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Airway morphology using computed tomography of patients diagnosed with neuroendocrine cell hyperplasia of infancy

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Title:
Airway morphology using computed tomography of patients diagnosed with neuroendocrine cell hyperplasia of infancy
Creator:
Cook, Marlijine C. ( author )
Place of Publication:
Denver, Colo.
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University of Colorado Denver
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English
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Degree:
Master's ( Master of Science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Bioengineering, CU Denver
Degree Disciplines:
Bioengineering
Committee Chair:
Hunter, Kendall
Committee Members:
Deterding, Robin R.
Benninger, Richard

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Paraneurons ( lcsh )
Lungs -- Diseases ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Review:
Neuroendocrine Cell Hyperplasia of Infancy (NEHI) is a rare diffuse lung disease presented in the first two years of life. It provides numerous diagnostic challenges due to poorly understood etiology and heterogeneous clinical presentations. In NEHI, lung biopsy show an increased count of neuroendocrine cells (NECs) in airway walls with otherwise normal histology reading. During fetal growth, NECs are associated with branch morphogenesis heading to our hypothesis that NEHI symptoms are correlated with changes in airway structure. To test this hypothesis we segmented airways from computed tomography of both NEHI and disease control patients to create a statistical shape model using both rigid and non-rigid registration techniques. Point-to-point correspondence was achieved and General Procrustes Analysis (GPA) oriented and normalized all shapes to a mean model. Principle Component (PC) Analysis was used to determine the axes of greatest variation in our model. Each patient can be estimated from the mean using the PC covariance matrix and its unique list of shape b parameters. Using Logistic Regression (LogR) and Akaike Information Criterion (AIC) model testing, we found that NEHI is classified by the b1, b3,, and b7 parameters. This model yields 76% accuracy in diagnosing NEHI from disease control patients. A receiver operator characteristic (ROC) curve yields an area under the curve (AUC) of b1 = 0:66, b3 = 0:73, and b7 = 0:77, which characterizes sensitivity and specificity of our shape parameters with the NEHI disease. We correlated available infant pulmonary function test (IPFT) results with our shape parameters. We found suggestive correlation between b7 and air flow and air trapping, both functional symptoms of NEHI patients. The following list correlated functional measures and their respective coefficient of determination from linear regression (LinR) analysis, R2: forced vital capacity (FV C) with R2 = 0:44, forced expiratory volume in 0.5 seconds (FEV0:5) with R2 = 0:48, residual volume over total lung capacity (RV=TLC) with R2 = 0:96, and functional residual capacity over total lung capacity (FRC=TLC) with R2 = 0:96. These results suggest that statistical shape models of the NEHI lung show promise for alternative disease diagnostics and stratification.
Thesis:
Thesis (M.S.)--University of Colorado Denver. Bioengineering
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Includes bibliographic references.
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Department of Bioengineering
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by Marlijine C. Cook.

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Full Text
AIRWAY MORPHOLOGY USING COMPUTED TOMOGRAPHY OF PATIENTS
DIAGNOSED WITH NEUROENDOCRINE CELL HYPERPLASIA OF INFANCY
by
MARLIJNE C COOK
B.S. Mathematics, University of New Hampshire, 2009
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Bioengineering
2014


This thesis for the Master of Science degree by
Marlijne C Cook
has been approved for the
Department of Bioengineering
by
Kendall Hunter, Chair
Robin R. Deterding
Richard Benninger
October 23, 2014
li


Cook, Marlijne C (M.S., Bioengineering)
Airway Morphology Using Computed Tomography of Patients Diagnosed with Neu-
roendocrine Cell Hyperplasia of Infancy
Thesis directed by Professor Kendall Hunter
ABSTRACT
Neuroendocrine Cell Hyperplasia of Infancy (NEHI) is a rare diffuse lung disease
presented in the first two years of life. It provides numerous diagnostic challenges due
to poorly understood etiology and heterogeneous clinical presentations. In NEHI, lung
biopsy show an increased count of neuroendocrine cells (NECs) in airway walls with
otherwise normal histology reading. During fetal growth, NECs are associated with
branch morphogenesis heading to our hypothesis that NEHI symptoms are correlated
with changes in airway structure. To test this hypothesis we segmented airways from
computed tomography of both NEHI and disease control patients to create a statisti-
cal shape model using both rigid and non-rigid registration techniques. Point-to-point
correspondence was achieved and General Procrustes Analysis (GPA) oriented and
normalized all shapes to a mean model. Principle Component (PC) Analysis was
used to determine the axes of greatest variation in our model. Each patient can be
estimated from the mean using the PC covariance matrix and its unique list of shape
fbf parameters. Using Logistic Regression (LogR) and Akaike Information Criterion
(AIC) model testing, we found that NEHI is classified by the 61,63, and 67 pa-
rameters. This model yields 76% accuracy in diagnosing NEHI from disease control
patients. A receiver operator characteristic (ROC) curve yields an area under the
curve (AUC) of 61=0.66, 63 = 0.73, and 67 = 0.77, which characterizes sensitivity
and specificity of our shape parameters with the NEHI disease. We correlated avail-
able infant pulmonary function test (IPFT) results with our shape parameters. We
found suggestive correlation between 67 and air flow and air trapping, both functional
in


symptoms of NEHI patients. The following list correlated functional measures and
their respective coefficient of determination from linear regression (LinR) analysis, R2:
forced vital capacity (FVC) with R2 = 0.44, forced expiratory volume in 0.5 seconds
(FEV^) with R2 = 0.48, residual volume over total lung capacity (RV/TLC) with
R2 = 0.96, and functional residual capacity over total lung capacity (FRC/TLC)
with R2 = 0.96. These results suggest that statistical shape models of the NEHI lung
show promise for alternative disease diagnostics and stratification.
The form and content of this abstract are approved. I recommend its publication.
Approved: Kendall Hunter
IV


ACKNOWLEDGMENT
I would like to thank for the following people for helping me form this final product:
Kendall Hunter, my advisor, for providing positive encouragement and incredible
insight
Robin Deterding for asking the question
Stephen Humphries and Emily DeBeor for technical and clinical support, collabo-
ration, and knowing more than I do on this subject
My Bioengineering cohort with special thanks to Ryan Delaney, Kathryn Gent, Phil
Bien and Tina Govindarajan
And finally, my parents, for encouraging me to chase more than one endeavor


TABLE OF CONTENTS
Tables..................................................................... ix
Figures .................................................................... x
Chapter
1.Introduction.............................................................. 1
1.1 Purpose............................................................ 1
1.2 Goals.............................................................. 1
1.2.1 Clinical..................................................... 1
1.2.2 Technical.................................................... 2
1.3 Overview of Methods................................................ 2
2. Background............................................................... 5
2.1 The Human Lung..................................................... 5
2.1.1 Basic Anatomy & Physiology................................... 5
2.1.2 Airway Structure and Function................................ 7
2.1.3 Airway Remodeling .......................................... 10
2.1.4 Pediatric Remodeling ....................................... 11
2.2 Modeling.......................................................... 13
2.2.1 Airway Models from Medical Images........................... 13
2.2.2 Image Registration.......................................... 15
2.2.3 Statistical Shape Analysis.................................. 16
2.3 Neuroendocrine Cell Hyperplasia of Infancy........................ 17
2.3.1 Clinical History & Challenges............................... 17
2.3.2 Test Results................................................ 18
2.3.2.1 Computed Tomography................................... 18
2.3.2.2 Infant Pulmonary Function Tests....................... 20
2.3.2.3 Bronchoalveolar Lavage................................ 20
2.3.2A Biopsy................................................ 21
vi


2.3.3 Significance of Neuroendocrine Cells............................ 22
3. Methods...................................................................... 25
3.1 Patient Population.................................................... 25
3.2 Imaging Techniques.................................................... 25
3.3 Segmentation and Skeletonization...................................... 27
3.4 Registration.......................................................... 30
3.4.1 Spline Method................................................... 31
3.4.2 Non-Rigid Registration ......................................... 31
3.5 General Procrustes Analysis .......................................... 32
3.6 Principal Component Analysis.......................................... 34
3.7 Statistical Analysis ................................................. 37
3.7.1 Logistic Regression............................................. 37
3.7.2 IPFT Correlation................................................ 40
4. Results...................................................................... 42
4.1 NEHI Patients......................................................... 42
4.2 Kernel Equalization................................................... 43
4.3 Landmark Registration................................................. 43
4.3.1 Coherent Point Drift Registration............................... 44
4.3.2 Spline Registration............................................. 46
4.4 Statistical Shape Analysis............................................ 46
4.4.1 Model Analysis.................................................. 46
4.4.2 Shape Deformation............................................... 48
4.5 Model Diagnostics..................................................... 55
4.6 Linear Regression..................................................... 56
5. Discussion................................................................... 62
5.1 NEHI Shape Deformities................................................ 62
5.2 Airway Image Registration............................................. 64
vii


5.3 Consideration and Limitations
66
5.3.1 Population Size............................................. 66
5.3.2 Further Clinical Comparisons................................ 67
5.3.3 Airway Registration......................................... 67
5.4 Conclusion......................................................... 68
6. Future Work.............................................................. 69
References................................................................ 71
Appendix
A. Branch Schematic........................................................ 80
B. Score Sheets............................................................ 81
B.l Clinical Score Sheet.......................................... 81
B.2 Radiology Score Sheet.............................................. 82
C. Normal Distribution of b Parameters..................................... 84
vm


TABLES
Table
3.1 Patient Population Clinical Values........................................ 26
3.2 Image Post-Processing..................................................... 27
3.3 Availabe IPFTs............................................................ 40
4.1 NEHI Clinical Information................................................. 43
4.2 Percent Variation......................................................... 47
4.3 Logistic Regression ...................................................... 49
4.4 Overdispersion Test ...................................................... 50
4.5 Odds Ratio................................................................ 50
4.6 Spline PCI................................................................ 51
4.7 Spline PC3................................................................ 52
4.8 Spline PC7................................................................ 53
4.9 CPD PC5................................................................... 54
4.10 Linear Regression Coefficients........................................... 57
A.l Branch Labeling Schematic................................................. 80
IX


FIGURES
Figure
2.1 The Respiratory System................................................... 7
2.2 Branch Generations ...................................................... 8
2.3 Fractal Lung............................................................. 9
2.4 Boundary Conditions on a Fractal Lung..................... 10
2.5 CFD with Segmented Airway............................................... 12
2.6 Pediatric Airway Shape.................................................. 13
2.7 CPD Registration ....................................................... 16
2.8 HRCT of Classic NEHI ....................................................19
2.9 NEHI IPFTs.............................................................. 21
2.10 BALF Profiles .......................................................... 22
2.11 NEC Distribution in Airways............................................. 23
2.12 Mammalian lung branching morphogenesis in vitro......................... 24
3.1 Kernel Comparison....................................................... 28
3.2 Branch Labeling Schematic............................................... 29
3.3 Branch Selection........................................................ 30
3.4 CPD Registration ....................................................... 33
3.5 Aligned Sets............................................................ 35
3.6 Principle Component of a 2D Point Cloud................................. 36
4.1 Kernel Comparison....................................................... 44
4.2 Stability of CPD........................................................ 45
4.3 ROC Curve for b Parameters ............................................. 56
4.4 Linear Regression and Residual for AirFlow Analysis with b7............. 59
4.5 Linear Regression and Residual of Lung Volumes with b7..... 60
4.6 Linear Regression and Residual of Lung Volumes with b3..... 61
x


1.Introduction
1.1 Purpose
Neuroendocrine Cell Hyperplasia of Infancy (NEHI) is an interstitial lung disease
with an unknown etiology [25, 31].It occurs as part of a recently defined schema
of children^ Interstitial Lung Disease (chILD) that describes rare and diffuse lung
disease. These lung disorders cause diagnostic confusion due to their uncommon
and heterogeneous presentations and varying mortality and morbidity [27]. NEHI
patients are a challenge diagnostically because of the disparity between their ill-
appearance clinically and the lack of suggestive disease state as seen in biopsy and
thoracic imaging. After years of biopsy analysis, a high count of neuroendocrine
cells (NECs) seen after immunohistochemical staining became associated with NEHI
clinical symptoms. This presentation in biopsies is consistent with NEHI patients
comparatively to other chILDs. Pulmonary NECs are expressed in high numbers
during fetal growth but decline in the neonatal period. Branch morphogenesis in
utero is influenced by pulmonary NECs [95]. With a lack of cellular and small airway
structural changes expressed, we speculate NEHI physiologic conditions are the result
of a large-scale structural change in pediatric airways. This project has set out to
determine if there is a significant change in NEHI large airways and ir it presents
correlation with disease symptoms.
1.2 Goals
1.2.1 Clinical
Pediatric patients diagnosed with NEHI syndrome express a variety of symptoms
that overlap with other chILDs and have mixed conditions within their own category.
This makes diagnosis difficult, especially for clinicians who do not often see this rare
disease. A lung biopsy showing high NEC count is the gold standard method of
diagnosis, but lung biopsy is often avoided due to risks from its invasive nature [95].
Patients being evaluated for NEHI and other chILDs typcially get a high resolution
1


computed tomography (HRCT) scan as a method to further distinguish between
chILDs. Data from these volumetric CTs can be used for qualitative imaging studies
including analysis of 3D large airway models [24]. Statistical shape modeling can
be used to determine variation of lung morphometry. This project seeks to classify
NEHI based upon airway modes of deformation from a disease control model. The
inclusion of NEHI infant pulmonary function test results with shape modes has the
potential to classify the severity of a patient^ NEHI condition [25].
1.2.2 Technical
Previous studies have been successful in determining pediatric airway dimensions
using CT scans [41,51,53, 75]. These methods required a specific nomenclature
of airway branches to perform point registration. Large airway structures follow a
common bifurcation pattern but topological variations exist. Branch labeling is a
tedious task that is susceptible to user error. This project purposes the comparison
of a previously characterized spline-fit registration method within out department to
a novel point-to-point alignment using established non-rigid registration techniques.
With this new method, greater patient variation is accepted, the editing time of
airway models is reduced, and it enables the inclusion of greater distal resolution.
1.3 Overview of Methods
Patients expressing NEHI-like symptoms are scheduled for additional clinical tests
such as infant pulmonary function tests (IFPTs) and thoracic imaging. Medical imag-
ing techniques using multi-detector CT scanners have drastically improved over the
last decade, providing clinicians with volumetric images while reducing radiation ex-
posure [9]. Our NEHI cohort is a collection of infants with single-center high resolu-
tion CT scans. This project utilized inspiratory images from patients diagnosed with
NEHI and NEHI-syndrome based on history, physical exam, and ancillary testing.
Our control group is a set of patients assessed for bone marrow transplant (BMT)
candidacy. A pediatric pulmonary doctor selected BMT patients with negative pul-
monary abnormalities in their radiology repots. Due to the young age of the NEHI
2


cohort, our disease control patients were relatively age and length-matched to our
NEHI population.
CT provides image stacks used in anatomical model reconstructions. A commer-
cially available package Apollo Workstation (VIDA Diagnostics, Coralville, I A) was
utilized for this project. Vida Diagnostics specifies in 3D airway models and pixel
densitometry techniques. This semi-automated software establishes the base model
while allowing for user edits such as bifurcation location and branch labeling.
Each patient scan was edited in Apollo following a protocol for branch labeling.
We received a mix of both sharp and soft kernel image post-processing scans. This
resulted in greater distal resolution of patients with a sharp kernel image reconstruc-
tion relative to the soft kernel. Our list of branch labels was adjusted to include those
bifurcation broadly expressed in both kernel sets.
Apollo patient packages were exported and processed in MathWorks Matlab
R2013a to retrieve airway skeletons and branch data in sub-directories. In coordina-
tion with Dijkstra^ path mapping algorithm, desired branches were called, allowing us
to establish a consistent representation of branches in each patient set. This negated
the kernel reconstruction affects on the segmentation process.
We established two techniques: a spline-fit method and non-rigid point set reg-
istration technique. Previously, point-to-point registration was completed using a
spline fit over each branch [41].This project suggested the use of Coherent Point
Drift (CPD) as a means to acquire image registration [62]. CPD provided benefit over
the spline method by not requiring defined landmarks and allowing for topological
variation. The algorithm uses a combination of Gaussian Mixture Model and Motion
Coherence Theory along with an Expectation Maximization process to converge on
a point-to-point coherence, removing outliers and establishing a 1-1 map. After each
technique was applied to our skeleton data, we processed the results identically.
Set registration was established using iteratively aligning General Procrustes
3


Analysis (GPA), which transformed each set to a mean shape. In our work, a scaling
factor was included to remove patient size as a mode deformation. Principal Com-
ponent Analysis is a method to reduce the dimensionality of a data set. Eigenvector
analysis of the residual covariance matrix of the data provided the main axis of the
landmark point cloud. Each axis can be ordered based upon greatest magnitude of
variation yielding our principal components of the data. The model expressed varia-
tion that is characterized by our eigenvectors and eigenvalues. Each individual airway
model was expressed as a deviation from the mean by a set of b parameters to the
covariance matrix [17]
Model parameters yielded shape deformation characteristics of the sample. This
information was used as covariates to Logistic Regression (LogR), a binomial pre-
dictor method [1].This statistical method can measure the relationship between a
categorical dependent variable and a continuous independent variable. Akaike Infor-
mation Criterion (AIC) was jointly used with LogR to determine the model goodness
of fit. We began with a set of candidate models and determined the model with least
amount of information loss. This process selected out the shape model parameters
that were used to associate NEHI shape deformation with other NEHI clinical re-
sults. An Odds Ratio was used to express the increase in belonging to the NEHI
population based upon an increase in our independent variable. We tested our model
with both Leave-One-Out cross validation process and Chi-Squared distribution of
the difference between our null hypothesis and the model residuals.
Pulmonary function tests provide a clinical measure that can be used to determine
the significant of our shape deformation. We determined the correlation coefficient of
available IPFT results and the significant shape parameters from PCA. If a test result
provided significant correlation with a shape parameter, we used Linear Regression
(LinR) to determine R2. The NEHI function results are highly variable as are the
shape parameters and together may indicate disease severity.
4


2. Background
2.1 The Human Lung
The human lung is an integrated system used to exchange oxygen (02) and car-
bon dioxide (C02) between the air space and our blood. The effectiveness of the
lungs lies in its ability to create an immense amount of surface area for passive dif-
fusion of gases. This is accomplished while simultaneously maintaining a thin region
defined by epithelium and endothelium layers within the thoracic cavity. It also
needs to evenly distribute fluid-flow throughout the complex network. The respira-
tory system is required to be very dynamic and elastic, allowing for stress from the
inspiratory-expiratory cycle. The lungs provide a boundary between internal tissue
and external environments, and are required to handle an infiltration of bacteria, air-
borne pathogens, and toxins through the secretion and movement of mucus [61,92].
By birth, the lungs have developed alveolar ducts that are expanded and capable
of transferring oxygen into the body. Formation of the alveoli and corresponding
capillary beds continues to develop during the first few years of life, allowing for lung
volume to increase in coordination with growth [68].
2.1.1 Basic Anatomy & Physiology
The lungs are situated within the thoracic cavity and are protected by bony
structures such as the ribs and sternum. Two pleurae bound the pleural cavity,
acting as a frictionless space and allowing for independent movement of the lungs
from the thoracic wall. The parietal pleura lines the inside of the thoracic cavity and
diaphragm, while the visceral pleura lines the lungs itself. The trachea is a singular
port for the entrance and exit of gas from the lungs. The respiratory tract leading
to the trachea is responsible for delivering warm, humia, and filtered air into the
lungs. It subdivides into the right and left main branch, which feed the right and
left lung, respectively. The carina is a cartilaginous ridge that is located at the base
of the trachea and establishes the first bifurcation. Each daughter branch continues
5


to subdivide, developing an airway tree network. The right lung contains three lobes
and the left only two, all of which are completely separated by fissures. The lingula
of the left upper lobe is geographically similar to the right middle lobe but lacks an
established fissure [3, 68, 91].
Approximately, the first 14 generations of branches are the conducting airways,
or physiologic dead space where no gas exchange occurs. The initial generations
are referred to as the bronchi and contain rings of cartilage and mucous-secreting
glands. Bronchioles are conducting airways under 2mm in diameter and no longer
have structural cartilage or glands. The bifurcation tree transitions into the acinar
airways were gas exchange begins. Alveoli are slowly integrated into the airway
wall until they become concentrated to the point of forming alveolar ducts. The
termination of the tree system is at the alveolar sacs, a cluster of alveoli roughly 27
generations from the trachea. The adult lung contains about 300 million alveoli, all
of which are ventilated and perfused. The expanse of the alveoli is roughly equivalent
to the size of a tennis court, or 130-185 sq meters [61,68, 91,92].
The hilum of the lung is the port for major blood vessels and the primary bronchi.
Pulmonary arties follow the bronchial tree, terminating with capillaries surrounding
the alveoli. The respiratory membrane is separated only by epithelial and endothelial
cells adjoined by their basement membrane. Other areas have a layer of interstitial
tissue that exist between epithelial and endothelial cells. This thin boundary coupled
with small diffusion coefficients allows for the most rapid diffusion rates [61,92].
Rather than following a parallel path to the bronchiole tree, oxygenated blood in the
veins follow a more direct route back to the hilum [68].
Fluid flow is caused by pressure gradients. A negative pressure in the lungs rela-
tive to atmospheric pressure exist during contraction of the diaphragm and intercostal
muscles, increasing the volume of the thoracic cavity and the intake of air. Partial
pressure of each gas species determines the direction of 02 and C2 diffusion. The
6


Figure 2.1: The human respiratory system from macro to microscopic views [7].
higher partial pressure of oxygen in the alveoli relative to the pulmonary capillaries
establishes a flow of 02 into the blood stream until equilibrium is reached at roughly
100 mmHG. Concurrently, this process occurs for C2 but in the other direction.
Surfactant proteins secreted by type II epithelial cells lower the surface tension of a
thin liquid film covering the sacs, inhibiting the collapse of the delicately thin alveoli
during the respiratory cycle [68]. A diagram of basic lung anatomy is presented in
Figure 2.1 in coordination with this discussion.
The majority of lung development into a well ordered structure occurs during
gestation. The initial lung bud will undergo morphogenesis, resulting in terminal
bronchioles by 16 weeks and alveolar ducts by 28 weeks. The lungs are functional by
36 weeks with surfactant production, vascular capillaries, and thin epithelium [68].
At this point, roughly 20 million alveoli exist in the form of ducts and expand to 300
million alveoli sacs in 3 years [91].
2.1.2 Airway Structure and Function
The structure of the lungs has been finely tuned to accomplish the necessary
functional requirement of providing adequate flow rate of 02 for metabolic needs
7


Figure 2.2: A diagram representing the progression of branch bifurcations. The paths
that are more straight are also wider [61].
[91].It is the largest organ in the human body and an adult lung is composed of
0.5L of tissue, 0.5L of blood and 4L of air [61].Fluid flow through the respiratory
system is defined by the characteristics of the branching tubes of the conducting
space. The lung is well developed to reduce energy loss in transporting 02 through
geometric arrangement of branch angles, lumen cross-sectional area and branch length
[2139, 91].
Human lungs classically branch in dichotomy and sometimes in trichotomy while
following a diameter and branch angle relationship. A larger lumen diameter of a
daughter branch follows a straighter path from the parent and a smaller lumen takes
a sharper angle as is shown in Figure 2.2 [87]. It is important to note that the sum
of the radii of daughter branches is greater than that of the parent branch [92]. The
lungs have also evolved such that the branch serving more distal gas exchange has a
smaller angle to the parent branch than the more proximal gas exchange branch. This
structure greatly reduces the velocity of gas as it reaches distal bronchioles extending
time for gas exchange [61,92].
Horsfield et al modeled the relationships between diameter ratio (Rd)j branch
ratio (i^) and length ratio (i?z) as ==61/3 and his measured finding agreed
with this evaluation [40]. Computation models from computed tomography images
by Tawhai et al.have shown agreement with the values that Horsfield calculated as


Figure 2.3: A representation of the fractal space-filling character of the Lung [92].
Rb = 2.8, Rb1^ =1.4, Rd =1.4, and Ri =1.4 [40, 84]. The consistency of these
values matches the well-ordered morphogenesis of the lungs. The bronchiole structure
is established during fetal growth and is based upon the interaction of epithelium of
the tracheal bud and mesenchyme, which will become the supportive network of the
lungs [91].As the individual grows, the lungs expand and fill more space, however,
the airway angles do not change relative to this growth [23].
The morphometry of the lungs is self-similar, or fractal in nature, and thus anal-
ysis of a small unit of the system can be informative of the whole airway [92]. This
complex system can be modeled and simplified by utilizing the space filling nature
of fractals as shown in Figure 2.3. The human lung is not symmetric, but its het-
erogeneity can be produced depending on boundary conditions applied to the system
and the adjustment of a fractal dimension (Df). This dimension characterizes the
irregularity of a shape. Smooth shapes have a low Df on du 1-2 scale (2-3 for 3D
shapes) and greater space-filling shapes will be characterized by a high Df [65].
As shown by Figure 2.4(a), the inclusion of various physical boundary conditions
and Df establishes a model more anatomically correct than WeibePs basic lung fractal
9


01 _
Df -1/94
(a) 2D Fractal Model [65]
(b) 3D Complex Fractal Model [47]
Figure 2.4: (a) Shows the affects of boundary conditions and Df on a simplistic 2D
fractal model and (b) expands complexity of the model to establish a more anatomical
representation.
(Figure 2.3). Optimal fluid flow requires specific formation. Kitaoka et al developed
a more complex model with greater generational accuracy by iteratively applying a
collection of rules [47, 82]. The end result is seen as a finite fractal airway tree set
into a thoracic shape. Models such as Figure 2.4(b) can be used to understand of
how lung formation affects physiology of the respiratory system. The structure of the
lungs that can be viewed through modeling techniques is similar to the structure we
cannot see.
2.1.3 Airway Remodeling
Disease pathophysiology described by visual radiology reading is a major unit
of clinical evaluation. Pulmonary diseases are described from CT image stacks by
radiologists as varying pixel attenuation, airway lumen thickness, lumen diameter
and structural abnormalities. Each disease has a specific visual characterization,
although some details overlap [20]. Quantitative analysis of CT images spans both 2D
10


image files and 3D image reconstruction through segmentation to describe remodeling
processes.
Various groups have studied the connection between disease physiology and image
representation. Fractal dimensions have been used to show correlation between space-
filling with Df values comparative to a control group [8, 36]. Airway lumen and
wall thickness measurement in chronic obstructive pulmonary disease (COPD) show
correlation with airflow limitations and air trapping from PFTs, a another classic
clinical measurement for determining lung physiology [5, 38, 48, 56, 57]. For example,
the COPDGene Study group assessed the difference between visual and quantitative
analysis of patients with emphysema. Their research using Apollo Workstation for
pixel attenuation, wall thickness, and lumen diameter has shown comparable results
between the methods. However, quantitative analysis is a more reproducible result
[6]. Determining the relation between shape changes and disease progression can aid
in earlier diagnosis [58].
3D segmented models from CT scans are used to link disease with structural mor-
phometry. Pu et al expressed a relation between airway tree volume calculated from
3D segmentation to pulmonary functional tests (PFTs) [73]. Airway segmentation
models are used with FEA and CFD studies as well[44]. De Backer et al.corre-
lated asthma with functional air flow values from PFTs. Regional structure changes
affected flow resistance in the CFD model, expressing the sensitivity of the lungs
to small changes [21].Figure 2.5 highlights how the use of bronchodilators affects
regional structural changes that correlate with resistance changes.
2.1.4 Pediatric Remodeling
Pulmonary diseases that exist in pediatrics provide addition imaging and radi-
ology reading challenges. Characteristics seen on adult and pediatric CTs do not
associate with the same pathophysiology. Radiation exposure and patient compli-
ance is also a concern with pediatrics and thus there are fewer available scans for
11


Figure 2.5: The relationship between changes in branch volume and airflow resistance
after treatment with a bronchodilator [21].
research. Protocols using sedation and controlled ventilation have been established
to provide repeatable results. Newer high resolution CT machines use fast scanners
that expose patients to low radiation doses, between 80 -120kV depending on pa-
tient size [51,76]. Quantitative results for pediatric CT scans are still able to identify
airway wall thickening and lumen diameter in Cystic Fibrosis that correlated with
PFTs [22, 53].
Additionally, pediatric patients are continually growing, which affects the struc-
tural shape of their respiratory system. Several studies have been completed to corre-
late patient length with quantitative analysis from CT segmentation. Lung volume,
air volume, and tissue volume all increase linearly with patient length. Densitome-
try of pediatric scans shows that alveoli increase in number as expected, and do not
increase in diameter [75]. DeBoer and Humphries have completed analysis showing
that correlation exists between bronchi area and length, and that airway angles do not
change with growth. A normative model was established and the expected bronchi
area and branch angles are depicted in Figure 2.6 [23, 41].
The extent of research completed with adults and pulmonary disease is extensive,
and specific consideration needs to be given when performing quantitative analysis
I

f I
12


I
(a) Airway Angles (b) Airway Diameter
Figure 2.6: A schematic of the normal pediatric airway branching angles (a) and
airway lumen diameter (b) [23, 41].
and image segmentation with a pediatric population. Methods for adult scans can
be transferred to pediatric scans but the results do not readily support the same
pathophysiology [51,76].
2.2 Modeling
2.2.1 Airway Models from Medical Images
Computer models can show how branch pattern and reduction of airway lumen
affects computational air flow [84, 94]. Finite element analysis (FEA) and compu-
tation fluid dynamics (CFD) are applied to respiratory computer models to study
correlation between air tree structure and pulmonary functional tests (PFTs) [85].
The Navier-Stokes equation, which describes fluid flow, shows how airway obstruc-
tion affects velocity profiles, flow rate, and pressure distribution in physical models
during both inspiration and expiration. Overall, such modeling suggests that the
lungs are sensitive to bifurcation configuration [82, 84, 94].
13


Applications of modeling systems to airway structure has made drastic improve-
ments with development of volumetric imaging techniques such as computed tomog-
raphy (CT) and magnetic resonance imaging (MRI) [22, 83]. A merge between math-
ematical models and patient specific anatomy allows better analysis of the relation
between structural design and functional capacity. These models can be used to
determine important dimensions such as airway wall diameter and wall thickness.
Imaging techniques are noninvasive and are used for in vivo studies in both human
and animal populations [18].
CT is the imaging modality of choice for the lungs and has been used for most
airway segmentation algorithms [74, 90]. The robustness of the algorithm is pertinent
to stable segmentations when dealing with various disease states and imaging proto-
cols. Region-growing methods have shown reliability and adaptations have improved
airway wall leak recognition [89]. Airway tree segmentations can be quantified fur-
ther by providing analysis of the skeleton structure. A fast, curve-thinning algorithm
iteratively removes border points of the segmentation while maintaining connectivity
to a singular line end point. This produces a one voxel wide skeleton of the airways.
Rough boundaries cause spurious branches that are removed based upon length and
airway branch relations using Dijkstra^ well known shortest path algorithm [67].
Adaptation and improvements of segmentation/skeletonization algorithms is on-
going, but commercially available packages provide these methods for clinical use.
Evaluation of airway changes are provided in groups of quantitative analysis for
parenchyma density, fissure integrity, and airway structure and dimension. Apollo
Workstation (Vida Diagnostic, Coral ville, I A) is one such package that provides a
graphical user interface for airway quantitative analysis. The underlying algorithms
of Apollo Workstation use region-growing and fast-thinning methods for segmentation
and skeletonization. Multiple studies have utilized the analysis provided by Apollo to
determine how remodeling processes correlate to disease state and lung functionality
14


[5, 6, 75].
2.2.2 Image Registration
Increased use of 3D models to visualize patient specific deformities has expanded
the field of point-set correspondence and statistical shapes models. Comparison of
similar objects is easy for the human eye to determine but provides significant compu-
tational challenges. Computer vision is a field based on finding the optimal transfor-
mation from one image to another [17,15]. Analysis of shape deformations within a
population provides valuable insight into correlation of disease state with pathophys-
iology. These highly dimensional sets can be simplified using modeling selectioning
techniques such as principal component analysis. Population models require addi-
tional processing in the form of image registration. Complex forms vary in position,
orientation and scale, which challenges alignment techniques. Correspondence al-
gorithms have been developed to automatically align landmarks through non-rigid
transformations [15, 62].
Feature-based methods map a source model to a target model through a spa-
tial transformation, determining point correspondence and transformation simulta-
neously. Optimization of the image registration technique is an integral part of the
established algorithm [15, 34, 62]. Coherent point drift (CPD) is a non-rigid image
registration technique established by Andriy Myronenko and Xubo Song that solves
correspondence and determines a non-rigid transformation as a probability density
estimation problem.
In CPD, physical landmarks are used by fitting a Gaussian mixture model (GMM)
of one set to the data points of another. The GMM is able to present subpopula-
tions of centroid within a population, rather than just a singular centroid. These
subpopulations are forced to move coherently with adjacent points by using Motion
Coherence Theory (MCT). The collective movement of points preserves topology
while maintaining similar soft assignment characteristics such as fuzzy connectivity
15


(a) The Point Set Registration Problem (b) CPD Image Registration Results
Figure 2.7: (a) A basic example showing similar but deformed and unequal point
sets, (b) CPD is a robust algorithm that iteratively registers images, even those with
missing points (2nd row) and outliers (3rd row) [62].
methods. Maximizing the likelihood estimation problem using an expectation max-
imization algorithm refines the result. The use of a non-parametric transformation,
which is ill-posed with no unique solution, is constrained by enforcing smoothness.
Regularization using operators of the displacement field and their variational deriva-
tives accomplish this. A displacement vector, from one state to another, is assigned
to all landmarks in the point cloud. CPD follows the basic form of using a feature
based similarity method, non-parametric transformation, and optimization accom-
plished through regularization. An example of the point set registration problem and
CPD solutions are shown in Figure 2.7. While this model represents a small, 2D
point set, Myronenko and Song have published work representing the robustness of
the algorithm for sets with high dimensionality, image noise, structural outliers and
various set sizes [14, 62, 63].
2.2.3 Statistical Shape Analysis
Statistical Shape Analysis (SSA) is immerging as a clinical method to study ge-
ometric properties of similar shapes or varying population groups. Morphometries is
a quantitative analysis of shape variability which removes information, such as loca-
tion, rotation, and scale that is not shape related [17, 28, 32, 50, 55, 78]. Landmarks
16


highlight similar physical locations or structures of a set of images within a similar
shape. Psuedo-landmarks are also included to describe shape between easily defined
landmarks measuring distance, curvature, and direction. Geometry of the point
configuration is retained under transformation and the distance between shapes is
obtained. Estimation of a mean shape determines the variability that exists from the
mean to each individual shape.
The general method for SSA is to established landmarks and psuedo-landmarks.
General Procrustes Analysis (GPA) removes non-shape related variations and collects
a proper shape model. Once sets become aligned to a common coordinate system,
Principal Component Analysis (PCA) reduces the dimensionality of large data set
and describes linear variation called Principal Components. These components are
organized by contribution to the total population variance [17, 28].
2.3 Neuroendocrine Cell Hyperplasia of Infancy
2.3.1 Clinical History & Challenges
chILD is a new classification schema used to characterize rare diffuse lung dis-
ease in pediatrics. This diverse group experiences compromised gas exchange and
diffuse infiltrates. Previously, this group was placed into adult ILD categories that
misrepresented pediatric disease-state or did not exist as an adult illness [31,27]. The
clinical definition of chILD is the presentation of 3 of 4 characteristics in the absence
of other disease:(1)Respiratory symptom, such as a cough or rapid respiratory rate,
(2) ^igns of respiratory symptoms like tachypnea or respiratory ranure, (3) Hypox-
emia, and (4) Diffuse abnormalities on thoracic imaging. Despite a new classification
scheme, pediatric rare diffuse lung disorders continue to challenge diagnostic bound-
aries by presenting a broad array of heterogeneous symptoms with poorly understood
etiology. Additionally, this overlap can diversify into drastically different patient out-
comes. Interstitial lung diseases occur at any age and in pediatrics the condition is
linked to both lung injury and lung development [25]. Disease mechanics are also
17


misinterpreted due to mixed physiologic patterns. The clinical illness of the patient
is severe, yet striking abnormalities are not present in radiological images and biopsy.
Understanding onset and progression of chILDs will support more directed treatment
plans.
NEHI classically presents with persistent tachypnea, crackles, retractions, and
hypoxemia during the first two years of life. Patient symptoms are not improved by
use of bronchodilators nor corticosteroids and the condition has no associated etiology
[31].NEHI patients also lack any inflammatory response in their condition. Based
upon an initial assessment with these presentations, patients are determined to have
a chILD but may require further tests for a more accurate assessment. Clinical tests
prescribed are infant pulmonary function tests (IPFTs), computed tomography scans,
bronchoalveolar lavage, and/or biopsy. With expert clinical opinion, yet without a
biopsy, a diagnosis of NEHI syndrome can still be made. There is a higher percentage
of male NEHI patients and a few cases of NEHI siblings, which suggests a genetic
susceptibility of NEHI as well [69, 54].
The characterization of NEHI is newly established, and only a few institutions
are actively studying its prevalence and expression. Patients with unknown ILDs are
being sent to large, specialty institutions for further evaluation. A diagnostic method
for NEHI is needed to provide a clear and concise result, allowing smaller institutions
accurate evaluation without need for patient referral.
2.3.2 Test Results
We present the classic test results of NEHI syndrome. These characteristics are
not necessarily distributed evenly or consistent among the NEHI syndrome popula-
tion.
2.3.2.1 Computed Tomography
A CT scan on a patient thought to have NEHI can be highly informative. A
standard NEHI CT scan lacks major geographic or structural changes. However,
18


ABC
Figure 2.8: 40-month-old girl with typical appearance of neuroendocrine cell hyper-
plasia of infancy. A-C, Inspiratory high-resolution CT scans show sharply defined
areas of ground-glass opacification along mediastinal borders, peripherally, and most
prominently in right middle lobe and lingula (asterisks, C)[10].
non-specific presentation of ground glass opacity (GGO) is seen and often localized to
specific areas of the lung during inspiration. An increase in attenuation that presents
in a variety of patterns throughout the lung parenchyma is classified as GGO [16].
While the findings are consistent in NEHI, it leads to no further understanding to
the etiology of NEHI, in both identification and interpretation. Characterization of
GGO from adult ILDs is not always related to conditions present in pediatrics.
Known etiologies of GGO often appear on biopsy readings. NEHI patients, how-
ever, have a near normal biopsy relative to fibrosis, pulmonary hemorrhaging, and
increased cell density [9]. Localization of GGO is commonly found in the right mid-
dle lobe (RML) and lingula. In addition to GGO in the RML and lingula, select
patients present GGO in other areas or express other abnormalities such as fibrosis,
architectural distortion, reactive injury, or inflammation. Hyperlucent areas on expi-
ratory scan are the other most common finding in NEHI. This is an expression of air
trapping and high lung volume results from IPFTs [10].
19


2.3.2.2 Infant Pulmonary Function Tests
Pediatric functional tests provided accurate and reproducible results under cur-
rent study standards but do not provide sufficient data to diagnose NEHI. Patient
presentation of tachypnea, retraction, and hypoxemia express major physiological im-
pairments that can be supported by IPFTs. The procedure requires patient sedation
to measure tidal breathing, plethysomography, and raised volume rapid thoracoab-
dominal compression (RVRTC). Kerby et al evaluated the IPFT results of NEHI
patients diagnosed by biopsy and NEHI patients diagnosed by clinical presentations
and CT results (NEHI syndrome) to a disease control group. NEHI and NEHI syn-
drome patients did not differ from one another but expressed significant differences
from disease control and normal in both air trapping and obstructed airflow measure-
ments. Significant airflow obstruction was observed in NEHI patients given by low
forced expiratory flow between 25% 75% (FEF2^-7^). Low FEF values in NEHI
patients were exhibited by a low forced expiratory volume at 0.5 sec (FEV^). Addi-
tionally, all lung volume measures were high in NEHI patients. Residual volume over
total lung capacity (RV/TLC) in NEHI was unprecedentedly high, suggesting NEHI
patients are severely airtrapped.The results of this study are shown in Figure 2.9. It
can be concluded that patients expressing a spectrum of air flow obstruction and air
trapping have NEHI characteristics.
2.3.2.3 Bronchoalveolar Lavage
NEHI biopsy results are near-normal with little to no sign of inflammatory
changes in pulmonary tissue. A cytokine profile of NEHI syndrome patients was ex-
tracted via bronchoalveolar lavage. The results of lavage agree with biopsy readings
that inflammation is not significantly present in NEHI. Both neutrophils and white
blood cell count were significantly lower compared to disease control, cystic fibrosis,
20


(a) Air Flow Measurements (b) Air Trapping and Lung Volume
Figure 2.9: Comparison of NEHI/NEHI syndrome to disease control: (a) shows con-
sistently low air flow values in NEHI, which suggests obstructed airways; (b) shows
consistently high residual volumes relative to total lung volume, which suggests the
presence of air trapping in NEHI [45].
and follicular bronchiolitis (Figure 2.10). These values are closer to the expected
normal range in healthy patients [70].
2.3.2.4 Biopsy
The gold standard diagnostic for NEHI is a biopsy reading of a high count of
neuroendocrine cells (NECs) in distal airways and lacks other histology abnormalities
[31,95]. Initially, histological reports using hemotoxylin and eosin returned negative
results, with no discernable structural or inflammatory changes. They also lacked
changes in pulmonary vasculature such as medial thickening associated with hyper-
tension [26]. The observation of increased ^lear cells7, or hydrophobic epithelial cells,
gave cause to test bombesin immunohistochemistry. Bombesin-like peptides (BLPs)
are members of the bioactive profile of pulmonary neuroendocrine cells and are best
distinguished by gastrin-releasing peptides (GRP). Results of bombesin immunohisto-
chemistry staining showed a prominence in NECs relative to percent area in controls
(Figure 2.11).Co-localization of bombesin and a proliferative marker, Ki67, did not
21


V
NEH CF CteUM fB NB4 CF Dsm FB
CdtM* COrtTdt
Figure 2.10: Boxplots displaying the distribution of(A) absolute WBC counts and
(B) Neutrophil counts across the disease groups. The horizontal reference line and
shaded area correspond to the median and normal range of values in healthy patients
from previously published data. NEHI has more normal WBC and Neutrophil count
relative to other disease groups [70].
exist, thus, suggesting no new PNEC production. The 3-fold increase in PNECs was
well correlated with airway obstruction in small airways. Localized biopsy samples
in areas of GGO from CT scans did not show any relation. This suggests that the
non-descript presentation of GGO is not associated with NEC distribution [95].
2.3.3 Significance of Neuroendocrine Cells
Neuroendocrine cells have varying roles throughout fetal and neonatal lung de-
velopment. These cells are localized to the conducting airways, reaching from the
basement membrane to the airway lumen. Innervated clusters of NECs are called
neuroendocrine bodies (NEBs). NECs and NEBs produce a selection of bioactive
proteins such as serotonin, calcitonin, cholecystokinin, and GRP. During fetal growth,
these proteins promote branch morphogenesis, epithelial and mesenchymal cell pro-
liferation, and surfactant secretions [2, 26, 95]. This mechanism was classified by
Aquayo et al.in a mouse model, and the affects on airway branching is shown in
Figure 2.12. Cells producing BLPs peak during mid-gestation and decline rapidly
22


A





Figure 2.11: A, Schematic of proximal and distal airways. Proximal airways (B,C x
200) show fewer NECs than respiratory bronchiolesfD x 100) and alveolar ducts (F x
200). Resoiratory broncmole or disease control show rewer NECs than NEHI patients
(Ex 200) [95].
after neonatal period. After birth, PNECs are involved with oxygen chemosensing -
influencing bronchoconstriction and vasoactivity in response to hypoxemia [19]. The
function and role of NEBs relative to chronic lung disease is unknown, as well as the
prominence of NECs in NEHI. The condition exists in NEHI with uninjured airways
and no sign of inflammatory response.
A genetic study on chILDs has identified gene mutations affecting surfactant
protein production, lung development, and alveolar capillary dysplasia, as well as
pathways for select diffuse lung diseases [66]. NEHI does not present within the first
week of life, thus it is not a congenital disease. However, there is genetic susceptibility
between siblings with a higher expression rate in males than females. With little
evidence of environmental cause, study results support a genetic etiology [69, 54].
We speculate that the significance or increased NEU count in NEHI is related to
their role of branch morphogenesis during fetal growth. Research using a mouse model
23


Figure 2.12: (A) Embryonic lung rudiment dissected at gestation day 11 demon-
strating only four branching points and (B) the same embryonic lung after 3 days in
culture (gestation day 14) demonstrating 18 branching points [2].
genetically amplified BLP receptors in the embryonic lung. Treating the model with
both bombesin and an agonist ligand to the receptor resulted in changes to airway
cleft count, shown in Figure 2.12. The presence of bombesin related to an increase in
branching points with no significant change in cell proliferation. The analog, however,
reduced the number of clefts present [2]. The increased count of branches associated
with increased BLP leads us to believe that the compromised lung function of NEHI
patients is related to a structural change present in the airway of NEHI patients.
24


3. Methods
3.1 Patient Population
Our study was approved by the Colorado Multiple Institutional Review Board
(COMIRB) protocol 10-0934. We collected data from 21 patients with clinically and
radiology confirmed NEHI. Clinical evaluation was completed at Children^ Hospital
Colorado (CHC) and required 8 of 10 NEHI presentations as provided by Appendix
A. Radiology reports were completed by a pediatric ILD specialist at CHC. Patients
were classified into 4 categories in which three characterized NEHI (Appendiz B).
Three patients had to be removed from the study: one for excessive noise artifacts
confounding our segmentation process, another for slice thickness, and the final for
only having a CT from outside our radiology department at CHC.
The control group data was selected from bone marrow transplant (BMT) patients
that had acquired high resolution CT scans during their evaluation at CHC. The
BMT patients for this study had no report of lung abnormalities as determined by a
pediatric radiologist. We age and length matched the control group to the NEHI due
to the low mean age (9.7 months) and length (71.1cm) of our NEHI cohort. This left
us with a total of 7 control patients for our study. All CT images were acquired after
April 2010 with a thickness of either 0.6mm or 1.0mm.
Clinical values were collected day of scan and have been provided for both popu-
lation (Table 3.1). We used the range for each value rather than standard deviation
and confidence interval due to the small sample size. Body mass index (BMI =
kg/m2) has been recorded, using both calculated values and z-score to emphasize low
score values for NEHI patients. These values were assessed from the 2000 Center for
Disease Control Growth Charts for the US.
3.2 Imaging Techniques
Advances in computed tomography have drastically improved temporal and spa-
tial resolution while reducing ionizing radiation exposure, allowing for better image
25


Table 3.1: Study Demographics
Clinical Values NEHI (18) Disease Control(7)
Male (%) 12 (66.67%) 5 (71.42%)
Mean Age (range) in months 9.72 (4 22) 12.29 (5 20)
Mean Length (range) in cm 71.06 (60 85) 76.36 (63 87)
Mean Weight (range) in kg 7.75 (5.3 -12.1) 9.59 (6.5 -12.75)
Calculated BMI (range) in kg/m2 15.32 (13.7 -18.54) 16.28 (14.9 -17.53)
z-score BMI (range) -1.49 (-2.5 -1) -0.36 (-1.5 0.5)
quality in a pediatric population. Thin contiguous image slices for the thoracic cavity
are reduced down to 0.6mm -1mm in thickness. When considering an interstitial lung
disease, a sharp kernel process is recommended, allowing detail of the parenchyma to
be visualized.
Radiology images for this study were collected from Childrens Hospital Colorado
Radiology Department. Due to the age of our population and the inability to comply
with breathing instructions, patients were sedated for imaging. Controlled ventilation
allows a radiology tech to administer a breath in coordination with scanning. A full
volumetric image is taken at inspiration and a sectioned scan during tidal expiration.
The CT scanner at CHC is Siemans SOMATOM Sensation 40 and all patients
were imaged with this device. A few patients (4 of 23) had a z-stack thickness of 1mm
rather than 0.6mm. The radiation the patient is exposed to is between 80 -120 kV.
The exposure value is based upon the thoracic area imaged and thus is different from
patient to patient. A discrepancy existed in kernel reconstruction between the NEHI
and disease control (DC) group. Most all DC had a soft (B31f) kernel reconstruction
and the NEHI had a mix of both soft and sharp (B60f/B70f) kernels. A few NEHI
patients had both reconstructions. In this case, we chose the soft kernel to reduce
variability between populations. Table 3.2 exhibits the number of kernels present for
26


Table 3.2: Available kernel reconstruction for patient cohort. A soft kernel (B31f)
was used over a sharp kernel (B60f/B70f) when available.
Kernel Disease Control NEHI
B31f 6 (86%) 10 (56%)
B60f 0 4 (22%)
B70f 1(14%) 13 (72%)
each population.
3.3 Segmentation and Skeletonization
Apollo Workstation (Vida Diagnostics, Coralville IA) is a semi-automated, airway-
specific, segmentation package. It provides various clinical measures such as lung vol-
ume, airway dimensions, parenchymal analysis, and fissure integrity analysis. It was
used in this project for its ability to provide airway segmentation with user-defined
branch editing and labeling.
To accommodate for various CT field of views, we established a cutoff for the
trachea. The airway segmentation was initiated at the top of the lung airspace when
viewed in the axial plane. Following Apollo Workstation editing protocol, we began
by removing airway leaks and false branches. We checked to see if branch merging was
necessary throughout each scan; Apollo occasionally establishes erroneous branches.
We could then begin the process of branch labeling.
Using a defined list of branches for our statistical shape analysis was required
to equalize the representation of peripheral branches. The soft kernel reconstruction
greatly affected the number of generations present in our 3D model. Figure 3.1 shows
the contrast between sharp and soft kernel segmentations on the same scan from a
single patient.
A protocol was established for branch labeling (Figure 3.2) so that each scan had
roughly the same segments labeled relative to generation and orientation. We used
27


(a) Soft: B31f Kernel (b) Sharp: B70f Kernel
Figure 3.1: Both segmentations are from a single CT acquisition on a patient with
(a) a soft kernel reconstruction and (b) a sharp kernel reconstruction.
WeibePs generation scheme, which allocates the trachea as generation 0 and labeled
out to the 4-6th generation [92]. Topological variations existed between patients but
parent/daughter relations were maintained. For example, RBI, RB2, and RB3 do
not necessarily trifurcate from RUL. On occasion, Apollo Workstation establishes two
bifurcations within close proximity of one another. This was corrected by inserting a
short RB1+2 branch, for example. The list of branches with respect to parent and
daughter branches is in Appendix A.
Apollo export data was brought into MATLAB (2013a(version: 8.1.0.604), The
MathWorks, Natick, Massachusetts) for further analysis. In the patient directory
files, Apollo stores a skeletonization of the airway segmentation (Analyze image for-
mats) and linker data for bifurcation points (extensible Markup Language). The air-
way skeleton is easily extracted but branch point data is organized in tiers of branch
generation id, start branch point, end branch point, and centerlines. An in-house
XML parse code was utilized and adjusted for this study [41].
28


Tr*chea
LBU2
Figure 3.2: The general airway labeling scheme used in Apollo Workstation. Various
changes were made for topological differences between patients, not shown here.
Apollo has an ordered nomenclature system for all branches in the skeleton that
is overwritten during the labeling process. We extracted the start and end points of
only labeled branches from our protocol from the XML files. Not all branches were
present in each scan, in which case the end parent branch point and start daughter
branch point were used to establish a zero length branch. This accommodated the
small topological variations that existed bewteen patient sets. These relationships
have been established in our branch labeling protocol. Certain centerline data did
not exist in the Apollo export data. To adjust for this discrepancy, we used an open
source Dijkstra^ algorithm for finding the shortest path from one point to another
[46]. A distance map was created using the skeleton data, such that the distance from
each point to all others was established. A connectivity map removed information
from points that were not connected. Our skeleton data is represented as voxel
position from the CT scan. A connection is determined if the distance is greater
than 0 but less than >/3, which collects voxels that are side-by-side, edge-to-edge, or
corner-to-corner [41,67]. Figure 3.3 depicts this pruning method from the full Apollo
29


Reduction of a Sharp Kernel Skeleton
Frontal Axis (mm)
Figure 3.3: The process of pruning the airway tree to a select set of branches from
the Apollo segmentation. The black skeleton represents a full airway tree from the
segmentation, while the green skeleton represents only our selected branches and
their respective bifurcation points in blue. These are the airways used for our study
process.
skeleton to the selection of branches in MATLAB.
All skeleton data has been stored as voxel indices in a 3D matrix. To convert
this information into coordinate space, we extract the voxel dimensions from the CT
report. Each skeleton is adjusted into a millimeter unit system, which establishes
size variation between patients. The bifurcation points of our skeleton provide land-
marks with branch length described by psuedo-landmarks. These are required for our
statistical shape analysis.
3.4 Registration
Image registration is a difficult task when dealing with data that have a large
degree of freedom (DOF) and represents a intricate shape. Airway skeletons follow a
basic tree shape but present variation in branch length and angle. Slight changes in
the topology of branch generation exist, even within the large bronchi of the respira-
tory system. Two methods are discussed in this study.
30


3.4.1 Spline Method
Our first approach was to use a method adapted from previous work within our
department. A spline was fit to each branch segment. In the skeletonization process,
we pruned the airway tree to a select list of branches and retained the centerlines
of each specific branch. The spline fit an equal set of points to each branch, which
were organized based upon name. Select branches were given a zero length and
thus resulted in a spline of 50 points in the same location. We established image
registration as a byproduct of this method. We also accounted for common topological
variation that exists through this method through our labeling process. A total of
40 branches were evaluated, each with a 50 point spline. Our final data set for each
patient was 6000 DOFs ( for % = 2000(40x50)). This method automatically
creates corresponding data sets. Alignment of each data set is accomplished using
General Procrustes Analysis, which will be discussed.
3.4.2 Non-Rigid Registration
Our second method used non-ngia image registration. Coherent Point Drift
(CPD) is a well established non-rigid image alignment method that has been applied
in a variety of computer vision problems [14,15, 62, 63]. This is its first applica-
tion towards an airway skeleton alignment problem (based upon publication results).
Andriy Myronenko has established a CPD project page, which provides a MATLAB
toolbox including non-rigid image registration. The package allows for the input of a
target and source scan with user-defined function parameters. A target skeleton was
selected and mapped to the remaining airway skeletons. CPD aligns each scan to
the target based upon a probability density estimation problem. Gaussian mixture
model centroids, which characterize localized deformations, are fit between iterations
based upon maximization of the likelihood estimation function. This produces the
highest probability of model fit. The GMM moves coherently, restricted by Motion
31


Coherence Theory (MCT), and preserving topological structure. MCT assigns the
displacement vectors for all points in our skeleton data set from one state to another
as it is aligned with the target set. Regularization of the registration is accomplished
by use of the displacement field and variational calculus [62].
After each registration, a vector is produced that maps each skeleton set to the
target. This map can be applied to the source set and thus equilibrates all scans to
the same size, reducing each set down to the smallest data set. Figure 3.4 highlights
original scan orientation relative to another, the aligned scans, and the final corre-
spondence that is produced. The reduction of landmarks from our source scan (red)
is visible, yet no significant landmark information is lost.
3.5 General Procrustes Analysis
Set alignment to a common coordinate frame is accomplished by General Pro-
crustes Analysis (GPA). Our data exhibits variation from position in the scanner,
orientation, and patient size. We establish a reference shape by arbitrarily choosing
a scan and aligning all other scans to it. Our first mean model is then determined
and becomes our base shape. This mean model is iteratively adjusted as we align all
scans again until a minimum threshold is approached.
This process was completed using open source and in-house code with input
parameters to include scaling [41,71].Both codes follow the well established method
of Orthogonal or General Procrustes Analysis, which applies Procrustes Analysis to
a population of 5 > 2 [17, 28, 35, 43, 86]. The basis of this method is to minimize
a goodness-of-fit criterion (3.1), which is measured by the residual sum of squares
distance to a mean. In this equation, c7 is a translation row vector, p is our scale
factor, and A is our rotation and reflection matrix applied to X. For each shape, a
center of mass is determined, positioned at the origin and scaled to a unit size relative
to the centroid distance of each shape.
32


(a)
(b)
Correspondence ol &ouroe 1o Target Scan
I

.2 .

Figure 3.4: Illustration of a source scan (red) being registered to the target scan
(blue): (a) Patient size and orientation during scan affects spatial location and (b)
after CPD registration scans are oriented and normalized to target scan and (c) the
correspondence map is applied.
Before Sat Regtslratun
Amr Re^rslaring Source 1ci Target


33


| lc' + pX*(A)|
(3.1)
We iteratively adjust the mean shape and adjust scan transformation to the new
mean. We rescale the centroid distance C (Eq 3.2) to the new mean at each step until
convergence.
Procrustes distance (d) is our threshold value and it is the sum of squared distance
between corresponding points (x^y^z^) and our mean (ui^Vi^Wi) (eq 3.3).
Our end result is a scaled and aligned cloud of skeleton landmarks. In Figure 3.5,
the results of our GPA alignment is shown with the mean shape overlaid. A scale
factor was included to adjust for patient size by normalizing the centroid distance to
one.
3.6 Principal Component Analysis
After alignment and scaling of all skeletons, we can complete Principal Compo-
nent Analysis (PCA). This statistical method reduces the dimensionality of correlated
data by providing a distribution of uncorrelated variation. In our instance, this de-
scribes shape deformations that are orthogonal. Covariance is used to describe how
our each landmark varies relative to one another [17, 42, 80]. The results of PCA are
orthogonal vectors that describe the extent of deformation along a given axis. From
Figure 3.6, we see a representative point cloud established by a singular landmark
across a sample data. The main axis produced is given by eigenvector decomposition
of the covariance matrix. Both the Spline and the CPD registration methods provide
a consistent representation of each landmark within our skeleton. For example, the
(3.2)
d= ^(ui- Xi)2"+ (vi yi)2"+ {wi Zi)2
(3.3)
34


Aligninent of Sets to a Mean Shape Using GPA
^
10 20
Frontal Axis
Figure 3.5: GPA is a process to align skeletons iteratively to produce a mean shape
(green) and orient all patient skeletons (blue) such that the least squares distance to
the mean centroid is minimized.
cartesian location of the carina in one patient set has the same matrix position as the
carina in all other patients set.
First we establish each set with n degrees of freedom in d dimensions as a
nd vector of all landmarks. Both the spline and non-rigid registration points are
reshaped into the form of 3.4.

T
(3.4)
Due to the large number of landmarks represented in each set, especially the
Spline method (n = 2000), we adjust our covariance matrix (Eq. 3.5) as follows:
5
s 1

T
We establish a matrix D of resiauals
(3-5)
WIXVIeuIpn-Eucrl
35


Figure 3.6: A 2D example of PCA where p is a principal component (PC) of the point
cloud centered at x. Each point in the cloud has a representative point x! on the PC
that is a distance b from the mean [17].
D = ((x^ x)...(x8 x)) (3.6)
The covariance matrix S can be written as S7
S = ^DDt ^ S7 = ^DtD (3.7)
Rather than using S that will have dimension nd x nd, S7 yields a s x s matrix
and is used for basic eigenvector (e^)/ eigenvalue (A^) decomposition.
By organizing our by descending order of we have a list of principal com-
ponents with the first vector representing the deformation with the greatest weight
of all deformations. To reestablish our principal component matrix to nd degrees of
freedom, we evaluate De^ which yields a n x s matrix, called $ [17]. This adjustment
was validated with our CPD data set by comparing eigenvectors from $ and S, since
our landmark set for the CPD data was significantly smaller than with the Spline
data.
Each airway model x can be expressed as combination of the mean (x) airway tree
and the covariance matrix $ adjusted by a vector of parameters. These b parameters
36


express the distance along the PC to x^, a projection point of x onto the PC for
each data point (Fig 3.6). The parameters are used to classify the extent of shape
deformation. Equations 3.8 and 3.9 express the relation of b to each airway model.
These b parameters become the basis for our statistical analysis as a distinguisher for
NEHI. Note that for the mean model, all b parameters are zero.
x ^ x + $6 (3.8)
b = $T(x- x) (3-9)
3.7 Statistical Analysis
3.7.1 Logistic Regression
The b parameters determined from PC A provide a platform for determining how
shape deformations relate to our NEHI and disease control populations. These values
are organized by percent variation and it is common to consider the components that
explain 95% of the variance. Due to the large number of landmarks but only a few
samples, our variation is spread across a broad range of PCs. For our statistical
analysis we will only consider the PCs that express 75% of the population variance.
Logistic Regression (LogR) is a binomial model that evaluates the effects of ex-
planatory variables on a set of response values. We will be predicting classification
into the NEHI population based upon our bi parameters. Given only one predictor
6, our model is based upon the relation established in Eq 3.10 relative to the linear
regression equation /3 + /3i& for response variable Y and predictor variable X. Our
response Y is the distinction between NEHI or Disease Control. Regression coeffi-
cients from the maximum likelihood function are given by /3i where /3 is the intercept
of our linear regression.
37


fib) = P{Y = l\B = b) = l- P{Y = 0\B = b)
/=(3.10)
logit[f(b)] = = /3 + /3ib
For multiple predictor variables, our regression coefficients are established as:
logit[f (b)] = /3 + fi\bi + /32^2 + *** (3.11)
The sign of f3 determines the positive or negative relation with /(6), our NEHI
LR model, and the magnitude of /3 suggests the rate or increase along the logistic
distnoution [1,11].
Akaike Information Criterion (AIC) is a method to test the relative quality of a
model based upon a selection of variables. We initialize our logistic regression can-
didate model with the b parameters that describe 75% of the airway tree variation.
AIC systematically adds and removes the b parameters and tests for goodness of fit
and information loss. Our final model expresses the b parameters that best classify
NEHI from the disease control group based upon shape deformation [11].The statis-
tical computation was completed in RStudio(Version 0.98.501, RStudio 2013, Boston,
Massachusetts). The LogR function in RStudio provides the necessary summary and
regression values for this analysis.
To determine the plausibility of our model, we compared the null and residual
deviance and degrees of freedom (df) based upon a Chi-Squared distribution. The
null deviance is a model of constant coefficients and the residual deviance looks at
the number of independent variables. This can be characterized as over dispersion of
our model.A larger result indicates that the resiaual is a better model fit than the
null.Eq 3.12 represents our calculation method for this method.
X (,DcviciTicc]\[uii DevianceResi(Puaidfnuii dfResiduai) (3.12)
38


There are a few methods to determine the significance of our result and how well
our model fits. We looked at the odds ratio to quantify the likelihood of being in
the NEHI population based upon the b parameter value. Our significance is based
upon a p-value <0.1 due to the small sample size but large extent of variation. The
significant regression coefficients Pi for each b parameter predictor that is selected by
AIC are used in a Odds Ratio (OR). Eq 3.13 defines the odds of belonging to the
NEHI population relative to one unit change in our b parameters. This can easily be
adjusted to remove the ambiguity of a ^ne unit change7 by determining a standard
deviation (SD) increase in b.
OR =
OR = ef3iSD^
(3.13)
We can calculate the confidence ratio of the predictor b by:
Cl
^{pi ^l-QQ(standard error))
(3.14)
Leave-one-out cross validation (LOOCV) is a method that determines the per-
centage of correct classification of our model. This method systematically removes
one observation, re-establishes the model, and then catagorizes the removed obser-
vation based upon the new model. The result from LOOCV is the estimate of the
prediction error [1,11].
For clinical evaluation, we determined the Receiver Operator Characteristic
(ROC) curve of our significant b parameters. Due to the distribution of parame-
ters, we organized values numerical and completed a step-wise analysis of sensitivity
and specificity; we did not use ranges.
Finally, to justify the use of Guassian statistical methods, we evaluated the distri-
bution of our significant b parameters. We fit a normal distrubtion curve based upon
parameter SD and mean to a histrogram of b values. We compared this to a quantile-
quantile (QQ) plot with a QQ line. Generalized extreme Studentizied deviate (ESD)
39


Table 3.3: A list of the available IPFT results for our NEHI patient population
Number of Patients Available IPFT
14 of 18 NEHI Patients Force Vital Capacity (FVC) Forced Expiratory Volume in 0.5sec (FEV^) Functional Residual Capacity (FRC) Forced Expiratory Flow at 50% (FEF50) Forced Expiratory Flow at 25% (FEF2^) Forced Expiratory Flow at 85% (FEF8^) Forced Expiratory Flow between 25-75% (FEF25-75)
8 of 18 NEHI Patients Expiratory Reserve Volume (ERV) Residual Volume (RV) Total Lung Capacity (TLC) Residual Volume/Total Lung Capacity (RV/TLC) Functional Residual Volume/Total Lung Capacity (FRC/TLC)
was used to determine parameter outliers [77].
3.7.2 IPFT Correlation
Our NEHI cohort has been evaluated for lung function with a infant pulmonary
function test (IPFT). These tests use spirometry and plethysmography to measure
both flow rates and lung volumes. Of our NEHI cohort, 14/18 patients had a IPFT
performed at CHC. Of those 14, only 8 had successful lung volume collection. Table
3.3 lists the tests available for 14 patients and then the addition results from the
smaller group of 8 patients.
We looked at test results that quantify airflow and lung volume and linearly re-
gressed these values with our significant b parameters. A combintation of Matlab and
RStudio was used to determine correlation coefficients r, coefficient of determination
i?2, linear regression plots, and residuals. A Bonferonni test statistic was performed
in RStudio to highligh the most extreme observations. If a model outlier existed, it
was removed and the LinR model was re-evaluated. We also looked at the stability
40


of our regression analysis. Select data points were removed to see if the regression
relied heavily on a singular point. Our regression analysis reported on only significant
correlation (p < 0.05).
41


4. Results
4.1 NEHI Patients
The NEHI patient group express a variety of chILD characteristics through a
range of symptoms and test results. Table 4.1 represents NEHI clinical score and
NEHI Radiology score for our NEHI study population. Both the clinical score and
radiology score sheets are provided in Appendix B. Dr. Robin R. Deterding and Dr.
Leland Fan, both primary NEHI clinical investigators, evaluated the clinical scores.
Dr. Jason Weinmann, a pediatric radiologist with expertise in NEHI radiology char-
acteristics, evaluated the radiology scores. The right middle lobe (RML) presented
ground glass opacities (GGO) in all NEHI patients on the radiology reading. The
right and left perihilar and the lingula presented GGO in 85% of patients. Only 30%
of patients had GGO in the right upper lobe (RUL), right lower lobe (RLL), and
left lower lobe (LLL), while only 1 patient had GGO in the left upper lobe (LUL).
Various other bronchial, alveolar, and interstitial lung disease were present in select
patients. The IPFTs results were collected only from CHC and have been overread
by biostatistician Dr. Brandie Wagner. We have provided the pulmonary functional
values that were significant in our pulmonary structure versus function regression
analysis.
Our NEHI patients express a variety of pulmonary dysfunction and are char-
acterized by the following classic NEHI conditions: hypoxemia, failure to thrive,
intercostal retraction, tachypnea, crackles, and dyspnea. chILDs express a range of
heterogeneous presentations and our NEHI group present the following chILD symp-
toms that are not generally associated with the NEHI condition: aspiration, reactive
airway disease, acute bronchiolitis, post-inflammatory pulmonary fibrosis, and pleu-
ral effusion. This contributes to the diagnostic confusion associated with NEHI and
other heterogeneous chILDs.
42


Table 4.1: The results of a clinical score and radiology score (sheets are provided
in Appendix A). The IPFT results used for our linear regression analysis are also
provided in the form of percent predicted from a control database.
Case Number Clinical Score Radiology Score Infant FVC 3ulmonary Fu FEVm5sec net ion Test, RV/TLC Percent Predicted FRC/TLC
6 NA Yes NEHI 45.69 49.20 NA NA
33 NA Maybe NEHI Plus 51.35 52.70 203.38 162.37
98 10 Maybe NEHI 46.25 48.40 NA NA
101 NA Yes NEHI NA NA NA NA
111 NA Maybe NEHI Plus 81.25 81.16 88.23 91.37
112 NA Maybe NEHI Plus 75.74 67.79 122.64 124.40
113 8 Maybe NEHI Plus 55.01 51.08 NA NA
114 10 Maybe NEHI Plus NA NA NA NA
119 NA Yes NEHI 70.79 82.03 139.82 138.95
75 NA Yes NEHI 55.75 63.90 194.43 166.74
82 NA Yes NEHI 44.64 48.57 198.62 166.23
85 10 Yes NEHI 35.49 34.36 NA NA
90 8 Maybe NEHI NA NA NA NA
77 10 Maybe NEHI Plus 67.94 80.53 128.77 129.13
84 10 Yes NEHI 50.01 55.07 NA NA
95 9 Maybe NEHI NA NA NA NA
99 10 Yes NEHI 57.88 60.34 NA NA
117 NA Yes NEHI 41.37 46.50 218.66 178.22
4.2 Kernel Equalization
The kernel used for image post-processing created a discrepancy in our segmenta-
tion results. The significant variation is seen only in the extent of branch generation
and not in airway length or bifurcation angle. Figure 4.1 highlights the peripheral
variation that exists between models. By calling forth a set of select branches, we were
able to equalize each patient set to the same branch generation. This also provides a
stable platform during point-to-point registration.
4.3 Landmark Registration
We completed statistical shape analysis on two distinct methods for aligning
our landmark point cloud. The first is a novel method of applying CPD to airway
skeleton for correspondence. The second is a technique which applies a set of equal
43


Frontal Axis (mm) Frontal Axis (mm)
(a) Coronal View (b) Transverse View
Figure 4.1: An overlay of a B31 soft kernel reconstruction (blue) and B70 sharp kernel
reconstruction (red) from the same CT data viewed in the coronal (a) and transverse
(b) plane. This highlights the equality of the skeletonization process within a unique
patient despite different kernels used.
spline points to each labeled branch. This method has been established in previous
studies [24, 41].
4.3.1 Coherent Point Drift Registration
This research investigated the use of the non-rigid image registration technique
Coherent Point Drift [62]. Using airway skeletons with a set number of branches, the
non-rigid method adequately aligned shapes about the carina. The use of centroid
neighborhoods also provided good alignment around more distal airways. The number
of points along each branch decreases significantly in peripheral airways and we see
information loss. We adjusted various input parameters to provide the best visible
fit. It is difficult to determine the alignment of the right and left lower lobes. From
Figure 4.2 we see good correspondence at the right main branch (RMB), left main
branch (LMB), RUL, and LUL bifurcation. As the tracheobronchial airtree continues
to bifurcate, we see fuzzier correspondence. We also lose the appearance of distinct
Compansoo Soft and Sharp Kernel on a Single Patient Companswi Soft and Sharp Kernel on a Single Patient
branches and the airtree becomes more cloud-like than skeleton form.
44


Corresponoence Source 10 Target Scan
(a) Skeleton Correspondence
-
j
i.
. . r
(b) Right Lower Lobe (c) Left Lower Lobe
Figure 4.2: A review of the registration of the source scan (red) and target scand
(blue): (a) The airway alignment using CPD is accurate and correspondence of the
large bronchi is accurate. However, the correspondence between points of the (b)
RLL and (c) LLL shows poor mappin. This error becomes augmented in our PCA
analysis with the inclusion of the total population.
45


From just a single representation, we see a sub-optimal alignment between sets.
As we add sets into the model, we continue to make the correspondence more poorly
defined. For example, in some instances we may accurately align the target LB8 to the
source LB8, but in others, it may be aligned to the source LB7. In our labeling process,
each branch was defined based upon is anatomical position and parent branch. By
adding discrepancy in point correspondence, we add erroneous variation. The extent
of this inaccurate align has not been quantified and thus we carried the results from
CPD into our PCA.
4.3.2 Spline Registration
The spline method provides exact point correspondence based upon user-defined
branches. Our point cloud for each skeleton is exemplified in the matrix 4.1. We avoid
the need of a registration method but require the tedious task of branch labeling. The
list of all branches present for each scan in supplied in Appendix B.l
TracheaXl Tracheayi TracheaZl
L2000,3
TracheaXb0 TracheaV50 TracheaZb0
RMB,
Xl
RMByi RMBZ1
(4.1)
4.4 Statistical Shape Analysis
4.4.1 Model Analysis
For a total of s = 25 patient scans, d = 3 dimensions, and rispUne = 2000
and ncpD = 498 degrees of freedom from our model, our covariance matrices were
DespUne = (6000 x 25) and Decpu =(1494 x 25). The percent variation of each
component of the covariance matrix is shown in Table 4.2. The modes shown are
used in our LogR and account for 75% of the total population deformation. The
classic use of 95% of variance yields 19 PCs for the Spline method and 18 PCs for the
46


Table 4.2: Principle Components that explain 75% of the variance within our model
Principal Component Spline (Total) in % CPD (Total) in %
1 0.2064 (0.2064) 0.3306 (0.3306)
2 0.1256 (0.3320) 0.1199 (0.4505)
3 0.1090 (0.4410) 0.0989 (0.5495)
4 0.0851(0.5261) 0.0529 (0.6304)
5 0.0643 (0.5904) 0.0452 (0.6833)
6 0.0585 (0.6488) 0.0379 (0.7286)
7 0.0515 (0.7004) 0.0338 (0.7665)
8 0.0430 (0.7434) -
9 0.0369 (0.7803) -
CPD method. Due to a larger number of dffs and small sample size s, we have a large
spread of variation with a small percentage of the total variation. The inclusion of
these smaller weighted variances does not supply significant shape deformation and
leads to model overdispersion.
Using RStudio, we preformed a LogR paired with AIC to determine which b
parameters would predict the best classification of NEHI shape deformities from our
control. The results for both the Spline and CPD method are shown in Table 4.3.
The null and residual deviances were used to determine the plausibility of our NEHI
model relative to the null model; the null model is a consideration of only the logistic
intercept and no coefficients. By considering P{x\df XAdeviance) various models,
we tested overdispersion of our AIC method. The inclusion of 61,63,and67 provides
the best model compared to a simpler model containing only 2 predictor variables
(4.4). This is determined by the larger change in %2 and the increased p-value.
The same comparison was provided for the CPD method. With the inclusion
of AIC model selection for our LogR, we assumed the selected parameter was an
47


improvement. This information is provided to remain consistent with the data shown
for the Spline method.
We also tested test the OR of belonging to a NEHI population based upon the
results of our LogR. We present the factor change in odds for unit increase of each
model predictor and its 95% confidence interval. We also provided the change in odds
relative to 1.96 standard deviation increase for a specific b parameter.
4.4.2 Shape Deformation
Logistic regression was used to determine which shape modes characterize the
airway deformation in our NEHI population. This information gives no insight into
how the NEHI airway tree changes relative to our control cohort. We can visualize
this shape change by adjusting the Principle component matrix $ relative to each b
parameter. Expression of NEHI deformation relative to the mean shape is expressed
in the following images.
Each table (4.4.2 4.9) is presented in both transverse and coronal planes of the
whole airway tree and then an enlarged image of the RMB and LMB, respectively. The
central green airway is our mean model. For each landmark, the principle component
for a given b parameter is shown as +1.96 standard deviation in dark blue and -
1.96 standard deviation in light blue. In all b parameters determined as significant,
the NEHI tend towards a positive standard deviation from the mean and thus their
shape deformities are expressed in dark blue. The light and dark blue lines are
inherently collinear and thus movement along this track present equal and opposite
deformation from the mean. The NEHI shape deformation is qualitatively described
in each table caption. Shape changes toward the control group are merely in an equal
and oppostie direction from the mean. This information of movement is determined
by the collective change in landmark axis. Characterization of the shape mode is
48


Table 4.3: Logistic Regression results from the best model chosen by AIC. For this study, we consider significance to be p-value
<0.1 due to our small sample size but large df. The estimate and standard error values are used for odds ratio evaluation.
Spline Method CPD Method
Coefficients
Parameters Estimate Std. Error z- value Pr(> |z|) Parameters Estimate Std. Error z- value Pr(> |z|)
(intercept) 1.51679 0.71443 2.123 0.0337 (Intercept) 1.10260 0.50903 2.166 0.0303
bl 0.02731 0.01788 1.527 0.1267 b5 0.07405 0.04053 1.827 0.0677
b3 0.02698 0.01566 1.723 0.0849 - - - - -
b7 0.03552 0.02138 1.662 0.0966 - - - - -
AIC 27.611 AIC: 29.562


Table 4.4: A comparison of the goodness of fit based upon a %2 distribution for various
b parameter predictor models. Spline: The use of a 3-predictor model is better than
a more simple 2-predictor model based open this overdispersion test. CPD: The
inclusion of a single predictor is superior to the null model.
x2 df PV(XAdf ^ XAdeviance)
null 29.648 24 0.803295
Spline Model Parameters
61 + 63 22.978 22 0.9643867
63 + 67 23.510 22 0.9535164
61 + 67 23.185 22 0.9604988
61 + 63 + 67 19.611 21 0.9817443
CPD Model Parameters
65 25.562 23 0.9567513
Table 4.5: A presentation of the odds ratio of belonging to NEHI population with
a 95% Cl and the odds relative to the standard deviation of each model predictor b
parameters.
Spline Method CPD Method
011(95% Cl)
bl 1.028(1.000, 1.077) b5 1.077(1.002, 1.183)
b3 1.027(0.999, 1.066) - -
b7 1.036(0.998,1.089) - -
OR wrt 1.96 SD of parameter
bl 22.03895 b5 6.779386
b3 9.214471 - -
b7 7.464009 - -
50


TclblG 4.6! The majority of the shape deformation described by the 1st PC is a elevation of the carina from the
model centroid (positioned at (0, 0, 0)). The airway tree also becomes relatively narrower as the angle between the
right lung and left lung decreases. There is a slight inferior/superior separation of the RB4+5 and RLL. The LLL
extends more to the peripheral as it rotates in an anterior direction, while branches of the LUL remain constant with
respect to one another. The angle between the RUL and Brontlnt appears to narrow and the RUL branches become
shorter.
Spline:1st Principle Component
Transverse Plane Coronal Plane
Zoom of the Right Lung Branches
Zoom of the Left Lung Branches
51


TclblG 4.7i For the 3rd PC, we see a general leftward tracking of the trachea as the RMB extends and the LMB
shortens. On the right side, RB4+5 rotates internally while the RLL rotates externally and both lobular branches
appear within closer proximity to one another. The LUL and SDB also shorten towards the NEHI shape deformation.
LB7+8 elevates towards LB4+5, also increasing the proximity of the LLL and the branches to the lingula. There is
also noticeable elongation of the LB5 and LB9.
Spline: 3rd Principle Component
Transverse Plane
Coronal Plane
Zoom of the Right Lung Branches
Zoom of the Left Lung Branches
52


TclblG 4.8i For the 7th Principle component, the trachea, RMB, and LMB are relatively still; we see most of our
shape deformation in the more distal branches. RB4+5 and the RLL branches separate from each other with RB4+5
elevating more extensively than the RLL depresses. The angle between the RUL and RMB also visibly decrease.
Again we see a shortening of the LUL and SDB and closer proximity of LB4+5 and the LLL.
Spline: 7th Principle Component
Transverse Plane
Coronal Plane
Zoom of the Right Lung Branches
Zoom of the Left Lung Branches
53


TclblG 4.9i The variation seen with this PC from our CPD method is an artifact of a poor skeleton correspondence
across our population. There is not description adequate for how the CPD method characterizes the NEHI cohort.
CPD: 5th Princple Component
54


provided with each image set.
We see from the CPD deformation model (Table 4.9) great variation within each
branch specifically in the RLL and LLL. This highlights the instability of the CPD
method to accurately align more peripheral branches across a population. Correspon-
dence to a single set may be achievable, but the process is not robust for larger sets.
We cannot analyze the shape deformations provided from this method.
4.5 Model Diagnostics
Both Leave-One-Out cross validation (LOOCV) and receiver-operator character-
istic (ROC) curve provide methods for determine the stability of our logistic model
in predicting NEHI patients from our control cohort. Using the logistic returns from
RStudio and an in-house LOOCV classifier, we determined that the a logistic model
including 61,63, and 67 parameters returns a 76% correct classification of NEHI. In
comparison, other logistic models with only one or two of the three predictors yielded
lower classification percentages.
Standard evaluation of sensitivity and specificity was performed for each b pa-
rameter. The list of NEHI and control patients were organized by b parameter value,
with positive values trending towards NEHI. Figure 4.3 is the ROC curve from this
evaluation with area under curve (AUC) calculated. Our best result, AUC = 76.9%,
is given by 67. This is also the most significant parameter in our logistic analysis.
We evaluated the distrubution of our b parameters, including control values for
the LR model and removing them for our linear regression models. Plots are provided
in Appendix U. Deviation from the QQ line exist only near the tails and our central
points are within close linear proximity between -1 and 1 quantiles. While the fit is not
a perfect Guassian distribution, significant non-normal distribution is not apparent.
We used generalized ESD to determine data outliers; including the control group, 67
had two outliers. Only considering the NEHI group, there was only one outlier. Both
of these points lie in the far negative range of 67, as shown in the distribution plots
55


Splms Mslhod ROC
ADO
l?1:e&073
ba 0 73339
b?:07es^4
False Positive Rate
Figure 4.3: A ROC curve for the b parameters that are predictors of group membership
in our logistic regression model.
in Appendix C. We make a note of these outliers but did not remove them from our
analysis.
4.6 Linear Regression
We first determined the correlation coefficient between all three shape parameters
and the available IPFT results. Since we confirmed normal distribution, we used the
correlation p-value to determine significance. We performed linear regression on only
those values with a p-value < 0.05 and displayed results in Table 4.10. There is
inverse correlation between 67 and FVC and FEV^. It also shows a high degree
of similarity in relative change between 67 and RV/TLC and FRC/TLC. Note, 67
was also correlated with RV^ but since RV/TLC is a more informative measure of
airtrapping, it was used over RV. We also see that 63 changes inversely to RV^
RV/TLC and FRC/TLC but only the last two are analyzed. This information was
calculated in Matlab and Rstudio.
We reviewed the linear regression coefficient of determination, R2 and its stability
when model outliers are removed. The significant relations determined by correlation
analysis were not greatly affected by singular points and thus supported the results
of our linear regression. A few functional results and b3 were suddenly correlated
when we looked at the sample size of 8 relative to 14. It was determined that this
56
6,sbT
elByBAI'-BcrIBnJi


Table 4.10: We present the correlation coefficients and coefficient of determination
of any significant linear regression model when comparing all b parameters to the
following IPFT restuls: forced vital capacity (FVC), forced expiratory volume in 0.5
seconds (FEVo^)^ residual volume over total lung capacity (RV/TLC) and functional
residual capacity over total lung capacity (FRC/TLC)
IPFT Correlation uoefficient Significance Coefficient of Determination
67 Parameter
FVC r = 0.6631 p = 0.0097 R2 = 0.4397
fev.5 r = -0.6938 p = 0.0059 R2 = 0.4813
RV/TLC r = 0.8309 p = 0.0106 R2 = 0.6903
FRC/TLC r = 0.8592 p = 0.0063 R2 = 0.7382
67 with Significant Outliers removed
RV/TLC r = 0.9775 p = 0.0001 R2 = 0.9555
FRC/TLC r = 0.9798 p = 0.0001 R2 = 0.9600
63 Parameter
RV/TLC r = -0.8195 p = 0.0128 R2 = 0.6716
FRC/TLC r = -0.8609 p = 0.0060 R2 = 0.7411
57


was due to a coincidental removal of data points in a region, but not representative
of our population. In Figures 4.4 4.6 we provide the plots of each regression and
respective residual data. From the residuals, we do not see any relations that may
be better modeled by non-linear regression. The Bonferonni outlier test selected one
significant outlier, which was removed. The change in r, p-value, and R2 with the
removal of the singular data point is also provided in Table 4.10. We see improvement
in correlation and linear regression.
58


Figure 4.4: (a) LinR results of FVC and FEV^sec with the b7 shape parameter and
(b) the resepctive residuals.
NEHI Air Flow Regression with b7 Shape Parameter
(a) LinR: b7 and Spirometry
Residuals of FVC and FEV0.5 with b7 Parameter
50 60 70 80 90
Fitted
(b) Residual:b7 and Spirometry
o
o
FVC
FEV0.5
0 0
c c c c c
9 8 7 6 5
p-OIIDaylu8JSH
c

3
2
2
c/
3
s'nplsey
59


Figure 4.5: (a) LinR results of RV/TLC and FRC/TLC with the b7 shape parameter
and (b) the respective residuals.
NEHI Lung Volume Regression with b7 Shape Parameter
(a) LinR: b7 and Pleth
Residuals of RV/TLC and FRC/TLC with b7 Parameter
15
10
5
0
-5
-10
-15
~2%0 100 150 200 250
Fitted
(b) Residual:b7 and Pleth
V
4
V *
V V
*

* RWTLC v FRC/TLC * 1
910 9J0-UGOJ00-
s'nplwey
60


-Too -50 0 50 100
b3 Shape Parameter
(a) LinR: b3 and Pleth
Residuals of RV/TLC and FRC/TLC with b3 Parameter
40
30
20
I
100
-Linear Fit
RV/TLC: Rsquared = 0.67163
-Linear Fit
FRC/TLC: Rsquared = 0.74113
NEHI Lung Volume Regression with b3 Shape Parameter
30
-40
5%o
100
150
Fitted
200
250
(b) Residual:b3 and Pleth
Figure 4.6: (a) LinR results of RV/TLC and FRC/TLC with the b3 shape
and (b) the respective residuals.
parameter
2220
o o o _
8 6 4 _
IDGPIIDGJ0-U00J90-
2
s'nplsey
61


5. Discussion
NEHI patients present a discrepancy between their ill-appearance and results
from classic airway structure tests: CT and biopsy [26, 31].Their IPFTs suggest
air trapping and obstructed air flow with no known causation [45]. Our speculation
is that the structural changes leading to poor pulmonary function is not uncovered
by classic clinical tests. This is the first attempt to determine if a structural airway
change is present in NEHI patients and if it correlates with clinical diagnostics.
5.1 NEHI Shape Deformities
NEHI characteristically presents GGO in the right middle lobe, lingula and per-
ihilar areas [10]. The deformations described by our principle component analysis
show areas of airway movement in these regions but also in areas such as the RLL
and LLL; these regions have a lower percentage of GGO present. Through our shape
analysis, we have provided preliminary evidence that NEHI patients have abnormal
airways. There is noticeable change in the general airway shape described by the first
PC. This is classified as a decrease in carina angle and a lengthening of the airway
tree. In the other NEHI specific principle components, we see large bronchi changes.
The most significant changes presented by PC 3 are an internal rotation and elevation
of the lower lobes to the RML and lingula branches. In PC 7, we continue to see
condensing of LB4+5 to the LLL branches, where as RB4+5 elevates away from the
RLL branches.
The logistic regression model is able to correctly classify 76% of the NEHI pop-
ulation. For this model, we consider a p-value < 0.1 as a significant indicator. Thus
b parameters 3 and 7 are significant model coefficients. Our first parameter, 61,has
a p-value = 0.1267 and is required to provide the best goodness of fit for our logistic
model. As described by our Chi-squared over dispersion test, the inclusion of all three
parameters is the best model. The results of our odds ratio using the multivariate
coefficient for each parameter provide interesting results. It is undesirable for the
62


confidence interval to bracket one. This occurs for both 63 and 67, while the Cl of
61 is just greater than one. The odds ratio relative to 1.96 SD supports a stronger
tendency towards NEHI. The 61 parameter shows the largest increase towards NEHI.
Again, this is a surprising result as 61 does not strongly classify NEHI.
An ROC curve is typically used as a clinical diagnostic tool. The AUC values
for 63 and 67 are not high enough to be considered a true diagnostic tool, but show
good specificity and sensitivity towards selecting NEHI from disease control. The
individual 63 and 67 have an AUC = 73.3% and AUC = 76.9% respectively. We
see a transition from NEHI to control in b parameter numbers that are below zero.
Recall, the mean shape model is defined by b parameters that are equal to zero. This
suggests that our mean model is more weighted towards NEHI population. With a
small sample size and over double NEHI patients relative to control, this is expected.
IPFTs express both airflow and lung volume functionality of the lung but do not
provide localization of compromised areas; IPFTs quantify global function. NEHI
patients express high levels of air trapping and low airflow. This is easily quantified
by the percent-predicted values based upon a control group at CHC. We determined
linear correlation with two of our shape parameters and a few functional results.
Most significantly, 67 had good correlation and regression results with two spirometry
measurements and two plethsymography (pleth) measurements.
Forced vital capacity is the total amount of air that can be exhaled with force
relative to tidal volume, and expiratory/inspiratory reserve volumes. Forced expi-
ratory volume in 0.5 sec measures the rate at which gas can be expelled from the
lungs. Low values indicate airway obstruction. We see negative correlation between
airflow and 67 shape deformation, which supports the concept that increased airway
deformation is related to increased airway obstruction. For FVC, R2 = 0.44 and
for FEVq^^ R2 = 0.48, both considered good given the extent of variation we see
in our population. These are also supported by significant correlation coefficients of
63


r = 0.66 and r = 0.69, respectively. There was a single patient who had very
little airway obstruction and control-range shape parameters. Removing this patient
only slightly adjusted R2 and the slope. Their consideration helps explain a normal
structure-function relationship compared to disease structure-function.
Residual volume relative to total lung capacity and functional residual capacity
relative to total lung capacity both indicate air trapping with high percentages. Sev-
eral patients of our NEHI cohort are severely air trapped, upwards of 200% predicted.
Our 67 shape deformation is highly correlated with both RV/TLC and FRC/TLC for
our 8 patient sample size, reporting r = 0.98 for both. The resulting R2 values
were 0.95 and 0.95 for respective pleth measurements with 67. We speculate that
the airway structural change of RB4+5 elevating away from the RLL and LB4+5
condensing to the LLL is correlated with increased air trapping. The singular patient
with near-normal air flow measures also has lower percent predicted. Again, they
were removed and we see a decrease in i?2, but its value is still considered significant
and the linear regression slope does not change.
RV/TLC and FRC/TLC are inverse ly correlated with the 63 shape parameter.
Interestingly, some of the shape deformations expressed by PC 3 are the opposite
movement expressed by PC 7. In PC 7, we see a separation of RB4+5 from the
RLL but in PC 3, we see a condensing of those two branches. The results of our
correlation suggest that, in this area of the airway tree, a elevation of RB4+5 away
from the RLL is directly related to an increase in air trapping in NEHI patients. We
must consider the slight changes that exist between PC 3 and PC 7. PC 3 appears to
also internally rotate more peripheral branches and we see a lengthening of the RMB
and a shortening of the LMB.
5.2 Airway Image Registration
Our data supports the use of the previously established spline method but not
the CPD approach. While the spline method provides accurate point-to-point regis-
64


tration, it requires extensive airway branch labeling and adjustments made for topo-
logical variation.
The initial trial with CPD used no branch labeling, the goal being to reduce
airway editing time. We began with the complete skeleton produced from Apollo
Workstation. The sharp kernel airway trees extend out 6-8 generations, and the
airway tree complexity was too great for the CPD registration technique. Unrealistic
mapping between branches existed; some branches bending or twisting down to lower
generation branches. When attempting to map a soft kernel scan to a sharp kernel
scan, CPD was unable to classify higher generations in the sharp kernel as outliers
relative to the soft kernel scan. This created a registration such that the end genera-
tions of the soft kernel were mapped through the remaining generations of the sharp
kernel. For example, if RB9 was terminal branch for a soft kernel scan, but a sharp
kernel scan had RB9a and RB9ai, the RB9 of the soft kernel was registered out to
RB9ai of the sharp kernel.
We then utilized the branch labels to reduce the extent of the airway tree and
to equalize kernel reconstruction. This appeared to accurately map each skeleton
to a target skeleton. Its benefit over the spline method was allowing for topological
variation, since specific bifurcation points were not established. There was concern
about number of landmarks that remained after correspondence and if there would be
enough data points to accurately characterize lower lobe branches; the correspondence
appeared fuzzier in these regions. We carried the results of the CPD method into our
statistical shape analysis to determine how well the lower lobe was registered across
the entire sample size.
After completion of PCA and LogR to select out our binomial model predictors, it
became clear that CPD was not robust enough to align airway skeletons. The PC axes
did not transition smoothly along branches. The misalignment visualized in the lower
lobes when comparing a singular source scan to the target scan was augmented when
65


looking at the complete patient population. Fewer points are maintained in the lower
lobe registration and inter-branch registration occurs. Looking at individual scans
mapped to the target scan, an estimate of 5-10 points exist for the 4-5th generation
branches; our spline method maintains 50 points for each and every branch. The
reduction of points is a degradation of shape information for our statistical shape
model. In addition, select branches for patients are mapped inappropriately, which
we determined by manually viewing the correspondence results with position in our
branch-labeling tree. These effects cause great variation in PC direction for adjacent
points and disprove our CPD method.
5.3 Consideration and Limitations
5.3.1 Population Size
Our research for this study was based upon a small sample size with a larger
number of dfs in our data set. This provides statistical difficulty in trying to determine
significance. As seen with our b parameters, we have a shape distribution that is
nearly normal but with flat peaks and fat tails (Appendix C). This is due to our
wide range of shape variation that exist in a small sample size. We also see this issue
when reviewing the significance of our LR coefficients. For this study, we accepted
p < 0.1 as significant, compared to the standard relation of p < 0.05. Our results
show about 75% classification based upon shape. The inclusion of more patients may
increase our ability to correctly determine NEHI based upon shape. This would also
be supported by an increase in AUC from a ROC curve..
The number of patients at CHC that met our retrospective study protocol limited
our group sizes. In part, the rarity and young age of NEHI limits the number of
acceptable controls that can be used. Expanding our study population would require
a multi-institutional study.
The inclusion of more samples to our shape model will change PCs and the b
parameters. What we would look for in a larger patient population is an expression
66


of NEHI shape deformations that is consistent. Meaning, the PCs, no matter the
weight in total population variance, support the airway changes expressed in the
paper. Additionally, increasing our sample size may further refine the 7NEHI shape7.
5.3.2 Further Clinical Comparisons
Due to ongoing research with the NEHI population, CHC has collected various
clinical measures on NEHI patients. With the inclusion of airway shape deformation,
we have the potential to look more closely at their relationship with radiology read-
ings. Localization of GGO seen on CT scans can be established as a discrete variable
from our Radiology Score sheet (Appendix B). It can then be regressed with shape
parameters. Recall, there is no correspondence with GGO and the presence of NEC
count in biopsy. However, we have yet to determine the presence of GGO relative to
airway deformation. Co-localization of NEHI shape deformation with GGO provides
insight into the presence of GGO.
5.3.3 Airway Registration
This study attempted to use CPD as a method for airway registration. Its initial
benefit over the Spline method was a reduction in airway labeling time. This process
is tedious and time consuming in Apollo, especially when labeling to a higher gen-
erations. Without needing branch labels, extensive airway trees could be mapped to
each other. However, CPD was not robust enough for skeletons with 6-8 generations
from a sharp kernel scan. Even with a soft kernel, we were unable to accurately align
skeletons. Once we determined that branch labeling was necessary for CPD stability,
we lost a major benefit of the method. At this point, the only improvement that
CPD provided over the spline method was the acceptance of topological variations
without data manipulations.
Our end results using CPD were disappointing. We required accurate set registra-
tion to determine shape deformations after using statistical shape analysis techniques.
Across a group of variable airway changes, CPD removed important data points in
67


the lower lobes. Cross-over between distal branches also occured during registration.
The upper lobes, however, appeared to be aligned well. Potentially, CPD could be
used in future studies if airway deformations in the larger bronchi are significantly
different and shape changes still correlate with function.
5.4 Conclusion
We have provided exciting data relating NEHI airway dysfunction to structural
changes. Expanding our research to a larger cohort will strengthen the statistics
of our results and help to clarify what exact deformations are present. Continual
work to improve airway registration will help reduce editing time and allow for large
population studies.
68


6. Future Work
This research work was a speculative study. The results of our study show that in
a small sample population, NEHI patients present large airway structural abnormali-
ties relative to a disease control cohort. The expansion of our model to include more
NEHI and control patients may provide better statistical significance. This would
require a multi-institutional study following protocol for imaging techniques, IPFTs,
and segementation process. To reduce the extent of any errouneous data variation,
it is important to consider the platforms being used during protocol. Varying im-
age scanner and segmentation algorithms has affect on the establishment of airway
landmarks.
We have shown accommodation for collecting data with different post-processing
image kernels. It provides a slight inconvenience, but the need to manually label
airway branches is also required for Spline registration. Branch labeling algorithms
have been designed and airway statistical shape modeling supports continued work
in this field.
The non-rigid image registration method used in this paper provided poor cor-
respondence in peripheral airways. The inclusion of these peripheral airways may
or may not be needed. The simplification of our airway tree to fewer branches may
also result in a model that produces significant NEHI structural changes. This would
reduce the amount of time for branch labeling and negate the concerns around airway
kernels.
Our results have shown a shape model that varies in both the left and right main
branches. The use of FEA and CFD on these large bronchi could further investigate
how structural changes in NEHI patients lead to poor pulmonary function. The
agreement between airflow simulation in patient specific airways and IPFTs would
further support why NEHI patients express their clinical abnormalities.
69


With the results we have discussed here, we open the doors for continued and
extended research in determining the relationship between NEHI and airway struc-
tural changes. Branch morphology from shape modeling can improve diagnosis and
correlate with prognosis of NEHI. Distinguishable classification of NEHI from other
chILDs can aid smaller institions in diagnosing NEHI.
70


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APPENDIX A. Branch Schematic
Table A.l: Branch Labeling Schematic
Branch Parent Daughter 1 Daughter2 Branch Parent Daughterl Daughter2
1 Trachea Trachea RMB LMB 21 RB9+10 RLL RB9 RB10
2 RMB Trachea RUL Bronlnt 22 RB9 RB9+10 RB9 RB9
3 RUL RMB RB1+2 RB1+3 23 RB10 RB9+10 RB10 RB10
4 RB1+2 RUL RBI RBI 24 LMB Trachea LUL LLB6
5 RB2+3 RUL RB2 RB3 25 LUL LMB SDB LB4+5
6 RB1+3 RUL RB3 RB3 26 SDB LUL LB1+2 LB3
7 RBI RB1+2 RBI RBI 27 LB1+2 SDB LB1+2 LB1+2
8 RB2 RB2+3 RB2 RB2 28 LB3 SDB LB3 LB3
9 RB3 RB1+3 RB3 RB3 29 LB4+5 LUL LB4 LB5
10 Bronlnt RMB RB4+5 RLL6 30 LB4 LB4+5 LB4 LB4
11 RB4+5 Bronlnt RB4 RB5 31 LB5 LB4+5 LB5 LB5
12 RB4 RB4+5 RB4 RB4 32 LLB6 LMB LB6 LLB
13 RB5 RB4+5 RB5 RB5 33 LB6 LLB6 LB6 LB6
14 RLL6 Bronlnt RB6 RLL7 34 LLB LLB6 LB7+8 LB9+10
15 RB6 RLL6 RB6 RB6 35 LB7+8 LLB LB7 LB8
16 RLL7 RLL6 RLL RL7 36 LB7 LB7+8 LB7 LB7
17 RB7 RLL7 RB7 RB7 37 LB8 LB7+8 LB8 LB8
18 RLL8 RLL7 RLL RLL 38 LB9+10 LLB LB9 LB10
19 RLL RLL7 R.B8 RB9+10 39 LB9 LB9+10 LB9 LB9
20 R.B8 RLL R.B8 R.B8 40 LB10 LB9+10 LB10 LB10
The following list of branches are used to equalize our sets and to adjust for
topoligical variations between patients. Each branch is defined to have a singular
parent branch and two daughter branches. If it is a terminal branch of our airway
tree, then it is also its own daughter branch. This is required for calling specified
branches out of Apollo case files and to equalize set size for the Spline corresondence
method.
80


APPENDIX B. Score Sheets
B.l Clinical Score Sheet
A NEHI clinical score sheet was established at CHC that evaluates the presence
of NEHI characteristics on a 10 point scale. Each presentation is awarded 1 point.
Values for our research looked at the cumulative total.
Clinical Presentation Today Cumulative
Crackles
Hypoxemia
Tachypnea
Retractions
Barrel Chest
Absence of clubbing
No Wheezing When Well
No Cough When WE11
Failure to Thrive
Onset < 1 year old
Total
81


B.2 Radiology Score Sheet
CLASSIFICATION CRITERIA FOR POTENTIAL NEHI CASES
CRITERIA FOR "YESCONFIDENT NEHI RADIOLOGY)
1. Ground glass opacities in RML, lingula, parahilar and paramediastinal distribution
2. Absence of CT findings not typically associated with NEHI
CRITERIA FOR ,fMAYBEH (POSSIBLE NEHI SPECTRUM PATHOLOGY)
1. Ground glass opacities in atypical distribution
2. Typical NEHI pattern only demonstrated on expiratory images
3. Absence of CT findings not typically associated with NEHI
CRITERIA FOR ,fMAYBE PLUSM (POSSIBLE NEHI PLUS SPECTRUM PATHOLOGY)
1. Ground glass opacities in RML, lingula, parahilar and paramediastinal distribution
2. Presence of CT findings not typically associated with NEHI
a. Bronchiectasis
b. Bronchial wall thickening
C. Architectural distortion
d< Pleural effusion
e. Interlobular septal thickening
f. Focal consolidation (excluding dependent atelectasis)
g. Parenchymal cysts
h Honeycombing
CRITERIA FOR "MO" (NEHI PATHOLOGY IS CONFIDENTLY EXCLUDED)
1. Normal chest CT
2. Absence of typical ground glass distribution as well as other findings not associated
with NEHI
a. Bronchiectasis
b. Bronchial wall thickening
C. Architectural distortion
d. Pleural effusion
e. Interlobular septal thickening
f. Focal consolidation (excluding dependent atelectasis)
g. Parenchymal cysts
h. Honeycombing
82


PATHOLOGY DATA FORM FOR chILD REGISTRY CASES
Registry number:
Age of patient when CT(s) performed :
FOR SURFACTANT CASES (CHOOSE ONE
OR MORE):
Normal chest CT
Diffuse ground glass opacities
Interlobular septal thickening
Crazy paving
Cysts
Architectural distortion
Pectus excavatum
_____________________________________
CHOOSE RADIOLOGY CLASSIFICATION:
PROBABLE SURFACTANT
DISORDER
MAYBE SURFACTANT DISORDER
NO SURFACTANT DISORDER
FOR NEHI CASES {CHOOSE ONE OR
MORE):
Normal chest CT
Ground glass opacity
RML
RUL
RLL
R perihilar
Lingula
LUL (other than lingula)
LLL
L perihilar
OTHER LUNG DISEASE: Bronchial
a. Bronchiectasis
b. Bronchial wall thickening
c. Architectural distortion
d. Pleural effusion
e. Septal thickening
f. Focal consolidation
OTHER LUNG DISEASE: Alveolar
a. Focal consolidation
OTHER LUNG DISEASE: Interstitial
a. Architectural distortion
b. Septal thickening
c. OTHER (Add free text)
n oxtiEfi.

CHOOSE RADIOLOGY CLASSIFICATION
YES NEHI
MAYBE NEHI
MAYBE NEHI ,fPLUSw
NO NEHI
83


APPENDIX C. Normal Distribution of b Parameters
Below we present the distribution of our NEHI model b parameters. In the left
column, the density of each parameter range is presented by the green bar graph.
The normal distrubtion relative to sample standard deviation and mean overlays the
histograph in dark blue. To the right we present the Quantile-Quantile plot. For a
normal distribution, we expect our quantiles to lie along the solid red line and within
the confidence interval established by the dotted red lines. While we do not have
a perfect Gaussian distribution, there is no underlying nonlinearity that is readily
expressed. A few of the b parameter distributions have fat tails, and in some cases,
outliers.
84


The second set of plots describe only the NEHI shape parameters. This is nec-
essary to determine the characteristic of our linear regression predictors. We do see
further departure from the classic Gaussian distribution with further outliers. How-
ever, there is not nonlinear deviation from the QQ line and thus we can still assume
normal distribution.
85


Full Text

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AIRWAYMORPHOLOGYUSINGCOMPUTEDTOMOGRAPHYOFPATIENTS DIAGNOSEDWITHNEUROENDOCRINECELLHYPERPLASIAOFINFANCY by MARLIJNECCOOK B.S.Mathematics,UniversityofNewHampshire,2009 Athesissubmittedtothe FacultyoftheGraduateSchoolofthe UniversityofColoradoinpartialfulllment oftherequirementsforthedegreeof MasterofScience Bioengineering 2014

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ThisthesisfortheMasterofSciencedegreeby MarlijneCCook hasbeenapprovedforthe DepartmentofBioengineering by KendallHunter,Chair RobinR.Deterding RichardBenninger October23,2014 ii

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Cook,MarlijneCM.S.,Bioengineering AirwayMorphologyUsingComputedTomographyofPatientsDiagnosedwithNeuroendocrineCellHyperplasiaofInfancy ThesisdirectedbyProfessorKendallHunter ABSTRACT NeuroendocrineCellHyperplasiaofInfancyNEHIisararediuselungdisease presentedinthersttwoyearsoflife.Itprovidesnumerousdiagnosticchallengesdue topoorlyunderstoodetiologyandheterogeneousclinicalpresentations.InNEHI,lung biopsyshowanincreasedcountofneuroendocrinecellsNECsinairwaywallswith otherwisenormalhistologyreading.Duringfetalgrowth,NECsareassociatedwith branchmorphogenesisheadingtoourhypothesisthatNEHIsymptomsarecorrelated withchangesinairwaystructure.Totestthishypothesiswesegmentedairwaysfrom computedtomographyofbothNEHIanddiseasecontrolpatientstocreateastatisticalshapemodelusingbothrigidandnon-rigidregistrationtechniques.Point-to-point correspondencewasachievedandGeneralProcrustesAnalysisGPAorientedand normalizedallshapestoameanmodel.PrincipleComponentPCAnalysiswas usedtodeterminetheaxesofgreatestvariationinourmodel.Eachpatientcanbe estimatedfromthemeanusingthePCcovariancematrixanditsuniquelistofshape 0 b 0 parameters.UsingLogisticRegressionLogRandAkaikeInformationCriterion AICmodeltesting,wefoundthatNEHIisclassiedbythe b 1, b 3,and b 7parameters.Thismodelyields76%accuracyindiagnosingNEHIfromdiseasecontrol patients.AreceiveroperatorcharacteristicROCcurveyieldsanareaunderthe curveAUCof b 1=0 : 66, b 3=0 : 73,and b 7=0 : 77,whichcharacterizessensitivity andspecicityofourshapeparameterswiththeNEHIdisease.WecorrelatedavailableinfantpulmonaryfunctiontestIPFTresultswithourshapeparameters.We foundsuggestivecorrelationbetween b 7andairowandairtrapping,bothfunctional iii

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symptomsofNEHIpatients.Thefollowinglistcorrelatedfunctionalmeasuresand theirrespectivecoecientofdeterminationfromlinearregressionLinRanalysis, R 2 : forcedvitalcapacity FVC with R 2 =0 : 44,forcedexpiratoryvolumein0.5seconds FEV 0 : 5 with R 2 =0 : 48,residualvolumeovertotallungcapacity RV=TLC with R 2 =0 : 96,andfunctionalresidualcapacityovertotallungcapacity FRC=TLC with R 2 =0 : 96.TheseresultssuggestthatstatisticalshapemodelsoftheNEHIlung showpromiseforalternativediseasediagnosticsandstratication. Theformandcontentofthisabstractareapproved.Irecommenditspublication. Approved:KendallHunter iv

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ACKNOWLEDGMENT Iwouldliketothankforthefollowingpeopleforhelpingmeformthisnalproduct: KendallHunter,myadvisor,forprovidingpositiveencouragementandincredible insight RobinDeterdingforaskingthequestion StephenHumphriesandEmilyDeBeorfortechnicalandclinicalsupport,collaboration,andknowingmorethanIdoonthissubject MyBioengineeringcohortwithspecialthankstoRyanDelaney,KathrynGent,Phil BienandTinaGovindarajan Andnally,myparents,forencouragingmetochasemorethanoneendeavor v

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TABLEOFCONTENTS Tables........................................ix Figures.......................................x Chapter 1.Introduction...................................1 1.1Purpose..................................1 1.2Goals...................................1 1.2.1Clinical..............................1 1.2.2Technical.............................2 1.3OverviewofMethods..........................2 2.Background...................................5 2.1TheHumanLung............................5 2.1.1BasicAnatomy&Physiology..................5 2.1.2AirwayStructureandFunction.................7 2.1.3AirwayRemodeling.......................10 2.1.4PediatricRemodeling......................11 2.2Modeling.................................13 2.2.1AirwayModelsfromMedicalImages..............13 2.2.2ImageRegistration........................15 2.2.3StatisticalShapeAnalysis....................16 2.3NeuroendocrineCellHyperplasiaofInfancy..............17 2.3.1ClinicalHistory&Challenges..................17 2.3.2TestResults............................18 2.3.2.1ComputedTomography..................18 2.3.2.2InfantPulmonaryFunctionTests............20 2.3.2.3BronchoalveolarLavage..................20 2.3.2.4Biopsy...........................21 vi

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2.3.3SignicanceofNeuroendocrineCells..............22 3.Methods.....................................25 3.1PatientPopulation............................25 3.2ImagingTechniques...........................25 3.3SegmentationandSkeletonization...................27 3.4Registration...............................30 3.4.1SplineMethod..........................31 3.4.2Non-RigidRegistration.....................31 3.5GeneralProcrustesAnalysis......................32 3.6PrincipalComponentAnalysis.....................34 3.7StatisticalAnalysis...........................37 3.7.1LogisticRegression........................37 3.7.2IPFTCorrelation.........................40 4.Results......................................42 4.1NEHIPatients..............................42 4.2KernelEqualization...........................43 4.3LandmarkRegistration.........................43 4.3.1CoherentPointDriftRegistration................44 4.3.2SplineRegistration........................46 4.4StatisticalShapeAnalysis........................46 4.4.1ModelAnalysis..........................46 4.4.2ShapeDeformation........................48 4.5ModelDiagnostics............................55 4.6LinearRegression............................56 5.Discussion....................................62 5.1NEHIShapeDeformities........................62 5.2AirwayImageRegistration.......................64 vii

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5.3ConsiderationandLimitations.....................66 5.3.1PopulationSize..........................66 5.3.2FurtherClinicalComparisons..................67 5.3.3AirwayRegistration.......................67 5.4Conclusion................................68 6.FutureWork...................................69 References ......................................71 Appendix A.BranchSchematic................................80 B.ScoreSheets...................................81 B.1ClinicalScoreSheet...........................81 B.2RadiologyScoreSheet..........................82 C.NormalDistributionofbParameters.....................84 viii

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TABLES Table 3.1PatientPopulationClinicalValues.....................26 3.2ImagePost-Processing............................27 3.3AvailabeIPFTs................................40 4.1NEHIClinicalInformation..........................43 4.2PercentVariation...............................47 4.3LogisticRegression.............................49 4.4OverdispersionTest.............................50 4.5OddsRatio..................................50 4.6SplinePC1..................................51 4.7SplinePC3..................................52 4.8SplinePC7..................................53 4.9CPDPC5...................................54 4.10LinearRegressionCoecients........................57 A.1BranchLabelingSchematic.........................80 ix

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FIGURES Figure 2.1TheRespiratorySystem...........................7 2.2BranchGenerations.............................8 2.3FractalLung.................................9 2.4BoundaryConditionsonaFractalLung..................10 2.5CFDwithSegmentedAirway........................12 2.6PediatricAirwayShape...........................13 2.7CPDRegistration..............................16 2.8HRCTofClassicNEHI...........................19 2.9NEHIIPFTs.................................21 2.10BALFProles................................22 2.11NECDistributioninAirways........................23 2.12Mammalianlungbranchingmorphogenesisinvitro............24 3.1KernelComparison..............................28 3.2BranchLabelingSchematic.........................29 3.3BranchSelection...............................30 3.4CPDRegistration..............................33 3.5AlignedSets..................................35 3.6PrincipleComponentofa2DPointCloud.................36 4.1KernelComparison..............................44 4.2StabilityofCPD...............................45 4.3ROCCurvefor b Parameters........................56 4.4LinearRegressionandResidualforAirFlowAnalysiswithb7......59 4.5LinearRegressionandResidualofLungVolumeswithb7.........60 4.6LinearRegressionandResidualofLungVolumeswithb3.........61 x

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1.Introduction 1.1Purpose NeuroendocrineCellHyperplasiaofInfancyNEHIisaninterstitiallungdisease withanunknownetiology[25,31].Itoccursaspartofarecentlydenedschema ofchildren'sInterstitialLungDiseasechILDthatdescribesrareanddiuselung disease.Theselungdisorderscausediagnosticconfusionduetotheiruncommon andheterogeneouspresentationsandvaryingmortalityandmorbidity[27].NEHI patientsareachallengediagnosticallybecauseofthedisparitybetweentheirillappearanceclinicallyandthelackofsuggestivediseasestateasseeninbiopsyand thoracicimaging.Afteryearsofbiopsyanalysis,ahighcountofneuroendocrine cellsNECsseenafterimmunohistochemicalstainingbecameassociatedwithNEHI clinicalsymptoms.ThispresentationinbiopsiesisconsistentwithNEHIpatients comparativelytootherchILDs.PulmonaryNECsareexpressedinhighnumbers duringfetalgrowthbutdeclineintheneonatalperiod.Branchmorphogenesisin uteroisinuencedbypulmonaryNECs[95].Withalackofcellularandsmallairway structuralchangesexpressed,wespeculateNEHIphysiologicconditionsaretheresult ofalarge-scalestructuralchangeinpediatricairways.Thisprojecthassetoutto determineifthereisasignicantchangeinNEHIlargeairwaysandifitpresents correlationwithdiseasesymptoms. 1.2Goals 1.2.1Clinical PediatricpatientsdiagnosedwithNEHIsyndromeexpressavarietyofsymptoms thatoverlapwithotherchILDsandhavemixedconditionswithintheirowncategory. Thismakesdiagnosisdicult,especiallyforclinicianswhodonotoftenseethisrare disease.AlungbiopsyshowinghighNECcountisthegoldstandardmethodof diagnosis,butlungbiopsyisoftenavoidedduetorisksfromitsinvasivenature[95]. PatientsbeingevaluatedforNEHIandotherchILDstypciallygetahighresolution 1

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computedtomographyHRCTscanasamethodtofurtherdistinguishbetween chILDs.DatafromthesevolumetricCTscanbeusedforqualitativeimagingstudies includinganalysisof3Dlargeairwaymodels[24].Statisticalshapemodelingcan beusedtodeterminevariationoflungmorphometry.Thisprojectseekstoclassify NEHIbaseduponairwaymodesofdeformationfromadiseasecontrolmodel.The inclusionofNEHIinfantpulmonaryfunctiontestresultswithshapemodeshasthe potentialtoclassifytheseverityofapatient'sNEHIcondition[25]. 1.2.2Technical Previousstudieshavebeensuccessfulindeterminingpediatricairwaydimensions usingCTscans[41,51,53,75].Thesemethodsrequiredaspecicnomenclature ofairwaybranchestoperformpointregistration.Largeairwaystructuresfollowa commonbifurcationpatternbuttopologicalvariationsexist.Branchlabelingisa tedioustaskthatissusceptibletousererror.Thisprojectpurposesthecomparison ofapreviouslycharacterizedspline-tregistrationmethodwithinoutdepartmentto anovelpoint-to-pointalignmentusingestablishednon-rigidregistrationtechniques. Withthisnewmethod,greaterpatientvariationisaccepted,theeditingtimeof airwaymodelsisreduced,anditenablestheinclusionofgreaterdistalresolution. 1.3OverviewofMethods PatientsexpressingNEHI-likesymptomsarescheduledforadditionalclinicaltests suchasinfantpulmonaryfunctiontestsIFPTsandthoracicimaging.Medicalimagingtechniquesusingmulti-detectorCTscannershavedrasticallyimprovedoverthe lastdecade,providingclinicianswithvolumetricimageswhilereducingradiationexposure[9].OurNEHIcohortisacollectionofinfantswithsingle-centerhighresolutionCTscans.Thisprojectutilizedinspiratoryimagesfrompatientsdiagnosedwith NEHIandNEHI-syndromebasedonhistory,physicalexam,andancillarytesting. OurcontrolgroupisasetofpatientsassessedforbonemarrowtransplantBMT candidacy.ApediatricpulmonarydoctorselectedBMTpatientswithnegativepulmonaryabnormalitiesintheirradiologyrepots.DuetotheyoungageoftheNEHI 2

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cohort,ourdiseasecontrolpatientswererelativelyageandlength-matchedtoour NEHIpopulation. CTprovidesimagestacksusedinanatomicalmodelreconstructions.AcommerciallyavailablepackageApolloWorkstationVIDADiagnostics,Coralville,IAwas utilizedforthisproject.VidaDiagnosticsspeciesin3Dairwaymodelsandpixel densitometrytechniques.Thissemi-automatedsoftwareestablishesthebasemodel whileallowingforusereditssuchasbifurcationlocationandbranchlabeling. EachpatientscanwaseditedinApollofollowingaprotocolforbranchlabeling. Wereceivedamixofbothsharpandsoftkernelimagepost-processingscans.This resultedingreaterdistalresolutionofpatientswithasharpkernelimagereconstructionrelativetothesoftkernel.Ourlistofbranchlabelswasadjustedtoincludethose bifurcationbroadlyexpressedinbothkernelsets. ApollopatientpackageswereexportedandprocessedinMathWorksMatlab R2013atoretrieveairwayskeletonsandbranchdatainsub-directories.IncoordinationwithDijkstra'spathmappingalgorithm,desiredbrancheswerecalled,allowingus toestablishaconsistentrepresentationofbranchesineachpatientset.Thisnegated thekernelreconstructionaectsonthesegmentationprocess. Weestablishedtwotechniques:aspline-tmethodandnon-rigidpointsetregistrationtechnique.Previously,point-to-pointregistrationwascompletedusinga splinetovereachbranch[41].ThisprojectsuggestedtheuseofCoherentPoint DriftCPDasameanstoacquireimageregistration[62].CPDprovidedbenetover thesplinemethodbynotrequiringdenedlandmarksandallowingfortopological variation.ThealgorithmusesacombinationofGaussianMixtureModelandMotion CoherenceTheoryalongwithanExpectationMaximizationprocesstoconvergeon apoint-to-pointcoherence,removingoutliersandestablishinga1-1map.Aftereach techniquewasappliedtoourskeletondata,weprocessedtheresultsidentically. SetregistrationwasestablishedusingiterativelyaligningGeneralProcrustes 3

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AnalysisGPA,whichtransformedeachsettoameanshape.Inourwork,ascaling factorwasincludedtoremovepatientsizeasamodedeformation.PrincipalComponentAnalysisisamethodtoreducethedimensionalityofadataset.Eigenvector analysisoftheresidualcovariancematrixofthedataprovidedthemainaxisofthe landmarkpointcloud.Eachaxiscanbeorderedbasedupongreatestmagnitudeof variationyieldingourprincipalcomponentsofthedata.Themodelexpressedvariationthatischaracterizedbyoureigenvectorsandeigenvalues.Eachindividualairway modelwasexpressedasadeviationfromthemeanbyasetof b parameterstothe covariancematrix[17] Modelparametersyieldedshapedeformationcharacteristicsofthesample.This informationwasusedascovariatestoLogisticRegressionLogR,abinomialpredictormethod[1].Thisstatisticalmethodcanmeasuretherelationshipbetweena categoricaldependentvariableandacontinuousindependentvariable.AkaikeInformationCriterionAICwasjointlyusedwithLogRtodeterminethemodelgoodness oft.Webeganwithasetofcandidatemodelsanddeterminedthemodelwithleast amountofinformationloss.Thisprocessselectedouttheshapemodelparameters thatwereusedtoassociateNEHIshapedeformationwithotherNEHIclinicalresults.AnOddsRatiowasusedtoexpresstheincreaseinbelongingtotheNEHI populationbaseduponanincreaseinourindependentvariable.Wetestedourmodel withbothLeave-One-OutcrossvalidationprocessandChi-Squareddistributionof thedierencebetweenournullhypothesisandthemodelresiduals. Pulmonaryfunctiontestsprovideaclinicalmeasurethatcanbeusedtodetermine thesignicantofourshapedeformation.Wedeterminedthecorrelationcoecientof availableIPFTresultsandthesignicantshapeparametersfromPCA.Ifatestresult providedsignicantcorrelationwithashapeparameter,weusedLinearRegression LinRtodetermine R 2 .TheNEHIfunctionresultsarehighlyvariableasarethe shapeparametersandtogethermayindicatediseaseseverity. 4

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2.Background 2.1TheHumanLung Thehumanlungisanintegratedsystemusedtoexchangeoxygen O 2 andcarbondioxide C O 2 betweentheairspaceandourblood.Theeectivenessofthe lungsliesinitsabilitytocreateanimmenseamountofsurfaceareaforpassivediffusionofgases.Thisisaccomplishedwhilesimultaneouslymaintainingathinregion denedbyepitheliumandendotheliumlayerswithinthethoraciccavity.Italso needstoevenlydistributeuid-owthroughoutthecomplexnetwork.Therespiratorysystemisrequiredtobeverydynamicandelastic,allowingforstressfromthe inspiratory-expiratorycycle.Thelungsprovideaboundarybetweeninternaltissue andexternalenvironments,andarerequiredtohandleaninltrationofbacteria,airbornepathogens,andtoxinsthroughthesecretionandmovementofmucus[61,92]. Bybirth,thelungshavedevelopedalveolarductsthatareexpandedandcapable oftransferringoxygenintothebody.Formationofthealveoliandcorresponding capillarybedscontinuestodevelopduringtherstfewyearsoflife,allowingforlung volumetoincreaseincoordinationwithgrowth[68]. 2.1.1BasicAnatomy&Physiology Thelungsaresituatedwithinthethoraciccavityandareprotectedbybony structuressuchastheribsandsternum.Twopleuraeboundthepleuralcavity, actingasafrictionlessspaceandallowingforindependentmovementofthelungs fromthethoracicwall.Theparietalpleuralinestheinsideofthethoraciccavityand diaphragm,whilethevisceralpleuralinesthelungsitself.Thetracheaisasingular portfortheentranceandexitofgasfromthelungs.Therespiratorytractleading tothetracheaisresponsiblefordeliveringwarm,humid,andlteredairintothe lungs.Itsubdividesintotherightandleftmainbranch,whichfeedtherightand leftlung,respectively.Thecarinaisacartilaginousridgethatislocatedatthebase ofthetracheaandestablishestherstbifurcation.Eachdaughterbranchcontinues 5

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tosubdivide,developinganairwaytreenetwork.Therightlungcontainsthreelobes andtheleftonlytwo,allofwhicharecompletelyseparatedbyssures.Thelingula oftheleftupperlobeisgeographicallysimilartotherightmiddlelobebutlacksan establishedssure[3,68,91]. Approximately,therst14generationsofbranchesaretheconductingairways, orphysiologicdeadspacewherenogasexchangeoccurs.Theinitialgenerations arereferredtoasthebronchiandcontainringsofcartilageandmucous-secreting glands.Bronchiolesareconductingairwaysunder2mmindiameterandnolonger havestructuralcartilageorglands.Thebifurcationtreetransitionsintotheacinar airwaysweregasexchangebegins.Alveoliareslowlyintegratedintotheairway walluntiltheybecomeconcentratedtothepointofformingalveolarducts.The terminationofthetreesystemisatthealveolarsacs,aclusterofalveoliroughly27 generationsfromthetrachea.Theadultlungcontainsabout300millionalveoli,all ofwhichareventilatedandperfused.Theexpanseofthealveoliisroughlyequivalent tothesizeofatenniscourt,or130-185sqmeters[61,68,91,92]. Thehilumofthelungistheportformajorbloodvesselsandtheprimarybronchi. Pulmonaryartiesfollowthebronchialtree,terminatingwithcapillariessurrounding thealveoli.Therespiratorymembraneisseparatedonlybyepithelialandendothelial cellsadjoinedbytheirbasementmembrane.Otherareashavealayerofinterstitial tissuethatexistbetweenepithelialandendothelialcells.Thisthinboundarycoupled withsmalldiusioncoecientsallowsforthemostrapiddiusionrates[61,92]. Ratherthanfollowingaparallelpathtothebronchioletree,oxygenatedbloodinthe veinsfollowamoredirectroutebacktothehilum[68]. Fluidowiscausedbypressuregradients.Anegativepressureinthelungsrelativetoatmosphericpressureexistduringcontractionofthediaphragmandintercostal muscles,increasingthevolumeofthethoraciccavityandtheintakeofair.Partial pressureofeachgasspeciesdeterminesthedirectionof O 2 and C O 2 diusion.The 6

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Figure2.1:Thehumanrespiratorysystemfrommacrotomicroscopicviews[7]. higherpartialpressureofoxygeninthealveolirelativetothepulmonarycapillaries establishesaowof O 2 intothebloodstreamuntilequilibriumisreachedatroughly 100mmHG.Concurrently,thisprocessoccursfor C O 2 butintheotherdirection. SurfactantproteinssecretedbytypeIIepithelialcellslowerthesurfacetensionofa thinliquidlmcoveringthesacs,inhibitingthecollapseofthedelicatelythinalveoli duringtherespiratorycycle[68].Adiagramofbasiclunganatomyispresentedin Figure2.1incoordinationwiththisdiscussion. Themajorityoflungdevelopmentintoawellorderedstructureoccursduring gestation.Theinitiallungbudwillundergomorphogenesis,resultinginterminal bronchiolesby16weeksandalveolarductsby28weeks.Thelungsarefunctionalby 36weekswithsurfactantproduction,vascularcapillaries,andthinepithelium[68]. Atthispoint,roughly20millionalveoliexistintheformofductsandexpandto300 millionalveolisacsin3years[91]. 2.1.2AirwayStructureandFunction Thestructureofthelungshasbeennelytunedtoaccomplishthenecessary functionalrequirementofprovidingadequateowrateof O 2 formetabolicneeds 7

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Figure2.2:Adiagramrepresentingtheprogressionofbranchbifurcations.Thepaths thataremorestraightarealsowider[61]. [91].Itisthelargestorganinthehumanbodyandanadultlungiscomposedof 0.5Loftissue,0.5Lofbloodand4Lofair[61].Fluidowthroughtherespiratory systemisdenedbythecharacteristicsofthebranchingtubesoftheconducting space.Thelungiswelldevelopedtoreduceenergylossintransporting O 2 through geometricarrangementofbranchangles,lumencross-sectionalareaandbranchlength [21,39,91]. Humanlungsclassicallybranchindichotomyandsometimesintrichotomywhile followingadiameterandbranchanglerelationship.Alargerlumendiameterofa daughterbranchfollowsastraighterpathfromtheparentandasmallerlumentakes asharperangleasisshowninFigure2.2[87].Itisimportanttonotethatthesum oftheradiiofdaughterbranchesisgreaterthanthatoftheparentbranch[92].The lungshavealsoevolvedsuchthatthebranchservingmoredistalgasexchangehasa smallerangletotheparentbranchthanthemoreproximalgasexchangebranch.This structuregreatlyreducesthevelocityofgasasitreachesdistalbronchiolesextending timeforgasexchange[61,92]. Horseldetalmodeledtherelationshipsbetweendiameterratio R d ,branch ratio R b andlengthratio R l as R l = R d = R b 1 = 3 andhismeasuredndingagreed withthisevaluation[40].Computationmodelsfromcomputedtomographyimages byTawhaietal.haveshownagreementwiththevaluesthatHorseldcalculatedas 8

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Figure2.3:Arepresentationofthefractalspace-llingcharacteroftheLung[92]. R b =2 : 8, R b 1 = 3 =1 : 4, R d =1 : 4,and R l =1 : 4[40,84].Theconsistencyofthese valuesmatchesthewell-orderedmorphogenesisofthelungs.Thebronchiolestructure isestablishedduringfetalgrowthandisbasedupontheinteractionofepitheliumof thetrachealbudandmesenchyme,whichwillbecomethesupportivenetworkofthe lungs[91].Astheindividualgrows,thelungsexpandandllmorespace,however, theairwayanglesdonotchangerelativetothisgrowth[23]. Themorphometryofthelungsisself-similar,orfractalinnature,andthusanalysisofasmallunitofthesystemcanbeinformativeofthewholeairway[92].This complexsystemcanbemodeledandsimpliedbyutilizingthespacellingnature offractalsasshowninFigure2.3.Thehumanlungisnotsymmetric,butitsheterogeneitycanbeproduceddependingonboundaryconditionsappliedtothesystem andtheadjustmentofafractaldimension D f .Thisdimensioncharacterizesthe irregularityofashape.Smoothshapeshavealow D f ona1-2scale-3for3D shapesandgreaterspace-llingshapeswillbecharacterizedbyahigh D f [65]. AsshownbyFigure2.4a,theinclusionofvariousphysicalboundaryconditions and D f establishesamodelmoreanatomicallycorrectthanWeibel'sbasiclungfractal 9

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a2DFractalModel[65] b3DComplexFractalModel[47] Figure2.4:aShowstheaectsofboundaryconditionsand D f onasimplistic2D fractalmodelandbexpandscomplexityofthemodeltoestablishamoreanatomical representation. Figure2.3.Optimaluidowrequiresspecicformation.Kitaokaetaldeveloped amorecomplexmodelwithgreatergenerationalaccuracybyiterativelyapplyinga collectionofrules[47,82].Theendresultisseenasanitefractalairwaytreeset intoathoracicshape.ModelssuchasFigure2.4bcanbeusedtounderstandof howlungformationaectsphysiologyoftherespiratorysystem.Thestructureofthe lungsthatcanbeviewedthroughmodelingtechniquesissimilartothestructurewe cannotsee. 2.1.3AirwayRemodeling Diseasepathophysiologydescribedbyvisualradiologyreadingisamajorunit ofclinicalevaluation.PulmonarydiseasesaredescribedfromCTimagestacksby radiologistsasvaryingpixelattenuation,airwaylumenthickness,lumendiameter andstructuralabnormalities.Eachdiseasehasaspecicvisualcharacterization, althoughsomedetailsoverlap[20].QuantitativeanalysisofCTimagesspansboth2D 10

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imagelesand3Dimagereconstructionthroughsegmentationtodescriberemodeling processes. Variousgroupshavestudiedtheconnectionbetweendiseasephysiologyandimage representation.Fractaldimensionshavebeenusedtoshowcorrelationbetweenspacellingwith D f valuescomparativetoacontrolgroup[8,36].Airwaylumenand wallthicknessmeasurementinchronicobstructivepulmonarydiseaseCOPDshow correlationwithairowlimitationsandairtrappingfromPFTs,aanotherclassic clinicalmeasurementfordetermininglungphysiology[5,38,48,56,57].Forexample, theCOPDGeneStudygroupassessedthedierencebetweenvisualandquantitative analysisofpatientswithemphysema.TheirresearchusingApolloWorkstationfor pixelattenuation,wallthickness,andlumendiameterhasshowncomparableresults betweenthemethods.However,quantitativeanalysisisamorereproducibleresult [6].Determiningtherelationbetweenshapechangesanddiseaseprogressioncanaid inearlierdiagnosis[58]. 3DsegmentedmodelsfromCTscansareusedtolinkdiseasewithstructuralmorphometry.Puetalexpressedarelationbetweenairwaytreevolumecalculatedfrom 3DsegmentationtopulmonaryfunctionaltestsPFTs[73].Airwaysegmentation modelsareusedwithFEAandCFDstudiesaswell[44].DeBackeretal.correlatedasthmawithfunctionalairowvaluesfromPFTs.Regionalstructurechanges aectedowresistanceintheCFDmodel,expressingthesensitivityofthelungs tosmallchanges[21].Figure2.5highlightshowtheuseofbronchodilatorsaects regionalstructuralchangesthatcorrelatewithresistancechanges. 2.1.4PediatricRemodeling Pulmonarydiseasesthatexistinpediatricsprovideadditionimagingandradiologyreadingchallenges.CharacteristicsseenonadultandpediatricCTsdonot associatewiththesamepathophysiology.Radiationexposureandpatientcomplianceisalsoaconcernwithpediatricsandthustherearefeweravailablescansfor 11

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Figure2.5:Therelationshipbetweenchangesinbranchvolumeandairowresistance aftertreatmentwithabronchodilator[21]. research.Protocolsusingsedationandcontrolledventilationhavebeenestablished toproviderepeatableresults.NewerhighresolutionCTmachinesusefastscanners thatexposepatientstolowradiationdoses,between80-120kVdependingonpatientsize[51,76].QuantitativeresultsforpediatricCTscansarestillabletoidentify airwaywallthickeningandlumendiameterinCysticFibrosisthatcorrelatedwith PFTs[22,53]. Additionally,pediatricpatientsarecontinuallygrowing,whichaectsthestructuralshapeoftheirrespiratorysystem.SeveralstudieshavebeencompletedtocorrelatepatientlengthwithquantitativeanalysisfromCTsegmentation.Lungvolume, airvolume,andtissuevolumeallincreaselinearlywithpatientlength.Densitometryofpediatricscansshowsthatalveoliincreaseinnumberasexpected,anddonot increaseindiameter[75].DeBoerandHumphrieshavecompletedanalysisshowing thatcorrelationexistsbetweenbronchiareaandlength,andthatairwayanglesdonot changewithgrowth.Anormativemodelwasestablishedandtheexpectedbronchi areaandbranchanglesaredepictedinFigure2.6[23,41]. Theextentofresearchcompletedwithadultsandpulmonarydiseaseisextensive, andspecicconsiderationneedstobegivenwhenperformingquantitativeanalysis 12

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aAirwayAngles bAirwayDiameter Figure2.6:Aschematicofthenormalpediatricairwaybranchinganglesaand airwaylumendiameterb[23,41]. andimagesegmentationwithapediatricpopulation.Methodsforadultscanscan betransferredtopediatricscansbuttheresultsdonotreadilysupportthesame pathophysiology[51,76]. 2.2Modeling 2.2.1AirwayModelsfromMedicalImages Computermodelscanshowhowbranchpatternandreductionofairwaylumen aectscomputationalairow[84,94].FiniteelementanalysisFEAandcomputationuiddynamicsCFDareappliedtorespiratorycomputermodelstostudy correlationbetweenairtreestructureandpulmonaryfunctionaltestsPFTs[85]. TheNavier-Stokesequation,whichdescribesuidow,showshowairwayobstructionaectsvelocityproles,owrate,andpressuredistributioninphysicalmodels duringbothinspirationandexpiration.Overall,suchmodelingsuggeststhatthe lungsaresensitivetobifurcationconguration[82,84,94]. 13

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ApplicationsofmodelingsystemstoairwaystructurehasmadedrasticimprovementswithdevelopmentofvolumetricimagingtechniquessuchascomputedtomographyCTandmagneticresonanceimagingMRI[22,83].Amergebetweenmathematicalmodelsandpatientspecicanatomyallowsbetteranalysisoftherelation betweenstructuraldesignandfunctionalcapacity.Thesemodelscanbeusedto determineimportantdimensionssuchasairwaywalldiameterandwallthickness. Imagingtechniquesarenoninvasiveandareusedforinvivostudiesinbothhuman andanimalpopulations[18]. CTistheimagingmodalityofchoiceforthelungsandhasbeenusedformost airwaysegmentationalgorithms[74,90].Therobustnessofthealgorithmispertinent tostablesegmentationswhendealingwithvariousdiseasestatesandimagingprotocols.Region-growingmethodshaveshownreliabilityandadaptationshaveimproved airwaywallleakrecognition[89].Airwaytreesegmentationscanbequantiedfurtherbyprovidinganalysisoftheskeletonstructure.Afast,curve-thinningalgorithm iterativelyremovesborderpointsofthesegmentationwhilemaintainingconnectivity toasingularlineendpoint.Thisproducesaonevoxelwideskeletonoftheairways. Roughboundariescausespuriousbranchesthatareremovedbaseduponlengthand airwaybranchrelationsusingDijkstra'swellknownshortestpathalgorithm[67]. Adaptationandimprovementsofsegmentation/skeletonizationalgorithmsisongoing,butcommerciallyavailablepackagesprovidethesemethodsforclinicaluse. Evaluationofairwaychangesareprovidedingroupsofquantitativeanalysisfor parenchymadensity,ssureintegrity,andairwaystructureanddimension.Apollo WorkstationVidaDiagnostic,Coralville,IAisonesuchpackagethatprovidesa graphicaluserinterfaceforairwayquantitativeanalysis.Theunderlyingalgorithms ofApolloWorkstationuseregion-growingandfast-thinningmethodsforsegmentation andskeletonization.MultiplestudieshaveutilizedtheanalysisprovidedbyApolloto determinehowremodelingprocessescorrelatetodiseasestateandlungfunctionality 14

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[5,6,75]. 2.2.2ImageRegistration Increaseduseof3Dmodelstovisualizepatientspecicdeformitieshasexpanded theeldofpoint-setcorrespondenceandstatisticalshapesmodels.Comparisonof similarobjectsiseasyforthehumaneyetodeterminebutprovidessignicantcomputationalchallenges.Computervisionisaeldbasedonndingtheoptimaltransformationfromoneimagetoanother[17,15].Analysisofshapedeformationswithina populationprovidesvaluableinsightintocorrelationofdiseasestatewithpathophysiology.Thesehighlydimensionalsetscanbesimpliedusingmodelingselectioning techniquessuchasprincipalcomponentanalysis.Populationmodelsrequireadditionalprocessingintheformofimageregistration.Complexformsvaryinposition, orientationandscale,whichchallengesalignmenttechniques.Correspondencealgorithmshavebeendevelopedtoautomaticallyalignlandmarksthroughnon-rigid transformations[15,62]. Feature-basedmethodsmapasourcemodeltoatargetmodelthroughaspatialtransformation,determiningpointcorrespondenceandtransformationsimultaneously.Optimizationoftheimageregistrationtechniqueisanintegralpartofthe establishedalgorithm[15,34,62].CoherentpointdriftCPDisanon-rigidimage registrationtechniqueestablishedbyAndriyMyronenkoandXuboSongthatsolves correspondenceanddeterminesanon-rigidtransformationasaprobabilitydensity estimationproblem. InCPD,physicallandmarksareusedbyttingaGaussianmixturemodelGMM ofonesettothedatapointsofanother.TheGMMisabletopresentsubpopulationsofcentroidwithinapopulation,ratherthanjustasingularcentroid.These subpopulationsareforcedtomovecoherentlywithadjacentpointsbyusingMotion CoherenceTheoryMCT.Thecollectivemovementofpointspreservestopology whilemaintainingsimilarsoftassignmentcharacteristicssuchasfuzzyconnectivity 15

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aThePointSetRegistrationProblem bCPDImageRegistrationResults Figure2.7:aAbasicexampleshowingsimilarbutdeformedandunequalpoint sets.bCPDisarobustalgorithmthatiterativelyregistersimages,eventhosewith missingpoints nd rowandoutliers rd row[62]. methods.Maximizingthelikelihoodestimationproblemusinganexpectationmaximizationalgorithmrenestheresult.Theuseofanon-parametrictransformation, whichisill-posedwithnouniquesolution,isconstrainedbyenforcingsmoothness. Regularizationusingoperatorsofthedisplacementeldandtheirvariationalderivativesaccomplishthis.Adisplacementvector,fromonestatetoanother,isassigned toalllandmarksinthepointcloud.CPDfollowsthebasicformofusingafeature basedsimilaritymethod,non-parametrictransformation,andoptimizationaccomplishedthroughregularization.Anexampleofthepointsetregistrationproblemand CPDsolutionsareshowninFigure2.7.Whilethismodelrepresentsasmall,2D pointset,MyronenkoandSonghavepublishedworkrepresentingtherobustnessof thealgorithmforsetswithhighdimensionality,imagenoise,structuraloutliersand varioussetsizes[14,62,63]. 2.2.3StatisticalShapeAnalysis StatisticalShapeAnalysisSSAisimmergingasaclinicalmethodtostudygeometricpropertiesofsimilarshapesorvaryingpopulationgroups.Morphometricsis aquantitativeanalysisofshapevariabilitywhichremovesinformation,suchaslocation,rotation,andscalethatisnotshaperelated[17,28,32,50,55,78].Landmarks 16

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highlightsimilarphysicallocationsorstructuresofasetofimageswithinasimilar shape.Psuedo-landmarksarealsoincludedtodescribeshapebetweeneasilydened landmarks-measuringdistance,curvature,anddirection.Geometryofthepoint congurationisretainedundertransformationandthedistancebetweenshapesis obtained.Estimationofameanshapedeterminesthevariabilitythatexistsfromthe meantoeachindividualshape. ThegeneralmethodforSSAistoestablishedlandmarksandpsuedo-landmarks. GeneralProcrustesAnalysisGPAremovesnon-shaperelatedvariationsandcollects apropershapemodel.Oncesetsbecomealignedtoacommoncoordinatesystem, PrincipalComponentAnalysisPCAreducesthedimensionalityoflargedataset anddescribeslinearvariationcalledPrincipalComponents.Thesecomponentsare organizedbycontributiontothetotalpopulationvariance[17,28]. 2.3NeuroendocrineCellHyperplasiaofInfancy 2.3.1ClinicalHistory&Challenges chILDisanewclassicationschemausedtocharacterizerarediuselungdiseaseinpediatrics.Thisdiversegroupexperiencescompromisedgasexchangeand diuseinltrates.Previously,thisgroupwasplacedintoadultILDcategoriesthat misrepresentedpediatricdisease-stateordidnotexistasanadultillness[31,27].The clinicaldenitionofchILDisthepresentationof3of4characteristicsintheabsence ofotherdisease:Respiratorysymptom,suchasacoughorrapidrespiratoryrate, Signsofrespiratorysymptomsliketachypneaorrespiratoryfailure,Hypoxemia,andDiuseabnormalitiesonthoracicimaging.Despiteanewclassication scheme,pediatricrarediuselungdisorderscontinuetochallengediagnosticboundariesbypresentingabroadarrayofheterogeneoussymptomswithpoorlyunderstood etiology.Additionally,thisoverlapcandiversifyintodrasticallydierentpatientoutcomes.Interstitiallungdiseasesoccuratanyageandinpediatricstheconditionis linkedtobothlunginjuryandlungdevelopment[25].Diseasemechanicsarealso 17

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misinterpretedduetomixedphysiologicpatterns.Theclinicalillnessofthepatient issevere,yetstrikingabnormalitiesarenotpresentinradiologicalimagesandbiopsy. UnderstandingonsetandprogressionofchILDswillsupportmoredirectedtreatment plans. NEHIclassicallypresentswithpersistenttachypnea,crackles,retractions,and hypoxemiaduringthersttwoyearsoflife.Patientsymptomsarenotimprovedby useofbronchodilatorsnorcorticosteroidsandtheconditionhasnoassociatedetiology [31].NEHIpatientsalsolackanyinammatoryresponseintheircondition.Based uponaninitialassessmentwiththesepresentations,patientsaredeterminedtohave achILDbutmayrequirefurthertestsforamoreaccurateassessment.Clinicaltests prescribedareinfantpulmonaryfunctiontestsIPFTs,computedtomographyscans, bronchoalveolarlavage,and/orbiopsy.Withexpertclinicalopinion,yetwithouta biopsy,adiagnosisofNEHIsyndromecanstillbemade.Thereisahigherpercentage ofmaleNEHIpatientsandafewcasesofNEHIsiblings,whichsuggestsagenetic susceptibilityofNEHIaswell[69,54]. ThecharacterizationofNEHIisnewlyestablished,andonlyafewinstitutions areactivelystudyingitsprevalenceandexpression.PatientswithunknownILDsare beingsenttolarge,specialtyinstitutionsforfurtherevaluation.Adiagnosticmethod forNEHIisneededtoprovideaclearandconciseresult,allowingsmallerinstitutions accurateevaluationwithoutneedforpatientreferral. 2.3.2TestResults WepresenttheclassictestresultsofNEHIsyndrome.Thesecharacteristicsare notnecessarilydistributedevenlyorconsistentamongtheNEHIsyndromepopulation. 2.3.2.1ComputedTomography ACTscanonapatientthoughttohaveNEHIcanbehighlyinformative.A standardNEHICTscanlacksmajorgeographicorstructuralchanges.However, 18

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Figure2.8:40-month-oldgirlwithtypicalappearanceofneuroendocrinecellhyperplasiaofinfancy.A-C,Inspiratoryhigh-resolutionCTscansshowsharplydened areasofground-glassopacicationalongmediastinalborders,peripherally,andmost prominentlyinrightmiddlelobeandlingulaasterisks,C[10]. non-specicpresentationofgroundglassopacityGGOisseenandoftenlocalizedto specicareasofthelungduringinspiration.Anincreaseinattenuationthatpresents inavarietyofpatternsthroughoutthelungparenchymaisclassiedasGGO[16]. WhilethendingsareconsistentinNEHI,itleadstonofurtherunderstandingto theetiologyofNEHI,inbothidenticationandinterpretation.Characterizationof GGOfromadultILDsisnotalwaysrelatedtoconditionspresentinpediatrics. KnownetiologiesofGGOoftenappearonbiopsyreadings.NEHIpatients,however,haveanearnormalbiopsyrelativetobrosis,pulmonaryhemorrhaging,and increasedcelldensity[9].LocalizationofGGOiscommonlyfoundintherightmiddlelobeRMLandlingula.InadditiontoGGOintheRMLandlingula,select patientspresentGGOinotherareasorexpressotherabnormalitiessuchasbrosis, architecturaldistortion,reactiveinjury,orinammation.HyperlucentareasonexpiratoryscanaretheothermostcommonndinginNEHI.Thisisanexpressionofair trappingandhighlungvolumeresultsfromIPFTs[10]. 19

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2.3.2.2InfantPulmonaryFunctionTests PediatricfunctionaltestsprovidedaccurateandreproducibleresultsundercurrentstudystandardsbutdonotprovidesucientdatatodiagnoseNEHI.Patient presentationoftachypnea,retraction,andhypoxemiaexpressmajorphysiologicalimpairmentsthatcanbesupportedbyIPFTs.Theprocedurerequirespatientsedation tomeasuretidalbreathing,plethysomography,andraisedvolumerapidthoracoabdominalcompressionRVRTC.KerbyetalevaluatedtheIPFTresultsofNEHI patientsdiagnosedbybiopsyandNEHIpatientsdiagnosedbyclinicalpresentations andCTresultsNEHIsyndrometoadiseasecontrolgroup.NEHIandNEHIsyndromepatientsdidnotdierfromoneanotherbutexpressedsignicantdierences fromdiseasecontrolandnormalinbothairtrappingandobstructedairowmeasurements.SignicantairowobstructionwasobservedinNEHIpatientsgivenbylow forcedexpiratoryowbetween25%-75% FEF 25 )]TJ/F17 7.9701 Tf 6.587 0 Td [(75 .LowFEFvaluesinNEHI patientswereexhibitedbyalowforcedexpiratoryvolumeat0.5sec FEV 0 : 5 .Additionally,alllungvolumemeasureswerehighinNEHIpatients.Residualvolumeover totallungcapacity RV=TLC inNEHIwasunprecedentedlyhigh,suggestingNEHI patientsareseverelyairtrapped.TheresultsofthisstudyareshowninFigure2.9.It canbeconcludedthatpatientsexpressingaspectrumofairowobstructionandair trappinghaveNEHIcharacteristics. 2.3.2.3BronchoalveolarLavage NEHIbiopsyresultsarenear-normalwithlittletonosignofinammatory changesinpulmonarytissue.AcytokineproleofNEHIsyndromepatientswasextractedviabronchoalveolarlavage.Theresultsoflavageagreewithbiopsyreadings thatinammationisnotsignicantlypresentinNEHI.Bothneutrophilsandwhite bloodcellcountweresignicantlylowercomparedtodiseasecontrol,cysticbrosis, 20

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aAirFlowMeasurements bAirTrappingandLungVolume Figure2.9:ComparisonofNEHI/NEHIsyndrometodiseasecontrol:ashowsconsistentlylowairowvaluesinNEHI,whichsuggestsobstructedairways;bshows consistentlyhighresidualvolumesrelativetototallungvolume,whichsuggeststhe presenceofairtrappinginNEHI[45]. andfollicularbronchiolitisFigure2.10.Thesevaluesareclosertotheexpected normalrangeinhealthypatients[70]. 2.3.2.4Biopsy ThegoldstandarddiagnosticforNEHIisabiopsyreadingofahighcountof neuroendocrinecellsNECsindistalairwaysandlacksotherhistologyabnormalities [31,95].Initially,histologicalreportsusinghemotoxylinandeosinreturnednegative results,withnodiscernablestructuralorinammatorychanges.Theyalsolacked changesinpulmonaryvasculaturesuchasmedialthickeningassociatedwithhypertension[26].Theobservationofincreased'clearcells',orhydrophobicepithelialcells, gavecausetotestbombesinimmunohistochemistry.Bombesin-likepeptidesBLPs aremembersofthebioactiveproleofpulmonaryneuroendocrinecellsandarebest distinguishedbygastrin-releasingpeptidesGRP.ResultsofbombesinimmunohistochemistrystainingshowedaprominenceinNECsrelativetopercentareaincontrols Figure2.11.Co-localizationofbombesinandaproliferativemarker,Ki67,didnot 21

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Figure2.10:BoxplotsdisplayingthedistributionofAabsoluteWBCcountsand BNeutrophilcountsacrossthediseasegroups.Thehorizontalreferencelineand shadedareacorrespondtothemedianandnormalrangeofvaluesinhealthypatients frompreviouslypublisheddata.NEHIhasmorenormalWBCandNeutrophilcount relativetootherdiseasegroups[70]. exist,thus,suggestingnonewPNECproduction.The3-foldincreaseinPNECswas wellcorrelatedwithairwayobstructioninsmallairways.Localizedbiopsysamples inareasofGGOfromCTscansdidnotshowanyrelation.Thissuggeststhatthe non-descriptpresentationofGGOisnotassociatedwithNECdistribution[95]. 2.3.3SignicanceofNeuroendocrineCells Neuroendocrinecellshavevaryingrolesthroughoutfetalandneonatallungdevelopment.Thesecellsarelocalizedtotheconductingairways,reachingfromthe basementmembranetotheairwaylumen.InnervatedclustersofNECsarecalled neuroendocrinebodiesNEBs.NECsandNEBsproduceaselectionofbioactive proteinssuchasserotonin,calcitonin,cholecystokinin,andGRP.Duringfetalgrowth, theseproteinspromotebranchmorphogenesis,epithelialandmesenchymalcellproliferation,andsurfactantsecretions[2,26,95].Thismechanismwasclassiedby Aquayoetal.inamousemodel,andtheaectsonairwaybranchingisshownin Figure2.12.CellsproducingBLPspeakduringmid-gestationanddeclinerapidly 22

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Figure2.11:A,Schematicofproximalanddistalairways.ProximalairwaysB,Cx 200showfewerNECsthanrespiratorybronchiolesDx100andalveolarductsFx 200.RespiratorybronchioleofdiseasecontrolshowfewerNECsthanNEHIpatients Ex200[95]. afterneonatalperiod.Afterbirth,PNECsareinvolvedwithoxygenchemosensinginuencingbronchoconstrictionandvasoactivityinresponsetohypoxemia[19].The functionandroleofNEBsrelativetochroniclungdiseaseisunknown,aswellasthe prominenceofNECsinNEHI.TheconditionexistsinNEHIwithuninjuredairways andnosignofinammatoryresponse. AgeneticstudyonchILDshasidentiedgenemutationsaectingsurfactant proteinproduction,lungdevelopment,andalveolarcapillarydysplasia,aswellas pathwaysforselectdiuselungdiseases[66].NEHIdoesnotpresentwithintherst weekoflife,thusitisnotacongenitaldisease.However,thereisgeneticsusceptibility betweensiblingswithahigherexpressionrateinmalesthanfemales.Withlittle evidenceofenvironmentalcause,studyresultssupportageneticetiology[69,54]. WespeculatethatthesignicanceofincreasedNECcountinNEHIisrelatedto theirroleofbranchmorphogenesisduringfetalgrowth.Researchusingamousemodel 23

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Figure2.12:AEmbryoniclungrudimentdissectedatgestationday11demonstratingonlyfourbranchingpointsandBthesameembryoniclungafter3daysin culturegestationday14demonstrating18branchingpoints[2]. geneticallyampliedBLPreceptorsintheembryoniclung.Treatingthemodelwith bothbombesinandanagonistligandtothereceptorresultedinchangestoairway cleftcount,showninFigure2.12.Thepresenceofbombesinrelatedtoanincreasein branchingpointswithnosignicantchangeincellproliferation.Theanalog,however, reducedthenumberofcleftspresent[2].Theincreasedcountofbranchesassociated withincreasedBLPleadsustobelievethatthecompromisedlungfunctionofNEHI patientsisrelatedtoastructuralchangepresentintheairwayofNEHIpatients. 24

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3.Methods 3.1PatientPopulation OurstudywasapprovedbytheColoradoMultipleInstitutionalReviewBoard COMIRBprotocol10-0934.Wecollecteddatafrom21patientswithclinicallyand radiologyconrmedNEHI.ClinicalevaluationwascompletedatChildren'sHospital ColoradoCHCandrequired8of10NEHIpresentationsasprovidedbyAppendix A.RadiologyreportswerecompletedbyapediatricILDspecialistatCHC.Patients wereclassiedinto4categoriesinwhichthreecharacterizedNEHIAppendizB. Threepatientshadtoberemovedfromthestudy:oneforexcessivenoiseartifacts confoundingoursegmentationprocess,anotherforslicethickness,andthenalfor onlyhavingaCTfromoutsideourradiologydepartmentatCHC. ThecontrolgroupdatawasselectedfrombonemarrowtransplantBMTpatients thathadacquiredhighresolutionCTscansduringtheirevaluationatCHC.The BMTpatientsforthisstudyhadnoreportoflungabnormalitiesasdeterminedbya pediatricradiologist.WeageandlengthmatchedthecontrolgrouptotheNEHIdue tothelowmeanage.7monthsandlength.1cmofourNEHIcohort.Thisleft uswithatotalof7controlpatientsforourstudy.AllCTimageswereacquiredafter April2010withathicknessofeither0.6mmor1.0mm. ClinicalvalueswerecollecteddayofscanandhavebeenprovidedforbothpopulationTable3.1.Weusedtherangeforeachvalueratherthanstandarddeviation andcondenceintervalduetothesmallsamplesize.BodymassindexBMI= kg=m 2 hasbeenrecorded,usingbothcalculatedvaluesand z -scoretoemphasizelow scorevaluesforNEHIpatients.Thesevalueswereassessedfromthe2000Centerfor DiseaseControlGrowthChartsfortheUS. 3.2ImagingTechniques Advancesincomputedtomographyhavedrasticallyimprovedtemporalandspatialresolutionwhilereducingionizingradiationexposure,allowingforbetterimage 25

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Table3.1:StudyDemographics ClinicalValues NEHI DiseaseControl Male% 12.67% 5.42% MeanAgerangeinmonths 9.72-22 12.29-20 MeanLengthrangeincm 71.06-85 76.36-87 MeanWeightrangeinkg 7.75.3-12.1 9.59.5-12.75 CalculatedBMIrangein kg=m 2 15.32.7-18.54 16.28.9-17.53 z -scoreBMIrange -1.49 )]TJ/F15 11.9552 Tf 9.298 0 Td [(2 : 5-1 -0.36 )]TJ/F15 11.9552 Tf 9.298 0 Td [(1 : 5-0.5 qualityinapediatricpopulation.Thincontiguousimageslicesforthethoraciccavity arereduceddownto0.6mm-1mminthickness.Whenconsideringaninterstitiallung disease,asharpkernelprocessisrecommended,allowingdetailoftheparenchymato bevisualized. RadiologyimagesforthisstudywerecollectedfromChildren'sHospitalColorado RadiologyDepartment.Duetotheageofourpopulationandtheinabilitytocomply withbreathinginstructions,patientsweresedatedforimaging.Controlledventilation allowsaradiologytechtoadministerabreathincoordinationwithscanning.Afull volumetricimageistakenatinspirationandasectionedscanduringtidalexpiration. TheCTscanneratCHCisSiemansSOMATOMSensation40andallpatients wereimagedwiththisdevice.Afewpatientsof23hadaz-stackthicknessof1mm ratherthan0.6mm.Theradiationthepatientisexposedtoisbetween80-120kV. Theexposurevalueisbaseduponthethoracicareaimagedandthusisdierentfrom patienttopatient.AdiscrepancyexistedinkernelreconstructionbetweentheNEHI anddiseasecontrolDCgroup.MostallDChadasoftB31fkernelreconstruction andtheNEHIhadamixofbothsoftandsharpB60f/B70fkernels.AfewNEHI patientshadbothreconstructions.Inthiscase,wechosethesoftkerneltoreduce variabilitybetweenpopulations.Table3.2exhibitsthenumberofkernelspresentfor 26

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Table3.2:Availablekernelreconstructionforpatientcohort.AsoftkernelB31f wasusedoverasharpkernelB60f/B70fwhenavailable. Kernel DiseaseControl NEHI B31f 6% 10% B60f 0 4% B70f 1% 13% eachpopulation. 3.3SegmentationandSkeletonization ApolloWorkstationVidaDiagnostics,CoralvilleIAisasemi-automated,airwayspecic,segmentationpackage.Itprovidesvariousclinicalmeasuressuchaslungvolume,airwaydimensions,parenchymalanalysis,andssureintegrityanalysis.Itwas usedinthisprojectforitsabilitytoprovideairwaysegmentationwithuser-dened brancheditingandlabeling. ToaccommodateforvariousCTeldofviews,weestablishedacutoforthe trachea.Theairwaysegmentationwasinitiatedatthetopofthelungairspacewhen viewedintheaxialplane.FollowingApolloWorkstationeditingprotocol,webegan byremovingairwayleaksandfalsebranches.Wecheckedtoseeifbranchmergingwas necessarythroughouteachscan;Apollooccasionallyestablisheserroneousbranches. Wecouldthenbegintheprocessofbranchlabeling. Usingadenedlistofbranchesforourstatisticalshapeanalysiswasrequired toequalizetherepresentationofperipheralbranches.Thesoftkernelreconstruction greatlyaectedthenumberofgenerationspresentinour3Dmodel.Figure3.1shows thecontrastbetweensharpandsoftkernelsegmentationsonthesamescanfroma singlepatient. AprotocolwasestablishedforbranchlabelingFigure3.2sothateachscanhad roughlythesamesegmentslabeledrelativetogenerationandorientation.Weused 27

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aSoft:B31fKernel bSharp:B70fKernel Figure3.1:BothsegmentationsarefromasingleCTacquisitiononapatientwith aasoftkernelreconstructionandbasharpkernelreconstruction. Weibel'sgenerationscheme,whichallocatesthetracheaasgeneration0andlabeled outtothe4-6thgeneration[92].Topologicalvariationsexistedbetweenpatientsbut parent/daughterrelationsweremaintained.Forexample,RB1,RB2,andRB3do notnecessarilytrifurcatefromRUL.Onoccasion,ApolloWorkstationestablishestwo bifurcationswithincloseproximityofoneanother.Thiswascorrectedbyinsertinga shortRB1+2branch,forexample.Thelistofbrancheswithrespecttoparentand daughterbranchesisinAppendixA. ApolloexportdatawasbroughtintoMATLABaversion:8.1.0.604,The MathWorks R ,Natick,Massachusettsforfurtheranalysis.Inthepatientdirectory les,ApollostoresaskeletonizationoftheairwaysegmentationAnalyzeimageformatsandlinkerdataforbifurcationpointseXtensibleMarkupLanguage.Theairwayskeletoniseasilyextractedbutbranchpointdataisorganizedintiersofbranch generationid,startbranchpoint,endbranchpoint,andcenterlines.Anin-house XMLparsecodewasutilizedandadjustedforthisstudy[41]. 28

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Figure3.2:ThegeneralairwaylabelingschemeusedinApolloWorkstation.Various changesweremadefortopologicaldierencesbetweenpatients,notshownhere. Apollohasanorderednomenclaturesystemforallbranchesintheskeletonthat isoverwrittenduringthelabelingprocess.Weextractedthestartandendpointsof onlylabeledbranchesfromourprotocolfromtheXMLles.Notallbrancheswere presentineachscan,inwhichcasetheendparentbranchpointandstartdaughter branchpointwereusedtoestablishazerolengthbranch.Thisaccommodatedthe smalltopologicalvariationsthatexistedbewteenpatientsets.Theserelationships havebeenestablishedinourbranchlabelingprotocol.Certaincenterlinedatadid notexistintheApolloexportdata.Toadjustforthisdiscrepancy,weusedanopen sourceDijkstra'salgorithmforndingtheshortestpathfromonepointtoanother [46].Adistancemapwascreatedusingtheskeletondata,suchthatthedistancefrom eachpointtoallotherswasestablished.Aconnectivitymapremovedinformation frompointsthatwerenotconnected.Ourskeletondataisrepresentedasvoxel positionfromtheCTscan.Aconnectionisdeterminedifthedistanceisgreater than0butlessthan p 3,whichcollectsvoxelsthatareside-by-side,edge-to-edge,or corner-to-corner[41,67].Figure3.3depictsthispruningmethodfromthefullApollo 29

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Figure3.3:Theprocessofpruningtheairwaytreetoaselectsetofbranchesfrom theApollosegmentation.Theblackskeletonrepresentsafullairwaytreefromthe segmentation,whilethegreenskeletonrepresentsonlyourselectedbranchesand theirrespectivebifurcationpointsinblue.Thesearetheairwaysusedforourstudy process. skeletontotheselectionofbranchesinMATLAB. Allskeletondatahasbeenstoredasvoxelindicesina3Dmatrix.Toconvert thisinformationintocoordinatespace,weextractthevoxeldimensionsfromtheCT report.Eachskeletonisadjustedintoamillimeterunitsystem,whichestablishes sizevariationbetweenpatients.Thebifurcationpointsofourskeletonprovidelandmarkswithbranchlengthdescribedbypsuedo-landmarks.Thesearerequiredforour statisticalshapeanalysis. 3.4Registration Imageregistrationisadiculttaskwhendealingwithdatathathavealarge degreeoffreedomDOFandrepresentsaintricateshape.Airwayskeletonsfollowa basictreeshapebutpresentvariationinbranchlengthandangle.Slightchangesin thetopologyofbranchgenerationexist,evenwithinthelargebronchioftherespiratorysystem.Twomethodsarediscussedinthisstudy. 30

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3.4.1SplineMethod Ourrstapproachwastouseamethodadaptedfrompreviousworkwithinour department.Asplinewasttoeachbranchsegment.Intheskeletonizationprocess, weprunedtheairwaytreetoaselectlistofbranchesandretainedthecenterlines ofeachspecicbranch.Thesplinetanequalsetofpointstoeachbranch,which wereorganizedbaseduponname.Selectbranchesweregivenazerolengthand thusresultedinasplineof50pointsinthesamelocation.Weestablishedimage registrationasabyproductofthismethod.Wealsoaccountedforcommontopological variationthatexiststhroughthismethodthroughourlabelingprocess.Atotalof 40brancheswereevaluated,eachwitha50pointspline.Ournaldatasetforeach patientwas6000DOFs x i ;y i ;z i for i =2000 x 50.Thismethodautomatically createscorrespondingdatasets.Alignmentofeachdatasetisaccomplishedusing GeneralProcrustesAnalysis,whichwillbediscussed. 3.4.2Non-RigidRegistration Oursecondmethodusednon-rigidimageregistration.CoherentPointDrift CPDisawellestablishednon-rigidimagealignmentmethodthathasbeenapplied inavarietyofcomputervisionproblems[14,15,62,63].Thisisitsrstapplicationtowardsanairwayskeletonalignmentproblembaseduponpublicationresults. AndriyMyronenkohasestablishedaCPDprojectpage,whichprovidesaMATLAB toolboxincludingnon-rigidimageregistration.Thepackageallowsfortheinputofa targetandsourcescanwithuser-denedfunctionparameters.Atargetskeletonwas selectedandmappedtotheremainingairwayskeletons.CPDalignseachscanto thetargetbaseduponaprobabilitydensityestimationproblem.Gaussianmixture modelcentroids,whichcharacterizelocalizeddeformations,aretbetweeniterations baseduponmaximizationofthelikelihoodestimationfunction.Thisproducesthe highestprobabilityofmodelt.TheGMMmovescoherently,restrictedbyMotion 31

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CoherenceTheoryMCT,andpreservingtopologicalstructure.MCTassignsthe displacementvectorsforallpointsinourskeletondatasetfromonestatetoanother asitisalignedwiththetargetset.Regularizationoftheregistrationisaccomplished byuseofthedisplacementeldandvariationalcalculus[62]. Aftereachregistration,avectorisproducedthatmapseachskeletonsettothe target.Thismapcanbeappliedtothesourcesetandthusequilibratesallscansto thesamesize,reducingeachsetdowntothesmallestdataset.Figure3.4highlights originalscanorientationrelativetoanother,thealignedscans,andthenalcorrespondencethatisproduced.Thereductionoflandmarksfromoursourcescanred isvisible,yetnosignicantlandmarkinformationislost. 3.5GeneralProcrustesAnalysis SetalignmenttoacommoncoordinateframeisaccomplishedbyGeneralProcrustesAnalysisGPA.Ourdataexhibitsvariationfrompositioninthescanner, orientation,andpatientsize.Weestablishareferenceshapebyarbitrarilychoosing ascanandaligningallotherscanstoit.Ourrstmeanmodelisthendetermined andbecomesourbaseshape.Thismeanmodelisiterativelyadjustedaswealignall scansagainuntilaminimumthresholdisapproached. Thisprocesswascompletedusingopensourceandin-housecodewithinput parameterstoincludescaling[41,71].Bothcodesfollowthewellestablishedmethod ofOrthogonalorGeneralProcrustesAnalysis,whichappliesProcrustesAnalysisto apopulationof s > 2[17,28,35,43,86].Thebasisofthismethodistominimize agoodness-of-tcriterion.1,whichismeasuredbytheresidualsumofsquares distancetoamean.Inthisequation, c 'isatranslationrowvector, isourscale factor,and A isourrotationandreectionmatrixappliedto X .Foreachshape,a centerofmassisdetermined,positionedattheoriginandscaledtoaunitsizerelative tothecentroiddistanceofeachshape. 32

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a b c Figure3.4:Illustrationofasourcescanredbeingregisteredtothetargetscan blue:aPatientsizeandorientationduringscanaectsspatiallocationandb afterCPDregistrationscansareorientedandnormalizedtotargetscanandcthe correspondencemapisapplied. 33

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j X )]TJ/F15 11.9552 Tf 11.955 0 Td [( c 0 + X i A j .1 Weiterativelyadjustthemeanshapeandadjustscantransformationtothenew mean.WerescalethecentroiddistanceCEq3.2tothenewmeanateachstepuntil convergence. C X = v u u t k X i =1 X i )]TJ/F16 11.9552 Tf 13.671 2.889 Td [( X 2 .2 Procrustesdistance d isourthresholdvalueanditisthesumofsquareddistance betweencorrespondingpoints x i ; y i ; z i andourmean u i ;v i ;w i eq3.3. d = p u i )]TJ/F16 11.9552 Tf 11.955 0 Td [(x i 2 + v i )]TJ/F16 11.9552 Tf 11.955 0 Td [(y i 2 + w i )]TJ/F16 11.9552 Tf 11.955 0 Td [(z i 2 .3 Ourendresultisascaledandalignedcloudofskeletonlandmarks.InFigure3.5, theresultsofourGPAalignmentisshownwiththemeanshapeoverlaid.Ascale factorwasincludedtoadjustforpatientsizebynormalizingthecentroiddistanceto one. 3.6PrincipalComponentAnalysis Afteralignmentandscalingofallskeletons,wecancompletePrincipalComponentAnalysisPCA.Thisstatisticalmethodreducesthedimensionalityofcorrelated databyprovidingadistributionofuncorrelatedvariation.Inourinstance,thisdescribesshapedeformationsthatareorthogonal.Covarianceisusedtodescribehow oureachlandmarkvariesrelativetooneanother[17,42,80].TheresultsofPCAare orthogonalvectorsthatdescribetheextentofdeformationalongagivenaxis.From Figure3.6,weseearepresentativepointcloudestablishedbyasingularlandmark acrossasampledata.Themainaxisproducedisgivenbyeigenvectordecomposition ofthecovariancematrix.BoththeSplineandtheCPDregistrationmethodsprovide aconsistentrepresentationofeachlandmarkwithinourskeleton.Forexample,the 34

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Figure3.5:GPAisaprocesstoalignskeletonsiterativelytoproduceameanshape greenandorientallpatientskeletonsbluesuchthattheleastsquaresdistanceto themeancentroidisminimized. cartesianlocationofthecarinainonepatientsethasthesamematrixpositionasthe carinainallotherpatientsset. Firstweestablisheachset s i with n degreesoffreedomin d dimensionsasa nd vectorofalllandmarks.Boththesplineandnon-rigidregistrationpointsare reshapedintotheformof3.4. x i = x 1 ;:::;x n ;y 1 ;:::;y n ;z 1 ;:::;z n T .4 Duetothelargenumberoflandmarksrepresentedineachset,especiallythe Splinemethod n =2000,weadjustourcovariancematrixEq.3.5asfollows: S = 1 s )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 s X i =1 x i )]TJ/F16 11.9552 Tf 12.142 0 Td [(x x i )]TJ/F16 11.9552 Tf 12.142 0 Td [(x T .5 Weestablishamatrix D ofresiduals 35

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Figure3.6:A2DexampleofPCAwhere p isaprincipalcomponentPCofthepoint cloudcenteredat x .Eachpointinthecloudhasarepresentativepoint x 0 onthePC thatisadistance b fromthemean[17]. D = x i )]TJ/F16 11.9552 Tf 12.142 0 Td [(x ::: x s )]TJ/F16 11.9552 Tf 12.142 0 Td [(x .6 Thecovariancematrix S canbewrittenas S S = 1 s DD T S 0 = 1 s D T D .7 Ratherthanusing S thatwillhavedimension nd nd S 'yieldsa s s matrix andisusedforbasiceigenvector e i /eigenvalue i decomposition. Byorganizingour e i bydescendingorderof i ,wehavealistofprincipalcomponentswiththerstvectorrepresentingthedeformationwiththegreatestweight ofalldeformations.Toreestablishourprincipalcomponentmatrixto nd degreesof freedom,weevaluate De i whichyieldsa n s matrix,called[17].Thisadjustment wasvalidatedwithourCPDdatasetbycomparingeigenvectorsfromand S ,since ourlandmarksetfortheCPDdatawassignicantlysmallerthanwiththeSpline data. Eachairwaymodel x canbeexpressedascombinationofthemean x airwaytree andthecovariancematrixadjustedbyavectorofparameters.These b parameters 36

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expressthedistancealongthePCto x 0 i ,aprojectionpointof x ontothePCfor eachdatapointFig3.6.Theparametersareusedtoclassifytheextentofshape deformation.Equations3.8and3.9expresstherelationof b toeachairwaymodel. These b parametersbecomethebasisforourstatisticalanalysisasadistinguisherfor NEHI.Notethatforthemeanmodel,all b parametersarezero. x x + b .8 b = T x )]TJ/F16 11.9552 Tf 12.142 0 Td [(x .9 3.7StatisticalAnalysis 3.7.1LogisticRegression The b parametersdeterminedfromPCAprovideaplatformfordetermininghow shapedeformationsrelatetoourNEHIanddiseasecontrolpopulations.Thesevalues areorganizedbypercentvariationanditiscommontoconsiderthecomponentsthat explain95%ofthevariance.Duetothelargenumberoflandmarksbutonlyafew samples,ourvariationisspreadacrossabroadrangeofPCs.Forourstatistical analysiswewillonlyconsiderthePCsthatexpress75%ofthepopulationvariance. LogisticRegressionLogRisabinomialmodelthatevaluatestheeectsofexplanatoryvariablesonasetofresponsevalues.Wewillbepredictingclassication intotheNEHIpopulationbaseduponour b i parameters.Givenonlyonepredictor b ,ourmodelisbasedupontherelationestablishedinEq3.10relativetothelinear regressionequation 0 + 1 b forresponsevariable Y andpredictorvariable X .Our response Y isthedistinctionbetweenNEHIorDiseaseControl.Regressioncoecientsfromthemaximumlikelihoodfunctionaregivenby i where 0 istheintercept ofourlinearregression. 37

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f b = P Y =1 j B = b =1 )]TJ/F19 11.9552 Tf 11.955 0 Td [(P Y =0 j B = b f b = e 0 + 1 b 1+ e 0 + 1 b logit [ f b ]= log f b 1 )]TJ/F20 7.9701 Tf 6.586 0 Td [(f b = 0 + 1 b .10 Formultiplepredictorvariables,ourregressioncoecientsareestablishedas: logit [ f b ]= 0 + 1 b 1 + 2 b 2 + ::: .11 Thesignof determinesthepositiveornegativerelationwith f b ,ourNEHI LRmodel,andthemagnitudeof suggeststherateofincreasealongthelogistic distribution[1,11]. AkaikeInformationCriterionAICisamethodtotesttherelativequalityofa modelbaseduponaselectionofvariables.Weinitializeourlogisticregressioncandidatemodelwiththe b parametersthatdescribe75%oftheairwaytreevariation. AICsystematicallyaddsandremovesthe b parametersandtestsforgoodnessoft andinformationloss.Ournalmodelexpressesthe b parametersthatbestclassify NEHIfromthediseasecontrolgroupbaseduponshapedeformation[11].ThestatisticalcomputationwascompletedinRStudioVersion0.98.501,RStudio2013,Boston, Massachusetts.TheLogRfunctioninRStudioprovidesthenecessarysummaryand regressionvaluesforthisanalysis. Todeterminetheplausibilityofourmodel,wecomparedthenullandresidual devianceanddegreesoffreedom df baseduponaChi-Squareddistribution.The nulldevianceisamodelofconstantcoecientsandtheresidualdeviancelooksat thenumberofindependentvariables.Thiscanbecharacterizedasoverdispersionof ourmodel.Alargerresultindicatesthattheresidualisabettermodeltthanthe null.Eq3.12representsourcalculationmethodforthismethod. 2 Deviance Null )]TJ/F19 11.9552 Tf 11.955 0 Td [(Deviance Residual ;df Null )]TJ/F19 11.9552 Tf 11.955 0 Td [(df Residual .12 38

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Thereareafewmethodstodeterminethesignicanceofourresultandhowwell ourmodelts.Welookedattheoddsratiotoquantifythelikelihoodofbeingin theNEHIpopulationbaseduponthe b parametervalue.Oursignicanceisbased uponap-value < 0 : 1duetothesmallsamplesizebutlargeextentofvariation.The signicantregressioncoecients i foreach b parameterpredictorthatisselectedby AICareusedinaOddsRatioOR.Eq3.13denestheoddsofbelongingtothe NEHIpopulationrelativetooneunitchangeinour b parameters.Thiscaneasilybe adjustedtoremovetheambiguityofa'oneunitchange'bydeterminingastandard deviationSDincreasein b OR = e i OR = e i SD b .13 Wecancalculatethecondenceratioofthepredictor b by: CI = e i 1 : 96 standarderror .14 Leave-one-outcrossvalidationLOOCVisamethodthatdeterminesthepercentageofcorrectclassicationofourmodel.Thismethodsystematicallyremoves oneobservation,re-establishesthemodel,andthencatagorizestheremovedobservationbaseduponthenewmodel.TheresultfromLOOCVistheestimateofthe predictionerror[1,11]. Forclinicalevaluation,wedeterminedtheReceiverOperatorCharacteristic ROCcurveofoursignicant b parameters.Duetothedistributionofparameters,weorganizedvaluesnumericalandcompletedastep-wiseanalysisofsensitivity andspecicity;wedidnotuseranges. Finally,tojustifytheuseofGuassianstatisticalmethods,weevaluatedthedistributionofoursignicant b parameters.Wetanormaldistrubtioncurvebasedupon parameterSDandmeantoahistrogramof b values.WecomparedthistoaquantilequantileQQplotwithaQQline.GeneralizedextremeStudentizieddeviateESD 39

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Table3.3:AlistoftheavailableIPFTresultsforourNEHIpatientpopulation NumberofPatients AvailableIPFT 14of18NEHIPatients ForceVitalCapacityFVC ForcedExpiratoryVolumein0.5sec FEV 0 : 5 FunctionalResidualCapacityFRC ForcedExpiratoryFlowat50% FEF 50 ForcedExpiratoryFlowat25% FEF 25 ForcedExpiratoryFlowat85% FEF 85 ForcedExpiratoryFlowbetween25-75% FEF 25 )]TJ/F17 7.9701 Tf 6.587 0 Td [(75 8of18NEHIPatients ExpiratoryReserveVolumeERV ResidualVolumeRV TotalLungCapacityTLC ResidualVolume/TotalLungCapacityRV/TLC FunctionalResidualVolume/TotalLungCapacity FRC/TLC wasusedtodetermineparameteroutliers[77]. 3.7.2IPFTCorrelation OurNEHIcohorthasbeenevaluatedforlungfunctionwithainfantpulmonary functiontestIPFT.Thesetestsusespirometryandplethysmographytomeasure bothowratesandlungvolumes.OfourNEHIcohort,14/18patientshadaIPFT performedatCHC.Ofthose14,only8hadsuccessfullungvolumecollection.Table 3.3liststhetestsavailablefor14patientsandthentheadditionresultsfromthe smallergroupof8patients. Welookedattestresultsthatquantifyairowandlungvolumeandlinearlyregressedthesevalueswithoursignicant b parameters.AcombintationofMatlaband RStudiowasusedtodeterminecorrelationcoecients r ,coecientofdetermination R 2 ,linearregressionplots,andresiduals.ABonferonniteststatisticwasperformed inRStudiotohighlighthemostextremeobservations.Ifamodeloutlierexisted,it wasremovedandtheLinRmodelwasre-evaluated.Wealsolookedatthestability 40

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ofourregressionanalysis.Selectdatapointswereremovedtoseeiftheregression reliedheavilyonasingularpoint.Ourregressionanalysisreportedononlysignicant correlation p 0 : 05. 41

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4.Results 4.1NEHIPatients TheNEHIpatientgroupexpressavarietyofchILDcharacteristicsthrougha rangeofsymptomsandtestresults.Table4.1representsNEHIclinicalscoreand NEHIRadiologyscoreforourNEHIstudypopulation.Boththeclinicalscoreand radiologyscoresheetsareprovidedinAppendixB.Dr.RobinR.DeterdingandDr. LelandFan,bothprimaryNEHIclinicalinvestigators,evaluatedtheclinicalscores. Dr.JasonWeinmann,apediatricradiologistwithexpertiseinNEHIradiologycharacteristics,evaluatedtheradiologyscores.TherightmiddlelobeRMLpresented groundglassopacitiesGGOinallNEHIpatientsontheradiologyreading.The rightandleftperihilarandthelingulapresentedGG0in85%ofpatients.Only30% ofpatientshadGGOintherightupperlobeRUL,rightlowerlobeRLL,and leftlowerlobeLLL,whileonly1patienthadGGOintheleftupperlobeLUL. Variousotherbronchial,alveolar,andinterstitiallungdiseasewerepresentinselect patients.TheIPFTsresultswerecollectedonlyfromCHCandhavebeenoverread bybiostatisticianDr.BrandieWagner.Wehaveprovidedthepulmonaryfunctional valuesthatweresignicantinourpulmonarystructureversusfunctionregression analysis. OurNEHIpatientsexpressavarietyofpulmonarydysfunctionandarecharacterizedbythefollowingclassicNEHIconditions:hypoxemia,failuretothrive, intercostalretraction,tachypnea,crackles,anddyspnea.chILDsexpressarangeof heterogeneouspresentationsandourNEHIgrouppresentthefollowingchILDsymptomsthatarenotgenerallyassociatedwiththeNEHIcondition:aspiration,reactive airwaydisease,acutebronchiolitis,post-inammatorypulmonarybrosis,andpleuraleusion.ThiscontributestothediagnosticconfusionassociatedwithNEHIand otherheterogeneouschILDs. 42

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Table4.1:Theresultsofaclinicalscoreandradiologyscoresheetsareprovided inAppendixA.TheIPFTresultsusedforourlinearregressionanalysisarealso providedintheformofpercentpredictedfromacontroldatabase. Case Clinical Radiology InfantPulmonaryFunctionTest,PercentPredicted Number Score Score FVC FEV 0 : 5 sec RV=TLC FRC=TLC 6 NA YesNEHI 45.69 49.20 NA NA 33 NA MaybeNEHI"Plus" 51.35 52.70 203.38 162.37 98 10 MaybeNEHI 46.25 48.40 NA NA 101 NA YesNEHI NA NA NA NA 111 NA MaybeNEHI"Plus" 81.25 81.16 88.23 91.37 112 NA MaybeNEHI"Plus" 75.74 67.79 122.64 124.40 113 8 MaybeNEHI"Plus" 55.01 51.08 NA NA 114 10 MaybeNEHI"Plus" NA NA NA NA 119 NA YesNEHI 70.79 82.03 139.82 138.95 75 NA YesNEHI 55.75 63.90 194.43 166.74 82 NA YesNEHI 44.64 48.57 198.62 166.23 85 10 YesNEHI 35.49 34.36 NA NA 90 8 MaybeNEHI NA NA NA NA 77 10 MaybeNEHI"Plus" 67.94 80.53 128.77 129.13 84 10 YesNEHI 50.01 55.07 NA NA 95 9 MaybeNEHI NA NA NA NA 99 10 YesNEHI 57.88 60.34 NA NA 117 NA YesNEHI 41.37 46.50 218.66 178.22 4.2KernelEqualization Thekernelusedforimagepost-processingcreatedadiscrepancyinoursegmentationresults.Thesignicantvariationisseenonlyintheextentofbranchgeneration andnotinairwaylengthorbifurcationangle.Figure4.1highlightstheperipheral variationthatexistsbetweenmodels.Bycallingforthasetofselectbranches,wewere abletoequalizeeachpatientsettothesamebranchgeneration.Thisalsoprovidesa stableplatformduringpoint-to-pointregistration. 4.3LandmarkRegistration Wecompletedstatisticalshapeanalysisontwodistinctmethodsforaligning ourlandmarkpointcloud.TherstisanovelmethodofapplyingCPDtoairway skeletonforcorrespondence.Thesecondisatechniquewhichappliesasetofequal 43

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aCoronalView bTransverseView Figure4.1:AnoverlayofaB31softkernelreconstructionblueandB70sharpkernel reconstructionredfromthesameCTdataviewedinthecoronalaandtransverse bplane.Thishighlightstheequalityoftheskeletonizationprocesswithinaunique patientdespitedierentkernelsused. splinepointstoeachlabeledbranch.Thismethodhasbeenestablishedinprevious studies[24,41]. 4.3.1CoherentPointDriftRegistration Thisresearchinvestigatedtheuseofthenon-rigidimageregistrationtechnique CoherentPointDrift[62].Usingairwayskeletonswithasetnumberofbranches,the non-rigidmethodadequatelyalignedshapesaboutthecarina.Theuseofcentroid neighborhoodsalsoprovidedgoodalignmentaroundmoredistalairways.Thenumber ofpointsalongeachbranchdecreasessignicantlyinperipheralairwaysandwesee informationloss.Weadjustedvariousinputparameterstoprovidethebestvisible t.Itisdiculttodeterminethealignmentoftherightandleftlowerlobes.From Figure4.2weseegoodcorrespondenceattherightmainbranchRMB,leftmain branchLMB,RUL,andLULbifurcation.Asthetracheobronchialairtreecontinues tobifurcate,weseefuzziercorrespondence.Wealsolosetheappearanceofdistinct branchesandtheairtreebecomesmorecloud-likethanskeletonform. 44

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aSkeletonCorrespondence bRightLowerLobe cLeftLowerLobe Figure4.2:Areviewoftheregistrationofthesourcescanredandtargetscand blue:aTheairwayalignmentusingCPDisaccurateandcorrespondenceofthe largebronchiisaccurate.However,thecorrespondencebetweenpointsoftheb RLLandcLLLshowspoormappin.ThiserrorbecomesaugmentedinourPCA analysiswiththeinclusionofthetotalpopulation. 45

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Fromjustasinglerepresentation,weseeasub-optimalalignmentbetweensets. Asweaddsetsintothemodel,wecontinuetomakethecorrespondencemorepoorly dened.Forexample,insomeinstanceswemayaccuratelyalignthetargetLB8tothe sourceLB8,butinothers,itmaybealignedtothesourceLB7.Inourlabelingprocess, eachbranchwasdenedbaseduponisanatomicalpositionandparentbranch.By addingdiscrepancyinpointcorrespondence,weadderroneousvariation.Theextent ofthisinaccuratealignhasnotbeenquantiedandthuswecarriedtheresultsfrom CPDintoourPCA. 4.3.2SplineRegistration Thesplinemethodprovidesexactpointcorrespondencebaseduponuser-dened branches.Ourpointcloudforeachskeletonisexempliedinthematrix4.1.Weavoid theneedofaregistrationmethodbutrequirethetedioustaskofbranchlabeling.The listofallbranchespresentforeachscaninsuppliedinAppendixB.1 X 2000 ; 3 = 0 B B B B B B B B B B B @ Trachea x 1 Trachea y 1 Trachea z 1 . . . . Trachea x 50 Trachea y 50 Trachea z 50 RMB x 1 RMB y 1 RMB z 1 . . . . 1 C C C C C C C C C C C A .1 4.4StatisticalShapeAnalysis 4.4.1ModelAnalysis Foratotalof s =25patientscans, d =3dimensions,and n Spline =2000 and n CPD =498degreesoffreedomfromourmodel,ourcovariancematriceswere De Spline = 25and De CPD = 25.Thepercentvariationofeach componentofthecovariancematrixisshowninTable4.2.Themodesshownare usedinourLogRandaccountfor75%ofthetotalpopulationdeformation.The classicuseof95%ofvarianceyields19PCsfortheSplinemethodand18PCsforthe 46

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Table4.2:PrincipleComponentsthatexplain75%ofthevariancewithinourmodel PrincipalComponent SplineTotalin% CPDTotalin% 1 0.2064.2064 0.3306.3306 2 0.1256.3320 0.1199.4505 3 0.1090.4410 0.0989.5495 4 0.0851.5261 0.0529.6304 5 0.0643.5904 0.0452.6833 6 0.0585.6488 0.0379.7286 7 0.0515.7004 0.0338.7665 8 0.0430.7434 9 0.0369.7803 CPDmethod.Duetoalargernumberof df 0 s andsmallsamplesize s ,wehavealarge spreadofvariationwithasmallpercentageofthetotalvariation.Theinclusionof thesesmallerweightedvariancesdoesnotsupplysignicantshapedeformationand leadstomodeloverdispersion. UsingRStudio,wepreformedaLogRpairedwithAICtodeterminewhich b parameterswouldpredictthebestclassicationofNEHIshapedeformitiesfromour control.TheresultsforboththeSplineandCPDmethodareshowninTable4.3. ThenullandresidualdevianceswereusedtodeterminetheplausibilityofourNEHI modelrelativetothenullmodel;thenullmodelisaconsiderationofonlythelogistic interceptandnocoecients.Byconsidering P 2 df deviance ofvariousmodels, wetestedoverdispersionofourAICmethod.Theinclusionof b 1 ;b 3 ;andb 7provides thebestmodelcomparedtoasimplermodelcontainingonly2predictorvariables .4.Thisisdeterminedbythelargerchangein 2 andtheincreasedp-value. ThesamecomparisonwasprovidedfortheCPDmethod.Withtheinclusion ofAICmodelselectionforourLogR,weassumedtheselectedparameterwasan 47

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improvement.Thisinformationisprovidedtoremainconsistentwiththedatashown fortheSplinemethod. WealsotestedtesttheORofbelongingtoaNEHIpopulationbaseduponthe resultsofourLogR.Wepresentthefactorchangeinoddsforunitincreaseofeach modelpredictorandits95%condenceinterval.Wealsoprovidedthechangeinodds relativeto1.96standarddeviationincreaseforaspecic b parameter. 4.4.2ShapeDeformation Logisticregressionwasusedtodeterminewhichshapemodescharacterizethe airwaydeformationinourNEHIpopulation.Thisinformationgivesnoinsightinto howtheNEHIairwaytreechangesrelativetoourcontrolcohort.Wecanvisualize thisshapechangebyadjustingthePrinciplecomponentmatrixrelativetoeach b parameter.ExpressionofNEHIdeformationrelativetothemeanshapeisexpressed inthefollowingimages. Eachtable.4.2-4.9ispresentedinbothtransverseandcoronalplanesofthe wholeairwaytreeandthenanenlargedimageoftheRMBandLMB,respectively.The centralgreenairwayisourmeanmodel.Foreachlandmark,theprinciplecomponent foragiven b parameterisshownas+1.96standarddeviationindarkblueand1.96standarddeviationinlightblue.Inall b parametersdeterminedassignicant, theNEHItendtowardsapositivestandarddeviationfromthemeanandthustheir shapedeformitiesareexpressedindarkblue.Thelightanddarkbluelinesare inherentlycollinearandthusmovementalongthistrackpresentequalandopposite deformationfromthemean.TheNEHIshapedeformationisqualitativelydescribed ineachtablecaption.Shapechangestowardthecontrolgrouparemerelyinanequal andoppostiedirectionfromthemean.Thisinformationofmovementisdetermined bythecollectivechangeinlandmarkaxis.Characterizationoftheshapemodeis 48

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Table4.3:LogisticRegressionresultsfromthebestmodelchosenbyAIC.Forthisstudy,weconsidersignicancetobep-value < 0 : 1duetooursmallsamplesizebutlarge df .Theestimateandstandarderrorvaluesareusedforoddsratioevaluation. SplineMethod CPDMethod Coecients Parameters Estimate Std.Error z -value Pr > j z j Parameters Estimate Std.Error z -value Pr > j z j intercept 1.51679 0.71443 2.123 0.0337 Intercept 1.10260 0.50903 2.166 0.0303 b1 0.02731 0.01788 1.527 0.1267 b5 0.07405 0.04053 1.827 0.0677 b3 0.02698 0.01566 1.723 0.0849 b7 0.03552 0.02138 1.662 0.0966 AIC:27.611 AIC:29.562 49

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Table4.4:Acomparisonofthegoodnessoftbasedupona 2 distributionforvarious b parameterpredictormodels.Spline:Theuseofa3-predictormodelisbetterthan amoresimple2-predictormodelbasedopenthisoverdispersiontest.CPD:The inclusionofasinglepredictorissuperiortothenullmodel. 2 df Pr 2 df 2 deviance null 29.648 24 0.803295 SplineModelParameters b 1+ b 3 22.978 22 0.9643867 b 3+ b 7 23.510 22 0.9535164 b 1+ b 7 23.185 22 0.9604988 b 1+ b 3+ b 7 19.611 21 0.9817443 CPDModelParameters b 5 25.562 23 0.9567513 Table4.5:ApresentationoftheoddsratioofbelongingtoNEHIpopulationwith a95%CIandtheoddsrelativetothestandarddeviationofeachmodelpredictor b parameters. SplineMethodCPDMethod OR%CI b1 1.028.000,1.077 b5 1.077.002,1.183 b3 1.027.999,1.066 b7 1.036.998,1.089 ORwrt1.96SDofparameter b1 22.03895 b5 6.779386 b3 9.214471 b7 7.464009 50

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Table4.6: Themajorityoftheshapedeformationdescribedbythe1 st PCisaelevationofthecarinafromthe modelcentroidpositionedat,0,0.Theairwaytreealsobecomesrelativelynarrowerastheanglebetweenthe rightlungandleftlungdecreases.Thereisaslightinferior/superiorseparationoftheRB4+5andRLL.TheLLL extendsmoretotheperipheralasitrotatesinananteriordirection,whilebranchesoftheLULremainconstantwith respecttooneanother.TheanglebetweentheRULandBrontIntappearstonarrowandtheRULbranchesbecome shorter. Spline:1 st PrincipleComponent TransversePlane CoronalPlane ZoomoftheRightLungBranches ZoomoftheLeftLungBranches 51

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Table4.7: Forthe3 rd PC,weseeageneralleftwardtrackingofthetracheaastheRMBextendsandtheLMB shortens.Ontherightside,RB4+5rotatesinternallywhiletheRLLrotatesexternallyandbothlobularbranches appearwithincloserproximitytooneanother.TheLULandSDBalsoshortentowardstheNEHIshapedeformation. LB7+8elevatestowardsLB4+5,alsoincreasingtheproximityoftheLLLandthebranchestothelingula.Thereis alsonoticeableelongationoftheLB5andLB9. Spline:3 rd PrincipleComponent TransversePlane CoronalPlane ZoomoftheRightLungBranches ZoomoftheLeftLungBranches 52

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Table4.8: Forthe7 th Principlecomponent,thetrachea,RMB,andLMBarerelativelystill;weseemostofour shapedeformationinthemoredistalbranches.RB4+5andtheRLLbranchesseparatefromeachotherwithRB4+5 elevatingmoreextensivelythantheRLLdepresses.TheanglebetweentheRULandRMBalsovisiblydecrease. AgainweseeashorteningoftheLULandSDBandcloserproximityofLB4+5andtheLLL. Spline:7 th PrincipleComponent TransversePlane CoronalPlane ZoomoftheRightLungBranches ZoomoftheLeftLungBranches 53

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Table4.9: ThevariationseenwiththisPCfromourCPDmethodisanartifactofapoorskeletoncorrespondence acrossourpopulation.ThereisnotdescriptionadequateforhowtheCPDmethodcharacterizestheNEHIcohort. CPD:5 th PrincpleComponent TransversePlane CoronalPlane ZoomoftheRightLungBranches ZoomoftheLeftLungBranches 54

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providedwitheachimageset. WeseefromtheCPDdeformationmodelTable4.9greatvariationwithineach branch-specicallyintheRLLandLLL.ThishighlightstheinstabilityoftheCPD methodtoaccuratelyalignmoreperipheralbranchesacrossapopulation.Correspondencetoasinglesetmaybeachievable,buttheprocessisnotrobustforlargersets. Wecannotanalyzetheshapedeformationsprovidedfromthismethod. 4.5ModelDiagnostics BothLeave-One-OutcrossvalidationLOOCVandreceiver-operatorcharacteristicROCcurveprovidemethodsfordeterminethestabilityofourlogisticmodel inpredictingNEHIpatientsfromourcontrolcohort.Usingthelogisticreturnsfrom RStudioandanin-houseLOOCVclassier,wedeterminedthatthealogisticmodel including b 1, b 3,and b 7parametersreturnsa76%correctclassicationofNEHI.In comparison,otherlogisticmodelswithonlyoneortwoofthethreepredictorsyielded lowerclassicationpercentages. Standardevaluationofsensitivityandspecicitywasperformedforeach b parameter.ThelistofNEHIandcontrolpatientswereorganizedby b parametervalue, withpositivevaluestrendingtowardsNEHI.Figure4.3istheROCcurvefromthis evaluationwithareaundercurveAUCcalculated.Ourbestresult,AUC=76.9%, isgivenby b 7.Thisisalsothemostsignicantparameterinourlogisticanalysis. Weevaluatedthedistrubutionofour b parameters,includingcontrolvaluesfor theLRmodelandremovingthemforourlinearregressionmodels.Plotsareprovided inAppendixC.DeviationfromtheQQlineexistonlynearthetailsandourcentral pointsarewithincloselinearproximitybetween-1and1quantiles.Whilethetisnot aperfectGuassiandistribution,signicantnon-normaldistributionisnotapparent. WeusedgeneralizedESDtodeterminedataoutliers;includingthecontrolgroup, b 7 hadtwooutliers.OnlyconsideringtheNEHIgroup,therewasonlyoneoutlier.Both ofthesepointslieinthefarnegativerangeof b 7,asshowninthedistributionplots 55

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Figure4.3:AROCcurveforthe b parametersthatarepredictorsofgroupmembership inourlogisticregressionmodel. inAppendixC.Wemakeanoteoftheseoutliersbutdidnotremovethemfromour analysis. 4.6LinearRegression Werstdeterminedthecorrelationcoecientbetweenallthreeshapeparameters andtheavailableIPFTresults.Sinceweconrmednormaldistribution,weusedthe correlationp-valuetodeterminesignicance.Weperformedlinearregressionononly thosevalueswithap-value 0 : 05anddisplayedresultsinTable4.10.Thereis inversecorrelationbetween b 7and FVC and FEV 0 : 5 .Italsoshowsahighdegree ofsimilarityinrelativechangebetween b 7and RV=TLC and FRC=TLC .Note, b 7 wasalsocorrelatedwith RV ,butsince RV=TLC isamoreinformativemeasureof airtrapping,itwasusedover RV .Wealsoseethat b 3changesinverselyto RV RV=TLC and FRC=TLC butonlythelasttwoareanalyzed.Thisinformationwas calculatedinMatlabandRstudio. Wereviewedthelinearregressioncoecientofdetermination, R 2 anditsstability whenmodeloutliersareremoved.Thesignicantrelationsdeterminedbycorrelation analysiswerenotgreatlyaectedbysingularpointsandthussupportedtheresults ofourlinearregression.Afewfunctionalresultsandb3weresuddenlycorrelated whenwelookedatthesamplesizeof8relativeto14.Itwasdeterminedthatthis 56

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Table4.10:Wepresentthecorrelationcoecientsandcoecientofdetermination ofanysignicantlinearregressionmodelwhencomparingall b parameterstothe followingIPFTrestuls:forcedvitalcapacityFVC,forcedexpiratoryvolumein0.5 seconds FEV 0 : 5 ,residualvolumeovertotallungcapacityRV/TLCandfunctional residualcapacityovertotallungcapacityFRC/TLC IPFT CorrelationCoecient Signicance CoecientofDetermination b 7Parameter FVC r = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 6631 p =0 : 0097 R 2 =0 : 4397 FEV 0 : 5 r = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 6938 p =0 : 0059 R 2 =0 : 4813 RV=TLC r =0 : 8309 p =0 : 0106 R 2 =0 : 6903 FRC=TLC r =0 : 8592 p =0 : 0063 R 2 =0 : 7382 b 7withSignicantOutliersremoved RV=TLC r =0 : 9775 p =0 : 0001 R 2 =0 : 9555 FRC=TLC r =0 : 9798 p =0 : 0001 R 2 =0 : 9600 b 3Parameter RV=TLC r = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 8195 p =0 : 0128 R 2 =0 : 6716 FRC=TLC r = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 8609 p =0 : 0060 R 2 =0 : 7411 57

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wasduetoacoincidentalremovalofdatapointsinaregion,butnotrepresentative ofourpopulation.InFigures4.4-4.6weprovidetheplotsofeachregressionand respectiveresidualdata.Fromtheresiduals,wedonotseeanyrelationsthatmay bebettermodeledbynon-linearregression.TheBonferonnioutliertestselectedone signicantoutlier,whichwasremoved.Thechangein r ,p-value,and R 2 withthe removalofthesingulardatapointisalsoprovidedinTable4.10.Weseeimprovement incorrelationandlinearregression. 58

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aLinR:b7andSpirometry bResidual:b7andSpirometry Figure4.4:aLinRresultsofFVCand FEV 0 : 5 sec withtheb7shapeparameterand btheresepctiveresiduals. 59

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aLinR:b7andPleth bResidual:b7andPleth Figure4.5:aLinRresultsofRV/TLCandFRC/TLCwiththeb7shapeparameter andbtherespectiveresiduals. 60

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aLinR:b3andPleth bResidual:b3andPleth Figure4.6:aLinRresultsofRV/TLCandFRC/TLCwiththeb3shapeparameter andbtherespectiveresiduals. 61

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5.Discussion NEHIpatientspresentadiscrepancybetweentheirill-appearanceandresults fromclassicairwaystructuretests:CTandbiopsy[26,31].TheirIPFTssuggest airtrappingandobstructedairowwithnoknowncausation[45].Ourspeculation isthatthestructuralchangesleadingtopoorpulmonaryfunctionisnotuncovered byclassicclinicaltests.Thisistherstattempttodetermineifastructuralairway changeispresentinNEHIpatientsandifitcorrelateswithclinicaldiagnostics. 5.1NEHIShapeDeformities NEHIcharacteristicallypresentsGGOintherightmiddlelobe,lingulaandperihilarareas[10].Thedeformationsdescribedbyourprinciplecomponentanalysis showareasofairwaymovementintheseregionsbutalsoinareassuchastheRLL andLLL;theseregionshavealowerpercentageofGGOpresent.Throughourshape analysis,wehaveprovidedpreliminaryevidencethatNEHIpatientshaveabnormal airways.Thereisnoticeablechangeinthegeneralairwayshapedescribedbytherst PC.Thisisclassiedasadecreaseincarinaangleandalengtheningoftheairway tree.IntheotherNEHIspecicprinciplecomponents,weseelargebronchichanges. ThemostsignicantchangespresentedbyPC3areaninternalrotationandelevation ofthelowerlobestotheRMLandlingulabranches.InPC7,wecontinuetosee condensingofLB4+5totheLLLbranches,whereasRB4+5elevatesawayfromthe RLLbranches. Thelogisticregressionmodelisabletocorrectlyclassify76%oftheNEHIpopulation.Forthismodel,weconsiderap-value < 0 : 1asasignicantindicator.Thus b parameters3and7aresignicantmodelcoecients.Ourrstparameter, b 1,has ap-value=0 : 1267andisrequiredtoprovidethebestgoodnessoftforourlogistic model.AsdescribedbyourChi-squaredoverdispersiontest,theinclusionofallthree parametersisthebestmodel.Theresultsofouroddsratiousingthemultivariate coecientforeachparameterprovideinterestingresults.Itisundesirableforthe 62

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condenceintervaltobracketone.Thisoccursforboth b 3and b 7,whiletheCIof b 1isjustgreaterthanone.Theoddsratiorelativeto1.96SDsupportsastronger tendencytowardsNEHI.The b 1parametershowsthelargestincreasetowardsNEHI. Again,thisisasurprisingresultas b 1doesnotstronglyclassifyNEHI. AnROCcurveistypicallyusedasaclinicaldiagnostictool.TheAUCvalues for b 3and b 7arenothighenoughtobeconsideredatruediagnostictool,butshow goodspecicityandsensitivitytowardsselectingNEHIfromdiseasecontrol.The individual b 3and b 7haveanAUC=73.3%andAUC=76.9%respectively.We seeatransitionfromNEHItocontrolin b parameternumbersthatarebelowzero. Recall,themeanshapemodelisdenedby b parametersthatareequaltozero.This suggeststhatourmeanmodelismoreweightedtowardsNEHIpopulation.Witha smallsamplesizeandoverdoubleNEHIpatientsrelativetocontrol,thisisexpected. IPFTsexpressbothairowandlungvolumefunctionalityofthelungbutdonot providelocalizationofcompromisedareas;IPFTsquantifyglobalfunction.NEHI patientsexpresshighlevelsofairtrappingandlowairow.Thisiseasilyquantied bythepercent-predictedvaluesbaseduponacontrolgroupatCHC.Wedetermined linearcorrelationwithtwoofourshapeparametersandafewfunctionalresults. Mostsignicantly, b 7hadgoodcorrelationandregressionresultswithtwospirometry measurementsandtwoplethsymographyplethmeasurements. Forcedvitalcapacityisthetotalamountofairthatcanbeexhaledwithforce relativetotidalvolume,andexpiratory/inspiratoryreservevolumes.Forcedexpiratoryvolumein0.5secmeasurestherateatwhichgascanbeexpelledfromthe lungs.Lowvaluesindicateairwayobstruction.Weseenegativecorrelationbetween airowand b 7shapedeformation,whichsupportstheconceptthatincreasedairway deformationisrelatedtoincreasedairwayobstruction.ForFVC, R 2 =0 : 44and for FEV 0 : 5 R 2 =0 : 48,bothconsideredgoodgiventheextentofvariationwesee inourpopulation.Thesearealsosupportedbysignicantcorrelationcoecientsof 63

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r = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 66and r = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 69,respectively.Therewasasinglepatientwhohadvery littleairwayobstructionandcontrol-rangeshapeparameters.Removingthispatient onlyslightlyadjusted R 2 andtheslope.Theirconsiderationhelpsexplainanormal structure-functionrelationshipcomparedtodiseasestructure-function. Residualvolumerelativetototallungcapacityandfunctionalresidualcapacity relativetototallungcapacitybothindicateairtrappingwithhighpercentages.SeveralpatientsofourNEHIcohortareseverelyairtrapped,upwardsof200%predicted. Our b 7shapedeformationishighlycorrelatedwithbothRV/TLCandFRC/TLCfor our8patientsamplesize,reporting r =0 : 98forboth.Theresulting R 2 values were0 : 95and0 : 95forrespectiveplethmeasurementswith b 7.Wespeculatethat theairwaystructuralchangeofRB4+5elevatingawayfromtheRLLandLB4+5 condensingtotheLLLiscorrelatedwithincreasedairtrapping.Thesingularpatient withnear-normalairowmeasuresalsohaslowerpercentpredicted.Again,they wereremovedandweseeadecreasein R 2 ,butitsvalueisstillconsideredsignicant andthelinearregressionslopedoesnotchange. RV/TLCandFRC/TLCareinverselycorrelatedwiththe b 3shapeparameter. Interestingly,someoftheshapedeformationsexpressedbyPC3aretheopposite movementexpressedbyPC7.InPC7,weseeaseparationofRB4+5fromthe RLLbutinPC3,weseeacondensingofthosetwobranches.Theresultsofour correlationsuggestthat,inthisareaoftheairwaytree,aelevationofRB4+5away fromtheRLLisdirectlyrelatedtoanincreaseinairtrappinginNEHIpatients.We mustconsidertheslightchangesthatexistbetweenPC3andPC7.PC3appearsto alsointernallyrotatemoreperipheralbranchesandweseealengtheningoftheRMB andashorteningoftheLMB. 5.2AirwayImageRegistration Ourdatasupportstheuseofthepreviouslyestablishedsplinemethodbutnot theCPDapproach.Whilethesplinemethodprovidesaccuratepoint-to-pointregis64

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tration,itrequiresextensiveairwaybranchlabelingandadjustmentsmadefortopologicalvariation. TheinitialtrialwithCPDusednobranchlabeling,thegoalbeingtoreduce airwayeditingtime.WebeganwiththecompleteskeletonproducedfromApollo Workstation.Thesharpkernelairwaytreesextendout6-8generations,andthe airwaytreecomplexitywastoogreatfortheCPDregistrationtechnique.Unrealistic mappingbetweenbranchesexisted;somebranchesbendingortwistingdowntolower generationbranches.Whenattemptingtomapasoftkernelscantoasharpkernel scan,CPDwasunabletoclassifyhighergenerationsinthesharpkernelasoutliers relativetothesoftkernelscan.Thiscreatedaregistrationsuchthattheendgenerationsofthesoftkernelweremappedthroughtheremaininggenerationsofthesharp kernel.Forexample,ifRB9wasterminalbranchforasoftkernelscan,butasharp kernelscanhadRB9aandRB9ai,theRB9ofthesoftkernelwasregisteredoutto RB9aiofthesharpkernel. Wethenutilizedthebranchlabelstoreducetheextentoftheairwaytreeand toequalizekernelreconstruction.Thisappearedtoaccuratelymapeachskeleton toatargetskeleton.Itsbenetoverthesplinemethodwasallowingfortopological variation,sincespecicbifurcationpointswerenotestablished.Therewasconcern aboutnumberoflandmarksthatremainedaftercorrespondenceandiftherewouldbe enoughdatapointstoaccuratelycharacterizelowerlobebranches;thecorrespondence appearedfuzzierintheseregions.WecarriedtheresultsoftheCPDmethodintoour statisticalshapeanalysistodeterminehowwellthelowerlobewasregisteredacross theentiresamplesize. AftercompletionofPCAandLogRtoselectoutourbinomialmodelpredictors,it becameclearthatCPDwasnotrobustenoughtoalignairwayskeletons.ThePCaxes didnottransitionsmoothlyalongbranches.Themisalignmentvisualizedinthelower lobeswhencomparingasingularsourcescantothetargetscanwasaugmentedwhen 65

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lookingatthecompletepatientpopulation.Fewerpointsaremaintainedinthelower loberegistrationandinter-branchregistrationoccurs.Lookingatindividualscans mappedtothetargetscan,anestimateof5-10pointsexistforthe4-5 th generation branches;oursplinemethodmaintains50pointsforeachandeverybranch.The reductionofpointsisadegradationofshapeinformationforourstatisticalshape model.Inaddition,selectbranchesforpatientsaremappedinappropriately,which wedeterminedbymanuallyviewingthecorrespondenceresultswithpositioninour branch-labelingtree.TheseeectscausegreatvariationinPCdirectionforadjacent pointsanddisproveourCPDmethod. 5.3ConsiderationandLimitations 5.3.1PopulationSize Ourresearchforthisstudywasbaseduponasmallsamplesizewithalarger numberof dfs inourdataset.Thisprovidesstatisticaldicultyintryingtodetermine signicance.Asseenwithour b parameters,wehaveashapedistributionthatis nearlynormalbutwithatpeaksandfattailsAppendixC.Thisisduetoour widerangeofshapevariationthatexistinasmallsamplesize.Wealsoseethisissue whenreviewingthesignicanceofourLRcoecients.Forthisstudy,weaccepted p 0 : 1assignicant,comparedtothestandardrelationof p 0 : 05.Ourresults showabout75%classicationbaseduponshape.Theinclusionofmorepatientsmay increaseourabilitytocorrectlydetermineNEHIbaseduponshape.Thiswouldalso besupportedbyanincreaseinAUCfromaROCcurve.. ThenumberofpatientsatCHCthatmetourretrospectivestudyprotocollimited ourgroupsizes.Inpart,therarityandyoungageofNEHIlimitsthenumberof acceptablecontrolsthatcanbeused.Expandingourstudypopulationwouldrequire amulti-institutionalstudy. TheinclusionofmoresamplestoourshapemodelwillchangePCsandthe b parameters.Whatwewouldlookforinalargerpatientpopulationisanexpression 66

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ofNEHIshapedeformationsthatisconsistent.Meaning,thePCs,nomatterthe weightintotalpopulationvariance,supporttheairwaychangesexpressedinthe paper.Additionally,increasingoursamplesizemayfurtherrenethe'NEHIshape'. 5.3.2FurtherClinicalComparisons DuetoongoingresearchwiththeNEHIpopulation,CHChascollectedvarious clinicalmeasuresonNEHIpatients.Withtheinclusionofairwayshapedeformation, wehavethepotentialtolookmorecloselyattheirrelationshipwithradiologyreadings.LocalizationofGGOseenonCTscanscanbeestablishedasadiscretevariable fromourRadiologyScoresheetAppendixB.Itcanthenberegressedwithshape parameters.Recall,thereisnocorrespondencewithGGOandthepresenceofNEC countinbiopsy.However,wehaveyettodeterminethepresenceofGGOrelativeto airwaydeformation.Co-localizationofNEHIshapedeformationwithGGOprovides insightintothepresenceofGGO. 5.3.3AirwayRegistration ThisstudyattemptedtouseCPDasamethodforairwayregistration.Itsinitial benetovertheSplinemethodwasareductioninairwaylabelingtime.Thisprocess istediousandtimeconsuminginApollo,especiallywhenlabelingtoahighergenerations.Withoutneedingbranchlabels,extensiveairwaytreescouldbemappedto eachother.However,CPDwasnotrobustenoughforskeletonswith6-8generations fromasharpkernelscan.Evenwithasoftkernel,wewereunabletoaccuratelyalign skeletons.OncewedeterminedthatbranchlabelingwasnecessaryforCPDstability, welostamajorbenetofthemethod.Atthispoint,theonlyimprovementthat CPDprovidedoverthesplinemethodwastheacceptanceoftopologicalvariations withoutdatamanipulations. OurendresultsusingCPDweredisappointing.Werequiredaccuratesetregistrationtodetermineshapedeformationsafterusingstatisticalshapeanalysistechniques. Acrossagroupofvariableairwaychanges,CPDremovedimportantdatapointsin 67

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thelowerlobes.Cross-overbetweendistalbranchesalsooccuredduringregistration. Theupperlobes,however,appearedtobealignedwell.Potentially,CPDcouldbe usedinfuturestudiesifairwaydeformationsinthelargerbronchiaresignicantly dierentandshapechangesstillcorrelatewithfunction. 5.4Conclusion WehaveprovidedexcitingdatarelatingNEHIairwaydysfunctiontostructural changes.Expandingourresearchtoalargercohortwillstrengthenthestatistics ofourresultsandhelptoclarifywhatexactdeformationsarepresent.Continual worktoimproveairwayregistrationwillhelpreduceeditingtimeandallowforlarge populationstudies. 68

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6.FutureWork Thisresearchworkwasaspeculativestudy.Theresultsofourstudyshowthatin asmallsamplepopulation,NEHIpatientspresentlargeairwaystructuralabnormalitiesrelativetoadiseasecontrolcohort.Theexpansionofourmodeltoincludemore NEHIandcontrolpatientsmayprovidebetterstatisticalsignicance.Thiswould requireamulti-institutionalstudyfollowingprotocolforimagingtechniques,IPFTs, andsegementationprocess.Toreducetheextentofanyerrouneousdatavariation, itisimportanttoconsidertheplatformsbeingusedduringprotocol.Varyingimagescannerandsegmentationalgorithmshasaectontheestablishmentofairway landmarks. Wehaveshownaccommodationforcollectingdatawithdierentpost-processing imagekernels.Itprovidesaslightinconvenience,buttheneedtomanuallylabel airwaybranchesisalsorequiredforSplineregistration.Branchlabelingalgorithms havebeendesignedandairwaystatisticalshapemodelingsupportscontinuedwork inthiseld. Thenon-rigidimageregistrationmethodusedinthispaperprovidedpoorcorrespondenceinperipheralairways.Theinclusionoftheseperipheralairwaysmay ormaynotbeneeded.Thesimplicationofourairwaytreetofewerbranchesmay alsoresultinamodelthatproducessignicantNEHIstructuralchanges.Thiswould reducetheamountoftimeforbranchlabelingandnegatetheconcernsaroundairway kernels. Ourresultshaveshownashapemodelthatvariesinboththeleftandrightmain branches.TheuseofFEAandCFDontheselargebronchicouldfurtherinvestigate howstructuralchangesinNEHIpatientsleadtopoorpulmonaryfunction.The agreementbetweenairowsimulationinpatientspecicairwaysandIPFTswould furthersupportwhyNEHIpatientsexpresstheirclinicalabnormalities. 69

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Withtheresultswehavediscussedhere,weopenthedoorsforcontinuedand extendedresearchindeterminingtherelationshipbetweenNEHIandairwaystructuralchanges.Branchmorphologyfromshapemodelingcanimprovediagnosisand correlatewithprognosisofNEHI.DistinguishableclassicationofNEHIfromother chILDscanaidsmallerinstitionsindiagnosingNEHI. 70

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[57]ShinMatsuoka,YasuyukiKurihara,KunihiroYagihashi,MakotoHoshino,Naoto Watanabe,andYasuoNakajima.Quantitativeassessmentofairtrappingin chronicobstructivepulmonarydiseaseusinginspiratoryandexpiratoryvolumetricmdct. AmericanJournalofRoentgenology ,190:762{769,2008. [58]OMMets,PAdeJong,BVanGinneken,HAGietema,andJWJLammers. Quantitativecomputedtomographyincopd:possibilitiesandlimitations. Lung 190:133{145,2012. [59]OnnoMMets,EwoudJSmit,FirdausAAMohamedHoesein,HesterAGietema, ReinoudPHBokkers,MohamedAttrach,SaskiavanAmelsvoort-vandeVorst, ErnstThScholten,ConstantinusFMBuckens,MatthijsOudkerk,etal.Visual versusautomatedevaluationofchestcomputedtomographyforthepresenceof chronicobstructivepulmonarydisease. PloSone ,7:e42227,2012. [60]DavidKMeyerholz,DavidAStoltz,EmanNamati,ShyamRamachandran,AlejandroAPezzulo,AmandaRSmith,MichaelVRector,MelissaJSuter,Simon Kao,GeoreyMcLennan,etal.Lossofcysticbrosistransmembraneconductanceregulatorfunctionproducesabnormalitiesintrachealdevelopmentin neonatalpigsandyoungchildren. Americanjournalofrespiratoryandcritical caremedicine ,182:1251,2010. [61]JohnF.Murray.Thestructureandfunctionofthelung. TheInternational JounralofTuberculosisandLungDisease ,2010. [62]AndriyMyronenko. Non-rigidImageRegistration:Regularization,Algorithms andApplications .Dissertation,OreganHealthandScienceUniversity,2010. [63]AndriyMyronenkoandXuboSong.Pointsetregistration:Coherentpointdrift. PatternAnalysisandMachineIntelligence,IEEETransactionson ,3212:2262{ 2275,2010. [64]YasutakaNakano,JonathanCWong,PimAdeJong,LillianaBuzatu,Taishi Nagao,HarveyOCoxson,WMarkElliott,JamesCHogg,andPeterDPare.The predictionofsmallairwaydimensionsusingcomputedtomography. American journalofrespiratoryandcriticalcaremedicine ,171:142{146,2005. [65]TRNelsonandDKManchester.Modelingoflungmorphogenesisusingfractal geometries. MedicalImaging,IEEETransactionson ,7:321{327,1988. [66]LawrenceMNogee.Geneticbasisofchildrensinterstitiallungdisease. Pediatr AllergyImmunolPulmonol ,2010. [67]KalmanPalagyi,JuergTschirren,EricAHoman,andMilanSonka.Quantitativeanalysisofpulmonaryairwaytreestructures. Computersinbiologyand medicine ,36:974{996,2006. [68]KevinPattonandIreneGaryThibodeaue. Anatomy&Physiology .MosbyElsevier,St.Louis,MO,seventheditionedition,2010. 76

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APPENDIXA.BranchSchematic TableA.1:BranchLabelingSchematic Branch Parent Daughter1 Daughter2 Branch Parent Daughter1 Daughter2 1 Trachea Trachea RMB LMB 21 RB9+10 RLL RB9 RB10 2 RMB Trachea RUL BronInt 22 RB9 RB9+10 RB9 RB9 3 RUL RMB RB1+2 RB1+3 23 RB10 RB9+10 RB10 RB10 4 RB1+2 RUL RB1 RB1 24 LMB Trachea LUL LLB6 5 RB2+3 RUL RB2 RB3 25 LUL LMB SDB LB4+5 6 RB1+3 RUL RB3 RB3 26 SDB LUL LB1+2 LB3 7 RB1 RB1+2 RB1 RB1 27 LB1+2 SDB LB1+2 LB1+2 8 RB2 RB2+3 RB2 RB2 28 LB3 SDB LB3 LB3 9 RB3 RB1+3 RB3 RB3 29 LB4+5 LUL LB4 LB5 10 BronInt RMB RB4+5 RLL6 30 LB4 LB4+5 LB4 LB4 11 RB4+5 BronInt RB4 RB5 31 LB5 LB4+5 LB5 LB5 12 RB4 RB4+5 RB4 RB4 32 LLB6 LMB LB6 LLB 13 RB5 RB4+5 RB5 RB5 33 LB6 LLB6 LB6 LB6 14 RLL6 BronInt RB6 RLL7 34 LLB LLB6 LB7+8 LB9+10 15 RB6 RLL6 RB6 RB6 35 LB7+8 LLB LB7 LB8 16 RLL7 RLL6 RLL RL7 36 LB7 LB7+8 LB7 LB7 17 RB7 RLL7 RB7 RB7 37 LB8 LB7+8 LB8 LB8 18 RLL8 RLL7 RLL RLL 38 LB9+10 LLB LB9 LB10 19 RLL RLL7 RB8 RB9+10 39 LB9 LB9+10 LB9 LB9 20 RB8 RLL RB8 RB8 40 LB10 LB9+10 LB10 LB10 Thefollowinglistofbranchesareusedtoequalizeoursetsandtoadjustfor topoligicalvariationsbetweenpatients.Eachbranchisdenedtohaveasingular parentbranchandtwodaughterbranches.Ifitisaterminalbranchofourairway tree,thenitisalsoit'sowndaughterbranch.Thisisrequiredforcallingspecied branchesoutofApollocaselesandtoequalizesetsizefortheSplinecorresondence method. 80

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APPENDIXB.ScoreSheets B.1ClinicalScoreSheet ANEHIclinicalscoresheetwasestablishedatCHCthatevaluatesthepresence ofNEHIcharacteristicsona10pointscale.Eachpresentationisawarded1point. Valuesforourresearchlookedatthecumulativetotal. ClinicalPresentation Today Cumulative Crackles Hypoxemia Tachypnea Retractions BarrelChest Absenceofclubbing NoWheezingWhenWell NoCoughWhenWEll FailuretoThrive Onset < 1yearold Total 81

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B.2RadiologyScoreSheet 82

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83

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APPENDIXC.NormalDistributionofbParameters BelowwepresentthedistributionofourNEHImodel b parameters.Intheleft column,thedensityofeachparameterrangeispresentedbythegreenbargraph. Thenormaldistrubtionrelativetosamplestandarddeviationandmeanoverlaysthe histographindarkblue.TotherightwepresenttheQuantile-Quantileplot.Fora normaldistribution,weexpectourquantilestoliealongthesolidredlineandwithin thecondenceintervalestablishedbythedottedredlines.Whilewedonothave aperfectGaussiandistribution,thereisnounderlyingnonlinearitythatisreadily expressed.Afewofthe b parameterdistributionshavefattails,andinsomecases, outliers. 84

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ThesecondsetofplotsdescribeonlytheNEHIshapeparameters.Thisisnecessarytodeterminethecharacteristicofourlinearregressionpredictors.Wedosee furtherdeparturefromtheclassicGaussiandistributionwithfurtheroutliers.However,thereisnotnonlineardeviationfromtheQQlineandthuswecanstillassume normaldistribution. 85