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Application of CLM to urodynamic problems

Material Information

Title:
Application of CLM to urodynamic problems
Creator:
Joo, Kyung Sub
Place of Publication:
Denver, Colo.
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
x, 79 leaves : illustrations ; 29 cm

Thesis/Dissertation Information

Degree:
Master of Science
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Electrical Engineering, CU Denver
Degree Disciplines:
Electrical Engineering
Committee Chair:
Fermelia, Alfred
Committee Members:
Cox, David
Thomas, Joe E.

Subjects

Subjects / Keywords:
Urodynamics ( lcsh )
Urodynamics ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references.
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Electrical Engineering.
Statement of Responsibility:
by Kyung Sub Joo.

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Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
26152461 ( OCLC )
ocm26152461
Classification:
LD1190.E54 1992m .J66 ( lcc )

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Full Text
APPLICATION OF CLM TO URODYNAMIC PROBLEMS
by
Kyung Sub Joo
B.S., University of Colorado, 1989
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Electrical Engineering
1992
All
V.


This thesis for the Master of Science
degree by
Kyung Sub Joo
has been approved for the
Department of
Electrical Engineering
by
Alfred Fermelia
Date
Joe E. Thomas


Joo, Kyung sub (M.S., Electrical Engineering)
Application of CLM to Urodynamic Problems
Thesis directed by Professor Alfred Fermelia
ABSTRACT
In this thesis a different method of finding
urinary obstruction due to benign enlargement of the
prostate is presented. An equation(QJ that approxi-
mates a normal person's urinary flow rate(Q) has
been found, which is Qft = a,/t exp(-Y-t3)-c(l-exp(-dt)) where
a, b, c, and d are parameters. Using this equation
with Closed Loop Methodology (CLM), one can distin-
guish urinary obstruction from unobstruction. Also
two different types of obstruction can be defined.
A person is obstructed if covariance of[(Q-Qj/
Q^] is bigger than 0.1. Once an obstructed person
is separated, then, using a Kalman filter, compres-
sive and constrictive obstruction can be distin-
guished. When b is not changed during voiding time,
obstruction is compressive. On the contrary, con-
strictive obstruction produces significant changes
in b during voiding time.
This method is applied to 13 different urinary
flows that are already diagnosed, and the results
iii


agree with the diagnoses. This proves that the ap-
plication of CLM to the modeling of physical and
biological systems provides a systematic approach
for the analysis of such system.
This abstract accurately represents the content of
the candidates thesis. I recommend its publication.
signed
Alfred Fermelia
iv


ACKNOWLEDGMENTS
While working on this thesis I have had the
pleasure and privilege of interaction with many per-
sons. I am particularly grateful to Dr. David Cox
and Professor A1 Fermelia who guided me. I also want
to thank Professor Joe Thomas and nurse Jean Van
Etten for their help. Finally, I thank my family for
their support and encouragement.
v


CONTENTS
Chapter
1.0 Introduction ............................... 1
2.0 Urinary Flow Rate (Q)........................3
2.1 Introduction............................3
2.2 Urinary Flow Rate (Q) and Equation {Qa).6
3.0 Closed Loop Methodology.....................13
3.1 Introduction...........................13
3.2 Kalman Filter..........................15
3.2.1 Model of Urinary System...........15
3.2.2 Estimation & Identification . .16
3.2.3 Control............................17
3.2.4. Validation. . ...................19
3.3 Results................................20
4.0 Conclusion..................................63
Appendixes
A. Derivation of a, b, c, and d..................67
B. Derivation of Cv and .........................71
References.......................................78
vi


FIGURES
Figure
2.1. A preoperative and postoperative
micturition from same patient.
The pressure/flow curve with the
fitted curve is shown.......................5
2.2. A normal person's flow rate.
The data is filtered.........................7
2.3. A normal person's flow rate.
The data is not filtered.....................8
2.4.
2.5.
2.6.
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
Q and Qb..........................
Intravesical volume VA............
Contraction velocity C ..... .
The OLM approach...................
The CLM approach...................
Mechanization of Kalman filter. .
Mechanization of validation without
noise .............................
a is increased by 20%,
which is a=1.2a*...................
A A ^
a and a where a=a +da.............
10
11
12
13
15
18
24
25
26
A
3.7. Error between Qa and Qa......................27
3.8. b is increased by 20%,
which is b=1.2b*.............................28
A A
3.9. b and b where b=b*+db........................29
A
3.10. Error between Qa and Q&......................30
VI1


3.11. a and b are increased by 20% each,
which are a=1.2a, b=1.2b4...................31
A A <
3.12. a and a where a=a+da
A A
b and b where b=b*+db........................32
A
3.13. Error between Qa and Qa.......................33
3.14. Mechanization of validation
with noise...................................34
3.15. Qa with noise.................................35
A
3.16. Q4=Qa*+dQ0 where dQ=noise....................36
3.17. Qa with noise.................................37
A
3.18. Qa=QB*+dQB where dQB=noise....................38
3.19. QB with noise.................................39
A
3.20. QB=QB+dQB where dQB=noise....................40
3.21. QB with noise.................................41
A
3.22. QB=QB*+dQa where dQ=noise....................42
3.23. Qa with noise.................................43
A
3.24. Qft=QB+dQB where dQ=noise...................44
3.25. A normal person's urinary flow
rate (Q) and approximation (Qa)
before Kalman filter.........................45
3.26. Error before Kalman filter. ................46
3.27. A normal person's urinary flow
rate (Q) and approximation (Qa)
after Kalman filter..........................47
3.28. Error after Kalman filter .................... 48
viii


3.29. Behavior of a during voiding
time for a normal person..................49
3.30. Behavior of b during voiding
time for a normal person...................50
3.31. Urinary flow rate (Q) for compressive
type and approximation (QJ before
Kalman filter............................. 51
3.32. Error before Kalman filter ............... 52
3.33. Urinary flow rate (Q) for compressive
type and approximation (QJ after
Kalman filter..............................53
3.34. Error after Kalman filter..................54
3.35. Behavior of a during voiding time
for a compressive type.....................55
3.36. Behavior of b during voiding time
for a compressive type.....................56
3.37. Urinary flow rate (Q) for constrictive
type and approximation (QJ before
Kalman filter..............................57
3.38. Error before Kalman filter ............... 58
3.39. Urinary flow rate (Q) for constrictive
type and approximation (QJ after
Kalman filter..............................59
3.40. Error after Kalman filter. ........ 60
3.41. Behavior of a during voiding time
for a constrictive type....................61
3.42. Behavior of b during voiding time
for a constrictive type....................62
4.1. Error covariance E[ (Q-QJ* (Q-QJT].........65
4.2. Relative error covariance
E [ ((Q-QJ / ((0-QJ /Qm) *] 66
A.l. aVtexp(^-t3)...............................68
ix


A.2. c (1-exp (-dt)) ...........................69
A. 3. a,/t exp(~tJ) c(l exp(-dt)).............70
A. 4. Definition of Q,, ...............72
B. l. Contraction velocity C^ for
a compressive type.........................74
B.2. Intravesical volume Vi for
a compressive type.........................75
B.3. Contraction velocity Cv for
a constrictive type........................76
B.4. Intravesical volume V4 for
a constrictive type...................... 77
x


CHAPTER 1
INTRODUCTION
Urinary obstruction is very common and it has
been estimated that a 40 year old man has a 30%
chance of undergoing a prostatic operation [Glynn et
al., 1985]. According to NEWSWEEK August 5, 1991,
Corrective surgery has become a major industry
over the past half century; American urologists
now perform 400,000 operations each year, at a
cost of more than $3 billion. And demand could
soar in coming decades, as the elderly popu-
lation grows. The irony is that, in many cases,
no one knows how much good the operation does.
In fact, there are studies showing up to 25% of pa-
tients operated on are unobstructed [Rollema and van
Mastrigt, 1987; Jensen et al., 1988; Schafer et al.,
1988].
Although there is a great need to gain a better
understanding of the phenomenology, little work has
been done to define obstruction in quantitative uro-
dynamic terms [Spangberg et al., 1991]. In their
paper, Spangberg et al. conducted pressure/flow
studies preoperatively and postoperatively in pa-
tients with hypertrophy. Specifically, they were
able to develop a mathematical relationship between
1


urethral pressure/flow and urethral elasticity. In
his review of this paper, Dr. Griffiths of the De-
partment of Applied Sciences at the University of
Alberta made the following observation:
Although the classification parameters is
used to distinguish physiologically different
types of obstruction are of value, its appli-
cability for diagnosis of obstruction in indi-
vidual patients is not obvious.
In their rebuttal, Spangberg et al. concede
that when developing a method which increases patho-
physiological knowledge, it is impossible to know
what its ultimate utility will be. They go on to
state: "We need complete knowledge about a phenome-
non before it is possible to say whether it can be
analyzed in a simplified way.
The application of CLM(Closed Loop Methodology)
to the modeling of physical and biological systems
provides an innovative systematic approach for the
analysis of such systems. The approach is developed
around the design of a Kalman filter which adapts
from signals provided by the subject.
2


CHAPTER 2
URINARY FLOW RATE (Q)
2.1 Introduction
Urinary obstruction is very common in elderly
men. The main cause of urinary obstruction is an
enlargement of the prostate, called Benign Prostatic
Hypertrophy (BPH). Werner Schafer defined two types
of obstruction in his paper [1984]. One is a com-
pressive obstruction and the other is a constrictive
obstruction. The mechanism causing compressive ob-
struction is an elevation of the minimal opening
pressure, but once this pressure is reached the ure-
thra has normal distensibility. In constrictive ob-
struction, the urethra can easily be distended to a
small cross-sectional area, but when a certain area
is reached very high pressure is needed for further
distention. So to find out the different types of
obstruction, numerous attempts have been made to
describe the relationship between detrusor pressure
(Pdet) and urinary flow rate (Q) .
One description examines the urethral re-
sistance factor. It considers micturiction as a sim-
ple hydrodynamic and assumes the urethra as a rigid
3


pipe with turbulent flow. However, due to an inade-
quate assumption, the value of such a factor does
not show the proper relationship between P^t and Q,
and can be misleading physiologically.
A more realistic model for urethral hydrodynam-
ics considers the urethra as a distensible tube.
Very recently, Anders Spangberg and his
colleagues[1991] defined obstruction in quantitative
urodynamic terms based on Griffiths' model of flow
through elastic tubes [Griffiths 1980]. According to
their paper, there is a relationship between and
Q
Pd*t = Pmo + LmXQm t2-1*
where PTO is minimal opening pressure and m and Lm
are parameters. From the urethral pressure/flow
graph P,,,, Lm, and m can be found using curve fitting.
Figure 2.1 shows urethral pressure/flow graph and
curve fitting. Depending upon the values of P^, Lm,
and m, three different types of obstruction can be
defined:
In the first of these, PM is elevated corre-
sponding to Schafer's compressive obstruction.
The second is a constrictive type of obstruc-
tion in which m >= 4/3 and Lm is elevated and
the third is a low-complaint type of obstruc-
tion in which m <= 1 and LB is elevated.
4


DetruBor pressure (kPa)
Fig. 2.1 A preoperative and postoperative micturition from
same patient. The presaure/flow curve with the fitted curve
is shown.


In the beginning, the goal of this research
was to find P,,,,, Ln, and m using the Kalman filter to
identify the types of obstruction. However, initial-
ly, there was not enough information on flow rate.
But as more data was collected on Q, there was a
distinctive trend" in normal persons flow rate.
Figures 2.2 and 2.3 show this trend. If an equation
that follows this trend can be found, then the ab-
normal flow rate can be compared with the equation.
It may even be possible to distinguish different
types of obstruction using flow rate only. So the
purpose of this study is to search for an equation
that approximates the normal flow rate and to quan-
tify different types of obstruction based on how
much the abnormal flow rate deviates from the equa-
tion using the Kalman filter.
2.2 Urinary Flow Rate (Q) and Equation (Qa)
What is the urinary flow? Von Garrelts pointed
out that the urinary flow represents "the sum of the
function of the whole mechanism of bladder evacu-
ation* [Von Garrelts, 1958]. Since urinary flow rate
is related directly to the urinary flow, the role of
Q is significant in distinguishing different types
6


Flow rate (ml/s)
Fig. 2.2 A normal person's flow rate.
The data is filtered.
7


Flow rate (ml/s)
Fig. 2.3 A normal person's flow rate.
The data is not filtered.


of obstruction. Mathematically, Q is defined as vol-
ume of urine passing a given point over a short pe-
riod of time and is measured in cubic centimeters or
milliliters per second. Also the urinary flow rate
can be obtained from the first derivative of the
voided volume.
Q = dVv/dt (2.2)
As it was mentioned in section 2.1, Q has a
trend in the normal person. What kind of an equation
fits into the trend? It happens to be that
Q* = a^t exp(^-t3)-c(l exp(dt)) (2.3)
where a, b, c, and d are parameters. Q0 has been
found by empirical means. Even though it looks aw-
ful, a, b, c, and d can be calculated very easily.
It is shown on Appendix A.
Once Q is obtained, then contraction velocity
Cv and intravesical volume VA can be calculated.
Vi=Tv-Vv (2.4)
Cv 1.3xQ/V|1-5 (2.5)
where Tv is total volume in bladder. The derivation
for VL and Cv is explained on Appendix B. Figures 2.4
through 2.6 show how Q*approximates Q accurately.
9




400
T
a

§
300
200-
100
01----------L
0 5
Fig.
T
T
* *V4 from Q
' ' iV4 from Q.
10
15
20
25
Time (a)
2.5 Intravesical volume V4


dl/dt (mm/s)
0 5 10 15 20 25
Time(b)
Contraction velocity Cv
Fig. 2.6


CHAPTER 3
CLOSED LOOP METHODLOGY
3.1 Introduction
The methodology invoked to gain a better under-
standing of BPH is a technique known as CLM (Closed
Loop Methodology) This technique employs an adap-
tive processor that systematically modifies a mathe-
matical model used to predict the urethral function
during micturiction. CLM can be compared to Open
Loop Methodology (OLM). Open loop techniques modify
the a priori math model by trial and error opera-
tions in order to reduce the error resulting from
the comparison of predicted and actual laboratory
result [Fermelia, 1981].
AGREEMENT
FORCES A PRIORI PREOiCTlONS
M0OU .I
ACTUAL
FORCES TEST MEASURED DATA 4

NO
AGREEMENT
Figure 1: The OLM Approach.
As shown in figure 3.1, open loop methodology
results can range from complete agreement to no
agreement at all. In addition, the confidence level
13


of the results from a laboratory test on a subject
are typically low until a large statistical data
base indicates the attributes of the samples and
clinical symptoms are correlated. Typically, as the
correlation takes place and additional laboratory
data becomes available, the model is adjusted to
produce predictions to accommodate these findings.
This "knob tweaking" is usually conducted by methods
which are inconsistent with much of a priori knowl-
edge of the system under investigation. For example:
many data reduction schemes employ the classical
least squares method of analysis [Marquart, 1963;
Spangberg et al., 1991] in an attempt to minimize
the difference shown in figure 3.1.
Because the OLM has considerable shortcoming,
the need for a more systematic approach has become
evident in recent years. Modern system theory pro-
vides such an approach based on the CLM concept. The
CLM is illustrated in figure 3.2 using adaptive pro-
cedures that provide a model with quantified confi-
dence levels. Modern system theory recognizes that
potential difference in prediction can be attributed
to stimuli uncertainty, incorrect estimates of the
constituents of the governing equations, and the
14


possibility that the model order is insufficient to
describe the phenomenology. The design of the adap-
tive processor accommodates these uncertainties and
systematically drives the difference between model
predictions and laboratory test data to a minimum.
DISTURBANCE SYSTEM EQUATIONS
identification AND parameters
Figure 2: The CLM Approach.
3.2 Kalman Filter
3.2.1 Model of Urinary System
The model of the lower urinary tract system can
be characterized by a stochastic nonlinear algebraic
equation because the equation Qa approximates the
normal urinary flow rate Q very well. Based upon
this knowledge, the system can be expressed as fol-
lows
X = f(X,U) + W (3.1)
Z = h(X,U) +V (3.2)
15


The solution to the equation (3.1) and (3.2) may be
obtained by defining and solving the estimation,
identification, and control.
3.2.2 Estimation & Identification
Estimation is to estimate the independent vari-
able U and dependent variable X, and identification
is to identify the coefficient of equations f, h, Qw
and R where QW=E [W*WTJ and R=E [V*VT3. To avoid confu-
sion between Q (flow rate) and Q (input noise
covariance), the input noise covariance is defined
as Qh. As it is mentioned previously, Qa approximates
Q, which is a measurement. So let Qa be equal to
h(X,U)
h(X,U) = a^t expf-^t3) c(l exp(-dt))
= aJt exp(^-t3) a/f^T exp(^-Tjnd)(l exp(-^-t)) (3.3)
When h(X,U) is carefully examined, there are only
two variables, a and b. With varying a and b, Qtt can
fit any shapes of Q. So it is appropriate to say
that X is composed by a and b.
X =
a
b
(3.4)
To find f(X,U), a and b have to be defined. Appendix
A shows how a and b can be derived. From Appendix A
16


a=Qnutt X exp(l/6)/ jTm!a
a=0
(3.5)
b=0
(3.6)
Then f(X,U)=0. In this particular problem, U is
zero. It is not clear whether input noise W and mea-
surement noise V are gaussian white noise. However,
to make the problem simple they are assumed to be
gaussian white noise.
Control is to reduce the error between Z and Z.
Figure 3.3 shows how it can be done graphically.
Since the system is nonlinear, it has to be line-
arized. This also is shown in figure 3.3. The impor-
tant relationships are summarized:
3.2.3 Control
A
A dh/dxlx* = q q
Discrete A.
Linearize h(X).
Jt exp(-^t3) (f)(1 exp(-dt))
H=dh/dXlx* = , , t3
aVt exp(ft3)(£-)-c(^)(l exp(-dt))
Kalman filter algorithm.
17


M
00
Xo/o = Xo
Fig. 3.3 Mechanization of Kalman filter.


Pk+l/fc ^>PkA^*T + Qwk
Gk+i =Pfcvi/fcH^+1[Hk+iPfc+i&Hj+I +Rk+i]-1
Qak+I = Zfc+j = h(X)
Qk+I = Zm
A
dZk+i =Zfc+I -Zv+i
dXk+i/k+i =OdXk& +Gk+i[dZk+i -Hk+i Pk+i/k+i = [I Gk+jHk+i ]Pk+i&
Xk+i/k+i = Xk+i/k + dXk
3.2.4 Validation
When Kalman filter algorithm is applied, there
are many unknown variables to be handled. When E[Z-
A
Z] does not approach zero, it is very difficult to
find what is wrong in the Kalman filter algorithm.
So it is appropriate to check some variables now.
This process, called validation, eliminates some
ambiguity from some unknown variables such as nomi-
nal value (X*) and covariance of noise (Q^ R) Also
this validation verifies the correctness of the
partial differential equation of h(X).
The first step is to check the model and cor-
rectness of the partial differential equation of
h(X). Here is a procedure to do that:
19


1) Create pseudodata (h(X)).
2) Create nominal data (h(X*)) based upon nominal
value (X*).
A
3) Add perturbed data onto nominal data (h(X) where
X = X*+dX).
A A
4) Compare Z=h{X) and Z = h(X).
A
If E[Z-Z] is very close to zero, then the model and
partial equation of h(X) is correct. Figure 3.4
shows the mechanization of validation without noise.
Table 3.1 shows some examples. Once this is checked,
the next step is to add noises into the system and
repeat the above process. Figure 3.14 shows mechani-
zation of validation with noise and table 3.2 shows
some examples.
3.3 Results
Thirteen urinary flow rates were obtained from
Colorado Neurological Institute. The sampling time
was 0.1 second. When a Kalman filter was applied to
A
the data, E[Z-Z] approached zero. Figures 3.25
through 3.42 show this. Since a controls magnitude
of flow rate and b controls time, to fit the given
flow rate curve it is necessary to change either a
or b or both a and b, so there are two types of be-
havior on a and b. The first type of data requires
20


change in a and no change in b. Figures 3.31 through
3.36 show this. This type of obstruction is called
compressive. The second type of data requires change
in a and b. Figures 3.37 through 3.42 show this.
This is called constrictive obstruction.
21


X X* X = X* + dX Error
a=12 a=10 da=2 Fig. 3.7
b=4374 b*=4374 db=0
Fig, 3.5 Fig. 3,5 Fig. 3.6
a=10 a*=10 da=0 Fig. 3.10
b=5248.8 b=4374 db=874.8
Fig. 3.8 Fig. 3.8 Fig. 3.9
a=12 a =10 da=2 Fig. 3.13
b=5248.8 b*=4374 db=874.8
Fig. 3.11 Fig. 3.11 Fig. 3.12
Table 1. Validation without noise.
system + noise nominal value X=X*+dX
a=10 b=4374 Wa=le-3 Wb=le-3 R=le-3 Fig. 3.15 a'=10 b*=4374 da=0 db=0 W=le-3 Wb=le-3 R=le-3 Fig. 3.16
a=10 b=4374 WB=1 Wb=l R=le-3 Fig. 3.17 a*=10 b*=4374 da=0 db=0 Wa=l Wb=l R=le-3 Fig. 3.18
22


a=10 a*=10 da=0
b=4374 b=4374 db=0
Wa=le-3 Wft=le-3
Wb=400 Wb=400
R=le-3 R=le-3
Fig. 3.19 Fig. 3.20
a=10 a'=10 da=0
b=4374 b*=4374 db=0
Wa=le-3 W=le-3
Wb=le-3 Wb=le-3
R=4 R=4
Fig. 3.21 Fig. 3.22
a=10 a=10 da=0
b=4374 b=4374 db=0
Wa=l Wa=l
Wb=400 Wb=400
R=4 R=4
Fig. 3.23 Fig. 3.24
Table 2. Validation with noise.
23


to
kpk
Zk+1 = Qk+1
Fig. 3.4 Mechanization of validation without noise.


30
25
20
15
10
5
0
5 10 15 20 25
Time(a)
Fig. 3.5 a is increased by 20%,
which ia a=1.2a*.


Flow rate (ml/B)


(ml/e)
1
0.5
to c?
-j i

a
-0.5-
-1
0 5 10 15 20
Time (s)
A
Fig. 3.7 Error between Qa and Qa
i i------------------------------------1------------------------------------r
I____________________________________I____________________________________I____________________________________L
25


Flow rate (ml/s)
25
r
T
r
Time (s)
Fig. 3.8 b is increased by 20%,
which is b=1.2b*.


Plow rate (ml/s)


(ml/B)


Flow rate (ml/s)
Time(a)
Fig. 3.11 a and b are increased by 20% each,
which are a=1.2a, b=1.2b*.


Flow rate (ml/a)
A A
Fig. 3.12 a and a where a = a*+da.
b and b where b = b*+db.


(ml/s)


Zjcn =Qkti
U)
it*
Fig. 3.14 Mechanization of validation with noise.


u
in




U)
-J
m
3
JJ
IS
t
r-t
fa
-10'---------L
0 5
Fig
_J__________I__________l_
10 15 20
Time (b)
3.17 Q.with noiBe.


8£
Flow rate (ml/s)
"d
(-*
IQ
Ui
9
OD
O >
B
II
o
+

§
ffi
ffi
a
o
ii
s
0
H*
tn
0
CJl
*3
H-
s
ffi
D
C71
ro
to
cn
co
i
i


U)
vo
to
S
(U
jj
2
B
rS
tli
-101---------L
0 5
Fig
W=le-3
Wb=400
R=le-3
__I__________I___________L
10 15 20
Time (a)
3.19 Qa with noise.


30
T
O
N
H
a

u
E
g
rH
to
25-
20
15
10
5 I
01----------L
0 5
Fig
T
10
15
20
Time (e)
A
3.20 Qa = Q*+dQa where dQ,=noise.
25


40
T
CD
30-
0)
U
g
8
fa
20-
10 -
0i
-101---------l
0 5
Fig.
10 15
Time (b)
3.21 Q with noiBe.


40
T
t*
to
m
'v
rH
&
Q)
U
d
U
l
rH
-10
0
x
5
Fig.
10 15 20
A Time (b)
3.22 Q. = Q2+dQa where dQB=noiee.


40
T
CD
0
9
u
d
W H
tii
i
30
20
10
0
10
0
5
l
i
10 15
Time (b)
Fig. 3.23 Qa with noiBe.


40
T
if*
itk
a
30


10
U
I
r-i
tu
20
-10
0
-L
5
Fig. 3.24
10
20
15
Time (s)
Qa = Q*+dQa where dQ=noise


Flow rate (ml/e)
Fig. 3.25
A normal person's urinary flow rate
and approximation (Q) before Kalman
(Q)
filter.


1
r
Time (b)
Fig. 3.26 Error before Kalman filter.


Fig, 3.27 A normal person's urinary flow rate (Q)
and approximation (Qa) after Kalman filter.


0 5 10 15 20 25
Time (b)
Fig. 3.28 Error after Kalman filter.


10 E
VO
102 :
\r~
B 10-U
10-4:
10-7
0
J.
5
Fig. 3.29
T
T
10 15 20 25
Time (s)
Behavior of a during voiding time
for a normal person.


10*
108
i i i r
J________________________I________________________I_________________________L
0 5 10 15 20 25
Time (b)
Fig. 3.30 Behavior of b during voiding time
for a normal person.


Time (b)
Fig. 3.31 Urinary flow rate (Q) for compreBsive type
and approximation (Q) before Kalman filter.


Time (b)
Fig. 3.32 Error before Kalman filter.


Time (s)
Fig. 3.33 Urinary flow rate (Q) for compressive type
and approximation (Q) after Kalman filter.


3
T
T
T
T
in
it*
a
rH
6
of
i
a
40 60
Time (s)
Fig. 3.34 Error after Kalman filter.


(ml/s)
Time (a)
Behavior of a during voiding time
for a compressive type.
Fig. 3.35


Pig. 3.36
40 60
Time (s)
Behavior of b during voiding time
for a compressive type.


Flow rate (ml/B)
Fig. 3.37 Urinary flow rate (Q) for a constrictive type
and approximation (Q) before Kalman filter.


Time (s)
Fig. 3.38 Error before Kalman filter.




Time (s)
Fig. 3.40 Error after Kalman filter.


(ml/s)
Fig. 3.41 Behavior of a during voiding time
for a constrictive type.


Fig. 3.42 Behavior of b during voiding time
for a conBtrictive type.


CHAPTER 4
CONCLUSION
The primary purpose of this paper is to find an
equation that approximates the normal person's uri-
nary flow rate curve and to identify different types
of obstruction using a Kalman filter. Even though
there has been difficulty in finding the proper val-
ue of noise covariance, the results were excellent.
Also they support Werner Schafer's concept. He indi-
cated in his paper that the main difference between
the normal and the compressive obstruction is that
the compressive requires high opening pressure. Oth-
er than that the function of the lower urinary tract
is the same. Figures 3.29, 3.30, 3.35 and 3.36 show
this relation. There is a little difference between
a in normal and a in compressive.
Something else should be defined to distinguish
normal from compressive. One way is 'relative" E[ to-
ga)* {Q-Qa)T] .
Er = E[((Q Qa)/Qma*) X ((Q Qa)/Qma*)T]
If the value of E is less than 0.01, then that is
normal flow rate. If not, then that is abnormal flow
rate. The main reason for this is that for the
max
63


normal rate is much higher than for the abnormal.
Data 1, data 2, and data 3 are the normal. From fig-
ure 4.1 it is very hard to distinguish the normal
from the abnormal. However, when EH is used, then it
is clear what is the normal person's urinary flow
rate and what is not. Figure 4.2 shows this. Using
this information, three different types of Q can be
defined.
1. Normal: Relative noise covariance is less than
0.01 and b does not change.
2. Compressive obstruction: Relative noise covarian-
ce is higher than 0.01 and b does not change.
3. Constrictive obstruction: Relative noise covaria-
nce is higher than 0.01 and b changes.
64


140
Data
Fig. 4.1 Error covariance E[ (Q-QJ (Q-Qa)T] .


0.09
C\
C\
Fig
3 4 5 6 7 8 9 10 11 12 13
Data
4.2 Relative error covariance
E[((Q-QJ/QibJ*((Q-Q->/QJ


APPENDIX A
Derivation of a, b, c, and d
Qa^a^t exp(^-t3)-c(l-exp(-dt where a, b, c, and d
are parameters. Though it looks awful, a, b, c, and
d can be calculated very easily. Most of time
c(l-exp(-dt)) is negligible compared to a^t exp(^-t3).
Main existence of c(l-exp(-dt)) is to reduce "tail"
part of Qa to zero. Figures A.l, A.2, and A.3 show
this relation. From this knowledge, Q can be ex-
pressed as
QaSaVt exp(^-t3)
dQ/dt = exp(^-t3)-3a|-tZi exp(^-t3)
To calculate a and b, let dQa/dt=0. Then
|aVF Sa-g-t2-5 = 0 b= 613
If t^T,^, then Q^Q*.
Qmax a^/Tmax" Xp((l/Tmax)Tmax)
a s Qmax exp(l/6)/yT^r
After a and b have been found, c and d can be calcu-
lated from aVt exp(-~t3). To reduce tail part to zero
c = a/T^d expOf-T^)
c(l exp(dTend)) as 0.99c
dar-lnO.Ol/T^
Figure A. 4 shows Q^, Tm, and Tmd.
67


89
Flow rate (ml/s)


69
Flow rate (ml/s)


25
20
15
10
5
0
5 10 15
Time (b)
Fig. A.3 &J\ exp^t^-cO-expf-dt))
20


APPENDIX D
Derivation of Cr and VA
When bladder is full, 'Vi can be modeled as
Vi = fjrr3 (B.l)
where r is radius of bladder. And there is relation-
ship between intravesical volume and voided volume.
Vj =TVVv (B. 2)
where Tv is total volume in bladder. From equation
(B. 2)
Vv=Tv-Vi (B.3)
Substitute equation (B.l) to (B.3)
Vv = Tv yiir3
Q = dVy/dt = (dVv/dr)(dr/dt)= -4irr2dr/dt
From equation (B.l)
r = ({ltVi)1'3
dr/dt = -0.207Q/vP (b.4)
Contraction velocity is equivalent to the rate of
change in circumference of bladder (L).
L = 2nr
Cv = -dL/dt -2rcdr/dt { b 5)
Substitute equation (B.4) to (B.5)
Cv = lJQ/Vf5
71


Flow Rate
Fig. A.4 Definition of Tm, and T^.
72


Figures B.l and B.2 show contraction velocity and
intravesical volume of compressive type,
and B.4 show contraction velocity and
volume of constrictive type.
Figures B.3
intravesical
73


5
4
~ 3
2
<1 u
IP* \
rH
>o
1
0
-1
0 20 40 60 80 100
Time (b)
Fig. B.l Contraction velocity CT for a compressive type.
xlO-3


Time (s)
Intravesical volume V4 for a compressive type.
Fig. B.2


Time (a)
Fig. B.3 Contraction velocity Cwfor a constrictive type.


380
360
340
320
300
280
i
n 1
T
T
* sVi from Q
;VA from Qn
_____________I____________I_____________I_____________I
5 10 15 20
Time (b)
. B.4 IntraveBical volume VL for a constrictive type.


REFERENCES
Astrom K, Wittenmark B (1990): Computer-controlled
systems. Englewood Cliffs, N.J.: Prentice Hall, Inc.
Fermelia A (1981): "Adaptive processor definition
and design", Technical Report BDM/A-81-168-TR, BDM
Corporation, Albuquerque, N.M.
Gabel RA, Roberts RA (1980): Signals and Linear
Systems. New York: John Wiley & Sons, Inc.
Glynn RJ, Campion EW, Bouchard GR, Silbert JE(1985):
The development of benign prostatic hyperplasia
among volunteers in the normative aging study. Am J
Epidemiol 121:78-90
Griffiths DJ (1980): Urodynamics. The Mechanics and
Hydrodynamics of the Lower Urinary Tract. Bristol:
Adam Hilger. Chs 3 and 4, pp. 25-65.
Jensen KM-E, Jorgensen JB, Mogensen P (1988): Uro-
dynamics in prostatism. II. Prognostic value of
pressure-flow study combined with stop-flow test.
Scand J Urol Nephrol [Suppl 114]:72-77.
Kopp R, Orford R (1962): Linear regression applied
to system identification for adaptive control sys-
tems. Sorenson H (ed): Kalman Filtering: Theory and
Application. IEEE PRESS:83-89.
Marquart DW (1963): An algorithm for least square
estimation of non-linear parameters. J Soc Indust
Appl Math 11:431-441.
Roberts RA, Mullis CT (1987): Digital Signal
Processing. Addison-Wesley Publishing Company.
Rollema JH, van Mastrigt R (1987): Detrusor contrac-
tility before and after prostatectomy. Neurourol
Urodyn 6:220-221.
Schafer W (1983): The contribution of the bladder
outlet to the relation between pressure and flow
78


rate during micturition. In Hinman F, Jr(ed):
Benign Prostatic Hypertrophy. Berlin:Springer-
Verlag, pp. 470-498.
Schafer W, Noppeney R, Rubben H, Lutzeyer W (1988):
The value of free flow rate and pressure/flow
studies in the routine investigation of BPH patients
Neurourol Urodyn 7:219-221.
Shanmugan K. S, Breipohl A. M (1988): Random Sig-
nals.;_P^j^ctJLojL._Estimation and Data Analysis. New
York: John Wiley & Sons, Inc.
Spangberg A, Terio H, Ask P, Engberg A (1991):
Pressure/flow studies preoperatively and postopera-
tively in patients with benign prostatic hypertro-
phy: Estimation of the urethral pressure/flow
relation and urethral elasticity. Neurourol Urodyn
10:139-167.
Terio H, Spangberg A, Engberg A, Ask P (1989) : Es-
timation of elastic properties in the urethral flow
controlling zone by signal processing analysis of
urodynamic pressure/flow data. Med Biol Eng Comput
27:314-321.
Von Garrelts B (1958): Micturition in disorders of
the prostate and posterior urethra. Acta Chir Scand
115:227-241.
79


Full Text

PAGE 1

APPLICATION OF CLM TO URODYNAMIC PROBLEMS by Kyung Sub Joo B.S., University of Colorado, 1989 A .thesis submitted to the Faculty of the Graduate School of the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Department of Electrical Engineering 1992

PAGE 2

This thesis for the Master of Science degree by Kyung Sub Joo has been approved for the Department of Electrical Engineering by Alfred Fermelia ox Joe E. Thomas Et,b. z. Date

PAGE 3

Joo, Kyung Sub (M.S., Electrical Engineering) Application of CLM to Urodynamic Problems Thesis directed by Professor Alfred Fermelia ABSTRACT In this thesis a different method of finding urinary obstruction due to benign enlargement of the prostate is presented. An equation(Qa) that approxi-mates a normal person's urinary flow rate (Q) has been found, which is where a, b, c, and d are parameters. Using this equation with Closed Loop Methodology(CLM), one can distin-guish urinary obstruction from unobstruction. Also two different types of obstruction can be defined. A person is obstructed if covariance of[(Q-Qa}/ Qmax] is bigger than 0 .1. Once an obstructed person is separated, then, using a Kalman filter, compres-sive and constrictive obstruction can be distin-guished. When b is not changed during voiding time, obstruction is compressive. On the contrary, con-strictive obstruction produces significant changes in b during voiding time. This method is applied to 13 different urinary flows that are already diagnosed, and the results iii

PAGE 4

agree with the diagnoses. This proves that the application of CLM to the modeling of physical and biological systems provides a systematic approach for the analysis of such system. This abstract accurately represents the content of the candidates thesis. I recommend its publication. signed Alfred Fermelia iv

PAGE 5

ACKNOWLEDGMENTS While working on this thesis I have had the pleasure and privilege of interaction with many persons. I am particularly grateful to Dr. David Cox and Professor Al Fermelia who guided me. I also want to thank Professor Joe Thomas and nurse Jean Van Etten for their help. Finally, I thank my family for their support and encouragement. v

PAGE 6

CONTENTS Chapter 1. 0 Introduction . 2.0 Urinary Flow Rate (Q) 2.1 Introduction ..... 1 3 3 2.2 Urinary Flow Rate (Q) and Equation (Qa).6 3.0 Closed Loop Methodology ........ 13 3.1 Introduction. .......... 13 3.2 Kalman Filter ............. 15 3.2.1 3.2.2 Model of Urinary System ... 15 Estimation & Identification .... 16 3.2.3 Control .. 3.2.4. Validation. 3.3 Results ... 4.0 Conclusion Appendixes A. Derivation of a, b, c, and d. B. Derivation of cv and Vi. References. vi .17 .19 . . 20 . 63 . 67 . 71 . 7 8

PAGE 7

Figure 2.1. FIGURES A preoperative and pos.toperative micturition from same patient. The pressure/flow curve with the fitted curve is shown. 2.2. A normal persons flow rate. 5 The data is filtered ....... 7 2.3. 2.4. 2.5. 2.6. 3 .1. 3.2. 3.3. A normal persons flow rate. The data is not filtered Q and Q.. Intravesical volume V1 Contraction velocity Cv The OLM approach. The CLM approach. .. Mechanization of Kalman filter. 3.4. Mechanization of validation without 3.5. 3.6. noise a is increased by 20%, which is a=1.2a ... 1\ 1\ a and a where a=a +da 1\ 8 10 11 12 13 15 18 . 24 25 26 3.7. Error between Qa and Qa 27 3.8. b is increased by 20%, which is b=1. 2b. . . . 28 1\ 1\ 3.9. b and b where b=b.+db .......... 29 1\ 3.10. Error between Qa and Qa 30 vii

PAGE 8

3.11. a and bare increased by 20% each, which are a=l. 2a, b=1. 2b". . . 31 3.12. a and a where a=a +da b and b where b=b.+db. . 32 3.13. Error between Qa and Qa. . 33 3.14. Mechanization of validation with noise. .. 3.15. Qa with noise ........ ... 3.16. Q4=Qa"+dQa where dQa=noise .. 3.17. Qa with noise. . 3.18. Q4=Qa"+dQa where dQa=noise .. 3.19. Qa with noise .. ... 3.20. Q4=Q,."+dQa where dQa=noise .. 3.21. Qa with noise ..... 3. 22 .. Qa =Qa+dQa where dQa=noise 3. 23. Qa with noise. . 3.24. Q4=Qa"+dQa where dQa=noise 3.25. A normal persons urinary flow rate (Q) and approximation (Qa) before Kalman filter ..... 3.26. Error before Kalman filter .... 3.27. A normal persons urinary flow rate (Q) and approximation (Qa) 34 35 .. 36 3 7 38 39 40 41 .. 42 43 .44 45 46 after Kalman filter . . 47 3.28. Error after Kalman filter .. 48 viii

PAGE 9

3.29. Behavior of a during voiding time for a normal person . 3.30. Behavior of b during voiding time for a normal person . 3.31. Urinary flow rate (Q) for compressive type and approximation (Q6 ) before 49 50 Kalman f i 1 t er . 51 3.32. Error before Kalman filter 3.33. Urinary flow rate (Q) for compressive type and approximation (Q6 ) after 52 Kalman filter. . 53 3.34. Error after Kalman filter. . 3.35. Behavior of a during voiding time for a compressive type . . 3.36. Behavior of b during voiding time for a compressive type . 3.37. Urinary flow rate (Q) for constrictive type and approximation (Q6 ) before 54 55 56 Kalman filter. . 57 3.38. Error before Kalman filter 3.39. Urinary flow rate (Q) for constrictive type and approximation (Q6 ) after 58 Kalman filter. . . 59 3.40. Error after Kalman filter .. 60 3.41. Behavior of a during voiding time for a constrictive type. . . 61 3.42. Behavior of b during voiding time for a constrictive type. . 62 4.1. 4.2. Error covariance E [ (Q-Q6 ) (Q-Qa) T]. Relative error covariance E [ ( ( Q-Qa) ( ( Q-Qa) /QIIII>X) T] A.l. aJf ix 65 66 68

PAGE 10

A. 2. A.3. A. 4. B.l. B.2. B.3. c (1-exp a/f t3)-c(l-exp(-dt)). Definition of T_, Qmax, Tend Contraction velocity Cv for a compressive type Intravesical volume Vi for a compressive type ..... Contraction velocity Cv for a constrictive type. B.4. Intravesical volume Vi for 69 .70 .72 7 4 7 5 . 76 a constrictive type. ..... 77 X

PAGE 11

CHAPTER 1 INTRODUCTION Urinary obstruction is very common and it has been estimated that a 40 year old man has a 3 0% chance of undergoing a prostatic operation [Glynn et al., 1985]. According to NEWSWEEK August 5, 1991, Corrective surgery has become a major industry over the past half century; American urologists now perform 400,000 operations each year, at a cost of more than $3 billion. And demand could soar in coming decades, as the elderly population grows. The irony is that, in many cases, no one knows how much good the operation does. In fact, there are studies showing up to 25% of pa-tients operated on are unobstructed [Rollema and van Mastrigt, 1987; Jensen et al., 1988; Schafer et al., 1988]. Although there is a great need to gain a better understanding of the phenomenology, little work has been done to define obstruction in quantitative uro-dynamic terms [Spangberg et al., 1991]. In their paper, Spangberg et al conducted pressure/flow studies preoperatively and postoperatively in pa-tients with hypertrophy. Specifically, they were able to develop a mathematical relationship between 1

PAGE 12

urethral pressure/flow and urethral elasticity. In his review of this paper, Dr. Griffiths of the De-partment of Applied Sciences at the University of Alberta made the following observation: Although the classification parameters is used to distinguish physiologically different types of obstruction are of value, its applicability for diagnosis of obstruction in individual patients is not obvious. In their rebuttal, Spangberg et al. concede that when developing a method which increases pathophysiological knowledge, it is impossible to know what its ultimate utility will be. They go on to state: we need complete knowledge about a phenome-non before it is possible to say whether it can be analyzed in a simplified way. The application of CLM(Closed Loop Methodology) to the modeling of physical and biological systems provides an innovative systematic approach for the analysis of such systems. The approach is developed around the design of a Kalman filter which adapts from signals provided by the subject. 2

PAGE 13

CHAPTER 2 URINARY FLOW RATE (Q) 2.1 Introduction Urinary obstruction is very common in elderly men. The main cause of urinary obstruction is an enlargement of the prostate, called Benign Prostatic Hypertrophy (BPH). Werner Schafer defined two types of obstruction in his paper [1984]. One is a compressive obstruction and the other is a constrictive obstruction. The mechanism causing compressive obstruction is an elevation of the minimal opening pressure, but once this pressure is reached the urethra has normal distensibility. In constrictive obstruction, the urethra can easily be distended to a small cross-sectional area, but when a certain area is reached very high pressure is needed for further distention. So to find out the different types of obstruction, numerous attempts have been made to describe the relationship between detrusor pressure (Pdet.> and urinary flow rate (Q) One description examines the urethral resistance factor. It considers micturiction as a simple hydrodynamic and assumes the urethra as a rigid 3

PAGE 14

p1pe with turbulent flow. However, due to an inade-quate assumption, the value of such a factor does not show the proper relationship between and Q, and can be misleading physiologically. A more realistic model for urethral hydrodynam-ics considers the urethra as a distensible tube. Very recently, Anders Spang berg and his colleagues[1991] defined obstruction in quantitative urodynamic terms based on Griffiths model of flow through elastic tubes [Griffiths 1980]. According to their paper, there is a relationship between and Q (2 .1) where P1110 is minimal opening pressure and m and Lm are parameters. From the urethral pressure/flow graph P_Lm, and m can be found using curve fitting. Figure 2.1 shows urethral pressure/flow graph and curve fitting. Depending upon the values of P1110, Lm, and m, three different types of obstruction can be defined: In the first of these, P1110 is elevated corresponding to Schafers compressive obstruction. The second is a constrictive type of obstruction in which m >= 4/3 and Lm is elevated and the third is a low-complaint type of obstruction in which m <= 1 and Lm is elevated. 4

PAGE 15

U'1 14.0 12.0 as Q) 10.0 14 :::3 CD 8.0 CD Q) 14 PI 6.0 14 0 CD e 4.0 .u Q) t:l 2.0 0.0-. 0.0 4.0 preop 8.0 p (Q) =2. 2+1. 973Q213 .p(Q)=1.2+0.000467Q3 postop IZ.O 16.0 20.0 Flow rate (ml/s) Fig. 2.1 A preoperative and postoperative micturition from same patient. The pressure/flow curve with the fitted curve is shown.

PAGE 16

In the beginning, the goal of this research was to find Lm, and m using the Kalman filter to identify the types of obstruction. However, initial-ly, there was not enough information on flow rate. But as more data was collected on Q, there was a distinctive trend in normal person s flow rate. Figures 2. 2 and 2. 3 show this trend. If an equation that follows this trend can be 'found, then the ab-normal flow rate can be compared with the equation. It may even be possible to distinguish different types of obstruction using flow rate only. So the purpose of this study is to search for an equation that approximates the normal flow rate and to quan-tify different types of obstruction based on how much the abnormal flow rate deviates from the equation using the Kalman filter. 2.2 Urinary Flow Rate (Q) and Equation (Q.) What is the urinary flow? Von Garrelts pointed out that the urinary flow represents the sum of the function of the whole mechanism of bladder evacuation [Von Garrelts, 1958]. Since urinary flow rate is related directly to the urinary flow, the role of Q is significant in distinguishing different types 6

PAGE 17

30 -( \ CD "' r-4 Ei 20 I CJ) f .., as "" 10 I 0 \ r-4 rz.. J 9; J 0 20 Time (s) Fig. 2.2 A normal persons flow rate. The data is filtered. 7

PAGE 18

25 ID 20, ....... s Q) 15 .u ca CD J.i 10 rt. I 5 0 5 10 15 20 25 Time (s) Fig. 2.3 A normal person's flow rate. The data is not filtered.

PAGE 19

of obstruction. Mathematically, Q is defined as volume of urine passing a given point over a short pe-riod of time and is measured in cubic centimeters or milliliters per second. Also the urinary flow rate can be obtained from the first derivative of the voided volume. Q=dVv/dt (2.2) As it was mentioned in section 2. 1, Q has a trend in the normal person. What kind of an equation fits into the trend? It happens to be that Qa = a.Jt t3)-c(l-exp(-dt)) (2. 3) where a, b, c, and d are parameters. Q has been a found by empirical means. Even though it looks awful, a, b, c, and d can be calculated very easily. It is shown on Appendix A. Once Qa is obtained, then contraction velocity Cv and intravesical volume Vi can be calculated. (2. 4) where Tv is total volume in bladder. The derivation for Vi and Cvis explained on Appendix B. Figures 2.4 through 2.6 show how Qaapproximates Q accurately. 9

PAGE 20

., ora 0 t\1 / "' ,, "' ., .. "' ,./ lQ .....-4 0 .....-4 10 cJ '0 c:: Ill Ill 01 CD s P'4 N E-4 Ol P'4 rz.

PAGE 21

lO i N I I I I I I I : I I I 01 01 = I N G) I I ,.. ,.. I 1"'1 ""' ""' I 0 > ... ... > > I I .. -, 1"'1 ld I. lO u ..... .... m G) m > ld CD ,.. s c .... ....... 0 E-t ..... In N tn .... rs. 11

PAGE 22

II ...... I ...... ...... ....t l!oJ 'd 0.15 ,...--.--r-----y-----y-----r-----.., I o) I 0.05 from Q --1 :C.., from o. I 5 10 Time{s) #II.,., ,, ', ... -,, __./ I\\ \ \ \ t t \ \J 15 20 25 Fig. 2.6 Contraction velocity c ...

PAGE 23

CHAPTER 3 CLOSED LOOP METHODLOGY 3.1 Introduction The methodology invoked to gain a better understanding of BPH is a technique known as CLM (Closed Loop .Methodology). This technique employs an adap-tive processor that systematically modifies a mathematical model used to predict the urethral function during micturiction. CLM can be compared to Open Loop Methodology (OLM). Open loop techniques modify the a priori math model by trial and error opera-tions in order to reduce the error resulting from the comparison of predicted and actual laboratory result [Fermelia, 1981]. ACTUAL FORCES AGREEMENT NO AGREEMENT Figure 1: The OLM Approach. As shown in figure 3.1, open loop methodology results can range from complete agreement to no agreement at all. In addition, the confidence level 13

PAGE 24

of the results from a laboratory test on a subject are typically low until a large statistical data base indicates the attributes of the samples and clinical symptoms are correlated. TYPically, as the correlation takes place and additional laboratory data becomes available, the model is adjusted to produce predictions to accommodate these findings. This knob tweaking is usually conducted by methods which are inconsistent with much of a priori knowledge of the system under investigation. For example: many data reduction schemes employ the classical least squares method of analysis [Marquart, 1963; Spangberg et al., 1991] in an attempt to minimize the difference shown in figure 3.1. Because the OLM has considerable shortcoming. the need for a more systematic approach has become evident in recent years. Modern system theory provides such an approach based on the CLM concept. The CLM is illustrated in figure 3.2 using adaptive procedures that provide a model with quantified confidence levels. Modern system theory recognizes that potential difference in prediction can be attributed to stimuli uncertainty, incorrect estimates of the constituents of the governing equations, and the 14

PAGE 25

possibility that the model order 1s insufficient to describe the phenomenology. The design of the adap-tive processor accommodates these uncertainties and systematically drives the difference between model predictions and laboratory test data to a minimum. DISTURBANCE SYSTEM EOUA TIONS IDENTIFICA TIDN AND PARAMETERS ACTUAL FORCES MEASURED DATA '----' ERROR Figure 2: The CLM Approach. 3.2 Kalman Filter 3.2.1 Model of Urinary system The model of the lower urinary tract system can be characterized by a stochastic nonlinear algebraic equation because the equation Q,. approximates the normal urinary flow rate Q very well. Based upon this knowledge, the system can be expressed as fol-lows X=f(X,U)+W (3 .1) Z=h(X,U)+ V ( 3. 2) 15

PAGE 26

The solution to the equation (3.1) and (3.2) may be obtained by defining and solving the estimation, identification, and control. 3.2.2 Estimation & Identification Estimation is to estimate the independent vari-able U and dependent variable X, and identification is to identify the coefficient of equations f, h, Qw and R where Qw=E [W*WT] and R=E [V*VT]. To avoid confusion between Q (flow rate) and Q (input noise covariance) the input noise covariance is defined as Qw As it is mentioned previously, Q0 approximates Q. which is a measurement. So let Qo be equal to h{X,U) h(X, U) =a./f t3)-c(l-exp(-dt)) = a./t t3 ) -aJT end T!nJ(lexp( t)) ( 3 3) When h (X, U) is carefully examined, there are only two variables, a and b. With varying a and b, Qo can fit any shapes of Q. So it is appropriate to say that X is composed by a and b. X=[:] (3.4) To find f(X,U), a and b have to be defined. Appendix A shows how a and b can be derived. From Appendix A 16

PAGE 27

a= Qmax Xexp(l/6)/ JTmax a=O b=6T!wt b=O (3. 5) (3. 6) Then f(X,U)=O. In this particular problem, U is zero. It is not clear whether input noise W and mea-surement noise V are gaussian white noise. However, to make the problem simple they are assumed to be gaussian white no1se. 3.2.3 Control A Control is to reduce the error between Z and z. Figure 3 3 shows how it can be done graphically. Since the system is nonlinear, it has to be line-arized. This also is shown in figure 3.3. The important relationships are summarized: Discrete A. Linearize h (X) [ Jf t3)-(f)(l-exp(-dt)) ] H = ohlaXIx = a./f Kalman filter algorithm. 17

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1-' CD &v i Zkl -!.,,., 1\Xhi/IUI () l>O I ;:=t fiZkttlk -A BZk+tlk t" 1 m. I ilX Xt+11t BXklk xk 1\ Zk+tlk 1\ "'0-I I [:> h(Xktllk 1\ Xk,tlktt xlttllk GJlF 1\ 1\ Xoto =Xo Fig. 3.3 Mechanization of Kalman filter.

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1\ 1\ Qak+l = zk+l = h(X) 1\ dZk+I =Zk+l -zk+l 3.2.4 Validation When Kalman filter algorithm is applied, there are many unknown variables to be handled. When E[Z-Z] does not approach zero, it is very difficult to find what is wrong in the Kalman filter algorithm. So it is appropriate to check some variables now. This process, called validation, eliminates some ambiguity from some unknown variables such as nominal value (x) and covariance of noise (Q... R). Also this validation verifies the correctness of the partial differential equationof h(X). The first step is to check the model and correctness of the partial differential equation of h(X). Here is a procedure to do that: 19

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1) Create pseudodata (h(X)). 2) Create nominal data (h(X*)) based upon nominal value (X*). 3) Add perturbed data onto nominal data (h(X) where X=X.+dX). 4) Compare Z=h(X) and Z=h(X). If E[Z-Z] is very close to zero, then the model and partial equation of h(X) is correct. Figure 3.4 shows the mechanization of validation without noise. Table 3.1 shows some examples. Once this is checked, the next step is to add noises into the system and repeat the above process. Figure 3.14 shows mechani-zation of validation with noise and table 3.2 shows some examples. 3.3 Results Thirteen urinary flow rates were obtained from Colorado Neurological Institute. The sampling time was 0.1 second. When a Kalman filter was applied to the data, E[Z-Z] approached zero. Figures 3.25 through 3. 42 show this. Since a controls magnitude of flow rate and b controls time, to fit the given flow rate curve it is necessary to change either a or b or both a and b, so there are two types of behavior on a and b. The first type of data requires 20

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change in a and no change in b. Figures 3.31 through 3.36 show this. This type of obstruction is called compressive. The second type of data requires change in a and b. Figures 3. 3 7 through 3 42 show this. This is called constrictive obstruction. 21

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1\ X x X=X*+dX Error a=12 a=10 da=2 Fig. 3.7 b=4374 b=4374 db=O Fig. 3.5 Fig. 3.5 Fig. 3.6 a=10 a=1o da=O Fig. 3.10 b=5248.8 b=4374 db=874.8 Fig. 3.8 Fig. 3.8 Fig. 3.9 a=12 a=10 da=2 Fig. 3.13 b=5248.8 b=4374 db=874.8 Fig. 3.11 Fig. 3.11 Fig. 3.12 Table 1. Validation without noise. system nominal 1\ + value X=X*+dX noise a=10 a=10 da=O b=4374 b=4374 db=O W8=1e-3 W =1e-3 a Wb=1e-3 Wb=1e-3 R=1e-3 R=1e-3 Fig. 3.15 Fig. 3.16 a=10 a=10 da=O b=4374 b=4374 db=O W8=1 W8=1 Wb=1 Wb=1 R=1e-3 R=1e-3 Fig. 3.17 Fig. 3.18 22

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a=10 a"=10 da=O b=4374 b"=4374 db:::O W :::1e-3 D W =1e-3 D Wb=400 Wb=400 R=1e-3 R=1e-3 Fig. 3.19 Fig. 3.20 a=10 a"=10 da:::O b:::4374 b"=4374 db:::O WD=1e-3 WD=1e-3 Wb=1e-3 Wb=1e-3 R=4 R=4 Fig. 3.21 Fig. 3.22 a=10 a"=10 da=O b:::4374 b"=4374 db=O WD=1 WD=1 Wb=400 Wb=400 R=4 R=4 Fig. 3.23 Fig. 3.24 Table 2. Validation with noise. 23

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Zk-t-1 =Qk+l xk+l LJ-Ek+t 0 1 [> delay ..___j_ + 1\ 1\ Xk Zk+t =Qk+t I dXk+t AI t==;-r=======::l ax Xua ----, Q 8Fig. 3.4 Mechanization of validation without noise.

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Q1 ...... ,..... s Q) ....., to.) e U"' ,..... 25 20 15 10 5 .. ---........... .. /' ,, ,, ,, / ', I \ I \ I \ / \ I \ I I \ I \ I \ I \ I \ I \ I \ I \ I \ f 1--1 :Q .. based upon a. \ I \ I b d '" 1 1 1 : Q. ase upon a I \ I \ \ I \ ', ,, ,, :\:\,!oo. 0 5 Fig. 3.5 10 15 20 Time(s) a is increased by 20%, which is a=l. 2a'". 25

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0 N + II .0 Q) ..... GJ -; Ul ca d d Q) 0 0 a "0 0. 0. r-1 d ::s =' E-4 liS "0 "0 0 GJ Q) ..... ca al ID ca ca \0 ,.Q ,.Q M 0 <0 .. .. Cl r-1 rz.. 26

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I = 27 I .0 = I --.... I Q C\l
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.. 0 N ... .Q 'ON Q) ID.-1 as 11 Q).Q CD Sol tJID C..t r-i 15! .c r-i IDtJ E-t r-i r-i rc 'C 0 ..... ID ID as as .Q .Q CD c1 Ol M Ol r-i rz.. 28

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0 :6 C\J + .J:I II <.J:I (J) .r.l (J) i .0 <.J:I CD c c <.J:I 0 0 0. 0. (J) ro :::3 :::3 s c "" IU ro ro E-t CD Q) 0 .0 CD CD ca IU .0 .0 0'1 d M
PAGE 40

0 "' N
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...... m ...... r-t s Q.l +J Cd H 3 w 0 ..... M r:r.. 25 20 15 tol ;/ --:Q.based upon a & b :Q. based upon a & b*. 5 0 5 Fig. 3.11 10 15 20 Time(s) a and b are increased by 20% each, which are a=1.2a*, b=1.2b 25

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. .Q c-'1 a:r a: 0 Q. ::s '0 Q) m a:r .Q 01 .. 32 <.Q c-'1
PAGE 43

0
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w w" 11 zktl == \7 Xktl I I 9 I I j----.:::..:. ... ) 1[>()----{> delay vk >I==; I 0 + /\ + 1\ 1\ zhl == Qk+l 'T vk Fig. 3.14 Mechanization of validation with noise. wk

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C""'C""'C""' I I I CD CD CD II 331%: 35 0 N .c ._.. 0 ._.. CD (D s .,.; E-1 (D CD .,.; 0 d ,..l:l .j.J .,.; 3: d U"' C""' Cl .,.; rz,

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0 ru Q) !D o,..j 0 = II d '0 .. Q) m Q) i CD .. = 0 o,..j "0 8 + 1""11""11""1 0 I I I 0 (ll Ill Q) II .-1.-1.-1 .. 1111 II <0 3:3:C:: \D ....... .. 1""1 IJ) o,..j rz. (B/Tlii) MO"[.:J: 36

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\ C'f"l .J I ...-I ..-1 Q) ..-1 lie l!a II 37 0 C\l lQ _.. 0 _.. 0 0 I (1) In "" 0 s:: ..c: m .j.J "" (1) d Ei ..-1 E-t I."'-..-1 C'f"l t ""

PAGE 48

M I .-I 'C""'' Q) 'C""'' II l!_a II 38 lO N 0 N lO _,. = ....... = 0 ID (I) s I"'! E-t (I) a1 I"'! 0 II 01 ra (I) Q) .; + as Cl II as
PAGE 49

co C\l
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0 C\l CD 0 1 II 16n 'J:..'J:. 40 0 0 C\1 .0 0 0 0 til CD s .-I E-4 Q,) til .-I 0 c II Ol '0 CD 1-1 Q,) .; "' + ... Cl II "'
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0 N Q) en .-I 0 Q ..c en .j,.J .-I ) Q) a Ei 01 MM .-I I I E-4 Q) Q) 0 ..-I ..-1..-l.qt N lla l!a II ::c::cc:: M Cl .-I rz.. 41

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. Q) m 0 N 0 d II 01 rc CD J.i Q) 10 ...... m tl -Ct Q) + a ., Cl I I E-1 II Q)Q) 0 II II II ......
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0 C\J CD ID r-1 0 1::: .0 ,.c .u _... r-1 ID !J a CD 0 s r-1 E-4 M N 0 0 M 0 _... II II Cl g:: r-1 r:r.. 43

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0 0 t""''"":f:"":f: II l!_g II 3:3:et: 44 0 N .0 ....... 0 ....... 0 0 ....... I aJ Q) s ..... E-4 CD ID ..... 0 c: lid Q) Q) .; ., + ., Cl II .,
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U'1 ID r-i s Q) ...., e r-i 25 20 15 10 '\,, I_ I :Q I--I : Q. ', 0 I I I -----, 0 I 1-':..,_ '-..,,.._1 5 10 15 20 25 Time (a) Fig. 3.25 A normal person's urinary flow rate (Q) and approximation {Qa) before Kalman filter.

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. 0 J-1 Q) C\J J,J 1"""1 Il-l c IG s 1"""1 ca .... ID Q) J-1 0 Q) Il-l a Q) ,.Q E-t 0 J-1 .... 0 J-1 J-1 rzJ \D N tn r:.. ( s 1 IUI) o-o 46

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:Q Gl 201 I I \ A --'sQ. ....... r-t E1 Q) +J as 1-f 10 .....:1 0 .-I tz.l 0 0 5 10 15 20 25 Time (s) Fig. 3.27 A normal person's urinary flow rate (Q} and approximation (Q.) after Kalman filter.

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I 48 = C\1 = 0 N I ID Q) a o,..j E-4 J.4 (I) .j.J r-1 o,..j = as a r-1 as bl:: J.4 (I) .j.J as J.4 0 J.4 J.4 ll:l co N M tJI ,..j IZ.t

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m r-i 105 102 a to- a \D to- to-7 5 tO 15 20 25 Time (s) Fig. 3.29 Behavior of a during voiding time for a normal person.

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CJ'1 0 ... m ..Q 104 -1031_ --_I_ I -I I 0 5 10 15 20 25 Time (s) Fig. 3.30 Behavior of b during voiding time for a normal person.

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(11 ...... .,#fl' / / / ,.,, 10 / m ....... r-i Ei Q) I I I \ \ I..-I :Q I Q -.. 5 5-f \ \ r-i tl:! \ \ ', 0 ', ', ..... .... ......... ___ .. _____ 0 20 40 60 80 100 Time (s) Fig. 3.31 Urinary flow rate (Q) for compressive type and approximation (Q0 ) before Kalman filter.

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( s I l:lll) "0-0 52 0 cc 0 = 0 0 N 0 = ... I m Q) s E-1 1-f G) ., c as s as til:: Q) 1-f 0 G). ,Q 1-f 0 1-f 1-f Cl:1 N M M t:n rz,

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ID ...... .-. s -cv +J ca 1.11 w .-. A 1\ I V\f\ :Q --'Q D 5 0 0 20 40 60 80 100 Time (s) Fig. 3.33 Urinary flow rate (Q) for compressive type and approximation (Q .. ) after Kalman filter.

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. 0 Q) cc J.J r-1 .-4 = as Ei r-1 0 as = en Q) J.J Q) = as .-4 E-t 0 0 Ill M M 0 C\l tJl .-4 rz., 0 C\l I I (S/TUI) 'b-0 54

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0 0 .... (I) El 0 0) cc d rc 0 >(I) c. O>t 0 CQ Q) ID ::::! > rc ID (I) cam CD. Ei ....... oc. E-t 0 0 u > a:J a:J Q) 0 Ill ... 0 U'l N M M Cl rz.. = N e l 0 c Q c ..... ..... ..... ..... (S/tlll) g 55

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I I I I I I 11-I I 56 Q ..... c c ...... c = c cc 0 c N Ul (J) s .-t E-t G) s ,..j .u tn s::: .-t '0 .,..j 0 >G) a. tn:>. rot So! G) ::::! > '0 o,..j Ul .Cal G) 4-11-l 00. So! a 0 tJ .-4 > as as .CI-! CD 0 allf-l ID M M tn rot

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m ....... l'"'i a Q) +J Cd J-4 l1'1 ....:I l'"'i f1f 8 I 6HI I I I I 4 Ill 2 0 \ \ ' \ \ \ \ \ \ \ \ ,, I_ I :Q --:Q .. 0 5 10 15 20 Time (s) Fig. 3.37 Urinary flQw rate (Q) for a constrictive type and approximation (Q.) before Kalman filter.

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(sttm> -o-o 58 C\l I .0 ..... 0 .0 0 I rD -CD a r-1 E-t J.4 G) r-1 c ca s r""'4 ca CD J.4 0 G) ,Q J.4 0 J.4 J.4 rzl co M M tn r-1 rz,

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m ....... r-i ei Q) .u as H c.n \Q r-i I'll 10 I .P 8 II \ I \I\ :Q --I Q 6 4 2 0 0 5 10 15 20 Time (a) Fig. 3.39 Urinary flow rate (Q) for a constrictive type and approximation (Q.) after Kalman filter.

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( S/"[UI) V0-0 60 .... I 0 N lQ 0 .... m QJ s .-I E-t 1-4 Q) .u r-f .-I c ca El r-f ca til:: 1-4 QJ .u ca 1-4 0 1-4 1-4 rz:l 0 '"" t:n .-I r.z..

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Q\ f-A m ....... 103 102 101 Et too as to- to-s 5 10 15 20 Time (s) Fig. 3.41 Behavior of a during voiding time for a constrictive type.

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0'\ e.J ... tO .0 103 102 101 1 10 20 5 15 Time (s) Fig. 3.42 Behavior of b during voiding time for a constrictive type.

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CHAPTER 4 CONCLUSION The primary purpose of this paper is to find an equation that approximates the normal person's urinary flow rate curve and to identify different types of obstruction using a Kalman filter. Even though there has been difficulty in finding the proper value of noise covariance, the results were excellent. Also they support Werner Schafer's concept. He indicated in his paper that the main difference between the normal and the compressive obstruction is that the compressive requires high opening pressure. Oth er than that the function of the lower urinary tract is the same. Figures 3.29, 3.30, 3.35 and 3.36 show this relation. There is a little difference between a in normal and a in compressive. Something else should be defined to distinguish normal from compressive. One way is relative E[(Q Oa) (Q-Qa) T] Ea = E(((QQa)/QDWL) X ((QQa)/Qmax) T) If the value of ER is less than 0.01, then that is normal flow rate. If not, then that is abnormal flow rate. The main reason for this is that Qnm for the 63

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normal rate is much higher than for the abnormal. Data 1, data 2, and data 3 are the normal. From figure 4.1 it is very hard to distinguish the normal from the abnormal. However, when ER is used, then it is clear what is the normal person s urinary flow rate and what is not. Figure 4.2 shows this. Using this information, three different types of Q can be defined. 1. Normal: Relative noise covariance is less than 0.01 and b does not change. 2. Compressive obstruction: Relative noise covariance is higher than 0.01 and b does not change. 3. Constrictive obstruction: Relative noise covariance is higher than 0.01 and b changes. 64

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0'\ c.n 140 ..., i< cJ I 01 il 70 d I 01 ......... 50 f:il 40 :m 20 10 o I lll5l'iM ll?'i?SM MXX?I !5l'li"iM nmm ISXXXII I9ROSII !SXXXII !lXXXII IIXXXII liXXM IX"lD1 1 2 3 4 5 6 7 Data B 9 10 11 12 13 Fig. 4.1 Error covariance E [(Q-Q.)* (Q-Q.)'']

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0.09 0.08 ,.._ ..-. .. 0.07 1-J 0.06 ....... 1cJ 0.05 I 01 ,.._ -... 0.04 10'\ J O.OJ 0'\ ....... fcJ 0.02 I ,.._ 01 -...... 0.01 f-1':1:1 0 m m 1 2 3 4 5 6 7 B 9 10 11 12 13 Data Fig. 4.2 Relative error covariance E [ ((Q-Q.) /Q_.) ((Q-Q.) /Q_.)

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APPENDIX A Derivation of a, b, c, and d where a, b, c, and d are parameters. Though it looks awful, a, b, c, and d can be calculated very easily. Most of time c(l-exp(-dt}} is negligible compared to Main existence of c(l-exp(-dt}} is to reduce tail part of Qa to zero. Figures A.l, A. 2, and A. 3 show this relation. From this knowledge, Qa can be ex-pressed as Qa s a./f exp( t3 ) dQ/dt = a../f-1 t3)3aft2.5 t3 ) To calculate a and b, let dQa/dt=O. Then l.a../f -3al.t2.5 =0, b=6t3 2 b If t=Tmax, then Qa==Qmax. Qmax S aJTmax a= QID81 exp{l/6)/ JT max After a and b have been found, c and d can be calcu-lated from a./f To reduce tail part to zero c = aJT cmd exp( ;1 T!td) c(l exp(-dT = 0.99c d=-lnO. Ol/Tomc1 Figure A. 4 shows QINSX, Tmax, and Tend" 67

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68 0 C\l l.Q ..... 0 ..... 0 0 m CD Ei ..... E-t -.., 'i'I.D cs: >< 0 CIS M ...: t:n ..... r:r..

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. 0 69 lQ Q Q 0 m <= I 'c5 N < 01 r4 C%.1

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70 0 C\! lQ ...... 0 ...... 0 0 ID CD E! ..... E-1 --=-1 Q, :< G) I -Q I -f"' .;.o 'iS: :< G) M < Cl .-4

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APPENDIX B Derivation of c.,. and vi When bladder is full, V1 can be modeled as (B.l) where r is radius of bladder. And there is relation-ship between intravesical volume and voided volume. (B. 2) where Tv is total volume in bladder. From equation (B. 2) (B. 3) Substitute equation (B.l) to (B.3) V -T 4 3 vv-tm" Q:: dV vldt = (dV vldr)(dr/dt)= -4m2dr/dt From equation (B.l) dr/dt=-0.207QNfl (B. 4) Contraction velocity is equivalent to the rate of change in circumference of bladder (L). L=2m Cv = -dL/dt = -21tdr/dt ( B 5 ) Substitute equation (B.4) to (B.S) Cv=l.3QNfl 71

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.... --a:,-----s 0 u.. Qmax --f Ql f-.-Tmax--i Taad Time Fig. A.4 Definition of Tam, and T.a 72

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Figures B .1 and B. 2 show contraction velocity and intravesical volume of compressive type. Figures B.3 and B. 4 show contraction velocity and intravesical volume of constrictive type. 73

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....:I ro ........ a '0 ........ r-i '0 5 xto-s 4 ,---.. ,, ', ', I \ I A' I \ ,/ Af\1\A \ 3 ,l 2 1 0 // // / I / I / I 1 1 :c... from Q 1--1 :Cv from Q. 0 20 40 60 80 100 Time (s) Fig. B.l Contraction velocity c ... for a compressive type.

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-...J (11 r-t a Q) r-t 350 300 250 200 ', ' \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ' ' ,, :VJ. --:vi from Q from Q. ',, ,, 150 I I -.._ __ I 0 I -----1 I 20 40 60 80 100 Time Fig. B.2 Intravesical volume V1 for a compressive type.

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2 x10-3 1.5 ...... I'D ....... M 1 Ei .u '0 ....... -..J M 0'\ '0 0.5 0 -0.5 0 Fig. B.3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5 \ ,, 1 1 :c.. from Q 1 -1 : c .. from Q. 10 15 Time (s) 20 Contraction velocity C.,for a constrictive type.

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r-t Q) ....:I ....:I ....t 0 > 380 r--------.-----------.----------, 360 340 3201 300 ,, from Q 1--1 :V1 from Qa 280 .___ __ _...____ __ ____.. ___ ____._ ___ _.. 0 5 10 15 20 Time (B) Fig. 8.4 volume Vi for a constrictive type.

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REFERENCES Astrom K, Wittenmark B (1990): Computer-controlled systems. Englewood Cliffs, N.J.: Prentice Hall, Inc. Fermelia A (1981) : Adaptive processor definition and design, Technical Report BDM/A-81-168-TR, BDM Corporation, Albuquerque, N.M. Gabel RA, Roberts RA (1980): Signals and Linear ysteros. New York: John Wiley & Sons, Inc. Glynn RJ, Campion EW, Bouchard GR, Silbert JE(1985): The development of benign prostatic hyperplasia among volunteers in the normative aging study. AmLJ Epidemiol 121:78-90 Griffiths DJ (1980): Urodynaroics. The Mechanics and Hydrodynamics of the Lower UrinahY Tract. Bristol: Adam Hilger. Cbs 3 and 4, pp. 25-65. Jensen KM-E, Jorgensen JB, Mogensen P (1988): Urodynamics in prostatism. II. Prognostic value of pressure-flow study combined with stop-flow test. Scand J Urol Nephrol [Suppl 114]:72-77. Kopp R, Orford R (1962): Linear regression applied to system identification for adaptive control systems. Sorenson H (ed): Kalman Filtering: and Application. IEEE PRESS:83-89 Marquart DW (1963): An algorithm for least square estimation of non-linear parameters. J Soc Indust Appl Math 11:431-441. Roberts RA, Mullis CT (1987): Digital Signal Processing. Addison-Wesley Publishing Company. Rollema JH, van Mastrigt R (1987): Detrusor contractility before and after prostatectomy. Neurourol Urodyn 6:220-221. Schafer W (1983): The contribution of the bladder outlet to the relation between pressure and flow 79

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rate during micturition. In Hinman F, Jr(ed): Benign Prostatic Hypertrophy. Berlin:SpringerVerlag, pp. 470-498. Schafer W, Noppeney R, Rubben H, Lutzeyer W (1988): The value of free flow rate and pressure/flow studies in the routine investigation of BPH patients Neurourol Urodyn 7:219-221. Shanmugan K. s, Breipohl A. M (1988): Random Sig nals: Detection. Estimation and Data Analysis. New York: John Wiley & Sons, Inc. Spangberg A, Terio H, Ask P, Engberg A (1991): Pressure/flow studies preoperatively and postoperatively in patients with benign prostatic hypertrophy: Estimation of the urethral pressure/flow relation and urethral elasticity. Neurourol Urodyn 10:139-167. Terio H, Spangberg A, Engberg A, Ask P (1989): Estimation of elastic properties in the urethral flow controlling zone by signal processing analysis of urodynamic pressure/flow data. Med Biol Eng Comput 27:314-321. Von Garrelts B (1958): Micturition in disorders of the prostate and posterior urethra. Acta Chir Scand 115:227-241. 79