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June 2011 published online 2Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine

M K Lee, S H Lee, N Hur, S Kim, S Kim and B Choidynamics in benign prostatic hyperplasia

Correlation between intravesical pressure and prostatic obstruction grade using computational fluid

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Correlation between intravesical pressure and prostaticobstruction grade using computational fluid dynamicsin benign prostatic hyperplasiaM K Lee1, S H Lee1, N Hur1, S Kim2, S Kim2, and B Choi1*1Department of Mechanical Engineering, Sogang University, South Korea2Department of Urology, College of Medicine, Catholic University of Korea, South Korea

The manuscript was received on 8 October 2010 and was accepted after revision for publication on 7 April 2011.

DOI: 10.1177/0954411911408663

Abstract: An urodynamic test which measures various physiologic variables during voiding isgenerally used for accurate diagnosis of a bladder outlet obstruction (BOO) resulting frombenign prostatic hyperplasia (BHP). However, this method is difficult to directly apply to allpatients because it is an invasive test and many patients suffer from anxiety and embarrass-ment during the test. Thus, other diagnosis methods such as uroflowmetry and prostaticsymptom score are performed to measure the degree of BOO prior to the urodynamic test,and it is necessary to construct a quantitative relationship among the obstruction level, theintravesical pressure, and the uroflow rate. The aim of this paper is to analyse the variation ofintravesical pressure as a function of the extent of the obstruction and the uroflow rate fromgiven information on the size of the bladder and the urodynamic test using a computationalfluid dynamics approach. In order to analyse the intravesical pressure, a two-dimensional axi-symmetric model of the bladder including a narrowed region, i.e. the prostatic obstruction, iscreated. Then the variation of the intravesical pressure is quantitatively obtained as a functionof the magnitude of the uroflow rate and the extent of the obstruction. It is shown that theintravesical pressure significantly increases even for small obstructions and that at largeobstructions it can reach values higher than 100 cm H20, which is a dangerous value. It isshown that the intravesical pressure decreases as the uroflow rate decreases. This study canform the basis of a non-invasive test for the diagnosis of BHP.

Keywords: bladder, prostatic obstruction, computational fluid dynamics, urodynamics,

intravesical pressure

1 INTRODUCTION

Benign prostatic hyperplasia (BPH) is a common

benign neoplasm that can affect ageing men. Lower

urinary tract symptoms (LUTS) for prostatic hyper-

plasia include enlargement of the prostate, bladder

outlet obstruction (BOO), contractional disorders in

the detrusor muscle, and an overactive detrusor

muscle [1]. It is reported that BOO can lead to

neurogenic detrusor overactivity, impared detrusor

contractility, polyuria, and changes in cellular meta-

bolism [2].

The urodynamic test to measure various physio-

logic variables during voiding is generally used for

accurate diagnosis of BOO resulting from BPH.

Urodynamic investigation is performed with a 7 Fr

dual-lumen urethral catheter and a 9 Fr rectal bal-

loon catheter at a filling rate of 50 ml/min to mea-

sure the intravesical pressure (Pves) and the

abdominal pressure (Pabd), respectively (see Fig. 1).

A pressure flow study is performed in a sitting

position similar to cystometry. However, this

method is difficult to directly apply to all patients

*Corresponding author: Department of Mechanical Engineering,

Sogang University, #1 Shinsu-dong, Mapo-gu, Seoul, South

Korea.

email: [email protected]

1

Proc. IMechE Vol. 225 Part H: J. Engineering in Medicine



because it is an invasive test and many patients suf-

fer from anxiety and embarrassment during the test.

Therefore, other diagnosis procedures (uroflowme-

try and prostatic symptom score) are performed to

measure the BOO degree prior to performing an

urodynamic test. The international prostatatic

symptom score is obtained through responses to a

questionnaire, which can suffer from subjective

responses that can lead to low accuracy.

The literature contains reports on non-invasive

diagnosis procedures such as measurement of the

bladder wall thickness, prostate size, and prostatic

resistive index [3–5]. There has been a recent report

on the use of an inflatable penile cuff [6]. This

method requires measuring the uroflow rate and the

cuff pressure required to interrupt flow. Measuring

the bladder wall thickness using ultrasound visuali-

zation can be used to diagnose prostatic hyperpla-

sia. This technique is based on the clinical

observation that an increase in the size of the lower

urinary tract obstruction results in detrusor muscle

hypertrophy [7–9]. This method has the advantage

of being quick and simple to apply; however, it can

be highly inaccurate since the measured thickness

depends on the location of the markers used in the

measurement. The level of inaccuracy inherent in

this measurement technique means that it can be

difficult or even impossible to decide if an increased

thickness value is due to a measurement error or is

the result of BPH [8].

Presently, the most widely used non-invasive

diagnosis method for LUTS is uroflowmetry. This

technique is used in clinical practice to objectively

measure the uroflow strength. It is performed in

either a sitting or standing position to simulate the

normal voiding situations. Its result consists of a

maximum urinary flow and a flow pattern in the

shape of a curve. It is reported that a maximum uro-

flow rate of less than 10 ml/s has an approximately

90 per cent chance of being the result of an obstruc-

tion (abnormal). A rate between 10 and 15 ml/s has

a 65 per cent chance (equivocal), and a rate greater

than 15 ml/s has a 30 per cent chance (normal).

However, it has been reported in the literature that

it is difficult to distinguish between a lower bladder

obstruction and detrusor contractile dysfunction

[10, 11].

Since the intravesical pressure is related to the

prostatic obstruction, the constriction effect of the

obstruction has to be analysed. Several studies have

been performed in order to study the effect of a

constricted tube on the characteristics of the flow

Fig. 1 Typical recording taken in an urodynamics test on a healthy 35-year-old man

2 M K Lee, S H Lee, N Hur, S Kim, S Kim, and B Choi




[12–14] and the pressure drop [15, 16]. Transrectal

ultrasonography is a widely used method in clinical

practice to measure the volume of the prostate.

However, it is currently not possible to accurately

measure the degree of obstruction using this tech-

nique [17]. Thus, it is necessary to develop a quanti-

tative relationship between the extent of the

obstruction, the intravesical pressure, and the uro-

flow rate using a mathematical model.

There are reports in the literature on attempts to

develop a mathematical model of micturition based

on urodynamic data [18, 19] and to analyse a urin-

ary tract obstruction using the method of computa-

tional flow dynamics (CFD) [20]. In this study, the

CFD method is used to generate a model of the

bladder with various-sized prostatic obstructions

and uroflow rates. The aim of this paper is to ana-

lyse the variation of intravesical pressure based on

the extent of the obstruction and flowrate from

given information on the bladder size and the uro-

dynamic test for healthy men, and to construct a

contour map of the intravesical pressure for the spe-

cific obstruction grade and uroflow rate based on

the CFD results.

2 METHODS

Micturition occurs due to an increase in intravesical

pressure created by contraction of the detrusor

muscle. The intravesical pressure is defined by the

head loss in the urinary tract during detrusor con-

traction. Figure 2 shows that the bladder can be

considered as being a sphere whose radius

decreases during voiding: in fact its volume

decreases from 450 to 18 ml. In order to estimate

the effective variation of the pressure, a model of a

simplified bladder with an initial volume of 450 ml

was created; this model is based on what would be

expected for a healthy 35-year-old man (Fig. 3). The

two-dimensional (2D) axisymmetric model consists

of a bladder and a urinary tract including a nar-

rowed region (prostatic urethra) and it was created

using 61 340 fluid cells of the commercial CFD pro-

gram, STAR-CD [21]. The axisymmetric model is an

unrealistic representation of the human bladder;

however, it is a reasonable starting point to report

the correlation between the intravesical pressure

and the obstruction grade. The initial bladder radius

was set to a value of 47.54 mm which corresponds

to the volume of 450 ml. Based on clinical informa-

tion the length of the obstructed region was

assumed to have a value of 5 mm and to be located

at a distance of 20 mm from the point at which the

bladder and urethra meet, see Fig. 3.

The rheological properties of the urine in the blad-

der were considered to be those of water which is a

reasonable assumption since more than 90 wt% of

urine is in fact water. The flow characteristics of urine

in a urinary tract conform to the laws of mass conser-

vation (equation (1)) and momentum conservation

(equation (2)) for an unsteady incompressible flow

ru = 0 (1)

r∂u

∂t+ uru

� �= �rp +rm ruð Þ+ ruð ÞT

h i+ rg (2)

where u is the velocity vector in Cartesian coordi-

nates and t, p, and r are time, pressure, and density,

respectively. Also, m is the dynamic viscosity and g

is the vector of gravitational force.

Fig. 2 Variation of bladder size during urination by radiographic visualization

Correlation between intravesical pressure and prostatic obstruction grade 3




The motion implicit in shrinking the bladder dur-

ing micturition was simulated using the subroutine

ALE in STAR-CD which contains a movable mesh.

The flowrate of the incompressible urine excreted

via the urethra by contraction of the bladder was

described using

Q =∂V

∂t=

∂

∂t

4

3pR3

� �

= 4pR2 ∂R

∂t’4pR2

n�1

Rn � Rn�1

Dt

(3)

where Q denotes the flowrate of the urine, V denotes

the volume of the bladder, and R denotes the radius

of the bladder. The radius at the current time step (n)

is calculated from that of the previous time step (n-1)

using equation (4). Thus, the specific urinary flow rate

is obtained by changing the bladder radius over time

Rn = Rn�1 +Q

4pR2n�1

Dt (4)

The flow rate and the pressure obtained using the

CFD model duplicate the clinical result, which

shows a bell shape (rapidly increasing and then

slowly decreasing) for the uroflow rate and the

intravesical pressure during voiding (Fig. 1). Taking

Q to be the urinary flowrate profile of a healthy per-

son, it can be approximated as a fourth-order poly-

nomial function (equation (5)) and when this

function is substituted into equation (4) it is able to

replicate the clinically obtained flowrate (Fig. 4)

Q = 0:933 + 3:24t � 0:194t2

+ 0:003 79t3 � 0:000 0244t4(5)

The other profiles of the flow rate shown in

Fig. 4 are supplementary profiles to compare the

effect of a lower flowrate than the normal flowrate.

These profiles show different maximum values of

the flowrate at the same total volume. Next, the

diameter and the length of urinary tract were regu-

lated to be in a range of reasonable values to agree

Fig. 3 Model of a urinary system with BHP

Fig. 4 The profile of urinary flowrate for a healthy person and the various curves of urianry flow-rate used in this study





with the pressure profile of the clinical result

shown in Fig. 1.

The ratio of the area of the narrowed urethra to

the actual urethral area A# was defined (equation

(6)) and subsequently used to analyse the effect of

the extent of the obstruction (1 - A#). This ratio was

represented in eight steps between 1.0 and 0.3

A0 =Aobstruction

Aurethra(6)

Then, the variation of intravesical pressure was

analysed for the magnitude of flowrate as a function

of the extent of the obstruction. The result repre-

sents the intravesical pressure as a function of time

and pressure at a distance from the point at which

the bladder and urethra meet. The extent of the

obstruction is between 0 (A# = 0) and 70 per cent

(A# = 0.3) and the flowrate is varied between 8 and

18 ml/s. The obtained results are plotted onto a con-

tour map. In order to assess its accuracy and relia-

bility, the results obtained using the proposed CFD

model are compared with the results obtained in

urodynamic tests to measure the intravesical pres-

sure and the uroflow rate.

3 RESULTS

First, the intravesical pressure profile was obtained

using the CFD model for the case where there was

no obstruction; this was done in order to determine

the radius and the length of the urethra. The pres-

sure values for various radii were calculated in the

model at a length of 100 mm (Fig. 5(a)). The results

show that the intravesical pressure increases up to

13 s and then it decreases towards the end of void-

ing, which is similar to the flowrate shown in Fig. 4.

In addition, as the radius decreases, the maximum

value of the intravesical pressure increases due to

an increase in head loss. This means that a smaller

radius of the urethra created by an obstruction

requires additional pressure during voiding. The

length of the urethra is the main variable in the

developed model. Thus, the pressures for various

lengths were obtained at a fixed radius of 2.1 mm

(Fig. 5(b)). As the length increases, the maximum

pressure linearly increases due to the head loss in

the inner surface of the duct. It can be seen from

Fig. 5 that a length of 100 mm and a radius of

2.1 mm produce results that agree with the clinical

result and these values were used in all subsequent

simulations. The difference between the simulated

and clinical results in the initial stages of micturi-

tion is a result of the fact that the diameter of the

urethra instantaneously expands at the start of mic-

turition. The length of the urethra is long enough

that end effects can be ignored in the CFD

simulations.

The pressure distribution in all regions of the

bladder during voiding obtained using the proposed

model is presented in Fig. 6. At the start of micturi-

tion, the pressure in the urethra immediately

decreases due to a large head loss, and as the blad-

der shrinks, the gradient of the pressure along the

urethra decreases. The maximum pressure is 25 cm

H2O for a healthy person (A = 1). Figure 6 also shows

the pressure distribution as a function of the extent

of the obstruction at the times of 5, 10, and 15 s. As

the size of the obstruction increases the pressure

gradient increases over time. Particularly, the

Fig. 5 Evolution of the internal pressure for a healthy person (from Fig. 2); comparison theexperimental and simulation results as a function of (a) the urethral radius and (b) the ure-thral length





gradient is maximized at the upper region of the

obstruction and this suggests that the urethral wall

is under the maximum pressure.

Figure 7 shows the evolution of pressure during

voiding as a function of the extent of the obstruc-

tion. As the prostatic hyperplasia becomes severe,

the intravesical pressure is exponentially increased

for A# below 0.7. At some point between A# = 0.3 and

A# = 0.4 the intravesical pressure goes higher than

100 cm H20, which is a dangerous value. In fact at

A# = 0.3 the intravesical pressure reaches its maxi-

mum value of 120 cm H20 (Fig. 7(a)). This result

shows that additional detrusor pressure for voiding

is needed because of the increase in the intravesical

pressure for the larger obstructions, which might

impair the functioning of the bladder muscle. Also,

as the size of the obstruction increases a large pres-

sure gradient is developed in the urethra between

the negative pressure in the region of the obstruc-

tion and the large pressure at the point at which the

urethra attaches to the bladder (Fig. 7(b)). This pres-

sure could cause a reverse circulation of urine into

the endocrine organ which could result in an

enlarged prostate.

Figure 8 shows the evolution of the intravesical

pressure for A# = 0.5 as a function of the uroflow

rate. If the flowrate decreases then the intravesical

pressure also decreases because the head loss for

the constant gradient is reduced. When the flowrate

is reduced by 50 per cent then the maximum pres-

sure decreases from 45 to 16 cm H20 (Fig. 8(a)). The

value of the pressure above the obstruction is also

decreased as the flowrate is reduced (Fig. 8(b)).

4 DISCUSSION

The narrowing of the urethra due to hypertrophied

prostatic tissue induces voiding problems such as

weak urinary stream, frequency, residual urine sen-

sation, and so on [22]. Initially, men with BPH take

medicine to resolve their voiding problems and

most of them respond to this treatment option.

However, in some cases this treatment is ineffective.

For example, men with severe BPH may experience

acute urinary retention during medication. These

patients require surgical treatment to solve their

voiding problems. Therefore, it is important to pro-

vide a method of assessment to avoid inappropriate

medical surgery in men with severe BPH. The uro-

flowmetry test is the standard clinical method to

evaluate the degree of obstruction created by BPH

and the results of this test are used to inform the

decision as to whether or not surgery is required.

It is clinically important to measure the intravesi-

cal pressure using an urodynamic test for the diag-

nosis of BPH because the intravesical pressure is

used to define the degree of obstruction in terms of

detrusor pressure and the flowrate [23]. Normally

the standard maximum intravesical pressure would

be between 40 and 60 cm H2O during voiding.

Treatment is normally considered when the value of

the pressure is above 80–100 cm H20. Accurate infor-

mation about the extent of the obstruction would

help to inform the correct choice of treatment in

clinical practice i.e. medicine or surgery. Figure 9

shows a contour map of the intravesical pressure as

a function of the extent of the obstruction and the

Fig. 6 Pressure distribution as a function of the extent of the obstruction in BHP at: (a) 5 s; (b)10 s; and (c) 15 s





uroflow rate during voiding. This figure allows the

intravesical pressure to be predicted from informa-

tion on the obstruction and uroflow rate based on a

healthy person. The x-coordinates in Fig. 9 are the

resistance factor, which directly measures the extent

of the obstruction. This result is similar to nomo-

grams that have been previously used in standard

assessment procedures [23–25]. The intravesical

pressure during voiding has a specific profile

because it depends on the extent of detrusor con-

tractility. Thus, the urinary obstruction reduces the

uroflow rate at a specific intravesical pressure. For

instance, when the pressure has a value of 25 cm

H2O and the obstruction is 20 per cent, the flow rate

is reduced by 10 per cent as shown in Fig. 9 (point

A). Conversely, the contour map indicates the intra-

vesical pressure as a function of the degree of

obstruction and flowrate reduction. In addition, an

obstruction of 40 per cent reduces the flowrate by

22 per cent (point B) and that of 60 per cent reduces

it by 45 per cent for the same pressure (point C).

Thus, the flow rate is sharply reduced as the extent

of the obstruction increases and in turn this means

that a large contraction of the detrusor muscle is

required over a long time period in order to allow

voiding in a severe BOO case.

This research could be used for better diagnosis

of BPH by quantitatively considering the intravesical

Fig. 7 Evolution of the pressure as function of the extent of the obstruction (a) pressure profileduring voiding as a function of time and (b) pressure profile as a function of the distancefrom the base of the bladder

Fig. 8 Evolution of the pressure as a function of flowrate (a) pressure profile during voiding as afunction of time and (b) pressure profile as a function of the distance from the base of thebladder (A# = 0.5)





pressure for benign prostatic enlargement and uro-

flow rate. However, there are some limitations for

its clinical application. The data on pressure and

urinary flowrate collected in the urodynamic test

include an initial variation and the plot needs to be

validated and improved using data taken in other

urodynamic tests. Also, this method needs to incor-

porate the age of the patient using other non-

invasive methods such as uroflowmetry. Although

the presented results need to be generalized before

its routine adoption in clinical practice it can still be

used as a basis establish the relationship between

intravesical pressure and the prostatic size for diag-

nosis of BPH.

5 CONCLUSIONS

This paper has presented an analysis of the variation

of intravesical pressure in the presence of BPH

using a CFD modelling approach. It has been shown

that as the prostatic hyperplasia becomes severe

then the intravesical pressure exponentially

increases for A#\0.7 and in fact at some point

between A# = 0.3 and A# = 0.4 it goes higher than

100 cm H20, which is a dangerous value. Also, as

BOO increases, the pressure gradient in the region

of the obstruction in the urinary tract significantly

increases. The variation of uroflow is relatively less

affected by changes in the intravesical pressure for a

given value of A#. The concepts proposed in this

paper could be used to aid the diagnosis of BHP by

studying the intravesical pressure changes created

by benign prostatic enlargement and uroflow rate.

FUNDING

This work was supported in part by the develop-

ment program for future fundamental technology of

the Ministry of Education, Science and Technology

(No. 2010K000986) and the Healthy Medical Treat-

ment Research and Development Program of the

Ministry of Health & Welfare (No. A090481).

� Authors 2011

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