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Model-based estimation of male urethral resistance and elasticity using pressure–flow data
Computers in Biology and Medicine 31 (2001) 27–40 www.elsevier.com/locate/compbiomed
Model-based estimation of male urethral resistance and elasticity using pressure– ow data Ofer Barneaa ; ∗ , Gabriel Gillonb,c a
Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel b Department of Urology, Rabin Medical Center, Israel c Sackler School of Medicine, Tel Aviv University, Ramat Aviv, Israel Received 8 October 1999; accepted 3 July 2000
Abstract To assess urethral resistance and changes in the urethral elasticity during voiding, a lumped parameter model of the urethra was developed. The model uses pressure and ow measurements to estimate time-dependent resistance and elasticity factor. The model includes a resistance that has a function of the cross-section and urethral elasticity. Two resistivity types are compared in the constricted ow-controlling zone of the urethra: Poiseouille resistance and the Bernoulli e ect. Using real pressure– ow data sets, the model was used to estimate urethral resistance and changes in urethral elasticity during voiding. Estimation of the elasticity show that in a normal patient relaxation of the urethra is a process that continues until the end of voiding. This has important implications with regard to the present methods that are used in the clinic to assess urethral obstruction or constriction. The resistance as calculated by this model, may be a useful indicator of urethral constriction and obstruction, since it is especially independent of the bladder function. Changes in the urethral elasticity during voiding which are estimated by the model add a new diagnostic parameter to c 2000 Elsevier Science Ltd. All rights reserved. pressure– ow studies. Keywords: Urodynamics; Urethral resistance; Urethral elasticity; Mathematical model
1. Introduction The function of the bladder is to store and hold urine and empty itself completely when suitable. The micturition, or voiding, is achieved by a rise in the intravesical pressure ( uid pressure in the bladder cavity) that is sustained until the bladder is empty. This is preceded by the relaxation of the pelvic oor muscles and the relaxation of the urethral sphincteric area. Thus, normally, the proximal urethra at the bladder outlet, comprising the bladder neck, the prostatic urethra and the sphincteric ∗
Corresponding author. Tel.: +972-3-640-8658; fax: +972-3-640-7939. E-mail address: [email protected] (O. Barnea).
c 2000 Elsevier Science Ltd. All rights reserved. 0010-4825/00/$ - see front matter PII: S 0 0 1 0 - 4 8 2 5 ( 0 0 ) 0 0 0 2 0 - 2
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O. Barnea, G. Gillon / Computers in Biology and Medicine 31 (2001) 27–40
area, are all relaxed during micturition. The urethral resistance to ow is accordingly very low and the driving force, i.e. the bladder wall smooth muscle should exhibit low pressure for any ow rate. Urethral resistance is de ned by the inherent mechanical and morphological properties of the proximal urethral wall called ow-controlling zone [1]. During micturition, the bladder outlet or the
ow-controlling zone can be obstructive as a result of the neurological over-activity or abnormal structure of anatomical basis such as stricture or more frequently — enlargement of the prostate. Obstruction, being a physical concept, implies that the urethral resistance to ow is abnormally elevated. Intravesical pressure during micturition has been shown to be directly related to urethral resistance [2,3]. As urethral resistance increases, ow rate declines and higher intravesical pressures are measured. Since urethral resistance a ects intravesical pressure and ow rate, a direct measurement of this parameter would be desirable in the diagnostic procedure. However, in practice this is dicult. Therefore, standard urodynamic studies were developed based on indirect methods. Thus, urethral resistance is represented by a relationship between the pressure and the ow rate. This implies that simultaneous measurement of intravesical pressure and ow rate during micturition is required to study urethral resistance. To assess bladder function, both intravesical and intra-abdominal pressures are measured and the detrusor (bladder wall smooth muscle) pressure is obtained from the di erence between these two. The pressure– ow relationship is used to obtain the clinically meaningful information and to classify urethral resistance as normal or abnormally elevated. The most accurate procedure is a quasi-continuous plot showing many points of corresponding pressure and ow rate values. Simpler clinical methods involve plotting of only two or three pressure– ow points. These studies of pressure–
ow plots yield a variety of curves and it is not possible to reduce each of these plots to a single number — resistance factor. Therefore, current methods make use of a family of plots of similar form, e.g. shape of slopes or curvatures to grade severity of obstruction [4 – 6]. Alternatively, it is practical to look at these pressure– ow plots based on one point of the detrusor pressure at a maximum ow rate and classify groups of patients accordingly [7]. De nition and grading of urethral resistance has a paramount clinical importance though its measurement by standard urodynamic techniques is not simple. Pressure– ow studies have become a standard test for lower urinary tract obstruction and constriction. The concept of urethral resistance measurement remains confusing and has not been de ned uniquely despite several rigorous analyses and reviews of methodologies [3,8–10]. The statement issued by the International Continence Society regarding standardization of terminology in pressure–
ow studies de ned urethral resistance in a vague manner. It states that ‘urethral resistance relation’ is represented by the pressure– ow relations [9]. Schafer o ered an oversimpli ed approach to urodynamic pressure– ow relations, assuming that the urethra is no more than a hole in the bladder and calculated the uid velocity based on Bernoulli’s equation. This work was the basis to some later development of diagnostic methods such as the passive urethral resistance relation (PURR) [3,5]. PURR is based on the understanding that the whole curve is too complex and that time-varying viscoelastic properties of the urethra stabilize towards the end of micturition. In this method, a curve- tting technique is applied at the lower pressure part of the curve relating pressure and ow at the end of the process, beginning at the maximum ow point. This was followed by modi cation to a linear curve t [5]. The slope of the pressure– ow curve is assumed to indicate ‘urethral resistance relation’. The implicit hypothesis on which this method is based upon is that the urethral elasticity that is reduced during micturition,
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reaches a plateau and is invariable during the last portion of the pressure– ow curve. Another work, a detailed uid–dynamic analysis of pressure– ow relation in the urethra as a collapsible tube, was reported by Griths [8]. Abrams and Griths constructed a nomogram that classi es patients into three categories: obstructed, equivocal and non-obstructed, according to the detrusor pressure at the maximum ow [7]. This statistical method that was based on a large clinical research, often results in an equivocal result. None of these methods is able to detect urethral obstruction conclusively in several cases. The model that is reported in this paper was developed to o er a di erent solution with clinical relevance. Therefore, only the dominating e ects that are directly related to the pressure– ow relations were included. 2. The model A detailed analysis of urinary laminar ow dynamics requires the solution of the Navier–Stokes equation d V + V · ∇ V = −∇P + ∇2 V; (1) dt where P is pressure, V is the three-dimensional velocity vector, is the uid density and is uid viscosity. This equation indicates that two forces are involved in the relationship between pressure gradient and velocity: acceleration and velocity forces due to the uid mass (term on the left) and viscous forces due to the uid viscosity (term on the right.) Several observations and assumptions can simplify the analysis. The form of the equation as presented here already implies that body forces, such as gravitational force have been neglected. To enable numerical implementations of urodynamic models where average cross-sectional pressures and volumetric rates are of interest, a series of assumptions must be made to simplify the solution of this equation. In this analysis, two types of pressure– ow relations in a compliant tube were considered. In the rst, we consider only the viscous ow and in the second we consider Bernoulli’s equation that is also inherent in the Navier–Stokes equation. These are analyzed separately. The rst model was developed to describe viscous ow through a compliant urethra based on the Navier–Stokes equation and the continuity equation. In the second model, a constriction was added where the conversion of pressure to velocity is determined based on Bernoulli’s equation. Others who analyzed blood ow have initially ignored compliance of the vessel wall, radial ow and the nonlinear terms in the equation and then added the vessel properties. The initial analysis yielded the following pressure–velocity relationship [11]: dP dw 1 dw d 2 w − + 2 ; (2) = − dz dt r dr dr where r is radius and w is velocity in the z-axis direction. Assuming a steady ow and a parabolic velocity pro le as well as the relationship between volumetric ow rate and the velocity pro le, this equation was converted to a relationship between pressure and volumetric ow [11]: Pi − Po = RQo + I Q˙ o ; Qi − Qo = C P˙ i ;
(3)
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O. Barnea, G. Gillon / Computers in Biology and Medicine 31 (2001) 27–40
Fig. 1. An electrical analog model of a compliant tube.
where I=
L rv2
and
R=
8L rv4
(4)
R is the viscous resistance of the uid, I is the inertance of the uid, C is the urethral compliance and L is the e ective length. This form of the pressure– ow equation can be described by an electrical analog model (Fig. 1) that includes two series of elements: a resistance representing viscous forces and an inductor representing inertial forces (inertance). The e ect of the compliant vessel wall is introduced in the form of a parallel capacitor. The assumption of the parabolic velocity pro le may not hold at the entrance of the urethra where the velocity pro le is at or in the case of ow through an ori ce or a constriction. These two cases are considered. To evaluate the e ect of various velocity pro les on R and I , Barnea [12] derived a relationship between pressure gradient and volumetric ow based on Eq. (2). For a velocity pro le of the form rn w(r) = wn 1 − n ; (5) rv where wn is a normalized peak ow, he obtained an expression for I and R for the equation I=
L rv2
and
R=
2(n + 2)L : rv4
(6)
This shows that I is una ected by the change in velocity pro le whereas R does depend on the velocity pro le. As the velocity pro le becomes more at n increases but the form of the relationship is maintained. R and I are examined following the description of the third component that is required to satisfy the continuity equation in a compliant tube. The last element in the model is a compliance representing the compliance of the urethral wall. The urethral compliance C is de ned as dA=dP, where A is the cross-sectional area, and may be estimated from the pressure–cross-sectional area plot. Conversely, elasticity E is de ned as dP=dA. Bagi et al. [13] measured urethral compliance at several points along the urethra during the storage phase. Others had measured the cross-sectional area during voiding. A typical schematic plot of pressure–cross-sectional area during the storage phase is shown in Fig. 2 for increasing pressure and area (during the descending pressure range the behavior may be di erent.) Fig. 2 shows that the urethra is closed for pressures under the opening pressure P0 (30 cm H2 O in this graph) and opens gradually with the pressure. C is constant along a wide range of cross-sectional area. In the model, C will be regarded as a time-varying component during voiding.
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Fig. 2. Schematic pressure–cross-sectional area relation in the male urethra during the storage phase.
Fig. 3. Ratio of viscous resistance over inertance as a function of tube radius.
R and I depend on C since the latter relates pressure to the cross-sectional area and both are functions of the radius. Under these conditions, the relative contribution of R and I to the pressure drop per unit length is estimated using a model tube of di erent radii (0.025 – 0.5 cm) and a data set of urethral pressure and ow including time derivative of the ow. We use the following parameter ◦ values: = 1:00 (g cm−3 ) and = 0:07 (Pa s at 37 C). The smallest resistance is obtained in a parabolic pro le, i.e. n = 2. The actual resistance may be larger. For this choice, the ratio of R=I was calculated according to Eq. (4). The results are shown in Fig. 3 on a semi-logarithmic graph. Fig. 3 shows that in the geometrical conditions, similar to those in the urethra, R is much greater than I at small radii and 22 times greater at the largest
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Fig. 4. A typical data set of pressure and ow including time-derivative of ow.
radius of 0.5 cm. To assess the pressure drop resulting from each element, we must look at a typical ˙ pressure– ow data set (Fig. 4) and also compare Q and Q. Fig. 4 shows that as pressure increases, immediately after opening of the urethra, when pressure exceeds opening pressure, Q˙ is greater than Q. However, at that time the cross-sectional area is very small, since the urethra had just been opened (see Fig. 2.) In the high-pressure range, where the cross-sectional area is greatest and I is larger, the ow is almost constant and Q˙ is diminished. Based on these observations, the pressure drop due to acceleration of mass is negligible, relative to the viscous forces and I may be removed from the model. The outlet pressure is atmospheric pressure and equals to zero. This yields the following reduced model equations: Pi = RQo ; Qi − Qo = C P˙ i :
(7)
R due to viscous forces will be designated by Rv and can be expressed as a function of Av with Kv representing all constants including the correction factor for di erent velocity pro les: Kv (8) Rv = 2 : Av The sphincter and the prostate gland form a constriction of the urethra. This part of the urethra is called the ‘ ow control zone’ since most of the pressure drop in the urethra occurs in that zone. If the ow is high enough and the ori ce is small, viscous forces may be neglected and Bernoulli’s theorem may be applied: v12 v2 = P2 + 2 : 2 2 Substituting v with Q=A results in the following pressure– ow relation: Q2 1 1 P1 − P2 = : − 2 A22 A21 P1 +
(9)
(10)
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Fig. 5. Pressure over ow (Rv — thin line) and pressure over squared ow (Rc — thick line) during voiding.
Binder [14] further developed this relation and showed that in a constricted tube or an ori ce, with cross-sectional area Ac , the pressure — ow relation can be described as follows: P1 − P2 =
Q2 ; 2A2c CD
(11)
where CD is a ‘discharge coecient’ that depends on the ‘constriction coecient’. The latter is a function of the constriction geometry. Therefore, we may describe the pressure as a function of the squared ow and a resistance that is a function of the squared cross-sectional area P= or
Kc 2 Q A2c
Rc =
P Kc = 2: 2 Q Ac
(12)
(13)
Since only the input pressure and the out ow are available and detailed internal dynamics cannot be obtained, we must consider two resistances in the development of the lumped-parameter model: one that is due to viscous forces and the other that is due to the rapid velocity changes in the tube. This model allows us to use the pressure– ow data to obtain an important parameter that indicates urethral constriction by observing the ratio of pressure over ow or the pressure over squared ow as shown in Fig. 5. For both resistance de nitions, Fig. 5 shows that before and during opening of the urethra, the resistance is very high and decreases rapidly to a minimum value. During the end of voiding, resistance increases rapidly until the urethra is closed. Combining Eqs. (7) and (8) yields an expression for A, r Kv Qo Av = : (14) Pi
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Fig. 6. Cross-sectional area, calculated from viscous resistance (Av — thin line) and area calculate from Bernoulli’s equation applied to a constriction (Ac — thick line) as functions of time during voiding with the pressure curve shown in dotted line for reference.
Eq. (13) yields a di erent expression for Ac , s Kc Qo2 Ac = : Pi
(15)
Assigning an arbitrary value of 5000 for K1 enables us to present the graph in Fig. 6. This value was selected only to obtain the realistic numbers for the cross-sectional area for demonstration. Fig. 6 shows a relationship between pressure and the cross-sectional area that is similar to those experimental observations. The rst part of the curve relates pressure to the cross-section at time when the urethra is not yet relaxed. This part of the curve is similar to the curves measured by Bagi during the storage phase [13]. Relaxation begins close to peak pressure where we can see that in the presence of pressure decrease, the cross-sectional area is increased. It continues till the end of micturition. Unfortunately, estimation of C or elasticity E (1=C) from this data set is not straightforward since K is unknown. Accepting the straight line description for the pressure–cross-section relations, two points are required for the estimation of compliance. Due to the time-varying nature of the parameter value, two simultaneous points that are required for the estimation are not available. To accommodate time changes in urethral elasticity, we will extend the straight line description shown in Fig. 2. Pi (t) = E(t)(A(t) + a);
(16)
Pi (t) : A(t) + a
(17)
E(t) =
The constant a is estimated at the beginning of voiding before the urethra relaxes and the rst second of micturition is used to normalize this elasticity index to 100% at the beginning of the process.
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Fig. 7. Pressure as a function or cross-sectional area and the estimation of the maximal value of E and the value of the constant ‘a’.
Fig. 8. The elasticity factor as a function of time during voiding.
Fig. 7 shows a plot of pressure as a function of the cross-sectional area and a thick line showing the straight line estimation used to obtain maximum value of E and the constant ‘a’. Fig. 8 shows a plot of the normalized elasticity index E(t) as a function of time using both Av and Ac as the lumen cross-sectional area. Analysis of another set of measured data with low pressure and ow from a patient with voiding complaints is presented in Fig. 9.
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Fig. 9. Full analysis of a patient with low pressure and low ow. The analysis shows that despite the low levels of ow, the resistance is close to normal. The elasticity factor shows a very small reduction during voiding.
To simplify the application of this method, Fig. 10 summarizes the algorithm used to obtain the normalized elasticity factor using Bernoulli’s equation.
3. Discussion A model was developed with a diagnostic value in mind. To make the model clinically useful, only the minimum number of elements that represent rst order e ects were included. Moreover, to t a model to the clinically measured data, namely input pressure and output ow, a lumped parameter model must be used since detailed data on inner dynamics of the urethra are not available for each patient. This excludes the possibility of estimating the location of the constriction along the urethra. In addition, all the past reports have emphasized the importance of a compliant-tube urethral model [10]. To consider the time-dependent physiological relaxation of the urethra, the model includes a time-dependent compliance element that represents mean elasticity of the urethra and a resistive element. Two types of resistive elements were examined, frictional forces due to viscosity of the
uid and pressure loss due to velocity change in a constricted tube. In both cases, the resistance is a continuous function of the cross-sectional area. Thus, the resistance depends on the instantaneous
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Fig. 10. An algorithm for estimating the normalized E(t) function.
values of urethral compliance and pressure. The pressure drop due to acceleration forces has been shown to be insigni cant. Normally, clinicians use the pressure– ow plot to estimate urethral resistance. This plot, as shown for a normal person in Fig. 11, has di erent paths in the increasing pressure limb and in the decreasing pressure limb. During an increasing pressure, ow also increases almost in a straight line similar to its behavior in the storage phase. However, when pressure starts to decrease, ow does not begin to decrease immediately and does not follow the same path. The ow may either increase or remain constant for a while. This indicates that urethral cross-section continues to increase (relax) while pressure decreases. This ongoing relaxation of the urethra results in the di erent trajectories of the plot. The model demonstrates this behavior in Figs. 6 –8. Fig. 6 shows that the cross-sectional area continues to increase while pressure decreases. Fig. 8 shows the change in elastance during this phase. In both viscous ow analysis and Bernoulli type analysis, the results were very similar in their behavior. This model and its clinical predictions should be compared with two most popular methods, the Abrams–Griths [7] nomogram and the linPURR suggested by Schafer [5]. Schafer developed a curve- tting approach to assess urethral resistance from the end of the pressure– ow curve. This method is based on an assumption that the urethral compliance and the resistance do not alter during the analyzed segment of the curve. The model which we have developed treats the urethra as a compliant tube, shows that during the nal segment of voiding, urethral compliance is time dependent and therefore the curve tting at that time will not yield the desired result — i.e. a single
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O. Barnea, G. Gillon / Computers in Biology and Medicine 31 (2001) 27–40
Fig. 11. Pressure– ow plot for a normal urethra.
value that represent a time-varying parameter. Moreover, the di erence between patients with small compliance changes (Fig. 9) and normal patients may be overlooked or confused with resistance changes. Fig. 9 shows an example of a patient with resistance that is similar to the normal patient. The urethral elasticity changed in this patient to a very small degree, compared to the normal patient. This may indicate under di erent circumstances, i.e. higher detrusor pressure, that the urethra will not respond with the desired change in cross-sectional area. Our model shows that a consistent resistance index is not likely to be obtained using this method that estimates resistance from the end slope of the pressure- ow curve. Moreover, this may explain why this diagnostic method is often inconclusive. The Abrams–Griths nomogram is based on a statistical approach. In this method the pressure at maximum ow is drawn on the nomogram. Basically, this point, or the angle of a line connecting the origin to that point, re ects resistance as considered in this work. Therefore, the clinical results may be similar. Our model o ers one step more than the resistance: it o ers an index of elasticity and shows the change in this index during voiding. The estimation of the elasticity changes during voiding is an indicator of the ability of the urethra to respond to greater pressures. Further ongoing clinical experiments will demonstrate the clinical usefulness of this model that considers both resistance and elasticity changes of the urethra. 4. Summary To assess urethral resistance and changes in the urethral elasticity during voiding, a lumped parameter model of the urethra was developed. The model uses pressure and ow measurements to estimate time-dependent resistance and elasticity factor. It was developed with a diagnostic value in
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mind. Therefore, to make the model clinically useful, only a minimum number of elements that represent rst order e ects were included. These are: a resistance that is a function of the cross-section and urethral elasticity responding to pressure changes and changing with time. Two resistance types were compared in the constricted ow-controlling zone of the urethra: Poiseouille resistance and Bernoulli e ect in the ow-control zone. Using real pressure– ow data sets, the model was used to estimate urethral resistance and changes in urethral elasticity during voiding. The estimations of elasticity show in a normal patient, relaxation of the urethra is a process that continues until end of voiding. This ongoing relaxation of the urethra results in the di erent trajectories of the plot. This has important implications regarding present methods that are used in the clinic to assess urethral obstruction or constriction. The primary conclusion from this behavior is that the methods which estimate resistance from one or two points at a stage where the elasticity varies with time, results in values that may be misleading. The resistance as calculated by this model, may be a useful indicator of urethral constriction and obstruction especially since it is independent of the bladder function. Changes in the urethral elasticity during voiding that are estimated by the model add a new diagnostic parameter to the pressure– ow studies. References [1] D.J. Griths, Urodynamic assessment of bladder function, Br. J Urol. 49 (1977) 29–34. [2] W. Schafer, Detrusor as the energy source in micturition, in: F. Hinman Jr. (Ed.), Benign Prostatic Hypertrophy, Springer, New York, 1983, pp. 450–469. [3] W. Schafer, Urethral resistance? Urodynamic concepts of physiological and pathological bladder outlet function during voiding, Neurourol. Urodyn. 4 (1985) 161–201. [4] K. Hofner, A.E.J.L. Kramer, H.K. Tan, H. Krah, U. Jonas, CHESS classi cation of bladder out ow obstruction. A consequence in the discussion of current concepts, World J. Urol. 13 (1995) 59–64. [5] W. Schafer, Analysis of bladder-outlet function with the linearized passive urethral resistance relation, linPURR, and a disease-speci c approach for grading obstruction: from complex to simple, World J. Urol. 13 (1) (1995) 47–58. [6] A. Spangberg, Estimation of urethral resistance by curve- tting in the pressure- ow plot, World J. Urol. 13 (1) (1995) 65–69. [7] P.H. Abrams, D.J. Griths, The assessment of prostatic obstruction from urodynamic measurements and from residual urine, Br. J. Urol. 51 (19XX) 129–134. [8] D. Griths, The pressure within a collapsed tube, with special reference to urethral pressure, Phys. Med. Biol. 30 (9) (1985) 951–963. [9] D. Griths, K. Hofner, R. van Mastrigt, HJ. Rollema, A. Spangberg, . Gleason, Standardization of terminology of lower urinary tract function: pressure– ow studies of voiding, urethral resistance, and urethral obstruction. International Continence Society Subcommittee on Standardization of Terminology of Pressure–Flow Studies, Neurourol. Urodyn. 16 (1) (1997) 1–18. [10] R. Mastrigt van, M. Kranse, Analysis of pressure- ow data in terms of computer-derived urethral resistance parameters, World J. Urol. 13 (1) (1995) 40–46. [11] V.C. Rideout, D.E. Dick, Di erence-di erential equations for uid ow in distensible tubes, IEEE Trans. Biomed. Eng. 14 (3) (1967) 171–177. [12] O. Barnea, A blood vessel model based on velocity pro les, Comput. Biol. Med. 23 (4) (1993) 295–300. [13] P. Bagi, I. Vejborg, H. Colstrup, J.K. Kristensen, Pressure=cross-sectional area relations in the proximal urethra of healthy males, Part 1: Elastance and estimated pressure in the uninstrumented urethra, Eur. Urol. 28 (1) (1995) 51–57. [14] R.C. Binder, Fluid Mechanics, 5th Edition, Prentice-Hall, Englewood Cli s, NJ, 1973.
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Ofer Barnea received a B.Sc. degree in Electrical and Electronics Engineering in 1980 and a M.Sc. degree in Biomedical Engineering in 1983 both from Tel Aviv University. In 1987 he received a Ph.D. degree in Biomedical Engineering from Drexel University in Philadelphia. After teaching and doing research in the area of cardiac assistance for two more years at Drexel University, he joined the Department of Biomedical Engineering at Tel Aviv University. Presently, Dr. Barnea is an Associate Professor at Tel Aviv University. His research interests are analysis of physiological systems, biomedical signal processing, and medical instrumentation. Gabriel Gillon graduated from Tel Aviv University Medical School in 1974 and obtained his MD Diploma in 1977. He completed his residency training in Urology in 1982 at the Rabin Medical Center, Beilinson Campus. Since then, he is a Faculty Member of the Dept. of Urology at Rabin Medical Center. Dr. Gillon had further studies in London UK in 1984 in St. George’s Medical School in female urology as an honorary registrar. In 1987 he spent a year as a lecturer in Guy’s Hospital in neuro-urology and reconstructive surgery. In 1992 he was appointed Lecturer in the Dept. of Surgery at the Tel Aviv University Medical School. Currently he is the head of the Department of Urology at Tel Aviv Central Clinic Zamenhof and responsible for urodynamic and neuro-urology services at the Rabin Med Center Beilinson Campus.
Model-based estimation of male urethral resistance and elasticity using pressure– ow data Ofer Barneaa ; ∗ , Gabriel Gillonb,c a
Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel b Department of Urology, Rabin Medical Center, Israel c Sackler School of Medicine, Tel Aviv University, Ramat Aviv, Israel Received 8 October 1999; accepted 3 July 2000
Abstract To assess urethral resistance and changes in the urethral elasticity during voiding, a lumped parameter model of the urethra was developed. The model uses pressure and ow measurements to estimate time-dependent resistance and elasticity factor. The model includes a resistance that has a function of the cross-section and urethral elasticity. Two resistivity types are compared in the constricted ow-controlling zone of the urethra: Poiseouille resistance and the Bernoulli e ect. Using real pressure– ow data sets, the model was used to estimate urethral resistance and changes in urethral elasticity during voiding. Estimation of the elasticity show that in a normal patient relaxation of the urethra is a process that continues until the end of voiding. This has important implications with regard to the present methods that are used in the clinic to assess urethral obstruction or constriction. The resistance as calculated by this model, may be a useful indicator of urethral constriction and obstruction, since it is especially independent of the bladder function. Changes in the urethral elasticity during voiding which are estimated by the model add a new diagnostic parameter to c 2000 Elsevier Science Ltd. All rights reserved. pressure– ow studies. Keywords: Urodynamics; Urethral resistance; Urethral elasticity; Mathematical model
1. Introduction The function of the bladder is to store and hold urine and empty itself completely when suitable. The micturition, or voiding, is achieved by a rise in the intravesical pressure ( uid pressure in the bladder cavity) that is sustained until the bladder is empty. This is preceded by the relaxation of the pelvic oor muscles and the relaxation of the urethral sphincteric area. Thus, normally, the proximal urethra at the bladder outlet, comprising the bladder neck, the prostatic urethra and the sphincteric ∗
Corresponding author. Tel.: +972-3-640-8658; fax: +972-3-640-7939. E-mail address: [email protected] (O. Barnea).
c 2000 Elsevier Science Ltd. All rights reserved. 0010-4825/00/$ - see front matter PII: S 0 0 1 0 - 4 8 2 5 ( 0 0 ) 0 0 0 2 0 - 2
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O. Barnea, G. Gillon / Computers in Biology and Medicine 31 (2001) 27–40
area, are all relaxed during micturition. The urethral resistance to ow is accordingly very low and the driving force, i.e. the bladder wall smooth muscle should exhibit low pressure for any ow rate. Urethral resistance is de ned by the inherent mechanical and morphological properties of the proximal urethral wall called ow-controlling zone [1]. During micturition, the bladder outlet or the
ow-controlling zone can be obstructive as a result of the neurological over-activity or abnormal structure of anatomical basis such as stricture or more frequently — enlargement of the prostate. Obstruction, being a physical concept, implies that the urethral resistance to ow is abnormally elevated. Intravesical pressure during micturition has been shown to be directly related to urethral resistance [2,3]. As urethral resistance increases, ow rate declines and higher intravesical pressures are measured. Since urethral resistance a ects intravesical pressure and ow rate, a direct measurement of this parameter would be desirable in the diagnostic procedure. However, in practice this is dicult. Therefore, standard urodynamic studies were developed based on indirect methods. Thus, urethral resistance is represented by a relationship between the pressure and the ow rate. This implies that simultaneous measurement of intravesical pressure and ow rate during micturition is required to study urethral resistance. To assess bladder function, both intravesical and intra-abdominal pressures are measured and the detrusor (bladder wall smooth muscle) pressure is obtained from the di erence between these two. The pressure– ow relationship is used to obtain the clinically meaningful information and to classify urethral resistance as normal or abnormally elevated. The most accurate procedure is a quasi-continuous plot showing many points of corresponding pressure and ow rate values. Simpler clinical methods involve plotting of only two or three pressure– ow points. These studies of pressure–
ow plots yield a variety of curves and it is not possible to reduce each of these plots to a single number — resistance factor. Therefore, current methods make use of a family of plots of similar form, e.g. shape of slopes or curvatures to grade severity of obstruction [4 – 6]. Alternatively, it is practical to look at these pressure– ow plots based on one point of the detrusor pressure at a maximum ow rate and classify groups of patients accordingly [7]. De nition and grading of urethral resistance has a paramount clinical importance though its measurement by standard urodynamic techniques is not simple. Pressure– ow studies have become a standard test for lower urinary tract obstruction and constriction. The concept of urethral resistance measurement remains confusing and has not been de ned uniquely despite several rigorous analyses and reviews of methodologies [3,8–10]. The statement issued by the International Continence Society regarding standardization of terminology in pressure–
ow studies de ned urethral resistance in a vague manner. It states that ‘urethral resistance relation’ is represented by the pressure– ow relations [9]. Schafer o ered an oversimpli ed approach to urodynamic pressure– ow relations, assuming that the urethra is no more than a hole in the bladder and calculated the uid velocity based on Bernoulli’s equation. This work was the basis to some later development of diagnostic methods such as the passive urethral resistance relation (PURR) [3,5]. PURR is based on the understanding that the whole curve is too complex and that time-varying viscoelastic properties of the urethra stabilize towards the end of micturition. In this method, a curve- tting technique is applied at the lower pressure part of the curve relating pressure and ow at the end of the process, beginning at the maximum ow point. This was followed by modi cation to a linear curve t [5]. The slope of the pressure– ow curve is assumed to indicate ‘urethral resistance relation’. The implicit hypothesis on which this method is based upon is that the urethral elasticity that is reduced during micturition,
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reaches a plateau and is invariable during the last portion of the pressure– ow curve. Another work, a detailed uid–dynamic analysis of pressure– ow relation in the urethra as a collapsible tube, was reported by Griths [8]. Abrams and Griths constructed a nomogram that classi es patients into three categories: obstructed, equivocal and non-obstructed, according to the detrusor pressure at the maximum ow [7]. This statistical method that was based on a large clinical research, often results in an equivocal result. None of these methods is able to detect urethral obstruction conclusively in several cases. The model that is reported in this paper was developed to o er a di erent solution with clinical relevance. Therefore, only the dominating e ects that are directly related to the pressure– ow relations were included. 2. The model A detailed analysis of urinary laminar ow dynamics requires the solution of the Navier–Stokes equation d V + V · ∇ V = −∇P + ∇2 V; (1) dt where P is pressure, V is the three-dimensional velocity vector, is the uid density and is uid viscosity. This equation indicates that two forces are involved in the relationship between pressure gradient and velocity: acceleration and velocity forces due to the uid mass (term on the left) and viscous forces due to the uid viscosity (term on the right.) Several observations and assumptions can simplify the analysis. The form of the equation as presented here already implies that body forces, such as gravitational force have been neglected. To enable numerical implementations of urodynamic models where average cross-sectional pressures and volumetric rates are of interest, a series of assumptions must be made to simplify the solution of this equation. In this analysis, two types of pressure– ow relations in a compliant tube were considered. In the rst, we consider only the viscous ow and in the second we consider Bernoulli’s equation that is also inherent in the Navier–Stokes equation. These are analyzed separately. The rst model was developed to describe viscous ow through a compliant urethra based on the Navier–Stokes equation and the continuity equation. In the second model, a constriction was added where the conversion of pressure to velocity is determined based on Bernoulli’s equation. Others who analyzed blood ow have initially ignored compliance of the vessel wall, radial ow and the nonlinear terms in the equation and then added the vessel properties. The initial analysis yielded the following pressure–velocity relationship [11]: dP dw 1 dw d 2 w − + 2 ; (2) = − dz dt r dr dr where r is radius and w is velocity in the z-axis direction. Assuming a steady ow and a parabolic velocity pro le as well as the relationship between volumetric ow rate and the velocity pro le, this equation was converted to a relationship between pressure and volumetric ow [11]: Pi − Po = RQo + I Q˙ o ; Qi − Qo = C P˙ i ;
(3)
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Fig. 1. An electrical analog model of a compliant tube.
where I=
L rv2
and
R=
8L rv4
(4)
R is the viscous resistance of the uid, I is the inertance of the uid, C is the urethral compliance and L is the e ective length. This form of the pressure– ow equation can be described by an electrical analog model (Fig. 1) that includes two series of elements: a resistance representing viscous forces and an inductor representing inertial forces (inertance). The e ect of the compliant vessel wall is introduced in the form of a parallel capacitor. The assumption of the parabolic velocity pro le may not hold at the entrance of the urethra where the velocity pro le is at or in the case of ow through an ori ce or a constriction. These two cases are considered. To evaluate the e ect of various velocity pro les on R and I , Barnea [12] derived a relationship between pressure gradient and volumetric ow based on Eq. (2). For a velocity pro le of the form rn w(r) = wn 1 − n ; (5) rv where wn is a normalized peak ow, he obtained an expression for I and R for the equation I=
L rv2
and
R=
2(n + 2)L : rv4
(6)
This shows that I is una ected by the change in velocity pro le whereas R does depend on the velocity pro le. As the velocity pro le becomes more at n increases but the form of the relationship is maintained. R and I are examined following the description of the third component that is required to satisfy the continuity equation in a compliant tube. The last element in the model is a compliance representing the compliance of the urethral wall. The urethral compliance C is de ned as dA=dP, where A is the cross-sectional area, and may be estimated from the pressure–cross-sectional area plot. Conversely, elasticity E is de ned as dP=dA. Bagi et al. [13] measured urethral compliance at several points along the urethra during the storage phase. Others had measured the cross-sectional area during voiding. A typical schematic plot of pressure–cross-sectional area during the storage phase is shown in Fig. 2 for increasing pressure and area (during the descending pressure range the behavior may be di erent.) Fig. 2 shows that the urethra is closed for pressures under the opening pressure P0 (30 cm H2 O in this graph) and opens gradually with the pressure. C is constant along a wide range of cross-sectional area. In the model, C will be regarded as a time-varying component during voiding.
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Fig. 2. Schematic pressure–cross-sectional area relation in the male urethra during the storage phase.
Fig. 3. Ratio of viscous resistance over inertance as a function of tube radius.
R and I depend on C since the latter relates pressure to the cross-sectional area and both are functions of the radius. Under these conditions, the relative contribution of R and I to the pressure drop per unit length is estimated using a model tube of di erent radii (0.025 – 0.5 cm) and a data set of urethral pressure and ow including time derivative of the ow. We use the following parameter ◦ values: = 1:00 (g cm−3 ) and = 0:07 (Pa s at 37 C). The smallest resistance is obtained in a parabolic pro le, i.e. n = 2. The actual resistance may be larger. For this choice, the ratio of R=I was calculated according to Eq. (4). The results are shown in Fig. 3 on a semi-logarithmic graph. Fig. 3 shows that in the geometrical conditions, similar to those in the urethra, R is much greater than I at small radii and 22 times greater at the largest
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Fig. 4. A typical data set of pressure and ow including time-derivative of ow.
radius of 0.5 cm. To assess the pressure drop resulting from each element, we must look at a typical ˙ pressure– ow data set (Fig. 4) and also compare Q and Q. Fig. 4 shows that as pressure increases, immediately after opening of the urethra, when pressure exceeds opening pressure, Q˙ is greater than Q. However, at that time the cross-sectional area is very small, since the urethra had just been opened (see Fig. 2.) In the high-pressure range, where the cross-sectional area is greatest and I is larger, the ow is almost constant and Q˙ is diminished. Based on these observations, the pressure drop due to acceleration of mass is negligible, relative to the viscous forces and I may be removed from the model. The outlet pressure is atmospheric pressure and equals to zero. This yields the following reduced model equations: Pi = RQo ; Qi − Qo = C P˙ i :
(7)
R due to viscous forces will be designated by Rv and can be expressed as a function of Av with Kv representing all constants including the correction factor for di erent velocity pro les: Kv (8) Rv = 2 : Av The sphincter and the prostate gland form a constriction of the urethra. This part of the urethra is called the ‘ ow control zone’ since most of the pressure drop in the urethra occurs in that zone. If the ow is high enough and the ori ce is small, viscous forces may be neglected and Bernoulli’s theorem may be applied: v12 v2 = P2 + 2 : 2 2 Substituting v with Q=A results in the following pressure– ow relation: Q2 1 1 P1 − P2 = : − 2 A22 A21 P1 +
(9)
(10)
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Fig. 5. Pressure over ow (Rv — thin line) and pressure over squared ow (Rc — thick line) during voiding.
Binder [14] further developed this relation and showed that in a constricted tube or an ori ce, with cross-sectional area Ac , the pressure — ow relation can be described as follows: P1 − P2 =
Q2 ; 2A2c CD
(11)
where CD is a ‘discharge coecient’ that depends on the ‘constriction coecient’. The latter is a function of the constriction geometry. Therefore, we may describe the pressure as a function of the squared ow and a resistance that is a function of the squared cross-sectional area P= or
Kc 2 Q A2c
Rc =
P Kc = 2: 2 Q Ac
(12)
(13)
Since only the input pressure and the out ow are available and detailed internal dynamics cannot be obtained, we must consider two resistances in the development of the lumped-parameter model: one that is due to viscous forces and the other that is due to the rapid velocity changes in the tube. This model allows us to use the pressure– ow data to obtain an important parameter that indicates urethral constriction by observing the ratio of pressure over ow or the pressure over squared ow as shown in Fig. 5. For both resistance de nitions, Fig. 5 shows that before and during opening of the urethra, the resistance is very high and decreases rapidly to a minimum value. During the end of voiding, resistance increases rapidly until the urethra is closed. Combining Eqs. (7) and (8) yields an expression for A, r Kv Qo Av = : (14) Pi
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Fig. 6. Cross-sectional area, calculated from viscous resistance (Av — thin line) and area calculate from Bernoulli’s equation applied to a constriction (Ac — thick line) as functions of time during voiding with the pressure curve shown in dotted line for reference.
Eq. (13) yields a di erent expression for Ac , s Kc Qo2 Ac = : Pi
(15)
Assigning an arbitrary value of 5000 for K1 enables us to present the graph in Fig. 6. This value was selected only to obtain the realistic numbers for the cross-sectional area for demonstration. Fig. 6 shows a relationship between pressure and the cross-sectional area that is similar to those experimental observations. The rst part of the curve relates pressure to the cross-section at time when the urethra is not yet relaxed. This part of the curve is similar to the curves measured by Bagi during the storage phase [13]. Relaxation begins close to peak pressure where we can see that in the presence of pressure decrease, the cross-sectional area is increased. It continues till the end of micturition. Unfortunately, estimation of C or elasticity E (1=C) from this data set is not straightforward since K is unknown. Accepting the straight line description for the pressure–cross-section relations, two points are required for the estimation of compliance. Due to the time-varying nature of the parameter value, two simultaneous points that are required for the estimation are not available. To accommodate time changes in urethral elasticity, we will extend the straight line description shown in Fig. 2. Pi (t) = E(t)(A(t) + a);
(16)
Pi (t) : A(t) + a
(17)
E(t) =
The constant a is estimated at the beginning of voiding before the urethra relaxes and the rst second of micturition is used to normalize this elasticity index to 100% at the beginning of the process.
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Fig. 7. Pressure as a function or cross-sectional area and the estimation of the maximal value of E and the value of the constant ‘a’.
Fig. 8. The elasticity factor as a function of time during voiding.
Fig. 7 shows a plot of pressure as a function of the cross-sectional area and a thick line showing the straight line estimation used to obtain maximum value of E and the constant ‘a’. Fig. 8 shows a plot of the normalized elasticity index E(t) as a function of time using both Av and Ac as the lumen cross-sectional area. Analysis of another set of measured data with low pressure and ow from a patient with voiding complaints is presented in Fig. 9.
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Fig. 9. Full analysis of a patient with low pressure and low ow. The analysis shows that despite the low levels of ow, the resistance is close to normal. The elasticity factor shows a very small reduction during voiding.
To simplify the application of this method, Fig. 10 summarizes the algorithm used to obtain the normalized elasticity factor using Bernoulli’s equation.
3. Discussion A model was developed with a diagnostic value in mind. To make the model clinically useful, only the minimum number of elements that represent rst order e ects were included. Moreover, to t a model to the clinically measured data, namely input pressure and output ow, a lumped parameter model must be used since detailed data on inner dynamics of the urethra are not available for each patient. This excludes the possibility of estimating the location of the constriction along the urethra. In addition, all the past reports have emphasized the importance of a compliant-tube urethral model [10]. To consider the time-dependent physiological relaxation of the urethra, the model includes a time-dependent compliance element that represents mean elasticity of the urethra and a resistive element. Two types of resistive elements were examined, frictional forces due to viscosity of the
uid and pressure loss due to velocity change in a constricted tube. In both cases, the resistance is a continuous function of the cross-sectional area. Thus, the resistance depends on the instantaneous
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Fig. 10. An algorithm for estimating the normalized E(t) function.
values of urethral compliance and pressure. The pressure drop due to acceleration forces has been shown to be insigni cant. Normally, clinicians use the pressure– ow plot to estimate urethral resistance. This plot, as shown for a normal person in Fig. 11, has di erent paths in the increasing pressure limb and in the decreasing pressure limb. During an increasing pressure, ow also increases almost in a straight line similar to its behavior in the storage phase. However, when pressure starts to decrease, ow does not begin to decrease immediately and does not follow the same path. The ow may either increase or remain constant for a while. This indicates that urethral cross-section continues to increase (relax) while pressure decreases. This ongoing relaxation of the urethra results in the di erent trajectories of the plot. The model demonstrates this behavior in Figs. 6 –8. Fig. 6 shows that the cross-sectional area continues to increase while pressure decreases. Fig. 8 shows the change in elastance during this phase. In both viscous ow analysis and Bernoulli type analysis, the results were very similar in their behavior. This model and its clinical predictions should be compared with two most popular methods, the Abrams–Griths [7] nomogram and the linPURR suggested by Schafer [5]. Schafer developed a curve- tting approach to assess urethral resistance from the end of the pressure– ow curve. This method is based on an assumption that the urethral compliance and the resistance do not alter during the analyzed segment of the curve. The model which we have developed treats the urethra as a compliant tube, shows that during the nal segment of voiding, urethral compliance is time dependent and therefore the curve tting at that time will not yield the desired result — i.e. a single
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O. Barnea, G. Gillon / Computers in Biology and Medicine 31 (2001) 27–40
Fig. 11. Pressure– ow plot for a normal urethra.
value that represent a time-varying parameter. Moreover, the di erence between patients with small compliance changes (Fig. 9) and normal patients may be overlooked or confused with resistance changes. Fig. 9 shows an example of a patient with resistance that is similar to the normal patient. The urethral elasticity changed in this patient to a very small degree, compared to the normal patient. This may indicate under di erent circumstances, i.e. higher detrusor pressure, that the urethra will not respond with the desired change in cross-sectional area. Our model shows that a consistent resistance index is not likely to be obtained using this method that estimates resistance from the end slope of the pressure- ow curve. Moreover, this may explain why this diagnostic method is often inconclusive. The Abrams–Griths nomogram is based on a statistical approach. In this method the pressure at maximum ow is drawn on the nomogram. Basically, this point, or the angle of a line connecting the origin to that point, re ects resistance as considered in this work. Therefore, the clinical results may be similar. Our model o ers one step more than the resistance: it o ers an index of elasticity and shows the change in this index during voiding. The estimation of the elasticity changes during voiding is an indicator of the ability of the urethra to respond to greater pressures. Further ongoing clinical experiments will demonstrate the clinical usefulness of this model that considers both resistance and elasticity changes of the urethra. 4. Summary To assess urethral resistance and changes in the urethral elasticity during voiding, a lumped parameter model of the urethra was developed. The model uses pressure and ow measurements to estimate time-dependent resistance and elasticity factor. It was developed with a diagnostic value in
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mind. Therefore, to make the model clinically useful, only a minimum number of elements that represent rst order e ects were included. These are: a resistance that is a function of the cross-section and urethral elasticity responding to pressure changes and changing with time. Two resistance types were compared in the constricted ow-controlling zone of the urethra: Poiseouille resistance and Bernoulli e ect in the ow-control zone. Using real pressure– ow data sets, the model was used to estimate urethral resistance and changes in urethral elasticity during voiding. The estimations of elasticity show in a normal patient, relaxation of the urethra is a process that continues until end of voiding. This ongoing relaxation of the urethra results in the di erent trajectories of the plot. This has important implications regarding present methods that are used in the clinic to assess urethral obstruction or constriction. The primary conclusion from this behavior is that the methods which estimate resistance from one or two points at a stage where the elasticity varies with time, results in values that may be misleading. The resistance as calculated by this model, may be a useful indicator of urethral constriction and obstruction especially since it is independent of the bladder function. Changes in the urethral elasticity during voiding that are estimated by the model add a new diagnostic parameter to the pressure– ow studies. References [1] D.J. Griths, Urodynamic assessment of bladder function, Br. J Urol. 49 (1977) 29–34. [2] W. Schafer, Detrusor as the energy source in micturition, in: F. Hinman Jr. (Ed.), Benign Prostatic Hypertrophy, Springer, New York, 1983, pp. 450–469. [3] W. Schafer, Urethral resistance? Urodynamic concepts of physiological and pathological bladder outlet function during voiding, Neurourol. Urodyn. 4 (1985) 161–201. [4] K. Hofner, A.E.J.L. Kramer, H.K. Tan, H. Krah, U. Jonas, CHESS classi cation of bladder out ow obstruction. A consequence in the discussion of current concepts, World J. Urol. 13 (1995) 59–64. [5] W. Schafer, Analysis of bladder-outlet function with the linearized passive urethral resistance relation, linPURR, and a disease-speci c approach for grading obstruction: from complex to simple, World J. Urol. 13 (1) (1995) 47–58. [6] A. Spangberg, Estimation of urethral resistance by curve- tting in the pressure- ow plot, World J. Urol. 13 (1) (1995) 65–69. [7] P.H. Abrams, D.J. Griths, The assessment of prostatic obstruction from urodynamic measurements and from residual urine, Br. J. Urol. 51 (19XX) 129–134. [8] D. Griths, The pressure within a collapsed tube, with special reference to urethral pressure, Phys. Med. Biol. 30 (9) (1985) 951–963. [9] D. Griths, K. Hofner, R. van Mastrigt, HJ. Rollema, A. Spangberg, . Gleason, Standardization of terminology of lower urinary tract function: pressure– ow studies of voiding, urethral resistance, and urethral obstruction. International Continence Society Subcommittee on Standardization of Terminology of Pressure–Flow Studies, Neurourol. Urodyn. 16 (1) (1997) 1–18. [10] R. Mastrigt van, M. Kranse, Analysis of pressure- ow data in terms of computer-derived urethral resistance parameters, World J. Urol. 13 (1) (1995) 40–46. [11] V.C. Rideout, D.E. Dick, Di erence-di erential equations for uid ow in distensible tubes, IEEE Trans. Biomed. Eng. 14 (3) (1967) 171–177. [12] O. Barnea, A blood vessel model based on velocity pro les, Comput. Biol. Med. 23 (4) (1993) 295–300. [13] P. Bagi, I. Vejborg, H. Colstrup, J.K. Kristensen, Pressure=cross-sectional area relations in the proximal urethra of healthy males, Part 1: Elastance and estimated pressure in the uninstrumented urethra, Eur. Urol. 28 (1) (1995) 51–57. [14] R.C. Binder, Fluid Mechanics, 5th Edition, Prentice-Hall, Englewood Cli s, NJ, 1973.
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Ofer Barnea received a B.Sc. degree in Electrical and Electronics Engineering in 1980 and a M.Sc. degree in Biomedical Engineering in 1983 both from Tel Aviv University. In 1987 he received a Ph.D. degree in Biomedical Engineering from Drexel University in Philadelphia. After teaching and doing research in the area of cardiac assistance for two more years at Drexel University, he joined the Department of Biomedical Engineering at Tel Aviv University. Presently, Dr. Barnea is an Associate Professor at Tel Aviv University. His research interests are analysis of physiological systems, biomedical signal processing, and medical instrumentation. Gabriel Gillon graduated from Tel Aviv University Medical School in 1974 and obtained his MD Diploma in 1977. He completed his residency training in Urology in 1982 at the Rabin Medical Center, Beilinson Campus. Since then, he is a Faculty Member of the Dept. of Urology at Rabin Medical Center. Dr. Gillon had further studies in London UK in 1984 in St. George’s Medical School in female urology as an honorary registrar. In 1987 he spent a year as a lecturer in Guy’s Hospital in neuro-urology and reconstructive surgery. In 1992 he was appointed Lecturer in the Dept. of Surgery at the Tel Aviv University Medical School. Currently he is the head of the Department of Urology at Tel Aviv Central Clinic Zamenhof and responsible for urodynamic and neuro-urology services at the Rabin Med Center Beilinson Campus.