Fundamental aspects of isovolumetric contractility measurements of urinary bladder

In 1978 probably the fi rst clinical contractility parameter, based on isovolumetric bladder, was introduced [2]. In that time the need for a contractility parameter was born to be able to observe damage on contractile tissue that might be caused by the clinical application of fast or stepwise cystometry to evaluate pressure relaxation and visco-elastic properties of the bladder [3]. Since the introduction of the concept of contractility many other contractility parameters and methods of determination for clinical evaluation of active bladder function have been developed. However, different fundamental aspects of contractility may contribute to the seen chaos in these clinical applications. In present consideration this is illustrated for the isovolumetric method.


Introduction
In 2004 Griffi ths published: "Detrusor Contractility: Order Out of Chaos" [1]. It was a critical assessment of the many competing ways of assessing detrusor contractility in the urodynamic clinic. Different isovolumetric methods and pressure fl ow studies were considered.
In 1978 probably the fi rst clinical contractility parameter, based on isovolumetric bladder, was introduced [2]. In that time the need for a contractility parameter was born to be able to observe damage on contractile tissue that might be caused by the clinical application of fast or stepwise cystometry to evaluate pressure relaxation and visco-elastic properties of the bladder [3]. Since the introduction of the concept of contractility many other contractility parameters and methods of determination for clinical evaluation of active bladder function have been developed. However, different fundamental aspects of contractility may contribute to the seen chaos in these clinical applications. In present consideration this is illustrated for the isovolumetric method.
Contraction is synonym for shortening of active muscular tissue. Shortening of circumference of the bladder wall is the requisite for the evacuation phase of the bladder. Rate of expulsion Q of bladder contents is determined by velocity of shortening of bladder wall. This velocity of shortening is reduced by bladder pressure, which can be built up by the resistance to fl ow of the urethra. The relation between velocity of shortening v and load of smooth muscle F for maximal stimulated bladder strips have been evaluated of pig bladders [4], using the normalized classic equation of Hill [5]: (F/F 0 + a/F 0 )(v/l+b/l) = (1+a/F O )b/l (1) Here F is force across the strip and F o is the isometric force,  For these methods we need to assume that stimulation of contractile tissue is maintained during fl ow at maximum level.
The original method [2] is based on determination of the relative rate of increase of pressure ((dp/dt)/p) during activation of the isovolumetric bladder, i.e. just before expulsion has started. However, isovolumetric pressure increase during stimulation of CE depends on the stress-strain relation of SEE.
We relate stress S to pressure p by: where V t is volume of bladder tissue and is assumed to be constant. With (2) we can express for isovolumetric volume V variable (dp/dt)/p in stress: For an isovolumetric stimulated bladder the sho rtening where E is an elasticity parameter. Elastic properties of bladder tissue, studied by series of stepwise straining of tissue strips, show an exponential increase of elastic parameter E [6]. To describe this non-linear type of elasticity for large elongations it is appropriate to express strain relative to an actual reference length l o by natural strain defi ned by  = ln l/l o. This natural strain is associated with a preload S o which depends on chosen reference length l o . With these variables the experimentally found stress-strain relation of SEE with progressive elasticity modulus can be characterized by: where k is a constant elastic stiffness parameter.
Then dS/dt=kS (d/dt) = kS(dl E /dt) /l o , so that with (3) holds: Because under isovolumetric condition (dl E /dt) = -(d l C /dt), w e fi nd by dividing these velocities by reference length l = l o as length of the actual circumference of the bladder as reference length: with (6) we have related parameter v CE /l of a st imulated isovolumetric bladder to the relative rate of increase of bladder pressure (dp/dt)/p. From start of stimulation pressure rises till the level is reached for start of expulsion. This pressure recording is used to determine (dp/dt)/p along pressure increase p(t).
Gordon and Siegman found for taenia coli of length l that v max /l roughly is a constant [7] and have taken v max /l as a parameter for contractility. According to Hill's equation (1)  and related to parameter Max {(dp/dt) / p}. Theoretically for (dp/dt)>0 the value of Max {(dp/dt) /p} is infi nite large for p =0. We are not interested in contractility at start of activation, but we look for Max {(dp/dt) / p} attained along the rising pressure for p>0.
In a pilot study on 11 human subjects referred to in [2] Max {(dp/dt) /p} was found in the fi rst part of rising pressure. This maximum varied between 0.17-0.99 s -1 for bladder volume in the range of 150-650 ml. It is evident that v max /l in Hill's equation valid for p=0 for fully activated tissue is different to v CEmax /l that here is taken as a measure of velocity of shortening derived from Max {(dp/dt) /p} for p>0 attained at unknown level of activation. For two subjects Max {(dp/dt) /p} wa s determined in series of voluntarily interruption of micturition.
The parameter of contractility derived from Max {(dp/dt) /p} clearly was not reproducible. Bad reproducible results of this method were particularly ascribed to variation in the characteristics of elasticity in SEE [8]. To exclude an effect of inhibition of the activation by voluntarily interruption the   (4) and consequently also the original isovolumetric method.
More observations have shown that the development of isovolumetric pressure during activation dp/dt is slower than assumed by Gordon and Siegman [7] and depends on different stimulation variables. It turned out that the fi rst part of dp/dt increases almost exponentially with increasing p to a maximum and then decreases almost linearly with increasing p to maximum isovolumetric pressure p 0 [11].
Despite these complications with the use of vari able (dp/ dt) /p to derive a parameter for contractility its use was re- to generate a plot of (dp/dt) /p versus p. Extrapolation of this plot according to a fi tted hyperbolic function to the y-axis (p=0) and to the x-axis (v CE =0) is used as contractility parameter v CEmax and maximum isovolumetric pressure p o respectively. Without foundation of their interpretation, the obtained fi tted plot of (dp/dt) /p versus p is taken to be similar with velocity-force relation according to (1) [13]. The course of increasing pressure between 20%-80% of maxi mum of recorded detrusor pressure is used to fi t the hyperbolic function needed for extrapolation.
This maximum pressure is equal to opening pressure of urethra.
Duration t 20 -t 80 needed for the rise of pressure from 20%-80% of maximum is used for practical reasons as a contractility index DCP.
In a letter to editor Schaefer has given critical comments to this method [14] and has emphasized the clinical signifi cance to relate detrusor strength to outfl ow. Here we criticize their method by referring to the fundamental problems discussed in relation the original similar method [2].
As has been explained before, the maximum of v CE derived from (dp/dt) /p by backwards extrapolation to p=0, is not equal to v max in Hill's equation (1). Because v max depends on circumference l of the bladder, hence on V, it is expected that v CEmax also depe nds on V, which is pretended to be not the case.
Hill's equation is based on a maintained fully stimulated state.
The relation between elastic volume V E and pressure p is expressed by elastic compliance parameter C E : C E = (dV E / dp) [17]. This type of compliance differs from ICS-standard and from compliance that commonly is derived from a cystometrogram. In a study on not-stimulated pig bladders in vitro it was found that elastic volume V E , as part of differe nt values of total volume V, and C E varies considerably [17]. For an accommodated bladder with volume between 100 and 300 ml the percentage that is ascribed to elastic volume varies in the range of 10-50% of total volume.
We referred above to the observation of large variation of elastic length for stimulated pig bladder strips of 4.5-20.5% of initial length [6]. When we translate this variation to variation of elastic volume V E of the activated bladder then we fi nd a variation of approximately 13-50% of actual volume. This We try to benefi t from the remarkable property of constant elastic volume during isovolumetric pressure increase during activation to characterize clinically the contractile state of the bladder. If C E is constant then Q= dV/dt= C E dp/dt. If we assume that at start of micturition C E has reached a minimu m value during isovolumetric activation up to attained opening pressure of urethra and that this value of C E is constant for a small initial period, then we can derive this Min {C E } from init ial fl ow Q(0) and initial dp(0)/dt by using equation: Min {C E }= (dV(0)/dt)/ (dp(0)/dt). However, because of the observed, though still unexplained, large variation in elastic volume for passive and activated bladder we expect that parameter Min {C E } will also vary. Forced stops of fl ow during a micturition offer more opportunities to determine actual values of elastic compliance C E of a certain bladder. This proposed parameter Min {C E } and method of determination has not yet been clinically evaluated.

Conclusion
Although we may have contributed extra chaos in the many published methods of contractility measurements by referring to fundamental aspects of isovolumetric methods, the considered basic properties fi nally suggest an alternative clinical feasible method to evaluate actual contractilit y of the bladder.