1. Bladder in the collection phase

1.1. Introduction of the model: Elastic volume and rest volume   

In clinical cystometry, the relationship between detrusor pressure (p_d) and increasing bladder volume is measured, with stress (σ) in the bladder wall connecting these variables¹. For a filled spherical bladder, the relation between p_d and V can be approximated by Equation 1:

p_d ≈ (2/3 V_t) σ/V                             (1)

where V_t is the total volume of tissue of the bladder wall.

Equation 1 indicates that, for a given value of σ, p_d decreases as bladder volume increases. Equation 1 is based on the geometry of the bladder and is valid irrespective of the source of the σ, whether arising from the passive mechanical properties of the bladder or from the active contractions of the muscular tissue of the wall. It also indicates that, for a given level of p_d, σ is proportional to bladder volume.

The bladder wall mainly consists of a network of many interconnected small smooth muscle cells. Hence, mechanical models are used to describe experimentally observed mechanical phenomena of the bladder, in particular, the relationship between σ and the elongation of the bladder wall. The simple model in Figure 1 has been introduced to express observed passive and active properties, as well as the properties of spontaneous contractions of bladder tissue, in a single model ². Hence, this model is applicable to describe the properties of the bladder during the collection and expulsion phases. The model consists of a series arrangement of two elements: a series elastic element (SEE) and a plasto/contractile element (PCE), each representing two distinct characteristic properties of the mechanical stress–strain relations.

Figure 1. van Duyl’s model of the length of a strip of bladder tissue as the sum of two elements, a series elastic element and a plasto/contractile element, representing two separated mechanical properties of bladder tissue. Copyright W.A. van Duyl.³

The mechanical properties of bladder tissue are more or less homogeneously distributed in the bladder wall. In the model, the properties are separated into two types and lumped into the two discrete elements, SEE and PCE ^2,3. Here, SEE represents the distributed property of elasticity of bladder tissue, and PCE represents the distributed plasto-contractile property of bladder tissue. Element PCE expresses the phenomenon that an active contraction can restore a passive elongated state of bladder tissue. Hence, in PCE, passive elongations and active contractions have reverse effects on the elongated state of PCE. As a consequence of the separated properties of bladder tissue, bladder volume can be separated into two parts. The elastic component with volume (V_E) is exclusively related to p_d; V_E is the volume that must be rapidly withdrawn from the bladder to attain zero p_d. The elastic wall of the V_E is part of the bladder wall and hence follows the shape of the bladder. After withdrawal of V_E, the remaining volume, comprising its content with p_d = 0, is defined as the rest volume V_R, yielding V = V_E + V_R. In terms of the model of Figure 1, the V_E is determined by the elongated state of SEE, and the V_R is determined by the elongated state of PCE. Accounting for the geometry of the bladder, the elongated state of the bladder wall can be considered as a sum of the elongated states of SEE and PCE. Elastic elongation of SEE follows a varying σ, and it returns instantaneously to its original state when σ becomes zero. The wall’s stiffness, expressed as elastic compliance, is defined as C_E = V_E/p_d. The C_E used for this model differs from the standard clinical compliance defined in Abrams et al. ⁴  

The PCE is a more complicated element than SEE. In contrast to elasticity, the elongated state of PCE increases gradually as σ increases. The rate of this gradual elongation of PCE is ascribed to the mechanical property of viscosity, being an aspect of plasticity. However, viscous elongation stops when a certain plastic elongated state of PCE is attained. The attained plastic elongated state is maintained as long as σ remains below the previous σ. Hence, the set plastic elongated state acts as a threshold for σ, which must be exceeded to achieve, via viscosity, a more plastic elongated state. This threshold value for σ is higher for a more plastic elongated state ⁵.

1.2. Cystometry in terms of the model

Bladder volume during the collection phase increases slowly, accompanied by an almost constant or only a small increase in p_d  ⁶. Clinically, the properties of the bladder during the collection phase are evaluated by slow-filling cystometry (filling rate <1 mL/s), yielding a pseudo-static relationship between p_d and volume. According to the model, an increase in p_d during slow-filling cystometry is determined solely by an increase in V_E, with C_E held constant. The minimum volume that must be withdrawn from the volume to get p_d = 0 yields a V_E that depends on the bladder’s state of filling. It is expected that during a slow filling, both V_E and V_R increase. Thus, the combined increases in V_E and V_R produce the small, nearly linear rise in p_d observed in the p_d vs. volume graph ⁷. However, the effect of the increase in V_E on the graph differs from that of the increase in V_R. The small, sustained positive slope of the p_d vs. volume graph in a slow-filling cystometrogram masks differences between increasing V_E and increasing V_R ⁷. The increase of p_d in a cystometrogram depends on the increase of V_E or the elongated state of SEE, and the increase of V_R depends on the plastic elongated state of the rest length of PCE. The plastic elongated state of the bladder wall expressed in V_R is determined by the combination of the passive elongation of the bladder wall and the degree of active restoration of the plastic elongated state by contractions, stimulated or spontaneous. In particular, V_R is considerably reduced during micturition. Normally, after complete micturition, the bladder’s total residual volume (V_r) is almost zero. Minimal V_r is determined by the sum of the minimal length of SEE and PCE and is limited by the anatomy of the tissue expressed by tissue volume (V_t). Depending on how micturition is terminated, V_r may exceed the anatomical minimum. Except after complete emptying, V_R is always greater than V_r.

1.3. Adaptation of the bladder to various thicknesses, stiffnesses, and plasticities of the bladder wall

The continuous, gradual increase in p_d accompanying a slowly increasing bladder volume is determined by the distinct mechanical properties of V_E and V_R. As V_t remains constant, a gradual increase in bladder volume implies thinning of the bladder wall, with differential consequences for the characteristics of SEE and PCE. In contrast to slow bladder filling, a slow filling of an elastic balloon is followed by a phase of decreasing pressure caused by thinning of the balloon’s elastic wall. By analogy, thinning of the bladder wall would predict a similar phase of decreasing p_d with increasing volume. The observed continuous positive slope of p_d with increasing volume, as described by Equation 1, requires a concomitant increase in σ, even more than proportional to volume. An increase in σ during filling of the bladder causes an elongation of the SEE, accompanied by the thinning of the bladder wall. The elongation of SEE depends on its elastic stiffness, which progressively increases with elongation. This progressive stiffening ensures that bladder wall thinning does not disrupt the upward linear slope of a cystometrogram, unlike in the elastic balloon analogy. Such progressive stiffness of bladder tissue has been experimentally determined ^5,7. This type of progressive stiffness, which compensates for the effect of wall thinning on p_d with increasing volume, can be considered the bladder’s adaptation to maintain a continuous positive slope in a cystometrogram. In vitro studies showed that during slow-filling cystometry, C_E is not a constant ⁸. An increase in V_E implies a longer SEE. If pressure is not reduced by an increase in C_E, due to adaptation to elasticity, a continuous increase of V_E = C_E p_d, results in a continuous increase of p_d. During bladder filling, the threshold for plastic elongation of the bladder wall must also increase to resist increasing p_d, despite thinning of the bladder wall ⁷. This property can be considered an adaptation of the bladder wall’s plasticity to thinning, determining the V_R. The combination of elasticity adaptation and plasticity adaptation reproduces the observed continuous positive slope of the cystometrogram despite thinning of the bladder wall ⁷.  Theoretically, the smaller the V_E/V_R ratio during slow-filling cystometry, the steeper the slope of p_d vs. volume in the cystometrogram ⁷. Damage or loss of one of the two distinguished types of adaptation to thinning of the bladder wall may have different consequences for the course of a cystometrogram or for the ratio of V_E/V_R. The next section describes how spontaneous contractions can cause variations in the V_E/V_R ratio.

2. Spontaneous contractions and micromotions

2.1. Concept of micromotions and spontaneous contractions with and without clinical consequences     

Recordings of p_d during the collection phase show phasic waves, which are superimposed on a steady tonic pressure level ⁹. These pressure waves are spontaneously generated in the bladder under isovolumetric conditions. If the amplitude of the pressure waves is high enough, these transient pressure waves can be clinically associated with urgency or bladder instability, which may even lead to urinary leakage ¹⁰. According to the model in Figure 1, these waves can be attributed to transient increases in V_E. Then, under isovolumetric conditions, these transient increases in V_E can be caused by equal phasic transient decreases in V_R. The spontaneous contraction waves do not involve the entire muscular component of the bladder wall but are generated in specific regions. At the smallest scale, these localized contractions must be ascribed to individual smooth muscle cells. The concept of micromotion (MM) was introduced during the first observations in 1985 of spontaneous small motions distributed within isometric fixed strips of pig bladder ⁹. The clinical relevance of this observation is that such spontaneously generated MMs are not always identified as small waves in force variations across the strip ⁹. Patterns of similarly distributed spontaneous small contractions have been described in bladder tissue of different animals, e.g., in rabbits ¹¹ and guinea pigs ¹². In 1993, it was hypothesized that MM causes sensations of urge that are not associated with phasic increases of p_d ¹³.  In 1996, patterns of spontaneous MM were detected in the bladders of normal human subjects and in women suffering from chronic pelvic pain, including urinary urge ¹⁴. These findings were later discussed from a urological perspective ¹⁵. In the pilot study on women, the lack of coincidence of MM and spontaneous variations in p_d was considered. The results confirmed the hypothesis that MMs are a type of localized spontaneous small-contractile activity that may elicit sensations of urge ^14,15. However, not all observed MMs, while not detected as waves in p_d, are a source of any sensation. These MMs are supposed to be physiologically relevant ³. However, their observation raises concerns about potential pathophysiological consequences for bladder function ¹⁶. Sensory urge, detrusor overactivity, and bladder instability are now considered MM phenomena in the spectrum of spontaneous activity of the bladder ¹⁷. In 2007, MMs were observed in women with and without overactive bladder by means of a non-invasive detection technique based on ultrasound ¹⁸.

2.2. Network of contractile cellular strings

Normally, spontaneous waves in p_d return to the tonic pressure level and are therefore considered completely transient. Similarly, MM observed in pig bladder strips and in the human bladder are typically transient. The effects of local MMs, in terms of changes in size and σ in a region of the bladder wall, must be examined within the network of connected smooth muscle cells. The mechanical properties of the smooth muscle cell ¹⁹ indicate that the model shown in Figure 1, originally applied to the whole bladder, can also be used as elements in a network model of smooth muscle cells to represent the activity of smooth muscle regions. Within a smooth muscle cell, actomyosin strings, as illustrated in Figure 2, are connected to the cell membrane and generate cellular contraction.

Figure 2. Mechanical model of an actomyosin string. Reprinted from van Duyl ³.

In an inactive muscle, the overlapping thin and thick filaments can slide past one another. However, this slippage is resisted by latches between the thin and thick filaments. Sliding of the filaments takes place if the force across the string is higher than a threshold value. Slippage of the filaments of inactive muscle cells exhibits plasticity ²⁰ and can be represented by a PCE in Figure 1, which is used here to represent an actomyosin string. The filaments are elastic, and this elasticity can be represented by SEE. Using a model consisting of a network of interconnected elements in many series arrangements of PCE and SEE, regional microvariations can be expressed as variations in the lengths of the PCEs in the network. Using such a network, the results of localized PCE contractions, as variations of p_d, can be simulated by the distributed elastic elongations of SEEs in the network ²¹. In the bladder wall, each actomyosin string has its own maintained elongated state, fixed by its latches. Each string can be elongated by the tension generated by the elastic elongation of its filaments. The increasing elastic and plastic elongation of each string are related to each other and determine via the network V_E and V_R. In the previous section, it was noted that during slow bladder filling, a particular coupling between increases in V_E and V_R can explain the normally almost linear positive slope of p_d vs. volume ⁷. This coupled increase of  V_E and V_R with increasing volume can be explained by the combination of mechanical properties and states of all interconnected actomyosin strings in the network.

2.3. Synchronization of transient distributed micromotions and detrusor pressure

It has been shown that distributed transient MMs can synchronize ²².  Synchronization of MM eventually may lead to a significant increase in the amplitude of the phasic wave in p_d. Furthermore, it has been observed that transient MMs are not always completely transient. In such cases, local activity may persist, leading to a change in the size of the affected tissue region. In terms of the model, this implies that after a not-completely transient motion in a region of the bladder wall, the plastically elongated state of PCE becomes smaller than before that motion. In an isovolumetric bladder, a small region with a small change in size may contribute a minor increase in p_d, and may be too small to be observed. Addition or synchronization of not-completely transient MMs across different regions of the bladder wall may lead to a significant change in p_d and can be identified by an increase in the tonic pressure component of p_d. Such a spontaneous increase of tonic p_d may cause myogenic sensation of urge or leakage of urine. Not-completely transient contractions may explain the observed effect of bladder wall MM modulation on changes in tonic p_d ²⁴.  Moreover, synchronization of not-completely transient MMs may render the bladder unstable. From this perspective, understanding the conditions that lead to transitions from spontaneously normally completely transient MMs to not-completely transient MMs is clinically relevant. However, these conditions remain unknown ²⁵.

2.4. Physiological and pathophysiological meaning of micromotions

If bladder volume is reduced by a small amount, the incidentally decreased p_d is restored after a short time, possibly to its previous level. This phenomenon is known as pressure recovery. Recovery of pressure can be ascribed to the results of not-completely transient localized contractions or MMs. In other words, the generation of transient MMs and transitions to not-completely transient MMs can restore or compensate for small passive elongations of the bladder wall during the reservoir phase, as observed in the phenomenon of recovery. Small passive regional elongations in the bladder wall can be caused by the surrounding environment, e.g., bodily motions, and may result in small decreases in p_d. Maintenance of a state of p_d adapted to a certain bladder volume despite such elongations in the bladder wall can be understood as a state of equilibrium between small regional passive elongations and small regional active contractions ²⁶. Besides the pathophysiologic meaning of the generation of not-completely transient MMs in relation to urge or instability, spontaneous small contraction activity unrelated to sensations has also been observed. This activity may have a normal physiological meaning in a process of active accommodation of p_d to bladder volume ²⁵.  Hence, MM activity can manifest as a physiological source of accommodation, although it may become a pathophysiological source of urge or bladder instability ²⁵.

2.5. Role of history of elongations and contractions on the mechanical state of the bladder in the collection phase

The elongated state of each actomyosin string in the network of coupled smooth muscle cells depends on its history of passive elongations and active not-completely transient contractions. This makes the passive elongated state of the whole bladder wall in the collection phase dependent on its history of elongations and contractions of the distributed plastic elongated states of the PCEs and of SEEs in the network model. Consequently, the dependence of passive elongations and active contractions on this history makes V_R and V_E of a bladder, and also the V_E/V_R, in principle irreproducible. This means that, in principle, the course of a cystometrogram of an individual is also ambiguous. The lack of reproducibility of cystometrograms due to varying prior histories of elongations and contractions has recently been experimentally demonstrated by Kiem et al. ²⁶.

2.6. Completely transient spontaneous activity has no effect on elastic compliance

The effect of spontaneous contractions on V_E/V_R during outflow from a non-stimulated bladder has been studied in vitro using pig bladders ^3,8,21. Starting from different accommodated levels of p_d, pig bladders in vitro were allowed to empty via a constant flow resistor, driven by elasticity and by spontaneous contractions. The decay of the tonic pressure component during this passive outflow can be fitted by a mono-exponential function ⁸. Decay of tonic p_d during expulsion is ascribed to a gradually decreasing V_E at a rate dV_E/dt. The success of the fit of a mono-exponential function to tonic pressure decay indicates that C_E = V_E/p_d during this pressure decay is constant. Superimposed on the mono-exponential decay of tonic pressure are transient, spontaneously generated pressure waves. As these waves return to the level of mono-exponentially decaying tonic pressure waves, they become completely transient. The transient phasic increase in pressure causes a transient extra outflow. While the mono-exponential decay of tonic pressure can be ascribed to a decrease in V_E with constant C_E, the decrease in V_R can be ascribed to extra outflow caused by spontaneous contraction waves. The experiments showed that outflow from V_R contractions does not affect outflow via the elasticity of V_E and C_E ⁸. Hence, in these experiments, the outflow due to elasticity (dV_E/dt) and the spontaneous contractions (dV_R/dt) are distinct phenomena with different effects on the variation in the V_E/V_R ratio. The experiments have shown that, depending on the history of slow filling and spontaneous contraction activity during slow expulsion of not-stimulated pig bladders in vitro, V_E/V_R and C_E may vary considerably ⁸. These variations have been ascribed to distributed changes in the elongation states of the actomyosin strings in the network, influenced by the history of passive elongations and active contractions ²¹. In this way, the history of elongations and of contractions contributes to the irreproducibility of slow-filling cystometrograms ²⁶.

3. Isovolumetric responses to fast filling of a bladder

3.1. Pressure relaxation and recovery after fast change of bladder volume

The faster a bladder is filled, the steeper the p_d vs. volume graph ⁶. A fast addition of a certain volume to a bladder in the collection phase causes a considerably higher increase of p_d than a slow addition of the same amount. If fast filling is stopped, p_d may decrease to the level attained after slow pseudo-static filling to the same volume. The gradual decrease in tonic p_d after fast filling, while bladder volume remains constant, is called pressure relaxation. The initial rapid increase in pd is attributed to the rapid elastic elongation of SEE. During subsequent pressure relaxation, this elastic elongation is gradually released and transferred to PCE elongation. Elongation of PCE through viscous processes ceases once the threshold for plastic elongation is reached.

3.2. Stepwise cystometry explained with the model

Fast-filling or stepwise cystometry has been proposed as an alternative to slow-filling cystometry to reveal additional parameters derived from relaxation ²⁷. Results of stepwise cystometry, with filling rate of 10 mL/s up to a final pressure of 40 cm H₂O, performed on patients directly after a standard slow-filling cystometry, were compared with results of relaxation studies on human and pig bladder strips in vitro ^4,28. Pressure relaxation ended at a level corresponding to that reached after slow filling to the same volume. The course of the first part of relaxation of p_d after stepwise filling of pig bladders in vitro and of human bladders in situ can be fitted by a mono-exponential function ²⁸. The decay of p_d by relaxation after stepwise filling can be ascribed to a gradually decreasing V_E. The success of the fit of a mono-exponential function to pressure decay indicates that C_E = V_E/p_d during the mono-exponential decay by relaxation is constant and that decrease of V_E and increase of V_R are proportional to decaying part of p_d. Hence, the mono-exponential pressure decay during relaxation, related to the decrease in V_E, is similar to the pressure decay during the experimental passive expulsion via a constant flow resistance of a not-stimulated pig bladder in vitro, described in the previous section ²⁴. In passive expulsion of pig bladders, V_E decreases with outflow dV/dt, whereas during isovolumetric relaxation after stepwise filling, the decrease in V_E equals the increase in V_R. In both cases, decay of tonic pressure is proportional to actual tonic p_d, indicating that the C_E is constant. Under the isovolumetric condition during pressure relaxation, the decrease in V_E in dV_E/dt is equal to the increase in V_R in dV_R/dt. Hence, during isovolumetric relaxation, the following relationship (Equation 2) holds:

 −dV_E/dt = −C_E (dp_d/dt) = dV_R/dt                       (2)

In Section 2.4, it has been noted that during isovolumetric pressure recovery, V_E increases by the same amount as V_R decreases. Then, Equation 2 is valid with V_E = −V_R and dV_E/dt = −dV_R/dt. Given that isovolumetric pressure recovery is associated with a decrease in V_E that compensates for the decrease in V_R driven by contractile activity, the course of pressure recovery may not follow a simple mono-exponential function ²⁹.

4. The preparatory phase to micturition

4.1. Isovolumetric stimulation

When a bladder in situ in the collection phase is neurogenically stimulated while its volume cannot decrease, p_d increases under isovolumetric conditions. Pressure continues to increase until a level is reached that opens the urethra and initiates outflow. The model suggests that the increase in p_d during isovolumetric stimulation is due to an increase in V_E, which compensates for the decrease in V_R by stimulating contraction of the muscular component of the bladder wall. Assuming that the relatively large C_E present during the collection phase is maintained during isovolumetric stimulation implies that, during the rise in p_d, the increase in V_E and the corresponding decrease in V_R just before the onset of outflow are substantial. Outflow via a certain flow resistance of the urethra is proportional to p_d.  At the start of micturition, a certain outflow is driven by the p_d level attained just before the start. If p_d remains constant, determined by constant V_E and C_E, the initial outflow is sustained by continued contraction through a further decrease in V_R, now expressed as F = dV_R/dt. To keep the consideration simple, we assume that during the main part of micturition, the flow resistance of the opened urethra is constant. According to the explanation of isovolumetric pressure development given so far, V_R is expected to be considerably reduced, and V_E increased during the preparatory phase preceding the start of micturition. However, it has been experimentally shown that during the preparatory phase, stimulation of bladder tissue initiates another phenomenon that generates an isovolumetric pressure increase without a large increase in V_E and a large decrease in V_R. This phenomenon, therefore, needs to be considered when explaining the pressure increase during isovolumetric stimulation during the preparatory phase.  

4.2. Decrease of elastic compliance during isovolumetric stimulation

At the end of isovolumetric stimulation during the preparatory phase, the state of the bladder at the start of micturition is determined by a certain volume and p_d, with V = V_E + V_R, V_E/V_R, and C_E. By definition of elastic volume, given in Section 1.1, V_E equals the volume that must be stepwise withdrawn from the volume to attain zero p_d, and this is also applicable during increasing p_d. Thus, the actual value of C_E derived from V_E at each attained level of increasing p_d during isovolumetric stimulation is given by C_E = V_E/p_d. C_E depends on the stiffness of the elasticity of the bladder wall or of SEE.

The elasticity of bladder tissue during the development of increasing tension across a stimulated tissue strip has been studied in pig bladder tissue ³⁰. The quick release of a stimulated, isometrically fixed string, needed to attain zero tension across the strip, has been initiated at different levels of increasing isometric tension. Each downward step in tension is followed by recovery to a certain level. The remarkable and physiologically relevant observation is that, during stimulation, the strip is in the same elastic elongated state at all levels of increasing tension ³⁰. Hence, during stimulation, the elastic elongated state of the strip is independent of the increased isometric level of tension across the strip. This means that during isometric stimulation, the strip’s elasticity becomes stiffer. Translation of this property of stiffer elasticity to a property of  V_E during isovolumetric stimulation means that during the isovolumetric stimulation of the total bladder, V_E does not change while pressure increases. Because of the isovolumetric condition during stimulated pressure increase, neither V_E nor V_R changes. As a consequence of this property, the pressure increase during isovolumetric stimulation of the bladder cannot be ascribed to an increase in V_E with a constant C_E nor to compensation of a decrease in dV_R/dt due to contraction, as proposed in Section 4.1. Instead, the results of the quick-release studies indicate that the isovolumetric increase in p_d must be attributed to an increase in the stiffness of the bladder wall, that is, a decrease in C_E, while V_E remains constant. In other words, during the transition from the collection phase to the micturition phase, via a phase of pressure build-up induced by stimulation, the decrease in C_E must be considered, while V_E is largely maintained. According to this property, during isovolumetric stimulation, V_E maintains a value transferred from the collection phase just preceding the start of stimulation to just before the start of micturition. This means that V_E is a relevant factor that connects the end of the collection phase to the start of the expulsion phase via the isovolumetric neurogenic stimulation phase. Because of the specific properties of the isovolumetric neurogenic stimulation phase, it is meaningful to distinguish this phase, which connects the collection phase to the evacuation phase, as preparatory to micturition. During this preparatory phase, the increasing level of p_d rises to the urethral opening pressure, establishing the initial condition for outflow. This opening pressure is determined by the combination of a specific V_E carried over from the collection phase, and a reduced C_E during stimulation, starting from its value at the end of the collection phase.

4.3. Distinction of a preparatory phase before micturition

During isovolumetric neurogenic stimulation in the preparatory phase, a specific state of the contractile tissue is established by the recruitment of cross-bridges between the filaments of the actomyosin strings within the network of smooth muscle cells ³¹. Recruitment of cross-bridges makes the network of smooth muscle cells stiffer than during the collection phase, when dV_R/dt is limited by the latches between the filaments. The cross-bridges can be stimulated to move, promoting contraction by sliding of the filaments. The process of recruitment of cross-bridges between the sliding filaments needs to be distinguished from the motion of these cross-bridges. The effect of isometric stimulation of bladder strips, causing stiffening of elasticity and maintenance of elastic elongation, has been explained by reference to a model of a network of connected smooth muscle cells ²¹.

At the end of a preparatory phase, when the urethra is opened, a certain state of contractility, constituted by the recruited cross-bridges, the motion of the cross-bridges enables a continued contraction of the actomyosin strings during outflow, which is accompanied by a reduction of V_R and V_E. The higher the urethral opening pressure, which may be elevated in cases of obstructed urethra, the more cross-bridges need to be activated, leading to a decreased C_E.

5. Contractility

5.1. Bladder contraction during micturition

At the end of a preparatory phase, the built-up contractility state enables expulsion, leading to a continuously decreasing total bladder volume during micturition: V(t) = V_E(t) + V_R(t). The state of contractility of a bladder, related to the number of cross-bridges recruited during the preparatory phase, enables the contraction of the muscular component required to open the urethra. In the expulsion phase, the decreasing bladder volume is associated with changes in p_d and is no longer exclusively related to variation in C_E, as during the preparatory phase. Normally, during micturition, outflow (F = dV/dt) is almost constant or maintained within a certain large part of the decreasing volume range ³². To maintain a constant outflow rate within that period, while urethral flow resistance is assumed constant, the level of p_d must be maintained as volume decreases. The maintenance of an almost constant p_d during that period of constant outflow, hence within a certain range of decreasing volume, is a particular manifestation of the contractility property of bladder tissue developed in the preparatory phase. From Equation 1, if p_d remains constant while volume decreases, σ must decrease proportionally with the volume. A decrease in bladder volume during micturition while V_t is constant implies an increase in the thickness of the bladder wall. As explained in Section 1.3, the effect of wall thinning on pressure during the collection phase is compensated by a progressive increase in the stiffness of elasticity, so that p_d remains almost constant over a large range of volume. In other words, to maintain constant pressure during a decrease in volume, accompanied by thickening of the bladder wall, a similar, though reversed, course of decreasing σ needs to be generated by the contraction activity during outflow. The property of adaptation of SEE elasticity and PCE plasticity, which maintains nearly constant pressure over a large range of increasing volume during the collection phase, must be mirrored in the expulsion phase: the reversal of these properties ensures constant pressure as volume decreases. In the final phase of micturition, the outflow decreases and is driven by a lowered p_d, and ends when the urethra blocks outflow or when V = V_r. After micturition, stimulation ceases, and the bladder returns to the initial state of the collection phase. From this point, bladder volume slowly increases physiologically from V_r, with C_E resetting to the low value attained during the preparatory phase, varying during the expulsion phase, and eventually reaching the large value characteristic of the low-pressure–volume relationship in the collection phase, with a certain V_E /V_R.                                                                                

5.2. Velocity of shortening of the bladder wall during micturition

The rate of decrease of volume (−dV/dt) is related to the velocity of shortening of the circumference of the bladder. For a spherical bladder, the following relationship in Equation 3 holds:

F = dV/dt = 4πR² (dR/dt)  = 3V (dl_c/dt/l_c)                     (3)

with l_c = 2πR is the circumference of the bladder. According to van Duyl ³, a certain constant outflow  (F = dV/dt) corresponds to a velocity of shortening of the circumference of a bladder relative to the actual circumference (dl_c/d_t/l_c), and this velocity must increase as the volume decreases. The velocity of shortening of stimulated bladder tissue has been studied in vitro on strips from pig bladders ³³. The velocity of shortening of a strip is proportional to its initial rest length l_R and depends on the tension across the strip. The velocity of shortening (v_max) is maximum at zero tension and decreases with increasing tension. If the strip cannot shorten, as it is isometrically fixed at a certain rest length (l_R), so that v = 0, a certain isometric tension (T_iso) across the strip is generated. The relation between the velocity of shortening and the tension of a stimulated pig bladder strip can be fitted by a hyperbolic function ³³. According to the model shown in Figure 1, shortening of the strip with rest length is caused by PCE shortening. The experiments have shown that the shortening of an activated bladder strip with its rest length is inversely proportional to the level of tension. Evidently, the velocity of activated shortening and the velocity of viscous passive elongation of the length of PCE, as discussed in Section 1.2, are mutually inversely related to tension. The velocity of activated shortening determines the velocity of decrease in V_R, dV_R/dt.  According to Equation 1, maintaining a certain p_d requires a lower σ in the wall when the volume is smaller. A lower volume implies a thicker bladder wall, so that even a lower σ generated by stimulation may cause a higher tension across a circumferential strip as part of the bladder wall. Due to this higher tension for a certain σ, the velocity of shortening of the relative length of circumference of the bladder, which according to Equation 3 needs to increase with decreasing volume, can be realized due to the thickening of the bladder wall. Of course, notwithstanding constant p_d, a varying V_E accompanied by varying C_E during micturition is part of the total outflow. Variation in the thickness of the bladder wall during micturition is not only relevant in the collection phase but also a factor enabling the maintenance of a constant outflow for a certain period at the level of neurogenic stimulation.

5.3. A measure of contractility

In 1978, a contractility parameter was introduced to evaluate possible damaging effects of the fast elongations of the bladder wall during stepwise cystometry, as described in Section 3.2, on the contractile properties of the muscular component ³⁴. The maximum relative velocity of shortening of muscular tissue, max (|dp_d/dt/p_d|), derived from the pressure increase in the human bladder during isovolumetric neurogenic stimulation, i.e., during the preparatory phase of the bladder, was proposed as a measure of contractility ³⁴. The use of this measure of contractility was inspired by the publication of Gordon and Siegman ³⁵, who used the maximum of relative velocity of shortening  of muscular tissue max {dl_R/dt/l_R} as a contractility parameter of a stimulated smooth muscle strip of taenia coli. Provided that the progressively increasing stiffness of SEE with elongation is constant and known, max (dl_R/dt/l_R/_Rl) can be derived from max (|dp_d/dt/p_d |) ³⁴. However, in Section 4.2, it has been concluded that, in contrast to the assumption of constant stiffness during the preparatory phase, the stiffness and elasticity of the bladder wall are not constant but are built up by stimulation.  This makes the preparatory phase inappropriate for deriving the suggested measure of bladder contractility from isovolumetric pressure increase ³⁶.  Nevertheless, a contractility parameter similar to max (|dpd/dt/pd|) derived from the preparatory phase is still used ³⁷.

5.4. Stopping of micturition and consequences for contraction activity

After the introduction of a measure of bladder contractility, clinical interest in quantifying this property increased. Since then, many different parameters and evaluation methods have been proposed to express bladder contractility. In 2004, Griffiths ³⁸ compared five clinical methods and parameters to assess bladder contractility. In his publication, the particular methods based on isovolumetric p_d were recommended for clinical use. An isovolumetric method is known as the stop-flow test. In the stop-flow test, the outflow during micturition is abruptly mechanically stopped by blowing up a balloon in the urethra via a balloon catheter ³⁹. The total increase in p_d after a stop-flow is taken as a measure of the contractility of a particular bladder. McIntosh et al. ⁴⁰ concluded that such a mechanical stop of flow does not inhibit the detrusor contraction. According to the model in Figure 1, at the moment of stop-flow, compensation of ongoing dV_R/dt is taken over from outflow by increasing V_E. Hence, in contrast to the pressure increase in the preparatory phase, the pressure increase during a stop-flow test is caused by an increase in V_E, hence, Equation 2 is applicable. As part of the conclusion that actual contraction does not change during the abrupt stoppage of outflow, it can be assumed that, during this isovolumetric pressure increase, C_E also remains constant (Equation 4):

|dp_d/dt/p_d|  = 1/C_E (|dV_E/dt|) = 1/C_E (|dV_R/dt|)                       (4)

Nevertheless, C_E may still depend on the actual volume at the moment the flow is stopped, as discussed in the previous section.   

5.5. Stop-flow test as a measure of contractility

The properties of pressure increase during a stop-flow test have been studied on stimulated strips of pig bladder ⁴¹. Shortening of the strips during stimulated contraction was halted at different velocities, and the resulting rapid increase in tension across the isometric strips was measured. It has been observed that in the large middle portion of dT/dt vs. T graphs, the value of dT/dt decreases with increasing T, and this portion can be approximated by a straight line. In this linear region, the slope, determined by |dT/dt/T|, is constant. According to Laplace’s law ⁴², the tension per unit circumferential length is T” = pR/2.  Hence, according to Laplace’s law, p_d at a constant volume is proportional to total circumferential tension T’’ per unit circumferential length. Consequently, dp_d/dt/p_d is proportional to dT’/dt/T’. Therefore, in the middle linear portion of the strip graph, where dT/dt vs. T across a strip, the value of  |dT/dt/T| is constant; dp_d/dt/p_d is also constant across the whole bladder. In Equation 4, a constant value of |dp_d/dt/p_d| means that 1/C_E |dV_R/dt| has a certain constant value. As C_E may be assumed to be constant during the isovolumetric pressure increase just after stopping flow, the observed constant value of |dp_d/dt/p_d| within that course of pressure increase implies that the reduction of rest volume |dV_R/dt| is constant. In this phase of isovolumetric pressure increase, where dp_d/dt/p_d is constant, dV_R/dt is compensated by an equal increase in dV_E/dt. Hence, in the stop-flow test, the outflow dV/dt during the micturition phase is replaced by dV_E/dt. This suggests that a stop-flow test should ideally be performed during the part of micturition where dV/dt is approximately constant, as this ensures that the isovolumetric pressure increase corresponds to the linear portion of the dT/dt vs. T graph. In this way, dp_d/dt/p_d is not only constant but also independent of the starting point within this trajectory. 

Equation 4 indicates that in the range of constant dp_d/dt/p_d, with a certain constant C_E,  |dV_R/dt| caused by contraction is constant. At the start of the stop-flow, with C_E assumed constant during the isovolumetric pressure increase, dp_d/dt/p can be interpreted as a measure of dV_R/dt, i.e., the rate of contraction. Therefore, dp_d/dt/p derived from isovolumetric pressure increase after stop-flow—preferably started during the period of nearly constant outflow—can be used as a contractility parameter that reflects the rate of contraction of the V_R, with C_E as the proportionality factor: (dV_R/dt) /(dp_d/dt/p) = C_E. As discussed in Section 5.2, C_E increases as volume decreases during micturition. The rate of dV_R/dt is determined by the velocity of shortening of l_R. Since the shape of V_R follows that of the total bladder, Equation 3 can also be applied to as a spherical volume. Combining Equations 4 with Equation 3 yields Equation 5:

|dV_R/dt| =C_E |dp_d/dt/p_d |=3 V_R |dl_R/dt/l_R|                    (5) 

    Equation (5) relates relates dV_R/dt to dl_R /dt/l_{R ,} with variable V_R as a proportionality factor, or (dV_R/dt)/V_R = 3|dl_R /dt/l_R|. Accordingly:  max{(dl_R/dt/l_R }]=max {C_E/ 3V_R  |dp_d/dt/p_d|} =max {(1/(3V_R)) |dV_R/dt|}. Following the suggestion of Gordon and Siegman ³⁵ to take the value of max (dl_R/dt/l_R) as a measure of contractility, we can derive dl_R/dt/l_R/_Rl as a contractility factor; however, not directly from dp_d/dt/p_d but from the product of dp_d/dt/p_d and variable C_E/3V_R. dp_d/dt/p_d| can still be derived from a stop-flow test, preferably started at a point within the micturition period when outflow is constant, to obtain a measure of contractility. However, this measure must be corrected by the factor C_E/3V_R. In principle, C_E can be estimated during this period by measuring the pressure decrease per unit volume via stepwise withdrawal of volume from the bladder. Hence, to determine a measure of contractility based on the suggestion of Gordon and Siegman ³⁵, the pressure increase during the preparatory phase is not appropriate ³⁴, whereas the derivation of contractility from pressure increase during a stop-flow test in the expulsion phase ⁴³ is more appropriate, though complex.

6. Conclusion

Separation of bladder volume V in an elastic part V_E and a plastic part V_R, both referring to different mechanical properties of bladder tissue and represented by a simple mechanical model, offers a perspective on new  diagnostic criteria for urodynamics. The model can be used to evaluate results of both cystometry and flowmetry and connects the cyclic transitions between the storage and voiding phases of the bladder. During these phases the variable thickness of bladder wall is an important factor in the manifestation of the characteristic elastic, plastic and muscular properties of bladder tissue to normal results in cystometrograms and pressure-flow relations. Elastic compliance C_E is another significant factor connecting the phases of the cycle. The transition from storage phase to voiding phase is mediated by a preparatory phase where under isovolumetric condition contractility of bladder tissue is built up and the high value of elastic compliance in the storage phase decreases. In the then following voiding phase C_E recovers to the high value. The isovolumetric pressure increase during a stop-flow test is more appropriate to derive a figure for the available contractility than pressure increase during the preparatory phase. Volume V_R is determined by the balanced state between passive elongations and active contractions. In particular not completely transient spontaneous contraction activity may change V_R and tonic detrusor pressure.  This makes spontaneous contraction activity or micromotions physiologically significant for adaptation of detrusor pressure to volume and patho-physiologically relevant as it may make detrusor pressure unstable and cause complaints of urge or leakage.  Ratio V_E/V_R expressing the filled state of the bladder and depends on its history of passive elongations and active contractions.