Urodynamic Theory of the lower urinary tract.


Experiments with strips of pig bladder have yielded the dependence of force upon extension. It might be thought as a result of the shape of these curves that detrusor pressure would rise in a similar way with volume

however from the diagram below the Laplace equation is derived. It gives the balance of forces. takes geometry into account and because r squared is on the right hand side, detrusor pressure does not in fact rise particularly quickly with volume.

Thus we find that

Fast ( i.e. non-physiological) filling rates have always been used for the past 20 years as a convenience to make investigations possible in a reasonable time. With the recent development of ambulatory urodynamics the bladder is filled naturally and observation 1 has been quite convincingly confirmed.

The behaviour described in the second observation is consistent with a viscoelastic model. A theoretical model for the detrusor has been developed by Coolaset whereby the passive detrusor is modeled by 3 non-linear elastic elements E1-E3 in series with 3 dashpots h1- h3 3. These are in parallel with E0 which gives the static time - independent behaviour.

The pressure rise at fast filling can be marked - as much as 50 cm H2O. This is termed a low compliance bladder - compliance is the change in volume divided by the change in pressure. In ambulatory studies when the flow rate is by renal excretion these pressure rises are not present .

All of the above refers only to the stable bladder. One of the main reasons to perform urodynamics is to test for the unstable bladder (detrusor instability). This is a bladder which has involuntary phasic contraction.
As mentioned previously the bladder may contract involuntarily if the spinal cord is not intact, but Detrusor instability can also occur with no neurological pathology. These contractions can be as large as 200 cm H2O and can cause leakage of urine. They can also have disastrous social implications as the patient may have a urinary frequency of many more than once per hour day and night. Also they carry the risk of ureteric reflux which can lead to hydronephrosis ( destruction of kidney)


Contractile behaviour of Detrusor muscle strips.

During emptying of the bladder (micturition) there is an active contraction of the detrusor. When a muscle contracts actively its mechanical properties undergo a functional change and become quite different from those of the same muscle at rest. The behaviour of striated muscle has been studied extensively. It is often described in terms of a model consisting of 3 elements,

which represent mathematical concepts rather than discrete structures in the muscle.

The contractile element CE is responsible for the functional change. It is under nervous control. At rest it exerts no tension. When stimulated to contract it develops a tension which depends on the speed of shortening as well as the stimulation and the extension. The active tension exerted at zero speed of shortening is called the isometric tension. As speed increases the tension decreases in a characteristic way,

The parallel elastic element PE exerts a tension non-linearly dependent on its extension. The total tension in the muscle is the sum of the contributions from PE and CE. At rest, only the contribution from PE remains. The PE represents the passive mechanical properties of the muscle. The SE is a second non-linear elastic element in series with the CE. Its tension is always equal to the active tension in CE. Whenever the active tension is altered the length of SE alters with the result that sudden changes are smoothed out. But the detrusor is smooth muscle. The mechanical properties of smooth muscle are less well known. One might hope to represent it with the figure above with PE replaced by the viscoelastic properties discussed in the previous section. Fortunately during micturition the passive contribution to the tension is considerably smaller than the active so only CE and SE need be considered. The behaviour of the CE under given stimulation is described by the dependence of the tension F on the extension and speed of shortening u. The extension dependence is completely defined by the relation between Fiso and extension. The velocity dependence is described by the relation between F/ Fiso and u which follows approximately the equation for striated muscle (work done by Hill in 1938)

Equation 1

Where b and a/ Fiso are positive constants independent of extension. The equation is plotted in the figure below.

As u increases F/ Fiso falls monotonically reaching zero when u = bFiso/a. Extension simply shifts the curve to greater values.

Contractile behaviour of the complete bladder. (Bladder Output Relation)

The tension developed in a strip can be related to detrusor pressure by some simple geometry. Thus the above equation can be used to derive the Bladder output relation (BOR).

Bladder output relation (BOR)


B is the velocity parameter b appropriate to a strip equal to the circumference. This is the single most important equation in urodynamics. It is plotted below.

Bladder output relation (BOR)  

The relation predicts that at a given bladder volume the pressure generated by the detrusor depends on the flow rate out of the bladder. It is volume dependent because both Pdet,iso and Q* are. It is an automatic geometrical consequence of the well known relation between force and speed of shortening from muscles. It has a crucial role to play in our understanding of micturition. It tells us that in the presence of obstruction leading to low flow, the normal detrusor will void at high pressure. In the past, the measured high pressures in obstructed patients were erroneously ascribed to detrusor compensation; a belief that as the detrusor was having to work harder to empty it developed greater contractile strength leading to higher pressure. In fact, the obstructed detrusor tends to hypertrophy and has lower strength as the obstruction persists. In confirmation of our hypothesis, experiments have been performed whereby the urethra is instantly obstructed by a constriction, with the detrusor moving instantly to a high pressure low flow pattern. Thus the way is paved to solve a difficult diagnostic problem. Older men may present with poor flow and a history typical of prostatic obstruction. Resection of the prostate on symptoms alone however, may be unhelpful in 25 %. These have an underactive detrusor. Simultaneous detrusor pressure and flow measurement will discriminate.

Hydrodynamics of Micturition.

The pressure-flow relationship during micturition can be understood in terms of 2 equations both of which relate detrusor pressure to flow rate.

The bladder output relation describes how the detrusor muscle reacts to changes in the outlet resistance and has already been covered.


The urethral resistance relation is an attempt to model the hydrodynamic behaviour of the urethra. Initial work on the urethra was based on flow through rigid tubes. This could not have been much more erroneous; as already mentioned the normal urethra is highly distensible and this shows up in its hydrodynamic behaviour. A simplified equation relating detrusor pressure and flow for the normal urethra is

PURR Equation

The factor puo is the pressure required to distend the elastic wall of the urethra to start flow. The other term comes from energy conservation. A is the cross sectional area. Thus the relation between pressure and flow rate depends not only on the geometry of the outlet but also elasticity. The PURR is plotted in the figure below . Dotted lines are the BORs for different detrusor external powers.

Simultaneous solution of passive urethral resistance relation and bladder output relation.

Thus micturition involves the simultaneous solution of the BOR and PURR. As the bladder empties the BOR moves from Pext2towards Pext1. If the urethral resistance is changed - for example by patient voluntarily constricting the urethra, the PURR moves from lower to higher pressure. A real example of this effect is seen in the second left figure below

The effect of changing
detrusor power or
urethral resistance
on the pressure flow plot.
A patient was voiding well,
then asked to voluntarily
interrupt the flow.

The Abrams - Griffiths nomogram
is an empirical approach
to classification of obstruction.
It is the most widely used method.
Schafer has devised an alternative
classification for the pressure
flow plot based on his concept
of the PURR.

BACK to index