**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**

**In a stable bladder at physiological filling rates (<20 ml min) detrusor pressure rises very little****With fast filling rates of the order of 100 ml min -1 the detrusor pressure often rises to a few tens of cm water and this pressure decays after filling has ceased. This decay is termed accommodation.**

**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 E****0**** which gives the static
time - independent behaviour.**

**The pressure rise at fast filling can be marked - as
much as 50 cm H****2****O. 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.**

**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 F****iso****
and extension. The velocity dependence is described by the relation between F/
F****iso**** and u which follows
approximately the equation for striated muscle (work done by Hill in
1938)**

**Equation 1**

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

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

**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) |

**where**

**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 P****det,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.**

**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.

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

**Passive Urethral resistance relation (PURR).**

**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
p**_{uo}** 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
P**_{ext2}**towards P**_{ext1}**. 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**