Compliance is a measure of the distensibility of a spherical structure and is determined
by the change in volume for a change in pressure. A simple example is inflation of
a balloon with a known volume and then measuring the change in pressure across the
wall. It may seem surprising that this static property is a key determinant of flow,
which is a dynamic state. The importance of compliance is that the elastic recoil
force created by stretching the walls of vascular structures creates a potential force
that can drive flow when the downstream pressure is lower. Second, compliance is necessary
to allow pulsatile flow through a closed circuit (Fig. 1). Cardiac contractions create a volume wave that moves through the vasculature. The
walls of vessels must be able to stretch in order to transiently take up the volume.
The pressure created by the stretch of vascular walls moves the volume on to the next
vascular segment with a lower pressure. If vascular walls were all very stiff, pressure
generated by a pump at one end would be instantaneously transmitted throughout the
vasculature. The pressure would then be equal at the start and end of the circuit
and there would be no pressure gradient for flow.

Fig. 1. The importance of a compliant region in the circulation. a A bellows trying to pump fluid around a system with stiff pipes and no compliance.
Flow is not possible because pressing on the bellows instantly raises the pressure
everywhere and there is no pressure gradient for flow. b An open compliant region which allows changes in volume for changes in pressure.
Flow can occur and there are pulsations throughout. c The compliant region is much large than in (b). The pulsations are markedly dampened and only produce ripples on the surface of
the compliant region

The sum of compliances in a series is the sum of the compliances of all the parts.
The compliance of small venules and veins is almost 40 times greater than that of
arterial vessels 9], 10] and large veins; capillaries have an even smaller compliance; and the compliance
of the pulmonary arterial and venous compartments is about one-seventh that of the
systemic circulation 11]. Thus, the total compliance of the circulation is dominated by the compliance of
the systemic veins and venules, which contain over 70 % of total blood volume at low
pressure. Because most of the compliance resides in this one region, for a first approximation
the circulation can be considered as having one compliance lumped in the veins and
venules. This simplification creates an approximate 10 % error in the prediction of
changes in flow with changes in volume but it makes the mathematics much simpler.
The implications of this simplification will be discussed later. Of note, if the question
is what determines arterial pulse pressure rather than cardiac output, the small arterial
compliance is the key value to consider and total vascular compliance is not important.

As already discussed, when the vasculature is filled with a normal blood volume but
there is no flow, the vasculature still has a pressure and this pressure is the same
in all compartments of the circulation. It is called mean circulatory filling pressure
(MCFP) and is determined by the total stressed volume in the circulation and the sum
of the compliances of all regions, including the pulmonary and cardiac compartments
12]. By reducing the volume in the right heart and lowering diastolic pressure, the beating
heart allows the elastic recoil pressure in veins and venules to drain back to the
heart. The heart thus acts in a “permissive” role by allowing the recoil force that
is already present in the veins and venules to act. The heart also has a “restorative”
role in that it puts the blood that drained from the veins and venules back into the
systemic compartment. With each beat in the steady state, a stroke return is removed
from the vena cava to refill the right ventricle and an equal amount of volume is
added back to the arterial side as stroke volume. On the venous side stroke return
can continue during the whole cycle because atria take up volume even when the ventricles
are injecting, but on the arterial side the stroke volume only occurs during systole.
The stroke volume is all the volume that moves through the system on each beat.

Some argue that instead of the heart merely being permissive and just allowing venous
recoil, flow through the circulation occurs because the volume pumped out by the heart
creates an increase in arterial pressure that drives the flow through the system and
even determines the right atrial pressure 13], 14]. However, this type of reasoning ignores a number of issues. Flow occurs from areas
of high pressure to areas of lower pressure. The flow back to the heart occurs from
the upstream veins and venules. The pressure in this region is determined by the volume
these vessels contain and the compliance of their walls. As already noted this region
contains the bulk of circulating volume and the heart has little volume that it can
add to the veins and venules and cannot significantly increase the pressure in these
vessels. Thus, the pressure in this region remains relatively constant and flow occurs
by lowering the downstream right atrial pressure through the actions of the right
heart rather than by increasing the upstream pressure. If the heart rate were limited
to one beat per minute, the pressure in the system would equilibrate in all regions
before the next beat. The arterial pulse pressure is created by the single stroke
volume ejected by the heart and the resistance to its drainage from the arterial compartment
and the volume remaining in the aorta at the end of diastole. Widely different stroke
volumes can be observed with the same arterial pressure, depending upon the arterial
resistance. For example, in sepsis the cardiac output is high and blood pressure is
low. During exercise cardiac output can increase more than fivefold with little change
in mean arterial pressure 15].

A useful analogy for understanding the importance of the large compliance in veins
and venules, and why the pressure produced by the heart is not important for the return
of blood, is that of a bathtub 16]. The rate of emptying of a bathtub is dependent upon the height of water above the
opening at the bottom of the tub. The height of water creates a hydrostatic pressure
due to the mass of the water and the force of gravity on its mass, which pushes the
water through the resistance draining the tub. However, the flow out of the tub is
not affected by the pressure coming out of the tap. The tap can only alter the outflow
from the drain by adding volume and increasing the height of water in the tub. Only
the volume flowing into the tub per minute is important for outflow and not the inflow
pressure. Over short time periods the flow from the tap has very little effect on
the height of water because the surface of the tub is very large compared with the
height of water; that is, the tub is very compliant. The same is true in the circulation.
Arterial pressure flowing into veins and venules does not affect the flow out of the
veins. As in the bathtub, only the liters per minute flowing from the arteries into
the veins affects how the veins and venules empty. Furthermore, a bathtub has an unlimited
upstream source of volume that can be added to it but in the circulation there is
very little other volume that the heart can add to the veins and venules to change
their recoil pressure because they already contain the bulk of vascular volume. To
take the analogy further, if the bathtub is filled to the brim, any additional volume
just flows over the edge of the bathtub and does not change flow out of the drain.
The equivalent of this in the body is what occurs when veins and venules are overfilled,
whether by clinical intervention or retention of volume through renal mechanisms.
The increase in venous pressure increases leakage from the upstream capillaries into
the interstitial space and is like spilling the volume on the floor with only minimal
changes in venous return.

If a sink were considered instead of a bathtub, the inflow from the tap would have
a much greater effect on outflow because the sink is effectively much less compliant
than a bathtub. A much smaller change in volume is needed to increase the height of
water in the sink and therefore the outflow. Later, I will discuss the significance
of having the equivalence of a bathtub and sink in parallel and the potential to change
the distribution of flow going to each of them in what is called the Krogh model,
which was first described in 1912 5].