Haemodynamics
Haemodynamics is the study of the relationships between pressure,
resistance and the flow of blood in the cardiovascular system.
Although the properties of this flow are enormously complex, they can largely
be derived from simpler physical laws governing the flow of liquids through
single tubes.
When a fluid is pumped through a closed system, its flow (Q) is
determined by the pressure head developed by the pump (P1–P2
or ΔP), and by the resistance (R) to that flow, according to Darcy’s
law (analogous to Ohm’s law):
Q = P/R or
for the cardiovascular system as a whole: CO = (MABP - CVP)/TPR,
where CO is cardiac output, MABP is mean arterial blood
pressure, TPR is total peripheral resistance and CVP is central
venous pressure. Because CVP is ordinarily close to zero, MABP is
equal to CO × TPR.
Resistance to flow is caused by frictional forces within the fluid, and
depends on the viscosity of the fluid and the dimensions of the tube, as
described by Poiseuille’s law:
resistance = 8VL /πr 4 so that: flow =∆P(πr 4 /8VL).
Here, V is the viscosity of the fluid, L is the tube length
and r is the inner radius (= 1/2 the diameter) of the tube. Because flow
depends on the 4th power of the tube radius in this equation, small changes
in radius have a powerful effect on flow. For example, a 20% decrease in
radius reduces flow by about 60%.
Considering the cardiovascular system as a whole, the different types or
sizes of blood vessels (e.g. arteries, arterioles, capillaries) are arranged
sequentially, or in series. In this case, the resistance of the
entire system is equal to the sum of all the resistances offered by each
type of vessel:
Rtotal = Rarteries + Rarterioles + Rcapillaries
+ Rvenules + Rveins.
Calculations
taking into account the estimated lengths, radii and numbers of the various
sizes of blood vessels show that the arterioles, and to a lesser extent the
capillaries and venules, are primarily responsible for the resistance of the
cardiovascular system to the flow of blood. In other words, Rarteriole
makes the largest contribution to Rtotal. Because according
to Darcy’s law the pressure drop in any section of the system is proportional
to the resistance of that section, the steepest fall
in pressure is in the arterioles (Figure 18.2).
Although the various sizes of blood vessel are arranged in series, each
organ or region of the body is supplied by its own major arteries which emerge
from the aorta. The vascular beds for the various organs are therefore arranged
in parallel with each other. Similarly, the vascular beds within each
organ are mainly arranged into parallel subdivisions (e.g. the arteriolar
resistances Rarteriole are in parallel with each other). For
‘n’ vascular beds arranged in parallel:
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + 1/R4
…1/Rn.
An important consequence of this relationship is that the blood flow to a
particular organ can be altered (by adjustments of the resistances of the
arterioles in that organ) without greatly affecting pressures and flows in the
rest of the system. This can be accomplished, as a consequence of Poiseuille’s
law, by relatively small dilatations or constrictions of the arterioles within
an organ or vascular bed.
Because there are so many small blood vessels (e.g. millions of
arterioles, billions of venules, trillions of capillaries), the overall
cross-sectional area of the vasculature reaches its peak in the
microcirculation. As the velocity of the blood at any level in the system is
equal to the total flow (the cardiac output) divided by the cross-sectional
area at that level, the blood flow is slowest in the capillaries (Figure 18.2),
favouring O2–CO2 exchange and tissue absorption of
nutrients. The capillary transit time at rest is 0.5–2 s.
Blood viscosity
Very viscous fluids like motor oil flow more slowly than less viscous
fluids like water. Viscosity is caused by frictional forces within a
fluid that resist flow. Although the viscosity of plasma is similar to that of
water, the viscosity of blood is normally three to four times that of water,
because of the presence of blood cells, mainly erythrocytes. In anaemia,
where the cell concentration (haematocrit) is low, viscosity and therefore
vascular resistance decrease, and CO rises. Conversely, in the high-haematocrit
condi- tion polycythaemia, vascular resistance and blood pressure are
increased.
Laminar FLow
As liquid flows steadily through a long tube, frictional forces are
exerted by the tube wall. These, in addition to viscous forces within the
liquid, set up a velocity gradient across the tube (Figure 18.1) in which the
fluid adjacent to the wall is motionless, and the flow velocity is greatest at
the centre of the tube. This is termed laminar flow, and occurs in the
microcirculation, except in the smallest capillaries. One consequence of
laminar flow is that erythrocytes tend to move away from the vessel wall and
align themselves edgewise in the flow stream. This reduces the effective
viscosity of the blood in the microcirculation (the Fåhraeus–Lindqvist
effect), helping to minimize resistance.
Wall tension
In addition to the pressure gradient along the length of blood vessels,
there exists a pressure difference across the wall of a blood vessel. This
transmural pressure is equal to the pressure inside the vessel minus the
interstitial pressure. The transmural pressure exerts a circumferential tension
on the wall of the blood vessel that tends to distend it, much as high pressure
within a balloon stretches it. According to the Laplace/Frank law:
wall tension = Pt (r /π),
where Pt is the transmural pressure, r is the
vessel radius and μ is the wall thickness. In the aorta, where Pt
and r are high, athero- sclerosis may cause thinning of the arterial
wall and the development of a bulge or aneurysm (see Chapter 37). This
increases r and decreases μ, setting
up a vicious
cycle of increasing
wall tension reated, may result in vessel rupture.
