Hemodynamics
of
Large Arteries
85
where Taylor expansion is applied to the exponential term. When the
assumption that the peripheral resistance is much larger than the
characteristic impedance of the aorta, or
Rs
>>
Z,,
is also made, then the
effective arterial elastance becomes, again,
Rs
E,
z-
T
(4.1.17)
The effective arterial system elastance obtained in this manner is only
dependent on the peripheral resistance and the cardiac period.
It is
totally independent of the elastic properties of the arterial system.
In terms of ventricular function, a popular index used to describe its
contractility is the maximal elastance (Emax)
of the ventricle. It
is
derived
from the ventricular pressure-volume relation (Suga et al., 1973). In this
context, the ventricle is modeled with a time-varying compliance, C,(t),
the inverse of which is the time-varying elastance, E(t). The concept of
using
Em,,
as
an
"index of cardiac contractility" is more clearly
demonstrated when interventions that alter pumping ability of the heart
are imposed. For instance, with epinephrine infusion, the slope increased
and hence an increase in contractility.
Fig. 4.1.4 gives a schematic
drawing of left ventricular pressure plotted against left ventricular
volume.
The pressure-volume loop, or P-V loop, follows an anti-
clockwise direction. It can be seen that the end-systolic points of the P-V
loops lie on a straight he. This line intercepts the volume axis at
vd.
At
end-systole, the elastance (E(t)) slope is at its maximum and this
defines Emax:
(4.1
.I
8)
where
Em,
is the maximum elastance
of
the ventricle, V,, is the end-
systolic volume and V, is the dead volume, or the volume at which the
