Biomedical Engineering Reference
In-Depth Information
In the 1970s Kennish and colleagues tried to estimate the differential relation of Eq. (4.72)
using the ratio of finite changes in ventricular pressure and volume:
E
v
¼
D
p
v
D
V
v
ð
4
:
73
Þ
This approach leads to physically impossible results. For example, before the aortic valve
opens, the left ventricle is generating increasing pressure while there is not yet any change
in volume. The ratio in Eq. (4.73) gives an infinite elastance when the denominator is zero.
Suga and Sagawa [28] used the ratio of pressure to volume itself, rather than differential or
discrete changes, to estimate elastance:
p
v
ð
t
Þ
V
v
ð
t
Þ
V
d
E
v
ð
t
Þ¼
ð
4
:
74
Þ
In this equation,
is a dead volume that remains constant. All the other terms are allowed
to be varying with time. Ventricular elastance measured in this way leads to elastance curves
as depicted in Figure 4.39. These curves show wide variation, as suggested by the large error
bars. The distinctive asymmetric shape leads to a major contradiction. A simple experiment
involves clamping the aorta, thereby preventing the left ventricle from ejecting blood,
denoted an
V
d
isovolumic
beat. Equation (4.74) shows that under isovolumic conditions (
V
v
is
constant) ventricular pressure
). However,
experiments show that isovolumic pressure curves are symmetric, unlike Figure 4.39. A fur-
ther complication is the requirement of ejecting beats for measuring
p
v
must have the same shape as elastance
E
v
(
t
), which requires
not only the heart (a ventricle) but also a circulation (blood vessels). Hence, time-varying
elastance curves such as Figure 4.39 are measures of both a particular heart, the source,
combined with a particular circulation, its load. Experiments show that elastance curves
measured in this way are subject to vascular changes, as well as the desired ventricular prop-
erties. As such, this approach cannot uniquely separate out ventricular from vascular proper-
ties. Consequently, a new measure of the heart's mechanical properties is required.
The problems just described—inconsistent isovolumic and ejecting behavior and combined
heart-blood vessel properties—led to the development of a newmechanical description of the
E
v
(
t
1.0
0.5
0
0
0.5
1.0
1.5
Normalized Time
FIGURE 4.39
Time-varying ventricular elastance curves measured using the definition in Eq. (4.74). Measured
elastance curves exhibit distinctive asymmetry.
Adapted from [28].
