Biomedical Engineering Reference
In-Depth Information
We can write
Q
1
and
Q
2
as
Q
1
¼
C
s
dp
1
dt
Q
2
Z
0
Q
p
1
p
Q
1
R
s
C
s
FIGURE 4.38
Nodal analysis of three-element arterial load.
Q
2
¼
p
1
R
s
so
Q
¼
C
s
dp
1
dt
þ
p
1
R
s
From Ohm's law,
p
p
1
¼
QZ
0
Solving the last expression for
p
1
and substituting back into the flow expression:
Q
¼
C
s
d
1
R
s
½
p
QZ
0
dt
½
p
QZ
0
þ
¼
C
s
dp
dt
Z
0
C
s
dQ
R
s
p
Z
0
1
dt
þ
R
s
Q
Grouping terms for
Q
on the left and
p
on the right gives Eq. (4.71).
4.7.3 Heart Mechanics
Mechanical performance of the heart, more specifically the left ventricle, is typically
characterized by estimates of ventricular elastance. The heart is an elastic bag that stiffens
and relaxes with each heartbeat. Elastance is a measure of stiffness, classically defined as
the differential relation between pressure and volume:
E
v
¼
dp
v
dV
v
ð
4
:
72
Þ
Here,
denote ventricular pressure and volume, respectively. For any instant in
time, ventricular elastance
p
v
and
V
v
is the differential change in pressure with respect to volume.
Mathematically, this relation is clear. Measurement of
E
v
E
v
is much less clear.
