132
Dynamics
of
the Vascular System
The amount
of
outflow is equivalent to the pressure drop from the
arterial side
(P)
to the venous side
(P,)
due to the peripheral resistance,
Rs
At
steady flow and assume that P, is small, we obtain
a
familiar
expression for estimating the peripheral resistance, and with the total
inflow,
Q=Qi,
R,=
P/
Q
(4.5.50)
or mean arterial pressure to mean arterial flow.
The storage property can
be described by the use
of
arterial
compliance, which expresses the amount
of
change in blood volume
(dV) due to
a
change in distending pressure (dP) in the artery. In this
case, we have
c
=
dVfdP
(4.5.51)
The amount
of
blood flow stored, or
Q,,
due to arterial compliance, is
related to the rate of change in pressure distending the artery,
Qs
=
C
dP/dt
(4.5.52)
Substituting this equation and (3-2) into (3-1), we obtain from
Qi
=
Qs
+
Qo
(4.5.53)
an expression relating the arterial pressure to flow incorporating the
two
windkessel parameters,
C
and
R,:
Q
(t)
=
C
dP/dt
+
P/R,
(4.5.54)
In other words, the total arterial inflow
is
the sum
of
the flow stored and
the flow going into the periphery.