210
Dynamics
of
the Vascular System
Li et al. (1980) first provided analytical expressions to predict pulse
wave velocity and attenuation in the microcirculation. Linearized pulse
transmission
theory was utilized.
Subsequently, the same group
computed the pulse transmission from the
left
ventricle to the human
index finger vessel (Salotto et al., 1986 Fig. 7.3.1). Their computation
was based on Westerhof
s
viscoelastic tube theory, with complex elastic
modulus.
The results show wave velocity of a few centimeters per second and
attenuation of about 30 percent at
I
Hz in large arterioles.
With
increasing frequencies, the attenuation become substantial and pulse
transmission is greatly reduced
at
10
Hz.
These are shown in
Fig.
7.3.2
and Fig. 7.3.3. This explains in parts why the observed pressure and
flow waveforms, though pulsatile, are becoming more sinusoidal in the
microcirculation.
A
wave speed of 7.2 cm/s in the capillary with an exponential
attenuation of 83%/cm was calculated by Car0 et al. (1978). Estimated
phase velocity from Intaglietta et a1.k (1971) data would give 7-10 cm/s,
in general agreement. They also gave an analytical expression for the
propagation speed in the case of a sinusoidal pulse propagating through
an elastic vessel, assuming blood is Newtonian:
(7.3.4)
where d is capillary diameter and
D
is the distensibility. Since blood
viscosity appears to decrease when measured in capillary tubes of
decreasing diameter, blood, in fact, is non-Newtonian. This is known as
the Fahraeus-Lindqvist effect.
7.3.3 Modeling Aspects of the Microcirculation
Modeling of any microvascular bed is a challenge, particularly when
validation of predicted phenomena is necessary.
A
complete study
requires not only the stringent measurement techniques, but also the
understanding of the complexity of the underlying system properties.
