206
Dynamics
of
the Vascular System
7.3.
Pulse Transmission and Modeling Aspects
7.3,
I
Pressure and
Flow
Waveforms in Arterioles and Capillaries
Pulses, originating at the left ventricle, are modified as they propagate
toward the periphery. This is attributed to the effects of blood viscosity,
to arterial viscoelasticity resulting in frequency dispersion and selective
attenuation, and to site dependent summation of incident and reflected
pulses. Pulsations, however, persist even in the microcirculation.
Quantification of peripheral resistance has long been an interest to
both researchers and clinicians. Since the largest mean pressure drop
occur in the arteriolar beds.
These latter have been suggested to
contribute mostly to the peripheral resistance.
It has been presumed for decades that flow in the microcirculation,
particularly in the arterioles and capillaries,
is
entirely steady flow.
Consequently, Poiseuille's formula has been applied. Poiseuille in
1841
arrived at an empirical relationship relating pressure drop AP to steady
flow
[Q)
in a cylindrical vessel with diameter
D
and length
1.
Thus, the amount of steady
flow through
a
blood
vessel
is
proportional to the pressure drop and the fourth power of the diameter.
Independently, at about the same time in 1939, Hagen had performed
numerous experiments and, at about the same time, arrived at a similar
expression. This formula was later modified to the presently known
Hagen-Poiseuille equation, or simply, the Poiseuille's law:
-
71r4
Q=-Ap
8771
(7.3.1)
Although credit has been given fully to Poiseuille, it was Hagenbach
(1860)
who came up with an exact relation relating steady flow to the
fluid viscosity
q,
and the pressure gradient,
m4
dp
877
dz
Q
=
(7.3.2)
