Biomedical Engineering Reference
In-Depth Information
Fig. 1.1.
Representation of the relative importance of various factors in models of the different
hemodynamic scales: ++ indicates primary importance; - indicates secondary or negligible impor-
tance; ?? indicates potential or unclear importance (taken from Creative Commons)
At the largest scales, it has been shown reasonable to model the vascular net-
work analogously to an AC electrical circuit [1], where inductance and resistance
(i.e., impedance) represent inertia and frictional (viscous) losses of the pulsating
blood. Capacitance represents the compliance of the blood vessel walls, which act
analogously via the alternating local storage and release of blood down the vessel.
This latter feature largely determines the wave propagation phenomena - attenua-
tion, dispersion, reflection, etc. - that can be used to infer the functional state of
the vasculature from macroscopic pressure and flow measurements. For estimating
vascular impedance, vessel diameters and lengths are required, but otherwise the
specific shapes and connections of the vessel are largely immaterial, except perhaps
when its effects are modelled via the imposition of correction factors or impedance
mismatches.
1
Blood may be modelled as a Newtonian fluid, perhaps with adjust-
ments to the apparent viscosity based on the vessel sizes included in the circuit.
At the smallest scales, in the arterioles and capillaries where vessel diameters ap-
proach within one or two orders of magnitude of red blood cell (RBC) diameters,
the blood, normally comprising about 40-50 % RBC by volume, may no longer be
treated as a homogeneous, constant-viscosity fluid. Well-known phenomena such
as the development of cell-free layers near the wall (Fahreaus-Lindqvist effect) or
deformation of RBC through capillaries alter not only the apparent viscosity of the
fluid, but arterial transport phenomena in general. Here again the specific shape of
a vessel is relatively unimportant: simple tubes mimicking the lengths, connections
and vessel density per tissue-volume are often adequate domains. As will be dis-
cussed later, at these scales it is no longer appropriate to think of blood as a contin-
1
Even then, reflections arising from the microcirculation tend to dominate over the effects of such
local impedance mismatches.
