Page 114 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

PHYSICAL AND FLOW PROPERTIES OF BLOOD 91

FIGURE 3.18 Lumped-parameter electrical model of a multicompartment arterial segment.

For a system of vessels attached in series (or small units of a nonuniform vessel) a more complicated
scheme, composed of a series of compartments whose characteristics are represented by R , C , and
i
i
L (Fig. 3.18), is used. For this case, Kirchhoff’s law applied to each loop will yield
i
dQ
P − P i−1 = R Q + L i (3.50)
i
i
i
dt
V
P = i (3.51)
i
C
i
dV
Q − Q i−1 = i (3.52)
i
dt
The problem is reduced to a set of linear differential equations and can be solved for given bound-
ary conditions. The RCL characteristics of a given problem may be derived from the known physi-
cal properties of blood and blood vessels (Dinnar, 1981; Van der Twell, 1957). This compartmental
approach allowed for computer simulations of complex arterial circuits with clinical applications
(McMahon et al., 1971; Clark et al., 1980; Barnea et al., 1990; Olansen et al., 2000; Westerhof and
Stergiopulos, 2000; Ripplinger et al., 2001).
ACKNOWLEDGMENT
The authors are thankful to Dr. Uri Zaretsky for his technical assistance.

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