Biomedical Engineering Reference
In-Depth Information
Figure 2.1a-2 Single-compartment circuit representation. P is pressure; R is resistance; C is vascular compliance; q
1
, q
2
, and q
3
are
blood flow rates; n1, n, nþ1 are compartment indexes; P
bias
, external pressure. From Heldt et al. (2002).
cava are separately identified. The model thus consists of
10 compartments, each of which is represented by a linear
resistance,
R
and a capacitance,
C.
There are many simi-
larities with the PHYSBE system in Chapter 2.2, but the
readerwill findPHYSBE to be amoredetailedmodel of the
cardiovascular system.
Themodel of Heldt et al. is described by 12 differential
equations similar to Eq. (2.1a.13). The authors used an
adaptive step-size fourth-order Runge-Kutta integration
routine to solve the system of differential equations nu-
merically. The results reported by Heldt et al. use in-
tegration steps that range from 6.1
10
4
to 0.01 s with
Figure 2.1a-3 Circuit diagram of the hemodynamic system. lv, left ventricle; a, arterial; up, upper body; kid, kidney; sp, splanchnic; ll, lower
limbs; ab, abdominal vena cava; inf, inferior vena cava; sup, superior vena cava; rv, right ventricle; p, pulmonary; pa, pulmonary artery;
pv, pulmonary vein; ro, right ventricular outflow; lo, left ventricular outflow; th, thoracic; bias, as defined in
Fig. 2.1a-2
. From Heldt et al. (2002).
