Journal of Applied Physiology, Vol 77, Issue 2 660-670, Copyright © 1994 by American Physiological Society
Impact of parallel heterogeneity on a continuum model of the pulmonary arterial tree
G. S. Krenz, J. Lin, C. A. Dawson and J. H. Linehan
Biomedical Engineering Department, Marquette University, Milwaukee 53233.
Model arterial trees were constructed following rules consistent with
morphometric data, Nj = (Dj/Da)-beta 1 and Lj = La(Dj/Da)beta 2, where Nj,
Dj, and Lj are number, diameter, and length, respectively, of vessels in
the jth level; Da and La are diameter and length, respectively, of the
inlet artery, and -beta 1 and beta 2 are power law slopes relating vessel
number and length, respectively, to vessel diameter. Simulated
heterogeneous trees approximating these rules were constructed by assigning
vessel diameters Dm = Da[2/(m + 1)]1/beta 1, such that m-1 vessels were
larger than Dm (vessel length proportional to diameter). Vessels were
connected, forming random bifurcating trees. Longitudinal intravascular
pressure [P(Qcum)] with respect to cumulative vascular volume [Qcum] was
computed for Poiseuille flow. Strahler-ordered tree morphometry yielded
estimates of La, Da, beta 1, beta 2, and mean number ratio (B); B is
defined by Nk + 1 = Bk, where k is total number of Strahler orders minus
Strahler order number. The parameters were used in P(Qcum) = Pa [formula:
see text] and the resulting P(Qcum) relationship was compared with that of
the simulated tree, where Pa is total arterial pressure drop, Q is flow
rate, Ra = (128 microLa)/(pi D4a (where mu is blood viscosity), and Qa
(volume of inlet artery) = 1/4D2a pi La. Results indicate that the
equation, originally developed for homogeneous trees (J. Appl. Physiol. 72:
2225-2237, 1992), provides a good approximation to the heterogeneous tree
P(Qcum).
