IMPACT OF PARALLEL HETEROGENEITY ON A CONTINUUM MODEL OF THE PULMONARY ARTERIAL TREE

Model arterial trees were constructed following rules consistent with morphometric data, N-j = (D-j/D-a)(-beta 1) and L(j) = L(a)(D-j/D-a)(beta 2), where N-j, D-j, and L(j) are number, diameter, and length, respectively, of vessels in the jth level; D-a and L(a) 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 D-m = D-a[2/(m + 1)](1/beta 1), such that m - 1 vessels were larger than D-m (vessel length proportional to diameter). Vessels were connected, forming random bifurcating trees. Longitudinal intravascular pressure [P(Q(cum))] with respect to cumulative vascular volume [Q(cum)] was computed for Poiseuille flow. Strahler-ordered tree morphometry yielded estimates of L(a), D-a, beta(1), beta(2), and mean number ratio (B); B is defined by N-k + 1 = B-k, where It is total number of Strahler orders minus Strahler order number. The parameters were used in P(Q(cum)) = Pa [GRAPHICS] and the resulting P(Q(cum)onship was compared with that of the simulated tree, where Pa is total arterial pressure drop, Q is flow rate, R(a) = (128 mu L(a))/(pi D-a(4)) (where mu is blood viscosity), and Q(a) (volume of inlet artery) = 1/4D(a)(2) pi L(a). Results indicate that the equation, originally developed for homogeneous trees (J. Appl. Physiol. 72: 2225-2237, 1992), provided a good approximation to the heterogeneous tree P(Q(cum)).