Key result
Homogeneous tree equations accurately approximate the longitudinal pressure-volume relationship in heterogeneous pulmonary arterial trees.
Why the study?
The applicability of a continuum model equation originally developed for homogeneous pulmonary arterial trees to heterogeneous arterial trees constructed with morphometric data was uncertain.
A continuum model equation developed for homogeneous trees provides a good approximation for longitudinal intravascular pressure in heterogeneous pulmonary arterial trees.
May aid simplified pulmonary vascular modeling; leaves open in vivo validation and clinical translation.
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).
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Krenz et al. (1994) studied this question. Continuum model equation for homogeneous trees vs. Simulated heterogeneous trees was evaluated on Longitudinal intravascular pressure with respect to cumulative vascular volume. An equation originally developed for homogeneous trees provides a good approximation to the longitudinal intravascular pressure-cumulative vascular volume relationship in heterogeneous pulmonary arterial trees.