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Coupling hemodynamics with vessel wall growth and remodeling (G&R) is crucialfor understanding pathology at distal vasculature to study progression ofincurable vascular diseases, such as pulmonary arterial hypertension. Thepresent study is the first modeling attempt that focuses on defininghomeostatic baseline values in distal pulmonary vascular bed via, a so-called,homeostatic optimization. To define the vascular homeostasis and totalhemodynamics in the vascular tree, we consider two time-scales: a cardiac cycleand a longer period of vascular adaptations. An iterative homeostaticoptimization is performed at the slow-time scale and incorporates: an extendedMurray's law, wall metabolic cost function, stress equilibrium, andhemodynamics. The pulmonary arterial network of small vessels is represented bya fractal bifurcating tree. The pulsatile blood flow is described by aWomersley's deformable wall analytical solution. A vessel wall mechanicalresponse is described by the constrained mixture theory for an orthotropicmembrane and then linearized around mean pressure. Wall material parameters arecharacterized by using available porcine pulmonary artery experiments and humandata from literature. Illustrative examples for symmetric and asymmetricfractal trees are presented to provide homeostatic values in normal subjects.We also outline the key ideas for the derivation of a temporal multiscaleformalism to justify the proposed one-way coupled system of governing equationsand identify the inherent assumptions. The developed framework demonstrates apotential for advanced parametric studies and future G&R and hemodynamicsmodeling in pulmonary arterial hypertension.

A Multiscale Framework for Defining Homeostasis in Distal Vascular Trees: Applications to the Pulmonary Circulation