Multiscale biomechanical modeling of arterial networks

Cardiovascular diseases are the leading cause of death all around the world. With the expansion of our understanding in biomedical sciences, a variety of factors associated with the onset and progression of such diseases have been identified. In particular, mechanical stresses such as wall shear stress and circumferential stress have been proven to be primary factors for the mechanobilogy, and their homeostatic conditions are regarded as a bridge between biomechanics and cardiovascular biology. The study of vascular growth and remodeling (G&R) is a field that exploits computational modeling to study the changes in mechanical structure and function of blood vessels in response to altered stimuli. During the past decade, vascular G&R modeling has made significant contributions to the field of biomedical engineering through all areas of cardiovascular research. However, the previous modeling has mostly been devoted to arteries, and few studies developed vascular G&R models of the microvasculature. Additionally, other remaining tasks for the modeling include: 1) consolidation of different physical models and taking into account their interactions (e.g., fluid-solid-interactions, fluid-solid-growth) and multiscale levels in space and time and 2) realization of the modeling for the clinical practice. To this end, we developed a novel computational framework that incorporates biofluid and biosolid mechanics of arterial networks in physiological conditions and expanded it to model different vascular adaptation processes. This framework integrated essential features from a constrained mixture model of G&R and blood circulation with an extension of Murray's law to construct a spatially multiscale vascular tree. We formulated the framework as a cost optimization problem where the design of the vasculature was governed by minimization of the metabolic dissipation under mechanical equilibrium as a constraint. Subsequently, we presented two implementations of the model to study two multiscale problems: pulmonary arterial hypertension (PAH) and coronary flow regulation. In the case of PAH, we used the framework to estimate the homeostatic characteristics of the arterial tree as well as their hemodynamics. The results showed good agreement with the available experimental data in the pulmonary arterial vasculature. Furthermore, we used Womersley's analytical solution combined with the theory of small-on-large in finite elasticity to simulate the pulsatile hemodynamics in the pulmonary arterial tree. This study lays the groundwork for further temporally multiscale studies of PAH where long-term G&R in the vasculature (days to weeks) are coupled with short-term hemodynamics (cardiac cycle) in a fluid-solid-growth modeling (FSG) framework. In the case of coronary network, the baseline properties of two myocardial arterial trees distal to left anterior descending coronary artery were established using the presented method. Consequently, three different coronary flow regulation mechanisms (flow-induced, myogenic, and metabolic) were implemented using the constrained mixture models of small arteries and arterioles. The model was then calibrated against the experimental autoregulatory pressure-flow relations. Moreover, the prediction capability of the model was evaluated by simulations of exogenous adenosine infusion and inhibition of nitric oxide synthesis. In closing, the developed framework exhibited great promise for applications in the study of vascular adaptations in physiological and pathophysiological conditions. Particularly, after the homeostatic baseline of an arterial tree is established, the kinetics of production and removal of constituents from stress-mediated G&R models can be used to simulate the short- and long-term evolution of vascular tissues in disease conditions. Furthermore, this research will set the cornerstone for much needed in-silico experiments on palliative or curative managements of vascular diseases.