Constrained Mixture Models of Arterial Homeostasis and Adaptation

Abstract

Phenomenological models of the mechanical behavior of the arterial wall continue to play important roles in vascular mechanics. Indeed, such models revealed the importance of residual stresses in homogenizing the transmural distribution of stress in normalcy [1], which in turn led to one of the most important hypotheses in vascular mechanobiology — the existence of a mechanical homeostasis [2]. Nevertheless, classical models are not able to exploit the growing information on the different mechanical properties and rates and extents of turnover of different structurally significant constituents within the arterial wall. To address this need, we have proposed a structurally-motivated, materially nonuniform model of the arterial wall based on a theory of constrained mixtures [cf. 3]. Key features of this model include the ability to prescribe individual stored energy functions for different structurally significant constituents that are constrained to move together within the overall wall while being allowed to possess individual evolving natural (stress-free) configurations, and the ability to prescribe separate stress-mediated constitutive relations for constituent production and removal. We have shown that this constrained mixture approach can capture many salient features of arterial adaptations (e.g., evolving changes in geometry, overall material behavior, and collagen to elastin ratios) to both altered mechanical loading (e.g., altered blood flow and pressure as well as axial stretch) and disease progression (e.g., enlargement of intracranial aneurysms and the development and resolution of cerebral vasospasm). We submit that, in contrast to models built on the assumption of kinematic growth, this constrained mixture approach can incorporate increasingly detailed biological information on cell and matrix turnover and can thereby begin to generate and test novel hypotheses on mechanisms of arterial homeostasis and adaptation. We will show, for example, that the constrained mixture model suggests a possible mechanism for the origin of residual stresses and axial prestretches, the importance of cellular deposition of new extracellular matrix proteins within stressed states, the complementary roles of vasoactivity and matrix remodeling, and stress mediation of matrix turnover [4,5]. We note, in particular, the importance of residual stress and axial prestress in establishing arterial homeostasis and thus targets for subsequent adaptations [5,6].