Not long ago it was thought that the most important characteristics of the mechanics of soft tissues were their complex mechanical properties: they often exhibit nonlinear, anisotropic, nearly incompressible, viscoelastic behavior over finite strains. Indeed, these properties endow soft tissues with unique structural capabilities that continue to be extremely challenging to quantify via constitutive relations. More recently, however, we have come to appreciate an even more important characteristic of soft tissues, their homeostatic tendency to adapt in response to changes in their mechanical environment. Thus, to understand well the biomechanical properties of a soft tissue, we must not only quantify their structure and function at a given time, we must also quantify how their structure and function change in response to altered stimuli. In this paper, we introduce a new constrained mixture theory model for studying growth and remodeling of soft tissues. The model melds ideas from classical mixture and homogenization theories so as to exploit advantages of each while avoiding particular difficulties. Salient features include the kinetics of the production and removal of individual constituents and recognition that the neighborhood of a material point of each constituent can have a different, evolving natural (i.e. stress-free) configuration.

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The mechanisms by which intracranial aneurysms develop, enlarge, and rupture are unknown, and it remains difficult to collect the longitudinal patient-based information needed to improve our understanding. We submit, therefore, that mathematical models hold promise by allowing us to propose and test competing hypotheses on potential mechanisms of aneurysmal enlargement and to compare predicted outcomes with limited clinical information--in this way, we may begin to narrow the possible mechanisms and thereby focus experimental studies. In this paper, we present a constrained mixture model of evolving thin-walled, fusiform aneurysms and compare multiple competing hypotheses with regard to the production, removal, and alignment of the collagen that provides the structural integrity of the wall. The results show that this type of approach has the capability to infer potential means by which lesions enlarge and whether such changes are likely to produce a stable or unstable process. Such information can better direct the requisite histopathological examinations, particularly on the need to quantify collagen orientations as a function of lesion geometry.

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