A Theoretical Model of Enlarging Intracranial Fusiform Aneurysms

Abstract

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.

A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms

“…Correlating cell response with, say, the Cauchy stress (cf., for example, Baek et al (2006)) has the advantage that only knowledge of the current deformed state (together with loads and boundary conditions) is required. On the other hand, the use of a strain (deformation) measure requires knowledge of two states, since strain is, by definition, defined as the deformation change between two states.…”

“…Baek et al (2006); Humphrey and Rajagopal (2002); Kroon and Holzapfel (2007a,b); Rachev et al (1996); Ryan and Humphrey (1999); Taber and Humphrey (2001); Watton et al (2004)). In the present paper, we propose a new theoretical model for the growth of human cerebral saccular aneurysms.…”

Initiation of aneurysms as a mechanical bifurcation phenomenon

“…However, how such factors manifest themselves in changing the mechanical behaviour of arteries before aneurysm formation is still not fully understood. Existing studies in the bio-mechanical community have largely focussed on modeling the material properties of mature aneurysm tissues and the growth of aneurysms when they have already formed; see, e.g., Humphrey and Rajagopal [1], Venkatasubramaniam et al [2], Watton et al [3], Baek et al [4,5], Vande Geest et al [6], Vorp [7], Watton and Hill [8], and the references therein. Such studies are obviously important in guiding a clinician when to intervene when an aneurysm has been diagnosed.…”

Preface

“…In the area of biomechanics, Rajagopal has worked on problems in hemodynamics [32][33][34], arterial mechanics [35], and biological growth [36,37]. Rajagopal and co-workers have also devoted considerable attention to electromechanical materials [38][39][40][41], geomaterials [42][43][44][45], and traffic flow [46][47][48].…”