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.
Arteries exhibit a remarkable ability to adapt to sustained alterations in biomechanical loading, probably via mechanisms that are similarly involved in many arterial pathologies and responses to treatment. Of particular note, diverse data suggest that cell and matrix turnover within vasoaltered states enables arteries to adapt to sustained changes in blood flow and pressure. The goal herein is to show explicitly how altered smooth muscle contractility and matrix growth and remodelling work together to adapt the geometry, structure, stiffness and function of a representative basilar artery. Towards this end, we employ a continuum theory of constrained mixtures to model evolving changes in the wall, which depend on both wall shear stress-induced changes in vasoactive molecules (which alter smooth muscle proliferation and synthesis of matrix) and intramural stress-induced changes in growth factors (which alter cell and matrix turnover). Simulations show, for example, that such considerations help explain the different rates of experimentally observed adaptations to increased versus decreased flows as well as differences in rates of change in response to increased flows or pressures.
Cerebral vasospasm is a poorly understood clinical condition that appears to result from complex biochemical and biomechanical processes that manifest as yet another example of vascular growth and remodeling. We submit that mathematical modeling holds great promise to help synthesize diverse types of data and thereby to increase our understanding of vasospasm. Toward this ultimate goal, we present constitutive relations and parametric studies that illustrate the potential utility of a new theoretical framework that combines information on wall mechanics, hemodynamics, and chemical kinetics. In particular, we show that chemical and mechanical mediators of cellular and extracellular matrix turnover can differentially dominate the progression and resolution of vasospasm. Moreover, based on our simulations, endothelial damage can significantly alter the time-course and extent of vasospasm as can impairment of autoregulation. Although the present results are consistent with salient features of clinically reported vasospasm, and thus provide some new insight, we suggest that most importantly they reveal areas of pressing need with regard to the collection of additional experimental data. Without appropriate data, our understanding of cerebral vasospasm will remain incomplete.
Complementary advances in medical imaging, vascular biology and biomechanics promise to enable computational modelling of abdominal aortic aneurysms to play increasingly important roles in clinical decision processes. Using a finite-element-based growth and remodelling model of evolving aneurysm geometry and material properties, we show that regional variations in material anisotropy, stiffness and wall thickness should be expected to arise naturally and thus should be included in analyses of aneurysmal enlargement or wall stress. In addition, by initiating the model from best-fit material parameters estimated for non-aneurysmal aortas from different subjects, we show that the initial state of the aorta may influence strongly the subsequent rate of enlargement, wall thickness, mechanical behaviour and thus stress in the lesion. We submit, therefore, that clinically reliable modelling of the enlargement and overall rupture-potential of aneurysms may require both a better understanding of the mechanobiological processes that govern the evolution of these lesions and new methods of determining the patient-specific state of the pre-aneurysmal aorta (or correlation to currently unaffected portions thereof ) through knowledge of demographics, comorbidities, lifestyle, genetics and future non-invasive or minimally invasive tests.
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