Advances in saccular aneurysm biomechanics : enlargement via rate-sensitive inelastic growth, bio-mathematical stages of aneurysm disease, and initiation profiles.

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2016-12

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I have created the first simulation of saccular aneurysm initiation and development from a healthy artery geometry. It is capable of growing saccular aneurysm geometries from patient-specific data. My model describes aneurysm behavior in a way that bridges fields. I assume arteries are made of a rate-sensitive inelastic material which produces irreversible deformation when it is overstressed. The material is assumed to consist of a 3D hyperelastic background material embedded with 1D transversely-isotropic fibers. I optionally use a Winkler foundation term to model support of external organs and distinguish healthy tissue from diseased tissue. Lesions are defined as a local degradation of artery wall structure. My work suggests passive mechanisms of growth are insufficient for predicting saccular aneurysms. Furthermore, I identify a new concept of stages of aneurysm disease. The stages connect mathematical descriptions of the simulation with clinically-relevant changes in the modeled aneurysm. They provide an evocative framework through which clinical descriptions of arteries can be neatly matched with mathematical features of the model. The framework gives a common language of concepts---e.g., collagen fiber, pseudoelastic limit, inelastic strain, and subclinical lesion---through which researchers in different fields, with different terminologies, can engage in an ongoing dialog: under the model, questions in medicine can be translated into equivalent questions in mathematics. A new stage of “subclinical lesion” has been identified, with a suggested direction for future biomechanics research into early detection and treatment of aneurysms. This stage defines a preclinical aneurysm-producing lesion which occurs before any artery dilatation. It is a stage of aneurysm development involving microstructural changes in artery wall makeup. Under the model, this stage can be identified by its reduced strength: its structural support is still within normal limits, but presumably would perform more poorly in ex vivo failure testing than healthy tissue from the same individual. I encourage clinicians and biomechanicians to measure elastin degradation, and to build detailed multiscale models of elastin degradation profiles as functions of aging and tortuosity; and similarly for basal tone. I hope such measurements will to lead to early detection and treatment of aneurysms. I give specific suggestions of biological tissue experiments to be performed for improving and reinforming constitutive modeling techniques.

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