Modelling the growth and stabilization of cerebral aneurysms

Watton, P. N. , Ventikos, Y. and Holzapfel, G. A. (2009) Modelling the growth and stabilization of cerebral aneurysms. Mathematical Medicine and Biology, 26(2), pp. 133-164. (doi: 10.1093/imammb/dqp001)

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Experimental and theoretical guidance is needed to understand how the collagen fabric evolves during the development of aneurysms. In this paper, we model the development of an aneurysm as a cylindrical/spherical membrane subject to 1D enlargement; these conceptual models reflect the development of fusiform and saccular cerebral aneurysms. The mechanical response is attributed to the elastin and collagen. We introduce variables which define the elastin and collagen fibre concentration; these evolve to simulate growth/atrophy of the constituents. A hypothetical aneurysm model is analysed: collagen stretch is constant, elastin degrades and collagen fibre concentration can adapt to maintain mechanical equilibrium. An analytic expression for the rate of evolution of the fibre concentration is derived. The functional form is dependent on (i) the current collagen fibre concentration, (ii) the deviations in the collagen fibre stretch from the attachment stretch, (iii) the rate of change of fibre stretch, (iv) the rate of loss of elastin and (v) the ratio of load borne by elastinous and collagenous constituents. Finally, numerical examples of aneurysm development are considered. Suitable candidates for the fibre concentration evolution equations are identified that yield stabilization of the aneurysm even when there is complete loss of elastin. This theoretical analysis provides the basis for the development of physiologically realistic models of aneurysm development.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Holzapfel, Professor Gerhard and Watton, Dr Paul
Authors: Watton, P. N., Ventikos, Y., and Holzapfel, G. A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematical Medicine and Biology
Publisher:Oxford University Press
ISSN (Online):1477-8602
Published Online:20 February 2009

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