Colloquium

Modelling Abdominal Aortic Aneurysms

Nicholas Hill
University of Glasgow, Scotland, UK
Wednesday, December 5, 2007
Higgins 310, 4 pm

This is the first mathematical model to account for the evolution of the abdominal aortic aneurysm. The artery is treated as a two-layer, cylindrical membrane using nonlinear elasticity and a physiologically realistic constitutive model. It is subject to a constant systolic pressure and a physiological axial prestretch. The development of the aneurysm is assumed to be a consequence of the remodelling of its material constituents. Microstructural recruitment and fibre density variables for the collagen are introduced into the strain energy density functions. This enables the remodelling of collagen to be addressed as the aneurysm enlarges. An axisymmetric aneurysm, with axisymmetric degradation of elastin and linear differential equations for the remodelling of the fibre variables, is simulated numerically. Using physiologically determined parameters to model the abdominal aorta and realistic remodelling rates for its constituents, the predicted dilations of the aneurysm agree with those observed in vivo. An asymmetric aneurysm with spinal contact is also considered, and the stress distributions are consistent with previous studies. Additionally, the dynamic properties of the AAA are calculated for different stages in its development, and the evolution of clinically measurable mechanical properties compare well with published physiological data.

Reference: Watton, P.N., Hill, N.A. & Heil, M. “A mathematical model for the growth of the abdominal aortic aneurysm." Biomechan Model Mechanobiol (2004) 3: 98–113.