Watton, P. N., Hill, N. A. & Heil, M. (2004) A mathematical model for
the growth of the abdominal aortic aneurysm.
Biomechanics and Modeling in Mechanobiology 3
We present the first mathematical model to account for the
evolution of the abdominal aortic aneurysm. The artery is modelled
as a two-layered, 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 are
consistent with those observed in vivo. An asymmetric aneurysm
with spinal contact is also modelled and the stress distributions
are consistent with previous studies.
Page last modified: October 01, 2003
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