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Temesgen M. Kindo
| Speaker: |
Temesgen M. Kindo
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| Date: |
Thursday October 26, 2006
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| Title: |
Mathematical
Models for Mechanical Degradation and Remodelling of Cerebral Arteries
(Master's Thesis Presentation)
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Abstract
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In the
sense of blood vessels, aneurysms are focal dilatations that result
from a local “weakening" of the arterial vessel walls. They can result
from congenital malformations, infections, or hypertension. Rupture is
the ultimate danger of this disease. Rupture can be fatal or disabling.
The size and geometry of the aneurysm have been hypothesized to be
indicators of the danger of rupture.
It is currently believed that aneurysm growth/rupture is governed by
mechanical quantities such as stretch and stress in the arterial
tissue. Elastin and collagen are two constituents of the artery which
are responsible for much of its mechanical properties. Aneurysms are
considered to result from weakening/degradation of elastin. It has been
hypothesized, based on data from real aneurysms, that collagen
“remodels" so as to avoid weakening of the tissue while maintaining a
certain equilibrium value of stretch.
The large deformations involved and the non-linear constitutive
properties of arterial walls call for the use of finite deformation
theories. In addition to the non-linear elasticity equations, evolution
equations governing the remodelling process are involved. Using a
combination of analytical and numerical procedures, we characterized
the cerebral artery and investigated the effect of degradation and
remodelling parameters on the growth and resulting stresses in the
tissue.
In this talk, we will present results for thin-walled spherical and
cylindrical membranes inflated by a quasi-static haemodynamic pressure
and subjected to uniform elastin degradation. A comparison of the
different geometries, material anisotropy conditions, degradation
functions, and remodelling equations will be provided. Finally we
select the model which best fits relevant experimental results. We will
also briefly comment on the finite element simulation of aneurysms.
This work was carried out at Philips Medical Systems (PMS).
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