Biomedical Engineering Reference
In-Depth Information
=
load control group ( p
0 . 005 and 0 . 003), but also significantly lower compared to
the group clamped at 0.5 N ( p
0 . 020 and 0 . 020). There was no significant differ-
ence between the zero load control group and the 0.5 N-group. When repeated for
more loading levels, these experiments will enable the definition of an unambiguous
relation between mechanical loading and experimental clamping force.
This section showed how the relation between 'macroscopic' mechanical loading
and 'macroscopic' damage can be found experimentally for a specific loading situ-
ation, but is not useful in general. When the boundary conditions of the mechanical
loading change, or when the force is applied in a different location or with a differ-
ent orientation, the connection between this new loading situation and the damage
is still unknown.
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10.4 A Material Model for Arteries
Practical and ethical issues impede the purely experimental characterization of this
generalized relation between mechanical loading and damage and favor the use
of numerical simulations. To this end, a realistic material model for arteries is re-
quired, capable of capturing features such as vasoregulation and damage. This sec-
tion presents a material model suitable to simulate the damage process during the
clamping of an artery.
Through an additive decomposition of the strain energy, the following consti-
tutive model for active healthy and degraded arterial tissue characterizes the prop-
erties of (i) an isotropic matrix material constituent, (ii) an anisotropic constituent
attributed to the dispersed collagen fibers and (iii) an anisotropic smooth muscle
cell constituent. The first two constituents are motivated by the Holzapfel-material
model as proposed in Holzapfel et al. ( 2000 ), whereas the third component is mo-
tivated by the mechanical smooth muscle activation model described by Murtada
et al. ( 2010 ). The damage accumulating in the different constituents during mechan-
ical loading is characterized through a strain-energy-driven damage function for
each individual constituent, motivated by the formulation of Balzani et al. ( 2006 ).
In the remainder of this chapter, the material model will be referred to as the three-
constituent damage model.
10.4.1 Constitutive Equations
Since the tissue is assumed to be nearly incompressible, it is common to additively
decompose the strain-energy function Ψ ,i.e.
Ψ = Ψ vol
+ Ψ dev
= Ψ vol
+ Ψ mat
+ Ψ fib 1
+ Ψ fib 2
+ Ψ smc ,
(10.1)
into a volumetric Ψ vol and a deviatoric Ψ dev part. The latter consists of an iso-
tropic contribution of the matrix material Ψ mat , an anisotropic contribution of two
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