Abstract:
This study investigated the performance of orthotropic constitutive laws describing
the passive mechanical behaviour of the myocardium. The performance
was validated against simple shear experiments of pig hearts which
were available from earlier studies.
First, a homogeneous deformation model was developed which captured
the main features of the deformation process. This served as the basis for a
comparative study between three phenomenological material laws that had
been published in the literature. Two of these laws exhibited certain limitations
and two further constitutive laws were therefore developed that removed
these limitations. Thus, five material laws were investigated in terms of their
performance to fit the given experimental data by reducing a least-square
objective function between the experimental and model data. Furthermore
the consistency of the material parameters amongst experiments was investigated.
As part of this study, a modified least-squares objective function
was developed that decreased the computational time involved by about two
orders of magnitude with comparable error.
Second, the assumption of a homogeneous deformation of simple shear
was removed and the parameters were estimated using a finite element environment
using an inverse estimation technique and therefore fulfilling the
equations of motion that underpin continuum mechanics. It was found that
the material parameters of all laws were in the same range compared to those
obtained from the homogeneous study. Relaxing the homogeneous assumptions
slightly reduced the objective function error although the computational
time increased by three orders of magnitude.
Third, the experimental protocol of six simple shear modes was supplemented
with three uniaxial deformations modes. The material parameters
for the same constitutive relations were estimated. It was possible to show
that the material parameters that were associated with shear strain were very
similar to those obtained from the simple shear study. The axial material
parameters, however, were considerably different.
Finally, since it is recognised that phenomenological material laws do
not provide insight into the underlying micro-structural mechanisms, the
framework for a multi-scale constitutive relation was developed. This is
based on multi-scale images of rat myocardium.