Biomedical Engineering Reference
In-Depth Information
permeability. The material modeling is derived from a thermo-mechanical inves-
tigation of the transversely isotropic biphasic mixture body. Thermodynamically
consistent constitutive relations are formulated describing the anisotropic behavior
of both the solid matrix and the fluid flow. In particular, a new description of the
transverse isotropic permeability has been discussed and enhanced with an evolu-
tionary approach for the preferred flow direction caused by the inner remodeling
process.
In the framework of the finite element method, the governing model equations
have been treated within a standard Galerkin procedure. This procedure leads to a
system of algebraic differential equations in time which can be efficiently solved by
an appropriate time integration scheme.
The numerical simulation model reflects the time-evolution of the hepatic vas-
cular remodeling process in response to a focal outflow obstruction as observed by
intravital microscopy. Philosophically speaking, the liver tries to 'escape' the in-
creased sinusoidal pressure, caused by the obstruction, by forming new vascular
structures called sinusoidal canals derived from multiple dilated sinusoids that fol-
low the direction of the highest pressure gradient. Therefore, we hypothesized that
the reorientation of the sinusoidal flow and the remodeling of the sinusoidal struc-
ture depends mainly on the fluid pressure and the fluid pressure gradient caused by
the outflow obstruction. We tested this hypothesis with a numerical simulation and
compared the results to experimental findings.
Due to the incorporated transverse isotropic permeability relation it was possible
to define a remodeling approach that captured the process of re-establishing hepatic
venous drainage via redirection of blood flow and formation of new vascular struc-
tures along fluid flow. It should be pointed out that the proposed model is based on
a phenomenological description and macroscopic observations. Micromechanical
influences are not taken into account at this stage.
In conclusion, we developed a modeling concept that reflects the experimental
observation of the remodeling process. We propose to use this concept for future
modeling steps on our way to simulate the individual response of a patient with focal
outflow obstruction after liver resection. We aim to do so by integrating additional
physiological data.
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326
