Biomedical Engineering Reference
In-Depth Information
Fig. 20.2
Macro (liver, lobes and segments), meso (lobule) and micro (microcirculation in sinu-
soids) structure of the liver
in soft tissues is mathematically defined as the increase of mass via an increase of
cells and/or via a synthesis of an extracellular matrix (ECM), whereas remodeling is
characterized by a change in structure that is achieved by reorganizing existing con-
stituents. As pointed out by Garikipati et al. (
2006
), remodeling and growth can be
separated although they appear simultaneously in biological tissue. In this contribu-
tion we focus on remodeling the inner structure instead of the growth phenomenon
as done by Epstein and Maugin (
2000
), Ambrosi and Mollica (
2002
), Kuhl and
Steinmann (
2003
), Kuhl et al. (
2003
) regarding one phasic approaches, or Klisch
et al. (
2001
), Humphrey and Rajagopal (
2002
), Guillou and Ogden (
2006
), Ehlers
et al. (
2003
), Garikipati et al. (
2004
), or Ricken et al. (
2007
) for multiphase models.
The first descriptions of remodeling are given by Lee (
1969
) and Cowin and
Hegedus (
1976
) in the context of plasticity. A general study of biological remodel-
ing is given in Garikipati et al. (
2006
) where both evolution of the reference config-
uration and the concept of internal variables is investigated. In the present study, the
latter concept has been used by integrating a preferred flow direction into the model.
Mechanical impact often influences the inner structures of biological tissues as,
e.g., the remodeling of collagen fiber in arterial walls is considered stress driven
where the fiber orientation follows the direction of principle stresses, see, e.g., Hari-
ton et al. (
2007
). Gleason et al. (
2004
) suggested that carotid arteries be modeled as
a flow-induced mixture in order to describe alterations in geometry, structure, and
properties.
The simulation was based on the concept of mechanical-induced remodeling
from Humphrey et al. (
2009
). The fluid is incorporated directly into the model as
a solid-fluid mixture. We hypothesized that the reorientation of the sinusoidal flow
and the remodeling of the sinusoidal structure depends mainly on the fluid pressure
and the fluid pressure gradient caused by the outflow obstruction, see Dahmen et al.
(
2007
) and Dirsch et al. (
2008
).
We tested this hypothesis with a numerical simulation and compared the results
to the experimental findings. As we did not implement liver resection in the math-
ematical model presented here, but concentrated on focal outflow obstruction only,
liver growth (
=
regeneration) was not addressed.
