Biomedical Engineering Reference
In-Depth Information
19.2 Continuum-Mechanical Modeling of Human Brain Tissue
The continuum-mechanical description of human brain tissue was always an im-
portant task of biomechanical studies. In the context of the hydrocephalus problem,
Hakim and Adams (
1965
) presented an early hypothesis that the occurring effects
can only be described by the interplay of several brain-tissue components. The first
satisfying mathematical approach, assuming the brain as a porous medium contain-
ing a viscous fluid in the extracellular space (ECS), was carried out two decades
later by Nagashima et al. (
1987
) including a simple numerical simulation of a two-
dimensional (2D) slice of the brain. Since then, various singlephasic and biphasic
brain-tissue models (see, e.g., Taylor and Miller,
2004
; Franceschini et al.,
2006
;
Dutta-Roy et al.,
2008
) have been developed treating the hydrocephalus problem.
For the specific application to CED, models have been proposed by, e.g., Smith and
Humphrey (
2007
), Chen and Sarntinoranont (
2007
) or Linninger et al. (
2008
). How-
ever, there are still open questions concerning the coupling effects, the description
of the deformable porous tissue and its entire pore content. To contribute to the solu-
tion of these questions, the present approach is based on the comprehensive Theory
of Porous Media (TPM) in order to describe the multiphasic nature of brain tissue
including the brain solid, the interstitial fluid and the vascular system.
19.2.1 Multiphasic Modeling Based on the TPM
The TPM is a macroscopic continuum theory, which is based on the Theory of Mix-
tures (TM), cf. Bowen (
1976
), combined with the concept of volume fractions. For
more details on its foundation, cf., e.g., Ehlers (
2002
,
2009
) and citations therein.
19.2.1.1 Basic Anatomy of the Human Brain Tissue
To obtain an overview of the modeling problem, the underlying structure of human
brain tissue is briefly summarized. Situated in the rigid scull, the brain is surrounded
by the cerebrospinal fluid (CSF), which is also found in the inner ventricles of the
brain hemispheres. The intracellular space (ICS) of the nervous brain tissue consists
of grey matter at the cerebral cortex (neural cell bodies) and of white-matter tracts
(myelinated axons) in the inner regions. The ECS of the nervous brain tissue is filled
with mobile interstitial fluid. Furthermore, the entire brain is crossed by a highly
branched blood-vessel system.
19.2.1.2 Constituents, Volume Fractions and Densities
In order to enable the numerical simulation of the CED process, a biphasic four-
constituent model is presented in accordance to Wagner and Ehlers (
2010
). The
