Biomedical Engineering Reference
In-Depth Information
16,17
edema;
this approach continues to appear as the mathematical model of
choice in many cases,
18
in large part because of its linearity, which translates
into computational advantages that are lost when complex constitutive rela-
tionships are modeled.
Very recently, brain deformation modeling has appeared in the context of
image-guided neurosurgery as a vehicle for estimating tissue motion during
surgical intervention.
represented the brain
as a three-compartment system consisting of bone, fluid, and soft tissue where
rigid-body transformations were applied to bone, fluid regions were uncon-
strained, and smooth deformation was applied to the parenchyma. Several
energy models were compared in 2D with data from an epilepsy patient
where preoperative MR and postoperative CT were available for analysis. The
Skrinjar et al.
19, 20
The study by Edwards et al.
21
20
study modeled the brain as a homogeneous linear viscoelastic
medium with finite elements on relatively coarse discretizations of the tissue
continuum (
250 nodes in 2D, 1000 nodes in 3D). Simulations of an artificial
parietal craniotomy were reported in two and three dimensions, illustrating
time sequences of the computed deformation field which showed settling
effects due to gravity that cause not only posterior movements near the cran-
iotomy but also motion in the superior and inferior directions.
The remainder of this chapter focuses on the work of Paulsen and Miga
19,22,23
as representative of the state of the art in biomechanical modeling with finite
elements for intraoperative use during image guidance. These investigators
have developed a 3D computational framework based on consolidation
which exploits high resolution meshes derived from high definition preoper-
ative medical images. Studies of the performance of both the computational
mathematics and the computational physics have been undertaken through
benchmark problem analysis and
experiments in animal and human
brains. As such, this work can be used to illustrate many of the issues associ-
ated with this type of modeling which are generic to the concept of intraop-
erative updating of preoperative images with deformation models driven by
the physical events occurring in the OR. It is worth noting that finite element
models are also being exploited in the more conventional image registration
and segmentation contexts.
in vivo
24,25
15.3
Brain Tissue Model Description
In the neurosurgery setting, consolidation theory represents the brain as a
linearly elastic biphasic medium consisting of a solid matrix with interstitial
fluid saturating the intramatrix spaces. Tissue motion is characterized by an
instantaneous displacement at the site of mechanical loading followed by addi-
tional deformation resulting from hydrodynamic changes from prescribed or
strain-induced pressure gradients in the interstitial fluid. The equations of
motion can be written as coupled partial differential equations (PDEs)
