Biomedical Engineering Reference
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the removal from the brain of as much diseased tissue as possible and meanwhile
the removal of normal tissue must be minimized and the disruption of important
anatomical structures must be avoided. Therefore, it is crucial to capture the brain
deformation during the neurosurgical interventions on patients by aligning preop-
eratively acquired image data with intraoperative images. To be practical, the brain
deformation simulation has to meet real-time constraints as well as achieve robustness
and high accuracy.
5.2 ANISOTROPIC DIFFUSION SIMULATION IN WHITE
MATTER TRACTOGRAPHY
5.2.1 Background
The solution of the general unsteady-state anisotropic diffusion equation could be
important in the development of improved approaches for the analysis of DT-MRI.
DT-MRI is an extension of conventional MRI with the added capability of measur-
ing the random motion of water molecules in all three dimensions, usually referred
to as diffusion or “Brownian motion.” As water diffusion is influenced by the
microstructure, architecture, and physical properties of tissues, DT-MRI can ren-
der the information about how water diffuses in biological tissues containing a large
number of fibers, like muscles or brain white matter, into intricate three-dimensional
representations of the tissues architecture. Thus, it can be exploited to visualize and
extract information about the brain white matter and nerve fibers by reconstructing
the fiber pathways, which has raised promises for achieving a better comprehension
of the fiber tract anatomy of the human brain. In combination with functional MRI,
it might potentially bring tremendous improvements in deeply understanding the
crucial issue of anatomical connectivity and functional coupling between different
regions of the brain [1-3]. Therefore, the neuroanatomical knowledge on connec-
tivity interpreted from the DT-MRI information has been playing an indispensable
role in neurosurgery planning [4] and in tackling a lot of brain diseases and disor-
ders, such as Alzheimer's disease [5, 6], attention-deficit hyperactivity disorder, and
schizophrenia [7, 8].
It is known that water diffusion is anisotropic in brain white matter. The significant
anisotropy presented in white matter reveals microscopic properties of the anatomy
of the nerve fibers, because water tends to diffuse predominantly along the long axis
of the fibers, because the longitudinally oriented structures, the dense packing of
axons, and the inherent axonal membranes, which are widely assumed to be the main
barrier, hinder water diffusion perpendicular to the fibers [9]. DT-MRI is sensitive
to this structural anisotropy and is able to characterize it by noninvasively quanti-
fying and assessing the self-diffusion of water in vivo. The information concerning
the local orientation of fibers, extracted from the water anisotropic diffusion in white
matter, forms the basis of utilizing DT-MRI to track fiber pathways and build con-
nectivity mapping in vivo. The water diffusion behavior elucidated by the diffusion
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