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Bioinformatics of the Brain

5.5

Brain Modeling

The first stage in modeling brain tumor simulator is to model the brain itself

from medical imaging techniques. Among different medical imaging modality,

Diffusion Tensor MRI (DTI) is widely used in that process as it will provide

sufficient data to model the 3 main components of the brain namely WM, GM

and CSF.

5.5.1

Diffusion Tensor Imaging (DTI)

A magnetic resonance imaging method called diffusion tensor imaging (DTI)

makes it possible to assess the limited diffusion of water in tissue [25–30].

The generalized diffusion tensor in three dimensions is given by a symmetric,

positive definite, second-order 3 × 3 matrix D. D’s three eigenvectors, or ma-

jor coordinate directions, e1, e2, and e3, are orthogonal since it is symmetric

and positive definite. Accordingly, λ1, λ2, and λ3 are the appropriate eigen-

values (diffusion coefficients) for these vectors, such that λ1 > λ2 >= λ3.

The two remaining eigenvectors point in the cross-fiber direction, whereas the

first eigenvector, e1, indicates the major diffusion direction, which is the fiber

direction.

D = EΛE^T = [e1| e2| e3]





λ1

0

0

0

λ2

0

0

0

λ3









e1

e2

e3





(5.20)

DTI data can be described using rotational invariant quantities (Table

5.1, Figure 5.1) such as Mean Diffusivity (MD), Fractional Anisotropy (FA),

Rational Anisotropy (RA), Linear Anisotropy(Cl), Spherical Anisotropy(Cs),

Volume Ratio (VR), Angular Anisotropy (AA), and Diffusion Volume (DV),

Aitchison Anisotropy (Aita), Matusita Anisotropy (MA), and Kullback-

Leibler Anisotropy (KLA).

5.5.2

Brain Model Segmentation

A thorough understanding of the intricate structure of the brain’s constituent

parts as well as the DTI scanner’s operation principle would enable more accu-

rate selection of the appropriate scalar index to best characterize the targeted

tissue in light of its biological properties [31, 32]. These features lead to the

conclusion that WM and GM contain the least water, while CSF contains the

most. Additionally, the way that the water is contained in each of these com-

ponents varies: the water in WM is ordered in axon cells, whereas the water in

CSF is entirely free (isotropic) (extremely limited or highly anisotropic). Un-

like WM and CSF, the organization of GM’s water contents is not as severely

constrained. Based on these facts, rational quantities like the FA, RA, or