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Bioinformatics of the Brain

FIGURE 5.1

Illustration of some Scalar Indices at an axial slice.

and 2.5 mm, respectively, as is the distance between two consecutive slices.

FA and MD are used to classify brain scan model to WM, GM and CSF.

5.5.3

Finite Element Modeling RDE

The solution to Equation 5.1 can be written in discrete form as follows:

c^t+1 = c^t + dt[∇.(D∇c^t)] + dtR(c)

(5.21)

where dt is the time step and c^t+1 and c^t represents the next and the current

values of the variable respectively. The initial value of R(c) is taken to be

equal zero. The diffusion term can be written as:

∇.(D∇c) =





d11 ^∂2c

∂x^{2 + d22 ∂2c}

∂y^{2 + d33 ∂2c}

∂z^{2 +}

2d12 ^∂2c

∂x∂y ^{+ 2d23 ∂2c}

∂y∂z ^{+ 2d13 ∂2c}

∂x∂z⁺

∂c

∂x



∂d11

∂x ^{+ ∂d21}

∂y ^{+ ∂d31}

∂z



+

∂c

∂y



∂d12

∂x ^{+ ∂d22}

∂y ^{+ ∂d32}

∂z



+

∂c

∂z



∂d13

∂x ^{+ ∂d23}

∂y ^{+ ∂d33}

∂z







(5.22)