S 04 03 02 01 0 01 02 03 04

Figure 11.11. (continued) (See the comment in parentheses in Figure 11.10.)

ary effects and more complex patterns of invasion due to the heterogeneous distribution of grey and white matter. We now discuss the model application to the human brain geometry and investigate the implications of heterogeneous diffusion on the spread of an introduced virtual tumour.

A major development which let us apply our model of tumour invasion to the human brain was provided by the BrainWeb database1 (Collins et al. 1998) and EMMA, mentioned above. Briefly, EMMA (Extensible MATLAB Medical Analysis) is a tool for manipulating medical images. The Brain Web database was created using an MRI simulator and defines the locations and distribution of grey and white matter in the brain in three spatial dimensions ona181 x 217 x 181 grid. It was created to visualize frozen images in MATLAB so that they could be manipulated and studied. In this section, we describe some of the numerical simulations of the model system (11.10) and (11.11) presented by Swanson et al. (2000). The results are for two-dimensional slices of the brain for ease of representation. Three-dimensional studies have been carried out and some of these will be discussed below.

Growth and diffusion until t =2.5 with h= 0.01 and y=0 1

1http://www.bic.mcgill.ca/brainweb.

Growth and diffusion until t =3.3333 with h= 0.01 and y =0.1

Growth and diffusion until t =3.3333 with h= 0.01 and y =0.1

■0.3

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