2.5. Computation of tissue probability maps

Bayes' theorem was used to calculate the posterior probability P(C_i|X) of each voxel intensity X, belonging to tissue class C_i where i∈{1, …,7} using,

where P(C_i) is the a priori probability of a voxel intensity X, belonging to tissue class C_i, and p(X|C_i) is the probability of tissue class C_i for a specific value of X. In this study, X = (x₁, x₂, x₃, x₄) is a feature vector comprising the four mMRI intensities (i.e. p, q, T2n & PDn, see red rectangle in Fig. 3a). The a priori probabilities were calculated from the 4D tissue PDDs as follows,

Illustration of the method for computation of tissue-type maps. (a) Data acquisition included T1w, T2w and PDw, FLAIR and diffusion tensor images (from which isotropic p and anisotropic q maps were computed). All acquired images were co-registered and resliced to the DTI space. (b) p, q, T2-weighted and PD-weighted images (red box) were used to compute voxelwise tissue probability maps by application of Bayesian statistics and tissue-type prior probability density distributions. Tissue probability maps were computed for grey matter, white matter, cerebrospinal fluid (CSF), vasogenic oedema, low-grade tissue, high-grade tissue and necrosis. (c) p, FLAIR and PD-weighted images (yellow box) were used to compute the superpixel map. The superpixel spatial resolution was chosen to identify major tissue boundaries. (d) Mean tissue probabilities were calculated within each superpixel and were used to identify high-grade tumour tissue (i.e. p(GIV)) shown in red, low-grade core or tumour infiltrated tissue (i.e. p(GII)) in green, and necrotic tissue (p(Ne)) in blue. (e) The composite RGB tissue-type colour map generated by the images illustrated in (d) is shown overlaid on the FLAIR image and provides a visual tissue-type assessment for all superpixels that contain abnormal tissue (i.e. p(VO) + p(GII) + p(GIV) + p(Ne) > 0.5). Red regions correspond to high-grade tissue, green regions to low-grade or tumour infiltrated tissue, blue regions to necrotic tissue and black regions to vasogenic oedema. A colour wheel showing all possible tissue-type colours is illustrated in Fig. 4.

Tissue probability maps (Fig. 3b) were computed for all tumour patients on a voxel-wise basis using the data from the four image modalities.