The focus of this study is the development of a statistical modelling procedure for characterising
intra-tumour heterogeneity, motivated by recent clinical literature indicating that a variety
of tumours exhibit a considerable degree of genetic spatial variability. A formal spatial statistical
model has been developed and used to characterise the structural heterogeneity of a
number of supratentorial primitive neuroecto-dermal tumours (PNETs), based on diffusionweighted
magnetic resonance imaging. Particular attention is paid to the spatial dependence
of diffusion close to the tumour boundary, in order to determine whether the data provide
statistical evidence to support the proposition that water diffusivity in the boundary region of
some tumours exhibits a deterministic dependence on distance from the boundary, in excess
of an underlying random 2D spatial heterogeneity in diffusion. Tumour spatial heterogeneity
measures were derived from the diffusion parameter estimates obtained using a Bayesian
spatial random effects model. The analyses were implemented using Markov chain Monte
Carlo (MCMC) simulation. Posterior predictive simulation was used to assess the adequacy
of the statistical model. The main observations are that the previously reported relationship
between diffusion and boundary proximity remains observable and achieves statistical significance
after adjusting for an underlying random 2D spatial heterogeneity in the diffusion
model parameters. A comparison of the magnitude of the boundary-distance effect with the
underlying random 2D boundary heterogeneity suggests that both are important sources of
variation in the vicinity of the boundary. No consistent pattern emerges from a comparison of
the boundary and core spatial heterogeneity, with no indication of a consistently greater level
of heterogeneity in one region compared with the other. The results raise the possibility that
DWI might provide a surrogate marker of intra-tumour genetic regional heterogeneity, which
would provide a powerful tool with applications in both patient management and in cancer
research.