A model of tumour induced brain deformation as bio-physical prior for non-rigid image registration

The present paper introduces extensions to a novel model of tumour induced brain deformation in order to aid non-rigid registration of images displaying brain tumour pathology to a standard reference atlas. The model serves as a bio-physical prior and by that resolves the inherent irregularities that naturally arise in the considered registration problem. The proposed model is formulated in terms of a constrained optimisation problem. At this, the data term is modelled on the basis of the population density of cancerous cells obtained from the solution of an initial boundary value problem. A soft constraint allows for approximating bio-mechanical properties of brain tissue. It is demonstrated that introducing a non-linear weighting functional with respect to the computed density of cancerous cells into both - the data term and the soft constraint - allows for an adaptive control of the deformation pattern. Additionally, we explicitly penalise deformations of rigid structures and extend the numerical scheme by exploiting analytical derivatives as well as the compact support of the employed parametric deformation model during optimisation. Further, we have made available a strategy for re-orientation of diffusion tensors subject to spatial deformation.