An efficient, variational non-parametric model of tumour induced brain deformation to aid non-diffeomorphic image registration

In the present work we propose a novel, efficient strategy for modelling tumour induced brain deformation as a prior for non-rigid image registration in non-diffeomorphic registration problems seen in serial or cross-population brain tumour imaging studies. Here, the presence of pathology dramatically alters the morphological and textural appearance of the anatomical structures under consideration and by that induces changes in topology in the considered images rendering the registration problem non-diffeomorphic. In the present work we extend on a model of tumour induced brain deformation that has been formulated as a parametric optimisation problem and translate it to a non-parametric model, for which efficient solution strategies are available. More precisely, we exploit the fact that diffusive regularisation can efficiently be approximated via successive Gaussian convolution. To generate diffeomorphic deformation patterns, a regridding strategy is employed. The resulting (point-wise) regularity of the mapping allows for accounting for mass preservation during deformation. Numerical experiments demonstrate the flexible control of the deformation pattern. A qualitative comparison to imaging data substantiates the potential of the proposed model. The generic variational framework makes this model generally applicable for an integration into any non-parametric image registration algorithm. The discussed implementation makes it particularly suited for demons-type registration approaches.