Coupling Tumor Growth with Brain Deformation: A Constrained Parametric Non-Rigid Registration Problem

A novel approach for coupling brain tumor mass effect with a continuous model of cancer progression is proposed. The purpose of the present work is to devise an efficient approximate model for the mechanical interaction of the tumor with its surroundings in order to aid registration of brain tumor images with statistical atlases as well as the generation of atlases of brain tumor disease. To model tumor progression a deterministic reaction-diffusion formalism, which describes the spatio-temporal dynamics of a coarse-grained population density of cancerous cells, is discretized on a regular grid. Tensor information obtained from a probabilistic atlas is used to model the anisotropy of the diffusion of malignant cells within white matter. To account for the expansive nature of the tumor a parametric deformation model is linked to the computed net cell density of cancerous cells. To this end, we formulate a constrained optimization problem using an inhomogeneous regularization that in turn allows for approximating physical properties of brain tissue. The described coupling model can in general be applied to estimate mass effect of non-convex, diffusive as well as multifocal tumors so that no simplification of the growth model has to be stipulated. The present work has to be considered as a proof-of-concept. Visual assessment of the computed results demonstrates the potential of the described method. We conclude that the analogy to the problem formulation in image registration potentially allows for a sensible integration of the described approach into a unified framework of image registration and tumor modeling.