tumor interaction biophysical models for medical image registration

State-of-the art algorithms for deformable image registration are based on the minimization of an image similarity functional that is regularized by adding a penalty term on the deformation map. The penalty function typically represents a smoothness regularization. In this article, we use a constrained optimization formulation in which the image similarity functional is coupled to a biophysical model. This formulation is pertinent when the data have been generated by imaging tissue that undergoes deformations due to an actual biophysical phenomenon. Such is the case of coregistering tumor-bearing brain images from the same individual. We present an approximate model that couples tumor growth with the mechanical deformations of the surrounding brain tissue. We consider primary brain tumors—in particular, gliomas. Glioma growth is modeled by a reaction-advection-diffusion PDE, with a two-way coupling with the underlying tissue elastic deformation. Tumor bulk, infiltration, and subsequent mass effects are not regarded separately but are captured by the model itself in the course of its evolution. Our formulation allows for updating the tumor diffusion coefficient following structural displacements caused by tumor growth/infiltration. Our forward problem implementation builds on the PETSc library of Argonne National Laboratory. Our reformulation results in a very small parameter space, and we use the derivative-free optimization library APPSPACK o