A robust framework for soft tissue simulations with application to modeling brain tumor mass effect in 3D MR images

We present a framework for black-box and flexible simulation of soft tissue deformation for medical imaging and surgical planning applications. Our main motivation in the present work is to develop robust algorithms that allow batch processing for registration of brains with tumors to statistical atlases of normal brains and construction of brain tumor atlases. We describe a fully Eulerian formulation able to handle large deformations effortlessly, with a level-set-based approach for evolving fronts. We use a regular grid-fictitious domain method approach, in which we approximate coefficient discontinuities, distributed forces and boundary conditions. This approach circumvents the need for unstructured mesh generation, which is often a bottleneck in the modeling and simulation pipeline. Our framework employs penalty approaches to impose boundary conditions and uses a matrix-free implementation coupled with a multigrid-accelerated Krylov solver. The overall scheme results in a scalable method with minimal storage requirements and optimal algorithmic complexity. We illustrate the potential of our framework to simulate realistic brain tumor mass effects at reduced computational cost, for aiding the registration process towards the construction of brain tumor atlases.