A Framework for Soft Tissue Simulations with Application to Modeling Brain Tumor Mass-Effect in 3 D Images

We present a framework for black-box and flexible simulation of soft tissue deformation for medical imaging and surgical planning applications. We use a regular grid 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. When using discretizations that do not conform to the boundary however, it becomes challenging to impose boundary conditions. Moreover, the resulting linear algebraic systems can require excessive memory storage and solution times. 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 also describe an Eulerian formulation to allow for large deformations, with a level-set based approach for evolving fronts. Finally, 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.