In-silico oncology: an approximate model of brain tumor mass effect based on directly manipulated free form deformation

Abstract

The present work introduces a novel method for approximating mass effect of primary brain tumors. The spatio-temporal dynamics of cancerous cells are modeled by means of a deterministic reaction-diffusion equation. Diffusion tensor information obtained from a probabilistic diffusion tensor imaging atlas is incorporated into the model to simulate anisotropic diffusion of cancerous cells. To account for the expansive nature of the tumor, the computed net cell density of malignant cells is linked to a parametric deformation model. This mass effect model is based on the so-called directly manipulated free form deformation. Spatial correspondence between two successive simulation steps is established by tracking landmarks, which are attached to the boundary of the gross tumor volume. The movement of these landmarks is used to compute the new configuration of the control points and, hence, determines the resulting deformation. To prevent a deformation of rigid structures (i.e. the skull), fixed shielding landmarks are introduced. In a refinement step, an adaptive landmark scheme ensures a dense sampling of the tumor isosurface, which in turn allows for an appropriate representation of the tumor shape. The influence of different parameters on the model is demonstrated by a set of simulations. Additionally, simulation results are qualitatively compared to an exemplary set of clinical magnetic resonance images of patients diagnosed with high-grade glioma. Careful visual inspection of the results demonstrates the potential of the implemented model and provides first evidence that the computed approximation of tumor mass effect is sensible. The shape of diffusive brain tumors (glioblastoma multiforme) can be recovered and approximately matches the observations in real clinical data.