I have currently been working on the development of complex mathematical models to predict cancer tumor growth and deformation of surrounding tissue to help brain cancer treatment. We basically utilize linear and finite deformation mechanical theories coupled with mixture theory to accurately capture both mechanical and growth effects. Developing models for such purpose needs the understanding of the biological system and underlying physics. We have been using magnetic resonance imaging to understand the characteristics such as cell proliferation, vessel permeability of the tumors. Quantitative data obtained by the medical imaging is used to calibrate these models. We employ computational methods such as the finite element method to solve the system of partial differential equations resulting from the mathematical modeling of the tumor growth. Currently, my focus is to work on the murine models of glioma and to use the know-how to adapt or improve these models to predict and treat human cancers.
Prediction of a murine glioma growth on a 3D brain model driven by magnetic resonance imaging. Diffusion weighted contrast enhanced images and T2 weighted imaged are used to calibrate model.