Mathematical modeling of cancer cell movement through biological fiber networks

Cancer is classified into various stages of malignancy. The highest and most lethal stage is characterized by tumor invasion and  metastasis. There are basically two mechanisms for cancer metastasis, (i) transport of malignant cells through the blood  stream and (ii) active movement of tumor cells into healthy tissue. In this project we are interested in the second mechanism.

 In close collaboration with a biomedical research team in Nijmegen, The Netherlands, we will investigate individual tumor cells and try to understand how they move and how they invade a collagen tissue.  While the colleagues in Nijmegen do experiments on mice skin cancer, we will complement their research through mathematical modeling. Our models will be based on two approaches, (a) individual based models and (b) partial differential equations. Both classes of models have been extensively used for other applications (such as bacterial aggregations or slime model aggregations), and we plan to adapt  these models to cancer invasion. While the experiments are done on skin of mice, the research will have relevance to the understanding  of brain tumor growth (glioma) as well.

 The methods for this research will be based on a solid education in applied mathematics (numerics, dynamical systems, differential equations) and methods from data analysis (inference). We expect that this research can help to predict how a tumor will grow and as a consequence help to design targeted treatment strategies.

Aditya Jain
Faculty Supervisor: 
Dr. Thomas Hillen