Mathematical Oncology

Cancer is one of the leading causes of disease-related death worldwide. In recent years, rapid increase in the molecular understanding of cancer has unraveled significant additional complexity of the disease. Although large amounts of data on cancer genetics and molecular characteristics are available and accumulating with increasing speed, adequate interpretation of these data still represents a major bottleneck. This is exactly where mathematics can be applied to oncology: Through mathematical modeling of complex biological processes we are able to gain novel, unprecedented medical insights. The fields of application of mathematical models include the analysis of biological concepts and medical hypotheses about cancer evolution, and the prediction of clinical outcomes using existing clinical and molecular information. On the other hand, the medical applications give rise to mathematical challenges, which can lead to new methods and algorithms in various fields of mathematics, like data analysis, mathematical modeling and machine learning. Therefore, applying mathematics in the field of oncology will facilitate data interpretation and improve our understanding of carcinogenic processes.

We implement mathematical modeling on the example of Lynch syndrome (LS). LS is the most common inherited cancer syndrome and predisposes affected individuals to developing cancer in the large bowel (colorectal cancer) and other organs. LS is reflects general principles of tumorigenesis and tumor immunology beyond the hereditary context in an exemplary manner. We are focusing on three main parts:

• Mathematically modeling the evolution of hereditary tumors to improve the existing prevention strategies
• Elevating tumor immunology to a genome-wide level
• Predicting the efficacy of clinical approaches for diagnostics, prevention and treatment

As the research on the project, my responsibilities included:

• Image analysis of large-scale tumor images
• Data analysis of genetic data
• Development of mathematical models for the description
• Communication with tumor biologists, medical experts, clinicians, and mathematical oncologists