Modelling of cancer treatment
Improved treatment of cancer is one of the most important challenges for medical science. Tailoring treatment for individual patients has long been an objective for oncologists. While many biological techniques and mathematical models have been devised to predict the course of treatment, none have applied routinely to clinical oncology. Our model, which describes the complexities of the responses of tumor cells over time to both anticancer drugs and radiation, has considerable impact on our ability to advance individualization of cancer therapy. This process is in advanced stages of implementation. Over the last few years, we have developed sophisticated mathematical equations describing the behavior of cancer cells as they progress through the cell division cycle. Which stage in the cycle the cells are actually in, can be differentiated by their DNA content and this enables model outcomes to be compared directly to experimental results. These equations describe the response of human tumors to chemotherapy and radiotherapy. Firstly we propose a model of the cell-cycle which gives rise to challenges in the non-local calculus involved. We then incorporate programmed cell death (apoptosis) into the model. Then we introducer perturbations of model parameters by treatment and compare model results with data. This research will provide significant new analytical and computational insights into the area of non-local equations, where cause and effect are separated in space and time, as well as underpinning support to oncologists concerned with treatment, as well as drug companies producing drugs and management of clinics.
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