Mathematical Medicine and Biology

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The application of mathematics to medicine is an exciting and novel area of research within the discipline of Applied Mathematics. One aspect of this research, in which our department is actively involved, is the creation of mathematical models of various disease processes, taking into account the interactions between the different components of the complex biological system that underlies the process. This research has two main goals.  Firstly, one hopes to increase our understanding of the onset of the disease and of how it progresses. Secondly, one hopes that the mathematical analysis of the available treatment strategies will enable one to identify one that is optimal in each situation.

The research in mathematical medicine, which is carried out in collaboration with physicians at the Hospital for Sick Children and Princess Margaret Hospital in Toronto, includes the following topics:

  • Mathematical modeling of ovarian cancer treatments and the sequencing of surgery and chemotherapy
  • Effects of surgery, radiotherapy, and chemotherapy on the treatment of brain tumours
  • Mathematical modeling of hydrocephalus, syringomyelia, and brain tumours

The research in mathematical medicine is also enhanced by the involvement of our faculty in the Centre for Mathematical Medicine.

Current research in mathematical biology focusses on understanding biological organisms at the cellular level. One aspect of this research pertains to networks of genes and proteins interacting through biochemical reactions.  More specifically, the goal is to elucidate the two main processes that underlie life, namely replication and metabolism. This ambitious program, which relies in part on applying ideas from systems and control theory to molecular biology, is known as systems biology. A second aspect of this research pertains to the behaviour and function of neurons, the building blocks of the central nervous system. The long term goal of this research, which comprises the field of theoretical neuroscience, is to understand how neurons process information, in other words, how the brain coordinates the overall activity of an organism. 

The research in mathematical biology is enhanced by collaborations with researchers in the Department of Biology, and by the involvement of our faculty in the Centre for Theoretical Neuroscience 

The regular faculty whose primary research area is Mathematical Medicine and Biology are: