Ali Mahdipour Shirayeh
Applied Mathematics, University of Waterloo
Evolutionary Dynamics of Cancer: Spatial and Heterogeneous Effects
Despite significant advances in the study of cancer and associated combination therapeutic treatments, cancer still remains one of the most common and complex often-terminal diseases. Acquisition of high–throughput experimental data from diverse cellular perspectives has thrown light on some of the regulatory mechanisms underlying the development of cancer. However, in general there is a lack of a general pattern and coherent model which can explain the development and evolution of the disease. To this end, evolutionary dynamics has been used, as a mathematical tool, in numerous studies to model various aspects of cancer over time periods. Our main focus in this thesis is on the use of stochastic and statistic methods to study cellular interactions within cancer tissues in order to understand the role of spatial structure, heterogeneity, and the microenvironment in cancer development. By constructing multi-cellular structures and using both analytic approach and stochastic simulation, we have investigated the phenotypic hierarchy of stem cells within a heterogeneous system and in the presence of environmentally induced plasticity. Moreover, the effect of a random environment on the development of cancer has been explored in a general framework. As an important application of the multi-stage hierarchical model, the structure of the colonic/intestinal crypt has been taken into account to show the crucial role of these stem cells in the initiation and progression of colorectal/intestinal cancer. From an alternative viewpoint, we have envisaged the hierarchy of mutations as an evolutionary mechanism in the context of acute myeloid leukemia and carried out a statistical analysis of genetic data. Our findings in this manuscript are general and most likely have many implications across a wide array of fields including different blood and solid cancers, bacterial growth, drug resistance and social networks and should have important applications in diverse branches of evolution, ecology, and population genetics.