Mathematical modelling of cell population dynamics in the colonic crypt with application to colorectal cancer - Johnston, M (2008)
Colorectal cancer has the third highest mortality and incidence rates of all cancers worldwide, but the prognosis for long-term survival is good if diagnosed early. It is a well-characterised disease, and is initiated in colonic crypts which line the colon wall. The aim of this thesis is to use mathematical modelling to describe the heavily regulated cell renewal cycle in the crypt to determine the key features of the system kinetics, and help to explain the initiation of tumourigenesis. The dynamics of a single colorectal crypt is considered using a compartmental approach, which accounts for populations of stem, transit-amplifying and fullydifferentiated cells. A number of different model formulations are derived, and their validity and suitability are discussed. Two mechanisms are presented that could regulate the growth of cell numbers and maintain homeostasis (equilibrium), and it is illustrated how a model can describe both regulated and unregulated growth, with cancer-driving cells deriving from stem and/or transit cells. This model is used to explain the long lag phases observed in carcinogenesis, which occur between periods of rapid tumour expansion, before unlimited growth in cell numbers ensues. Significantly, it is found that, contrary to general belief, the proportion of cancer-driving cells in the exponential growth phase of a tumour may vary depending on tumour type. The process of cells accumulating mutations is also examined by considering both a stochastic individual cell-based model and an analytic approach. Finally, an ordinary differential equation model is shown to be valid by considering a simplified description of a one-dimensional spatial model, and the latter is used to consider the effect of changing the crypt shape. The suitability of this modelling approach to tracking stem cells in a niche, as well as mutant cell clones as they propagate in the crypt, is also discussed.