A new mathematical model for progression of colorectal cancer

Tumorigenesis can be regarded as an evolutionary process, in which the transformation of a normal cell into a tumor cell involves a number of limiting genetic and epigenetic events. To study the progression process, a time scheme has been presented for colorectal cancer through micro-adenoma, small-adenoma, large-adenoma early carcinoma, advanced carcinoma and metastasis processes by an extensive clinical investigation. In addition, a mathematical model has been designed to describe this biological process. It is a challenge to calculate the time required for the first mutation occurs and to determine the influence of tumor size on the mutation rate. In this work we present a general framework to remedy the shortcoming of existing models. By matching the clinical cancer time scheme, we determine the values of a number of parameters, including the selective advantage of cancer cells and initial mutation rate for individual patients. The averaged values of doubling time and selective advantage coefficient generated by our model are consistent with the predictions made by the published models.