Possible Source of the Gompertz Law of Proliferating Cancer Cells: Mechanistic Modeling of Tumor Growth

Induction and proliferation of cancer cells are complex processes whose ab initio mathematical description is virtually impossible. Nevertheless, some integral characteristics such as the Gompertz law, which is generally used to describe cancer development, can result from a simple mathematical consideration of biophysical processes. The simplified response to a single-source lesion created in a cell's DNA consists in the repair of the lesion or induction of a mutation which can lead to neoplastic transformation. This approach makes it possible to propose a single mathematical formula connecting the Gompertz curve with the simplified biophysical characteristics of tumor growth. Such an approach, which merges the process of neoplastic transformation with cancer development, is shown in the present paper based on the relatively simple analytical and Monte-Carlo models. The models operate with a small number of biophysical parameters and account, at least in part, for the mechanisms that operate in an organism exposed to low doses of ionizing radiation.