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

K.W. Fornalskia, b, J. Reszczyńskaa, c, L. Dobrzyńskia, P. Wysockid, M.K. Janiake aNational Centre for Nuclear Research (NCBJ), A. Sołtana 7, 05-400 Otwock-Świerk, Poland bEx-Polon Lab, Podleśna 81a, 05-552 Łazy, Poland cMedical University of Warsaw (WUM), Department of Biophysics and Human Physiology, Chałubińskiego 5, 02-004 Warszawa, Poland dFaculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warszawa, Poland eMilitary Institute of Hygiene and Epidemiology (WIHE), Kozielska 4, 01-163 Warszawa, Poland

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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.

DOI:10.12693/APhysPolA.138.854 topics: cancer biophysics, Gompertz curve, ionizing radiation, cancer cell dynamics