Mathematical modeling of malignant ovarian tumors

A. B. Goncharova ; E. P. Kolpak ; M. Yu. Vil ; A. V. Abramova ; E. A. Busko

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 1, pp. 120-134

Résumé

The article explores modeling the development of ovarian cancer, the treatment of this oncologicaldisease in women, the assessment of the time to achieve remission, and the assessment of the time of the onset of relapse. The relevance of the study is that ovarian cancer is one of the most common cancers in women and has the highest mortality rate among all gynecological diseases. Modeling the process of the development of the disease makes it possible to better understand the mechanism of the development of the disease, as well as the time frame of the onset of each stage, as well as the assessment of the survival time. The aim of the work is to develop a model of an ovarian tumor. It is based on a model of competition between two types of cells: epithelial cells (normal cells) and tumor cells (dividing cells). The mathematical interpretation of the competition model is the Cauchy problem for a system of ordinary differential equations. Treatment is seen as the direct destruction of tumor cells by drugs. The behavior of solutions in the vicinity of stationary points is investigated by the eigenvalues of the Jacobi matrix of the right side of the equations. On the basis of this model, the distribution of conditional patients by four stages of the disease is proposed. Biochemical processes that stimulate the accelerated growth of the tumor cell population are modeled by a factor that allows tumor cells to gain an advantage in a competitive relationship with epithelial cells. The spatio-temporal dynamics of an ovarian tumor leads to a modification of the competition model due to the introduction of additional factors into it, taking into account the presence of increased nutrition of ovarian tumors, the exit of the tumor from the plane of the ovary, as well as the effect of treatment on tumor cells. The new model describes the interaction conditions with a system of second-order partial differential equations. The results of computer modeling demonstrate an assessment of the distribution of conditional patients by stages of the disease, the time of onset of relapse, the duration of remission, the obtained theoretical results of modeling are compared with the real data.

Détail

Keywords: mathematical modeling, treatment model, malignant tumor of the ovary, reproductive system.