Tumor growth modeling via Fokker–Planck equation.

In the present investigation, a stochastic tumor growth model is presented based on the Morse potential. The solution of the Fokker–Planck equation is used to study the growth rate and the geometry of breast cancer with and without radiation therapy effects. In the second case, to estimate unknown parameters of the probability density function, breast data from the Surveillance, Epidemiology, and End Results program and machine learning algorithm are used. By considering three groups of women (35–85 years old), the results show that as time goes on, tumor size increases while its growth rate decreases, and the older women have a slower growth rate. Also, the simulation results of breast tumors of mice confirm that our results are consistent with the experimental evidence in both cases of radiotherapy and no treatment. Finally, the finding of this study implies that the present model is accurate than the Gompertz one in predicting tumor size, in the treatment case. • The time-dependent Fokker–Planck equation is solved for Morse potential. • The PDF of the tumor size is estimated by using experimental data and a machine learning algorithm. • The PDF of the tumor size is used to estimate the breast tumor boundary and its growth rate with and without therapy. • As time goes on, tumor size increases while its growth rate decreases, and older women have a slower growth rate. • The finding of this study implies that the present model is accurate than the Gompertz one in the treatment case. [ABSTRACT FROM AUTHOR]