Modeling of tumor radiotherapy with damage and repair processes

Background: Under irradiation, some cells are damaged permanently and die while some damaged cells can be self-repaired and become normal cells. The same situation happens in tumor radiotherapy. There has been several models to calculate the probability of cell survival after irradiation, and mathematical models for tumor growth to incorporate cell survival probability in radiotherapy. However, there is no detailed study about how both radiation damage process and cell repair process impact outcomes of tumor radiotherapy. This study will focus on impacts of these two processes on tumor radiotherapy. Methods: The study employs mathematical modeling. Based on established mathematical models for tumor growth and irradiation, a functional reaction diffusion system for tumor radiotherapy is proposed. The model has the tumor cell population and damaged tumor cell population, and tracks their movements in the tumor site. The model considers the repair time of damaged tumor cells as a delay parameter. Detailed analysis is conducted while numerical simulations are performed with glioma data. Results: We obtain the radiation threshold which combines the tumor growth rate, the damaged cell death rate, and damaged cell repair rate. The radiation threshold is a decreasing function of radiation dose while the radiation damage rate is a increasing function of radiation dose. The radiation damage rate and repair time determine the outcome of radiotherapy. When the radiation damage rate is greater than the radiation threshold, radiotherapy may destroy the tumor while radiotherapy may control tumor growth and the tumor load decreases as the radiation dose increases when the radiation damage rate is less than the radiation threshold. For both situations, we also observe oscillations of two cell populations occurring from Hopf bifurcations and Turing instability appearing from a large repair time of damaged tumor cells and different cell motilities. Conclusions: The damaged tumor cell repairing process increases the radiation threshold and complicates outcomes of radiotherapy. The medical implication of our results is that radiotherapy may control the tumor growth and the radiation dose can reduce the total tumor load when the damage rate is greater than the radiation threshold, and otherwise, radiotherapy may kill the tumor and the amount of the does not matter.

Discontinuous Galerkin method for a nonlinear age-structured tumor cell population model with proliferating and quiescent phases

We propose a nonlinear age-structured model of tumor cell population with proliferating and quiescent phases. We apply the discontinuous Galerkin (DG) method to study its dynamical behavior. The DG numerical approximation is used for the spatial discretization and then the strong-stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. This paper aims to establish more efficient results in the sense of computational approach and compare these with analogous estimates for Weighted Essentially and Non-Oscillatory (WENO) scheme. Finally, some test examples and numerical simulations are given to illustrate theoretical results and to examine the behavior of the solution.

Modeling of tumor radiotherapy with damage and repair processes

Background: Under irradiation, some cells are damaged permanently and die while some damaged cells can be self-repaired and become normal cells. The same situation happens in tumor radiotherapy. There has been several models to calculate the probability of cell survival after irradiation, and mathematical models for tumor growth to incorporate cell survival probability in radiotherapy. However, there is no detailed study about how both radiation damage process and cell repair process impact outcomes of tumor radiotherapy. This study will focus on impacts of these two processes on tumor radiotherapy.Methods: The study employs mathematical modeling. Based on established mathematical models for tumor growth and irradiation, a functional reaction diffusion system for tumor radiotherapy is proposed. The model has the tumor cell population and damaged tumor cell population, and tracks their movements in the tumor site. The model considers the repair time of damaged tumor cells as a delay parameter. Detailed analysis is conducted while numerical simulations are performed with glioma data.Results: We obtain the radiation threshold which combines the tumor growth rate, the damaged cell death rate, and damaged cell repair rate. The radiation threshold is a decreasing function of radiation dose while the radiation damage rate is a increasing function of radiation dose. The radiation damage rate and repair time determine the outcome of radiotherapy. When the radiation damage rate is greater than the radiation threshold, radiotherapy may destroy the tumor while radiotherapy may control tumor growth and the tumor load decreases as the radiation dose increases when the radiation damage rate is less than the radiation threshold. For both situations, we also observe oscillations of two cell populations occurring from Hopf bifurcations and Turing instability appearing from a large repair time of damaged tumor cells and different cell motilities.Conclusions: The damaged tumor cell repairing process increases the radiation threshold and complicates outcomes of radiotherapy. The medical implication of our results is that radiotherapy may control the tumor growth and the radiation dose can reduce the total tumor load when the damage rate is greater than the radiation threshold, and otherwise, radiotherapy may kill the tumor and the amount of the does not matter.

Modulation of gold nanoparticle mediated radiation dose enhancement through synchronization of breast tumor cell population

Objective: The incorporation of high atomic number materials such as gold nanoparticles (GNPs) into tumor cells is being tested to enhance the local radiotherapy (RT) dose. It is also known that the radiosensitivity of tumor cells depends on the phase of their cell cycle. Triple combination of GNPs, phase of tumor cell population, and RT for improved outcomes in cancer treatment. Methods: We used a double-thymidine block method for synchronization of the tumor cell population. GNPs of diameters 17 and 46 nm were used to capture the size dependent effects. A radiation dose of 2 Gy with 6 MV linear accelerator was used to assess the efficacy of this proposed combined treatment. A triple negative breast cancer cell line, MDA-MB-231 was chosen as the model cell line. Monte Carlo (MC) calculations were done to predict the GNP-mediated cell death using the experimental GNP uptake data. Results: There was a 1.5- and 2- fold increase in uptake of 17 and 46 nm GNPs in the synchronized cell population, respectively. A radiation dose of 2 Gy with clinically relevant 6 MV photons resulted in a 62 and 38 % enhancement in cell death in the synchronized cell population with the incorporation of 17 and 46 nm GNPs, respectively. MC data supported the experimental data, but to a lesser extent. Conclusion: A triple combination of GNPs, cell cycle synchronization, and RT could pave the way to enhance the local radiation dose while minimizing side effects to the surrounding healthy tissue. Advances in knowledge: This is the first study to show that the combined use of GNPs, phase of tumor cell population, and RT could enhance tumor cell death.