Mathematical Model Combined with Microdosimetric Kinetic Model for Tumor Volume Calculation in Stereotactic Body Radiation Therapy

Abstract

Purpose: We proposed a new mathematical model that combines an ordinary differential equation (ODE) and microdosimetric kinetic model (MKM) to predict the tumor-cell lethal effect of Stereotactic body radiation therapy (SBRT) applied to non-small cell lung cancer (NSCLC). Methods: The tumor growth volume was calculated by the ODE in the multi-component mathematical model (MCM) for the cell lines NSCLC A549 and NCI-H460 (H460). The prescription doses 48 Gy/4 fr and 54 Gy/3 fr were used in the SBRT, and the effect of the SBRT on tumor cells was evaluated by the MKM. We also evaluated the effects of (i) linear quadratic model (LQM) and the MKM, (ii) varying the ratio of active and quiescent tumors for the total tumor volume, and (iii) the length of the dose-delivery time per fractionated dose (tinter) on the initial tumor volume. We used the ratio of the tumor volume at 1 day after the end of irradiation to the tumor volume before irradiation to define the radiation effectiveness value (REV). Results: The combination MKM compared to the MCM and LQM resulted in a significant decrease in REVs at 48 Gy/4 fr. The ratio of active tumors and the prolonging of tinter affected the decrease in the REV for A549 and H460 cells. Conclusions: We evaluated the tumor volume considering a large fractionated dose and the dose-delivery time by combining the MKM with a mathematical model of tumor growth using an ODE in lung SBRT for NSCLC A549 and H460 cells.