Mathematical modeling and analysis of tumor-volume variation during radiotherapy

•We develop a tumor growth dynamical model on oxygenated tumor cells and hypoxic tumor cells with pulsed radiotherapy.•We investigate how the reoxygenation of hypoxic cells and the radiosensitivity influence the effect of tumor radiotherapy.•We simulate the volumetric imaging data from 12 available head-and-neck cancer patients and obtain a good fitting effect.•We investigate the similarities and differences of tumor patients and provide some guidance for personalized treatment. Based on tumor radiobiologic mechanisms, this paper develops a new tumor growth dynamic model with radiotherapy. It investigates how the reoxygenation of hypoxic cells and the radiosensitivity of radiotherpy influence the effect of tumor radiotherapy. The existence of the positive periodic solution, the asymptotic stabilities of the tumor-free equilibrium and the hypoxic tumor cell-free periodic solution and the corresponding sufficient criteria are obtained in this paper. The theoretical results indicate that when the value of the sensitivity coefficient of radiotherapy becomes bigger and the reoxygenation rate of tumor cells becomes higher, the radiotherapy of tumor is more effective. In addition, we apply our model to simulate the volumetric imaging data from 12 available head-and-neck cancer patients treated with an integrated computed tomography/linear accelerator system and obtain a very good fitting effect. Finally, we apply patient specific parameters obtained by simulating clinical data of 12 tumor cases to investigate their individual similarities and differences, so that we can provide some guidance for medical workers to implement personalized treatment strategies for tumor patients.