Mathematical Modeling of Persistent Treatment Responses After Cancer Radiotherapy

LaraSchmalenstroer

Group of Bioinformatics and Computational Biophysics, University of Duisburg-Essen

"Mathematical Modeling of Persistent Treatment Responses After Cancer Radiotherapy"

Solid tumors such as pancreatic cancer are major causes of cancer-related deaths worldwide. Despite the availability of multiple treatment options such as radiotherapy or chemotherapy, long-term survival rates of patients with solid tumors remain low due to the development of treatment resistance and tumor recurrence. It has been experimentally observed that irradiation induces shifts in tumor growth kinetics, highlighting the need to unravel both short- and long-term cellular responses to irradiation. Computational models have been used to complement experimental studies by quantifying complex interactions between radiation, tumor biology, and treatment variables. While the common approach of employing the linear-quadratic model and its derivatives by computing the survival fraction is successful in describing short-term effects of radiation on a tumor, it is not suitable for capturing dynamic, persistent, long-term treatment effects. In this study, we developed a phenomenological differential equation-based model that integrates both immediate and delayed radiotherapy effects. A key feature of our model is the inclusion of probabilistic proliferation dynamics. We incorporate cancer cell proliferation rates as the determinant of radiosensitivity, aligning with the well-established hypothesis that highly proliferative cells are more radiosensitive than slower proliferating cells. By using these proliferation rates to determine the rate of cell death after irradiation, the model predicts a heterogeneous cancer cell killing rate, resulting in a variable fraction of surviving cells and a subsequent shift in the composition of the tumor. Thus, the model provides mechanistic insights into relapse dynamics and heterogeneous treatment responses. In the future, we want to extend our model by including immune cell dynamics to investigate the impact of radiation on the tumor microenvironment and the reciprocal interactions between cancer cells and the immune system.
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