Towards a Reduced In Silico Model Predicting Biochemical Recurrence After Radiotherapy in Prostate Cancer

Objective: Purposes of this work were i) to develop an in silico model of tumor response to radiotherapy, ii) to perform an exhaustive sensitivity analysis in order to iii) propose a simplified version and iv) to predict biochemical recurrence with both the comprehensive and the reduced model. Methods: A multiscale computational model of tumor response to radiotherapy was developed. It integrated the following radiobiological mechanisms: oxygenation, including hypoxic death; division of tumor cells; VEGF diffusion driving angiogenesis; division of healthy cells and oxygen-dependent response to irradiation, considering, cycle arrest and mitotic catastrophe. A thorough sensitivity analysis using the Morris screening method was performed on 21 prostate computational tissues. Tumor control probability (TCP) curves of the comprehensive model and 15 reduced versions were compared. Logistic regression was performed to predict biochemical recurrence after radiotherapy on 76 localized prostate cancer patients using an output of the comprehensive and the reduced models. Results: No significant difference was found between the TCP curves of the comprehensive and a simplified version which only considered oxygenation, division of tumor cells and their response to irradiation. Biochemical recurrence predictions using the comprehensive and the reduced models improved those made from pre-treatment imaging parameters (AUC = 0.81 $\pm$ 0.02 and 0.82 $\pm$ 0.02 vs. 0.75 $\pm$ 0.03, respectively). Conclusion: A reduced model of tumor response to radiotherapy able to predict biochemical recurrence in prostate cancer was obtained. Significance: This reduced model may be used in the future to optimize personalized fractionation schedules.