A mathematical model for the investigation of combined treatment of radiopharmaceutical therapy and PARP inhibitors

Background: Although the combined treatment with radiopharmaceutical therapy (RPT) and poly (ADP-ribose) polymerase inhibitors (PARPi) shows promise, a critical challenge remains in the limited quantitative understanding needed to optimize treatment protocols. This study introduces a mathematical model that quantitatively represents homologous recombination deficiency (HRD) and facilitates patient-specific customization of therapeutic schedules. Methods: The model predicts therapeutic outcomes based on the absorbed dose by DNA and the resulting radiobiological responses, with DNA double-strand breaks (DSBs) being the critical determinant of cancer cell fate. The effect of PARPi is modeled by the accelerated conversion of single-strand breaks (SSBs) to DSBs due to PARP-trapping in the S phase, while HRD is represented by defects in DSB repair in replicated DNA. In vitro experiments are used to calibrate the model parameters and validate the model. In silico tests are designed to extensively investigate various combination protocols including the LuPARP trial. Results: Model calibration was performed using data from the treatment of NCI-H69 cells with [¹⁷⁷Lu]Lu-DOTA-TOC and PARPi. Previously published in vivo studies were integrated into the presented model. Model validation using in vitro data showed deviations within the experimental error margins, with average deviations of 5.3 ± 3.2% without PARPi, 6.1 ± 4.4% with Olaparib, and 12 ± 18% with Rucaparib. Rucaparib radiosensitization reduces number of tumor cells during lutetium therapy by 99.2% and 99.99% (HRD). The highest radiosensitizing effect in vivo and in vitro was observed with Talazoparib (IC50: 4.8 nM), followed by Rucaparib (IC50: 1.4 µM). The model predicts relative tumor shrinkage after 14 days of combination treatment with Olaparib (250 mg) based on patient body weight (e.g. 60 kg: 99.6%; 90 kg: 98.0%). Conclusion: Results demonstrate the potential of this computational model as a step toward the development of the digital twin for systematic exploration and optimization of clinical protocols.