Predicting Combined Radiotherapy-Immunotherapy Outcomes in Murine TNBC via Bayesian Calibration of Biology-Based Ode Models and [89zr]-Cd8 Pet Image

Triple-negative breast cancer (TNBC) is defined by the lack of hormone receptors and HER2 expression, and it is a biologically heterogeneous subtype that often shows limited benefit from single-modality therapies. Experimental studies suggest that radiotherapy can reshape the tumor microenvironment, promote pro-immune processes and potentially increase the effectiveness of immunotherapies. In this context, biology-based mathematical models calibrated to longitudinal measurements can help quantify heterogeneity and support the evaluation of combined treatment strategies. Development of a Bayesian framework for calibration, model selection, and predictive validation of biology-based ordinary differential equation (ODE) models describing tumor-volume dynamics under radiotherapy and immunotherapy, while explicitly quantifying uncertainty associated with model fitting. We apply the framework to radiation-sensitive and radiation-resistant murine TNBC cohorts and assess the impact of incorporating the imaging biomarker [89Zr]-CD8 PET, quantified using the standard uptake value (SUV), into the immunotherapy-effect formulation. Longitudinal tumor-volume data from 56 mice bearing 4T1 (radiation-sensitive) and RR-4T1 (radiation-resistant) tumors were used across control (n = 14), radiotherapy (n = 24), immunotherapy (n = 3), and combined-therapy (n = 15) groups. Post-radiotherapy CD8+ T-cell infiltration was quantified by [89Zr]-CD8 PET/CT, with SUV as the quantitative metric. Candidate ODE models included an intrinsic growth term and treatment-effect terms for radiotherapy and immunotherapy. Parsimonious formulations were identified using the Bayesian Information Criterion (BIC) and BIC weights. Bayesian parameter inference was performed via Markov chain Monte-Carlo (MCMC), yielding credible intervals and posterior predictive bands. Model performance was assessed using posterior concordance correlation coefficient (CCC) and Pearson correlation coefficient (PCC) under combined-therapy prediction and leave-one-out (LOO) validation. The selected model combined logistic growth with a delayed, time-decaying radiotherapy effect and a saturating immunotherapy effect term. When predicting outcomes in the combined-therapy group, posterior-median CCC and PCC were 0.867 and 0.870, respectively. Introducing SUV-dependence in the immunotherapy term led to comparable aggregate performance, with CCC/PCC of 0.880/0.883 under global calibration and 0.829/0.835 under LOO validation, supporting generalization while linking immunotherapy efficacy to a functional readout of the tumor microenvironment. The proposed framework integrates Bayesian calibration, model selection, and predictive validation to quantify uncertainty and capture phenotypic heterogeneity in TNBC response. Incorporating [89Zr]-CD8 PET (SUV) is not primarily aimed at improving overall fit, but at strengthening a biology-based connection between immunotherapy effect and CD8+ infiltration, reinforcing the role of imaging biomarkers in prediction and analysis of combined radiotherapy-immunotherapy regimens.