Mathematical Modeling to Simulate the Effect of Adding Radiation Therapy to Immunotherapy and Application to Hepatocellular Carcinoma

Purpose/Objective(s) To develop a comprehensive framework to simulate the response to immune checkpoint inhibitors (ICIs) in combination with radiotherapy (RT) and to apply the framework for investigating ICI-RT combination regimen in hepatocellular carcinoma (HCC) patients. Materials/Methods The mechanistic mathematical model is based on dynamic biological interactions between the immune system and the tumor using input data from patient blood samples and outcomes of clinical trials. The cell compartments are described by ordinary differential equations and represent irradiated and non-irradiated tumor cells and lymphocytes. The effect of ICI is modeled using an immune activation term that is based on tumor size changes observed in a phase 1/2 clinical trial for HCC. Simulated combination regimen are based on ongoing ICI-RT trials. Results The proposed framework successfully describes tumor volume trajectories observed in early-stage clinical trials of durvalumab monotherapy in HCC patients. For ICI-RT treatment regimen the irradiated tumor fraction is the most important parameter for the efficacy. For 90% of the tumor cells being irradiated, adding RT to ICI yields an increase in clinical benefit from 33% to 71% in non-irradiated tumor sites. The model agrees with clinical data showing an association of outcome with initial tumor volume and lymphocyte counts. We demonstrate model application in clinical trial design to predict progression-free survival curves, showing that the cohort size to show significant improvement heavily depends on the irradiated tumor fraction. Conclusion We present a framework extending radiation cell kill models to include circulating lymphocytes and the effect of ICIs and enable simulation of combination strategies. The simulations predict that a significant amount of the benefit from RT in combination with ICI stems from the reduction in irradiated tumor burden and associated immune suppression. This aspect needs to be included in the interpretation of outcomes and the design of novel combination trials.