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

Int J Radiat Oncol Biol Phys. 2022 Mar 15;112(4):1055-1062. doi: 10.1016/j.ijrobp.2021.11.008. Epub 2021 Nov 11.


Purpose: To develop a comprehensive framework to simulate the response to immune checkpoint inhibitors (ICIs) in combination with radiation therapy (RT) and to apply the framework for investigating ICI-RT combination regimen in patients with hepatocellular carcinoma (HCC).

Methods and materials: 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 nonirradiated 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 patients with HCC. 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 nonirradiated 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.

Conclusions: 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.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Carcinoma, Hepatocellular* / radiotherapy
  • Clinical Trials, Phase I as Topic
  • Clinical Trials, Phase II as Topic
  • Humans
  • Immunotherapy / methods
  • Liver Neoplasms* / radiotherapy
  • Models, Theoretical
  • Progression-Free Survival