Abstract:

Immunotherapy has dramatically transformed the cancer treatment landscape largely due to the efficacy of immune checkpoint inhibitors (ICIs). Although ICIs have shown promising results for many patients, they do not exhibit the same level of effectiveness across all cancers and individuals. To determine the critical factors affecting responses to ICIs and hypothesize optimal treatment strategies, we develop mathematical and computational models for in vivo tumor-immune dynamics involving the PD-1/PD-L1 immune checkpoint and ICIs. Our models are the first to incorporate tumor cells of high and low antigenicity and two distinct cytotoxic T lymphocyte (CTL) killing mechanisms, with the preferred mechanism depending on the antigenicity of tumor cells.

We leverage the predicative power of ordinary differential equations (ODEs) and agent-based models (ABMs). Continuous ODEs allow rapid simulations at a realistic scale but cannot describe the spatial structure in the tumor microenvironment. ABMs can model more detailed spatial heterogeneity that better reflects the complexity seen in vivo. Using both models, we construct virtual cohorts with diverse tumor and immune attributes to simulate the therapeutic outcomes in a heterogeneous population. We reveal relationships between the parameters and the volume or phenotypic composition of tumors to thus identity key tumor or immune characteristics associated with tumor elimination, dormancy, and escape. In addition, we underscore the importance of including spatial components in computational models of immunotherapy by elucidating the additional insights that the ABM provides regarding the spatial complexities of the TME and their impact on therapeutic outcomes.

We then highlight the necessity of sufficient experimental data and identifiability analysis to reliable model predictions of post-treatment outcomes by the ODE model. Without experimental data, we create a virtual cohort of mice by randomly sampling the parameter space. With in vivo data, we perform practical identifiability analysis to estimate the distributions of key model parameters. We show that virtual cohorts constructed from random sampling or distributions of unidentifiable parameters due to limited data yield a wide range of numerical predictions and overestimate the efficacy of ICIs. Moreover, adequate quantities and varieties of data are required for the practical identifiability of key immune parameters and the construction of realistic virtual cohorts, which in turn produce accurate and precise numerical predictions, such as percentage reduction of tumor volume and survival proportion of virtual mice after aPDL1 treatment.

Furthermore, we discuss the application of machine learning (ML) techniques to address a primary limitation of ABMs — their high computational costs. We demonstrate that it is possible to predict post-treatment tumor outcomes and tumor volume trajectory from parameters of the ABM and a brief ABM simulation period by training an ML surrogate model. Our proposed workflow suggests an effective way to reduce computational time of ABMs by potentially eliminating the need to simulate the ABM until equilibrium or using ML models trained on smaller-scale simulations to predict outcomes of larger-scale simulations.

Data-driven and biologically informed mathematical models of cancer control strategies are a powerful complement to experimental studies. A multi-model approach identifies critical patterns and uncovers underlying mechanisms in the tumor microenvironment that drive cancer progression and therapeutic resistance. Our methodology can be adapted to systematically explore a wide range of questions related to tumor-immune dynamics and immunotherapy. The proposed modeling framework can also provide valuable insights for the rational design of pre-clinical experiments and clinical trials.