A Spatial Quantitative Systems Pharmacology Platform spQSP-IO for Simulations of Tumor–Immune Interactions and Effects of Checkpoint Inhibitor Immunotherapy

Abstract

Quantitative systems pharmacology (QSP) models have become increasingly common in fundamental mechanistic studies and drug discovery in both academic and industrial environments. With imaging techniques widely adopted and other spatial quantification of tumor such as spatial transcriptomics gaining traction, it is crucial that these data reflecting tumor spatial heterogeneity be utilized to inform the QSP models to enhance their predictive power. We developed a hybrid computational model platform, spQSP-IO, to extend QSP models of immuno-oncology with spatially resolved agent-based models (ABM), combining their powers to track whole patient-scale dynamics and recapitulate the emergent spatial heterogeneity in the tumor. Using a model of non-small-cell lung cancer developed based on this platform, we studied the role of the tumor microenvironment and cancer–immune cell interactions in tumor development and applied anti-PD-1 treatment to virtual patients and studied how the spatial distribution of cells changes during tumor growth in response to the immune checkpoint inhibition treatment. Using parameter sensitivity analysis and biomarker analysis, we are able to identify mechanisms and pretreatment measurements correlated with treatment efficacy. By incorporating spatial data that highlight both heterogeneity in tumors and variability among individual patients, spQSP-IO models can extend the QSP framework and further advance virtual clinical trials.

Simulations of tumor growth and response to immunotherapy by coupling a spatial agent-based model with a whole-patient quantitative systems pharmacology model

“…Cancer cells growth and death. Following [36], we formulate an ordinary differential equation (ODE) version of the ABM rules for cancer cell growth dynamics to keep consistency between the QSP model and ABM. Calculations are summarized in Section A.2 of the S1 Supplementary Material.…”

“…Recent data from cancer studies prove the importance of modeling spatio-temporal features of cancer progression in order to understand the key role of the immune system and develop more effective combination immunotherapies [ 25 , 26 , 27 , 28 , 29 ]. Agent-based models, where entities called agents act and interact according to a set of rules, deterministic or stochastic, are excellent tools to represent the elements and processes that characterize the TME and the effects of immunotherapies with ICBs [ 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ].…”

“…Multiscale hybrid models are powerful tools that combine deterministic and stochastic scenarios that handle a wide range of spatio-temporal scales [ 44 , 45 ]. Here, we extend a novel and recently published spatial QSP model (spQSP) [ 36 , 37 ], where a whole-patient ordinary differential equations-based QSP model and a spatial ABM, each representing part of a whole tumor, are combined, to study the dynamics of tumor growth and the response to immunotherapy at different spatial and temporal scales. Different types of cancer cells, T cells, and myeloid-derived suppressor cells (MDSCs) in ABM are represented as agents that move and react, conforming to a set of probabilistic rules, whereas QSP model defines an average number of cells that changes over time.…”

“…Different types of cancer cells, T cells, and myeloid-derived suppressor cells (MDSCs) in ABM are represented as agents that move and react, conforming to a set of probabilistic rules, whereas QSP model defines an average number of cells that changes over time. Unlike previous studies [ 36 , 37 ], where the state of the species in the tumor is defined by combining the outcomes from QSP model and ABM, the presented approach replaces the spatially homogeneous QSP representation of cells in the tumor by the spatial ABM representation after applying a scaling factor. The QSP temporal dynamics of cells in the tumor is redefined in terms of propensity functions and probabilities, which establishes a simple methodology to transform QSP models into their equivalent spatial representations and guarantees a consistent coupling between QSP model and ABM.…”

Dynamics of tumor-associated macrophages in a quantitative systems pharmacology model of immunotherapy in triple-negative breast cancer

“…In the past few years, we have developed and expanded a large-scale QSP platform for the analyses of immune checkpoint inhibitors and bispecific T cell engagers in combination with other agents in non-small cell lung cancer ( Jafarnejad et al., 2019 ; Sové et al., 2020 ), colorectal cancer ( Ma et al., 2020a ; 2020b ) and breast cancer ( Wang et al., 2020a , 2021 ). We have also combined the QSP model with a spatial agent-based model of tumor to describe spatial heterogeneity of the tumor microenvironment ( Gong et al., 2021 ; Zhang et al., 2021a ). Here, by integrating a macrophage module into our previously published QSP platform ( Wang et al., 2020a , 2021 ), we are able to investigate the impact of TAMs on the cancer-immune cell interactions and provide a computational framework to predict clinical response to macrophage-targeted agents based on preclinical data.…”