CAR T-cell therapy, a revolutionary cancer treatment modality, has shown transformative results in hematological malignancies. This success stems from the ability to engineer T cells with chimeric antigen receptors (CARs) that recognize specific cancer cell antigens, leading to targeted destruction. However, translating this success to solid tumors remains a significant challenge. Solid tumors present a complex microenvironment that hinders CAR T-cell efficacy. Key challenges include antigen heterogeneity (variability in antigen expression across tumor cells), difficulties in CAR T-cell trafficking and infiltration into the tumor tissue, and an immunosuppressive tumor microenvironment. The ideal scenario would involve tumor-associated antigens (TAAs) being uniformly expressed on all tumor cells; however, this is rarely the case. Antigen heterogeneity limits the effectiveness of CAR T cells, as they can only target cells expressing the specific antigen. A critical question to address this heterogeneity is whether CAR T-cell therapy induces "bystander effects," where CAR T cells indirectly eliminate nearby cancer cells that do not express the target antigen. Bystander effects can involve indirect tumor cell killing (e.g., via cytokine release and activation of macrophages or NK cells) or antigen spreading (activation of endogenous antitumor CD8 T cells against additional antigens). Experimentally evaluating bystander effects presents several challenges, including the need for immunocompetent models and sophisticated techniques for quantifying antigen expression and CAR T-cell impact. This study uses mathematical modeling to address these challenges by developing a model that incorporates both antigen heterogeneity and bystander effects in solid tumor CAR T-cell therapy. The goal is to utilize the model to simulate treatment scenarios and analyze how bystander effects influence treatment outcomes, ultimately seeking to inform strategies for improving CAR T-cell therapy against solid tumors.

Existing mathematical models have explored aspects of CAR T-cell therapy, but, to the authors' knowledge, none have specifically investigated the bystander effect in solid tumors. Studies have focused on aspects like T-cell proliferation and exhaustion, or the effects of chemotherapy regimens, primarily in hematological malignancies. Some models have examined how antigen density affects cellular mechanisms in hematological cancers. However, a comprehensive model incorporating antigen heterogeneity, bystander effects (both indirect killing and antigen spreading), and the complex interactions within the solid tumor microenvironment was lacking. The authors' study aims to fill this gap and provide valuable insights into the dynamics of CAR T-cell therapy in solid tumors.

The researchers developed a mathematical model incorporating four cell populations: target antigen-positive tumor cells (Tpos), target antigen-negative tumor cells (Tneg), CAR T cells (C), and bystander cells (B). The model employs ordinary differential equations (ODEs) to describe the dynamics of these populations. Tumor growth is modeled using logistic growth equations with carrying capacity, accounting for competition between Tpos and Tneg. CAR T cell and bystander cell killing of tumor cells are represented using ratio-dependent terms (based on the ratio of immune cells to tumor cells), reflecting the observation that tumor cell lysis by T cells is not always linear. The recruitment of CAR T cells and bystander cells is modeled using Michaelis-Menten kinetics, capturing saturation effects. The model incorporates parameters representing proliferation rates, death rates, maximum killing rates, and other relevant factors. Parameter estimation was performed using in vivo data from a syngeneic mouse cancer model study (Klampatsa et al., 2020) that investigated bystander effects in mesothelioma. Data extraction was performed using Plot Digitizer. A sequential parameter fitting process was employed, using the control group data (without CAR T cells) to estimate tumor growth parameters, and then using data from CAR T-cell treatments (with and without cyclophosphamide pretreatment) to estimate parameters related to CAR T-cell and bystander cell dynamics. The model was calibrated to fit both the control group data (no bystander effect) and the data demonstrating bystander effect following CTX treatment. The authors used MATLAB's ‘fmincon’ for parameter fitting and ‘ode45’ for numerical solutions. Global sensitivity analysis was performed using sparse grid interpolation to identify the most influential parameters. A virtual patient (VP) cohort was generated by sampling parameters from ranges derived from the experimental data. Statistical analyses, including Kruskal-Wallis and Dunn's tests, were conducted to compare parameter distributions across different response groups (responders, partial responders, and non-responders) in the VP cohort. The study systematically varied parameters to assess their impact on treatment outcomes.

The Sobol sensitivity analysis revealed that parameters related to tumor growth rates (r1, r2), the exponent of tumor lysis (l), and the maximum killing rates of tumor cells by CAR T cells (dc) and bystander cells (db) were most influential in determining tumor progression. The model accurately reproduced the experimental data, showing a good fit for both control and treatment groups. Simulations showed that increasing CAR T cell dosage alone does not consistently improve outcomes, especially at low antigen expression levels. Instead, enhancing the cytotoxic capacity of bystander cells significantly increased the proportion of responders. Virtual patient analysis identified parameters (i, da, µg, dg) that were significantly different between responder and non-responder groups. Specifically, higher values of da (maximum killing rate of bystander cells) were strongly associated with responders. In contrast, increasing the maximum killing rate of bystander cells (da) consistently improved treatment outcomes in the virtual patient cohort. The Kruskal-Wallis test revealed that several parameters exhibited significant differences between responders and non-responders, with the largest effect sizes observed for parameters relating to bystander cell killing and tumor lysis function exponents. Dunn's post-hoc tests highlighted significant differences between responders and non-responders across multiple key parameters.

The findings strongly suggest that focusing on enhancing the bystander effect, rather than simply increasing CAR T-cell dosage, is crucial for improving CAR T-cell therapy in solid tumors. The model provides a framework to understand the complex interactions between CAR T cells, bystander cells, and tumor cells, highlighting the importance of bystander cell activity. The model's ability to accurately capture the experimental data, including the effects of cyclophosphamide pretreatment, validates its utility in studying bystander effects. The virtual patient analysis further strengthens the conclusions by demonstrating the consistent impact of bystander cell cytotoxicity on treatment success. This work aligns with experimental observations demonstrating the importance of endogenous CD8 T cells and the beneficial effect of cyclophosphamide pretreatment in triggering bystander effects.

This study presents a novel mathematical model that successfully incorporates antigen heterogeneity and bystander effects in CAR T-cell therapy for solid tumors. The findings highlight the critical role of enhancing bystander cell cytotoxicity, rather than solely increasing CAR T-cell dose, for improved therapeutic outcomes. Future research directions could include incorporating additional factors into the model, such as the role of regulatory T cells, the effects of cytokines, and the mechanisms of cross-presentation by antigen-presenting cells. Investigating spatial dynamics using partial differential equations would also enhance the model's realism and predictive power. The model's insights can guide the development of more effective strategies for CAR T-cell therapy in solid tumors.

The model relies on parameter values obtained from a combination of mouse models and human patient data, which may introduce uncertainties. The model is a simplification of the complex biology involved in CAR T-cell therapy and bystander effects; some processes are simplified or not explicitly modeled. The limited available data on bystander effects in solid tumors constrained the parameter estimation and model validation. Expanding the dataset through further experimental studies would improve the model's accuracy and predictive capabilities.