Modeling CAR T-Cell Therapy with Patient Preconditioning

Mathematical modeling insights into improving CAR T cell therapy for solid tumors with bystander effects

As an adoptive cellular therapy, Chimeric Antigen Receptor T cell (CAR T cell) therapy has shown remarkable success in hematological malignancies but only limited efficacy against solid tumors. Compared with blood cancers, solid tumors present a series of challenges that ultimately combine to neutralize the function of CAR T cells. These challenges include, but are not limited to, antigen heterogeneity - variability in the expression of the antigen on tumor cells, as well as trafficking and infiltration into the solid tumor tissue. A critical question for solving the heterogeneity problem is whether CAR T therapy induces bystander effects, such as antigen spreading. Antigen spreading occurs when CAR T cells activate other endogenous antitumor CD8 T cells against antigens that were not originally targeted. In this work, we develop a mathematical model of CAR T cell therapy for solid tumors that considers both antigen heterogeneity and bystander effects. Our model is based on in vivo treatment data that includes a mixture of target antigen-positive and target antigen-negative tumor cells. We use our model to simulate large cohorts of virtual patients to better understand the relationship involving bystander killing. We also investigate several strategies for enhancing bystander effects, thus increasing CAR T cell therapy's overall efficacy for solid tumors.

Using Spectral Flow Cytometry for CAR T-Cell Clinical Trials: Game Changing Technologies Enabling Novel Therapies

Monitoring chimeric antigen redirected (CAR) T-cells post-infusion in clinical trials is a specialized application of flow cytometry. Unlike the CAR T-cell monitoring for individual patients conducted in clinical laboratories, the data generated during a clinical trial will be used not only to monitor the therapeutic response of a single patient, but determine the success of the therapy itself, or even of an entire class of therapeutic compounds. The data, typically acquired at multiple testing laboratories, will be compiled into a single database. The data may also be used for mathematical modeling of cellular kinetics or to identify predictive biomarkers. With the expanded context of use, a robust, standardized assay is mandatory in order to generate a valuable and reliable data set. Hence, the requirements for assay validation, traceable calibration, technology transfer, cross-instrument standardization and regulatory compliance are high.

MCMC Methods for Parameter Estimation in ODE Systems for CAR-T Cell Cancer Therapy

Chimeric antigen receptor (CAR)-T cell therapy represents a breakthrough in treating resistant hematologic cancers. It is based on genetically modifying T cells transferred from the patient or a donor. Although its implementation has increased over the last few years, CAR-T has many challenges to be addressed, for instance, the associated severe toxicities, such as cytokine release syndrome. To model CAR-T cell dynamics, focusing on their proliferation and cytotoxic activity, we developed a mathematical framework using ordinary differential equations (ODEs) with Bayesian parameter estimation. Bayesian statistics were used to estimate model parameters through Monte Carlo integration, Bayesian inference, and Markov chain Monte Carlo (MCMC) methods. This paper explores MCMC methods, including the Metropolis-Hastings algorithm and DEMetropolis and DEMetropolisZ algorithms, which integrate differential evolution to enhance convergence rates. The theoretical findings and algorithms were validated using Python and Jupyter Notebooks. A real medical dataset of CAR-T cell therapy was analyzed, employing optimization algorithms to fit the mathematical model to the data, with the PyMC library facilitating Bayesian analysis. The results demonstrated that our model accurately captured the key dynamics of CAR-T cell therapy. This conclusion underscores the potential of parameter estimation to improve the understanding and effectiveness of CAR-T cell therapy in clinical settings.

Understanding the role of B cells in CAR T-cell therapy in leukemia through a mathematical model

Chimeric antigen receptor T (CAR T) cell therapy has been proven to be successful against a variety of leukemias and lymphomas. This paper undertakes an analytical and numerical study of a mathematical model describing the competition of CAR T, leukemia, tumor, and B cells. Considering its significance in sustaining anti-CD19 CAR T-cell stimulation, a B-cell source term is integrated into the model. Through stability and bifurcation analyses, the potential for tumor eradication, contingent on the continuous influx of B cells, has been revealed, showing a transcritical bifurcation at a critical B-cell input. Additionally, an almost heteroclinic cycle between equilibrium points is identified, providing a theoretical basis for understanding disease relapse. Analyzing the oscillatory behavior of the system, the time-dependent dynamics of CAR T cells and leukemic cells can be approximated, shedding light on the impact of initial tumor burden on therapeutic outcomes. In conclusion, the study provides insights into CAR T-cell therapy dynamics for acute lymphoblastic leukemias, offering a theoretical foundation for clinical observations and suggesting avenues for future immunotherapy modeling research.

Current advances in experimental and computational approaches to enhance CAR T cell manufacturing protocols and improve clinical efficacy

Since the FDA's approval of chimeric antigen receptor (CAR) T cells in 2017, significant improvements have been made in the design of chimeric antigen receptor constructs and in the manufacturing of CAR T cell therapies resulting in increased in vivo CAR T cell persistence and improved clinical outcome in certain hematological malignancies. Despite the remarkable clinical response seen in some patients, challenges remain in achieving durable long-term tumor-free survival, reducing therapy associated malignancies and toxicities, and expanding on the types of cancers that can be treated with this therapeutic modality. Careful analysis of the biological factors demarcating efficacious from suboptimal CAR T cell responses will be of paramount importance to address these shortcomings. With the ever-expanding toolbox of experimental approaches, single-cell technologies, and computational resources, there is renowned interest in discovering new ways to streamline the development and validation of new CAR T cell products. Better and more accurate prognostic and predictive models can be developed to help guide and inform clinical decision making by incorporating these approaches into translational and clinical workflows. In this review, we provide a brief overview of recent advancements in CAR T cell manufacturing and describe the strategies used to selectively expand specific phenotypic subsets. Additionally, we review experimental approaches to assess CAR T cell functionality and summarize current in silico methods which have the potential to improve CAR T cell manufacturing and predict clinical outcomes.

Chimeric Antigen Receptor T-Cell Therapy for Solid Tumors

We review chimeric antigen receptor (CAR) T-cell therapy for solid tumors. We discuss patient selection factors and aspects of clinical management. We describe challenges including physical and molecular barriers to trafficking CAR-Ts, an immunosuppressive tumor microenvironment, and difficulty finding cell surface target antigens. The application of new approaches in synthetic biology and cellular engineering toward solid tumor CAR-Ts is described. Finally, we summarize reported and ongoing clinical trials of CAR-T therapies for select disease sites such as head and neck (including thyroid cancer), lung, central nervous system (glioblastoma, neuroblastoma, glioma), sarcoma, genitourinary (prostate, renal, bladder, kidney), breast and ovarian cancer.

Model-informed drug development of autologous CAR-T cell therapy: Strategies to optimize CAR-T cell exposure leveraging cell kinetic/dynamic modeling

Autologous Chimeric antigen receptor (CAR-T) cell therapy has been highly successful in the treatment of aggressive hematological malignancies and is also being evaluated for the treatment of solid tumors as well as other therapeutic areas. A challenge, however, is that up to 60% of patients do not sustain a long-term response. Low CAR-T cell exposure has been suggested as an underlying factor for a poor prognosis. CAR-T cell therapy is a novel therapeutic modality with unique kinetic and dynamic properties. Importantly, "clear" dose-exposure relationships do not seem to exist for any of the currently approved CAR-T cell products. In other words, dose increases have not led to a commensurate increase in the measurable in vivo frequency of transferred CAR-T cells. Therefore, alternative approaches beyond dose titration are needed to optimize CAR-T cell exposure. In this paper, we provide examples of actionable variables - design elements in CAR-T cell discovery, development, and clinical practice, which can be modified to optimize autologous CAR-T cell exposure. Most of these actionable variables can be assessed throughout the various stages of discovery and development as part of a well-informed research and development program. Model-informed drug development approaches can enable such study and program design choices from discovery through to clinical practice and can be an important contributor to cell therapy effectiveness and efficiency.

Best Practices and Considerations for Clinical Pharmacology and Pharmacometric Aspects for Optimal Development of CAR-T and TCR-T Cell Therapies: An Industry Perspective

With the promise of a potentially "single dose curative" paradigm, CAR-T cell therapies have brought a paradigm shift in the treatment and management of hematological malignancies. Both CAR-T and TCR-T cell therapies have also made great progress toward the successful treatment of solid tumor indications. The field is rapidly evolving with recent advancements including the clinical development of "off-the-shelf" allogeneic CAR-T therapies that can overcome the long and difficult "vein-to-vein" wait time seen with autologous CAR-T therapies. There are unique clinical pharmacology, pharmacometric, bioanalytical, and immunogenicity considerations and challenges in the development of these CAR-T and TCR-T cell therapies. Hence, to help accelerate the development of these life-saving therapies for the patients with cancer, experts in this field came together under the umbrella of International Consortium for Innovation and Quality in Pharmaceutical Development (IQ) to form a joint working group between the Clinical Pharmacology Leadership Group (CPLG) and the Translational and ADME Sciences Leadership Group (TALG). In this white paper, we present the IQ consortium perspective on the best practices and considerations for clinical pharmacology and pharmacometric aspects toward the optimal development of CAR-T and TCR-T cell therapies.

A systems and computational biology perspective on advancing CAR therapy

In the recent decades, chimeric antigen receptor (CAR) therapy signaled a new revolutionary approach to cancer treatment. This method seeks to engineer immune cells expressing an artificially designed receptor, which would endue those cells with the ability to recognize and eliminate tumor cells. While some CAR therapies received FDA approval and others are subject to clinical trials, many aspects of their workings remain elusive. Techniques of systems and computational biology have been frequently employed to explain the operating principles of CAR therapy and suggest further design improvements. In this review, we sought to provide a comprehensive account of those efforts. Specifically, we discuss various computational models of CAR therapy ranging in scale from organismal to molecular. Then, we describe the molecular and functional properties of costimulatory domains frequently incorporated in CAR structure. Finally, we describe the signaling cascades by which those costimulatory domains elicit cellular response against the target. We hope that this comprehensive summary of computational and experimental studies will further motivate the use of systems approaches in advancing CAR therapy.

Data driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables

In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.

Current Developments in Cellular Therapy for Castration Resistant Prostate Cancer: A Systematic Review of Clinical Studies

Recently, the development of immunotherapies such as cellular therapy, monoclonal antibodies, vaccines and immunomodulators has revolutionized the treatment of various cancer entities. In order to close the existing gaps in knowledge about cellular immunotherapy, specifically focusing on the chimeric antigen receptors (CAR) T-cells, their benefits and application in clinical settings, we conducted a comprehensive systematic review. Two co-authors independently searched the literature and characterized the results. Out of 183 records, 26 were considered eligible. This review provides an overview of the cellular immunotherapy landscape in treating prostate cancer, honing in on the challenges of employing CAR T-cell therapy. CAR T-cell therapy is a promising avenue for research due to the presence of an array of different tumor specific antigens. In prostate cancer, the complex microenvironment of the tumor vastly contributes to the success or failure of immunotherapies.

Modeling Patient-Specific CAR-T Cell Dynamics: Multiphasic Kinetics via Phenotypic Differentiation

Chimeric Antigen Receptor (CAR)-T cell immunotherapy revolutionized cancer treatment and consists of the genetic modification of T lymphocytes with a CAR gene, aiming to increase their ability to recognize and kill antigen-specific tumor cells. The dynamics of CAR-T cell responses in patients present multiphasic kinetics with distribution, expansion, contraction, and persistence phases. The characteristics and duration of each phase depend on the tumor type, the infused product, and patient-specific characteristics. We present a mathematical model that describes the multiphasic CAR-T cell dynamics resulting from the interplay between CAR-T and tumor cells, considering patient and product heterogeneities. The CAR-T cell population is divided into functional (distributed and effector), memory, and exhausted CAR-T cell phenotypes. The model is able to describe the diversity of CAR-T cell dynamical behaviors in different patients and hematological cancers as well as their therapy outcomes. Our results indicate that the joint assessment of the area under the concentration-time curve in the first 28 days and the corresponding fraction of non-exhausted CAR-T cells may be considered a potential marker to classify therapy responses. Overall, the analysis of different CAR-T cell phenotypes can be a key aspect for a better understanding of the whole CAR-T cell dynamics.

Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?

Several mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the interaction of tumor cells with immune effector cells. The Kuznetsov model (Kuznetsov et al. in Bull Math Biol 56(2):295–321, 1994) is the most prominent of these models and has been used as a basis for many other related models and theoretical studies. However, none of these models have been validated with large-scale real-world data of human patients treated with cancer immunotherapy. In addition, parameter estimation of these models remains a major bottleneck on the way to model-based and data-driven medical treatment. In this study, we quantitatively fit Kuznetsov’s model to a large dataset of 1472 patients, of which 210 patients have more than six data points, by estimating the model parameters of each patient individually. We also conduct a global practical identifiability analysis for the estimated parameters. We thus demonstrate that several combinations of parameter values could lead to accurate data fitting. This opens the potential for global parameter estimation of the model, in which the values of all or some parameters are fixed for all patients. Furthermore, by omitting the last two or three data points, we show that the model can be extrapolated and predict future tumor dynamics. This paves the way for a more clinically relevant application of mathematical tumor modeling, in which the treatment strategy could be adjusted in advance according to the model’s future predictions.

Mapping CAR T-Cell Design Space Using Agent-Based Models

Chimeric antigen receptor (CAR) T-cell therapy shows promise for treating liquid cancers and increasingly for solid tumors as well. While potential design strategies exist to address translational challenges, including the lack of unique tumor antigens and the presence of an immunosuppressive tumor microenvironment, testing all possible design choices in vitro and in vivo is prohibitively expensive, time consuming, and laborious. To address this gap, we extended the modeling framework ARCADE (Agent-based Representation of Cells And Dynamic Environments) to include CAR T-cell agents (CAR T-cell ARCADE, or CARCADE). We conducted in silico experiments to investigate how clinically relevant design choices and inherent tumor features—CAR T-cell dose, CD4⁺:CD8⁺ CAR T-cell ratio, CAR-antigen affinity, cancer and healthy cell antigen expression—individually and collectively impact treatment outcomes. Our analysis revealed that tuning CAR affinity modulates IL-2 production by balancing CAR T-cell proliferation and effector function. It also identified a novel multi-feature tuned treatment strategy for balancing selectivity and efficacy and provided insights into how spatial effects can impact relative treatment performance in different contexts. CARCADE facilitates deeper biological understanding of treatment design and could ultimately enable identification of promising treatment strategies to accelerate solid tumor CAR T-cell design-build-test cycles.

Cellular kinetics: A clinical and computational review of CAR-T cell pharmacology

To the extent that pharmacokinetics influence the effectiveness of nonliving therapeutics, so too do cellular kinetics influence the efficacy of Chimeric Antigen Receptor (CAR) -T cell therapy. Like conventional therapeutics, CAR-T cell therapies undergo a distribution phase upon administration. Unlike other therapeutics, however, this distribution phase is followed by subsequent phases of expansion, contraction, and persistence. The magnitude and duration of these phases unequivocally influence clinical outcomes. Furthermore, the "pharmacodynamics" of CAR-T cells is truly dynamic, as cells can rapidly become exhausted and lose their therapeutic efficacy. Mathematical models are among the translational tools commonly applied to assess, characterize, and predict the complex cellular kinetics and dynamics of CAR-T cells. Here, we provide a focused review of the cellular kinetics of CAR-T cells, the mechanisms underpinning their complexity, and the mathematical modeling approaches used to interrogate them.

A combination therapy of oncolytic viruses and chimeric antigen receptor T cells: a mathematical model proof-of-concept

Combining chimeric antigen receptor T (CAR-T) cells with oncolytic viruses (OVs) has recently emerged as a promising treatment approach in preclinical studies that aim to alleviate some of the barriers faced by CAR-T cell therapy. In this study, we address by means of mathematical modeling the main question of whether a single dose or multiple sequential doses of CAR-T cells during the OVs therapy can have a synergetic effect on tumor reduction. To that end, we propose an ordinary differential equations-based model with virus-induced synergism to investigate potential effects of different regimes that could result in efficacious combination therapy against tumor cell populations. Model simulations show that, while the treatment with a single dose of CAR-T cells is inadequate to eliminate all tumor cells, combining the same dose with a single dose of OVs can successfully eliminate the tumor in the absence of virus-induced synergism. However, in the presence of virus-induced synergism, the same combination therapy fails to eliminate the tumor. Furthermore, it is shown that if the intensity of virus-induced synergy and/or virus oncolytic potency is high, then the induced CAR-T cell response can inhibit virus oncolysis. Additionally, the simulations show a more robust synergistic effect on tumor cell reduction when OVs and CAR-T cells are administered simultaneously compared to the combination treatment where CAR-T cells are administered first or after OV injection. Our findings suggest that the combination therapy of CAR-T cells and OVs seems unlikely to be effective if the virus-induced synergistic effects are included when genetically engineering oncolytic viral vectors.

Dose-dependent thresholds of dexamethasone destabilize CAR T-cell treatment efficacy

Chimeric antigen receptor (CAR) T-cell therapy is potentially an effective targeted immunotherapy for glioblastoma, yet there is presently little known about the efficacy of CAR T-cell treatment when combined with the widely used anti-inflammatory and immunosuppressant glucocorticoid, dexamethasone. Here we present a mathematical model-based analysis of three patient-derived glioblastoma cell lines treated in vitro with CAR T-cells and dexamethasone. Advanced in vitro experimental cell killing assay technologies allow for highly resolved temporal dynamics of tumor cells treated with CAR T-cells and dexamethasone, making this a valuable model system for studying the rich dynamics of nonlinear biological processes with translational applications. We model the system as a nonautonomous, two-species predator-prey interaction of tumor cells and CAR T-cells, with explicit time-dependence in the clearance rate of dexamethasone. Using time as a bifurcation parameter, we show that (1) dexamethasone destabilizes coexistence equilibria between CAR T-cells and tumor cells in a dose-dependent manner and (2) as dexamethasone is cleared from the system, a stable coexistence equilibrium returns in the form of a Hopf bifurcation. With the model fit to experimental data, we demonstrate that high concentrations of dexamethasone antagonizes CAR T-cell efficacy by exhausting, or reducing the activity of CAR T-cells, and by promoting tumor cell growth. Finally, we identify a critical threshold in the ratio of CAR T-cell death to CAR T-cell proliferation rates that predicts eventual treatment success or failure that may be used to guide the dose and timing of CAR T-cell therapy in the presence of dexamethasone in patients.

Bioengineering and gene-editing technologies have paved the way for advance immunotherapies that can target patient-specific tumor cells. One of these therapies, chimeric antigen receptor (CAR) T-cell therapy has recently shown promise in treating glioblastoma, an aggressive brain cancer often with poor patient prognosis. Dexamethasone is a commonly prescribed anti-inflammatory medication due to the health complications of tumor associated swelling in the brain. However, the immunosuppressant effects of dexamethasone on the immunotherapeutic CAR T-cells are not well understood. To address this issue, we use mathematical modeling to study in vitro dynamics of dexamethasone and CAR T-cells in three patient-derived glioblastoma cell lines. We find that in each cell line studied there is a threshold of tolerable dexamethasone concentration. Below this threshold, CAR T-cells are successful at eliminating the cancer cells, while above this threshold, dexamethasone critically inhibits CAR T-cell efficacy. Our modeling suggests that in the presence of high dexamethasone reduced CAR T-cell efficacy, or increased exhaustion, can occur and result in CAR T-cell treatment failure.

The potential of CAR T cell therapy for prostate cancer

Chimeric antigen receptor (CAR) T cell immunotherapy involves the genetic modification of the patient's own T cells so that they specifically recognize and destroy tumour cells. Considerable clinical success has been achieved using this technique in patients with lymphoid malignancies, but clinical studies that investigated treating solid tumours using this emerging technology have been disappointing. A number of developments might be able to increase the efficacy of CAR T cell therapy for treatment of prostate cancer, including improved trafficking to the tumour, techniques to overcome the immunosuppressive tumour microenvironment, as well as methods to enhance CAR T cell persistence, specificity and safety. Furthermore, CAR T cell therapy has the potential to be combined with other treatment modalities, such as androgen deprivation therapy, radiotherapy or chemotherapy, and could be applied as focal CAR T cell therapy for prostate cancer.

A Mathematical Description of the Bone Marrow Dynamics during CAR T-Cell Therapy in B-Cell Childhood Acute Lymphoblastic Leukemia

Chimeric Antigen Receptor (CAR) T-cell therapy has demonstrated high rates of response in recurrent B-cell Acute Lymphoblastic Leukemia in children and young adults. Despite this success, a fraction of patients' experience relapse after treatment. Relapse is often preceded by recovery of healthy B cells, which suggests loss or dysfunction of CAR T-cells in bone marrow. This site is harder to access, and thus is not monitored as frequently as peripheral blood. Understanding the interplay between B cells, leukemic cells, and CAR T-cells in bone marrow is paramount in ascertaining the causes of lack of response. In this paper, we put forward a mathematical model representing the interaction between constantly renewing B cells, CAR T-cells, and leukemic cells in the bone marrow. Our model accounts for the maturation dynamics of B cells and incorporates effector and memory CAR T-cells. The model provides a plausible description of the dynamics of the various cellular compartments in bone marrow after CAR T infusion. After exploration of the parameter space, we found that the dynamics of CAR T product and disease were independent of the dose injected, initial B-cell load, and leukemia burden. We also show theoretically the importance of CAR T product attributes in determining therapy outcome, and have studied a variety of possible response scenarios, including second dosage schemes. We conclude by setting out ideas for the refinement of the model.