The roles of T cell competition and stochastic extinction events in chimeric antigen receptor T cell therapy

Mathematical modeling unveils the timeline of CAR-T cell therapy and macrophage-mediated cytokine release syndrome

Chimeric antigen receptor (CAR)-T cell therapy holds significant potential for cancer treatment, although disease relapse and cytokine release syndrome (CRS) remain as frequent clinical challenges. To better understand the mechanisms underlying the temporal dynamics of CAR-T cell therapy response and CRS, we developed a novel multi-layer mathematical model incorporating antigen-mediated CAR-T cell expansion, antigen-negative resistance, and macrophage-associated cytokine release. Three key mechanisms of macrophage activation are considered: release of damage-associated molecular patterns, antigen-binding mediated activation, and CD40-CD40L contact. The model accurately describes 25 patient time courses with different responses and IL-6 cytokine kinetics. We successfully link the dynamic shape of the response to interpretable model parameters and investigate the influence of CAR-T cell dose and initial tumor burden on the occurrence of cytokine release and treatment outcome. By disentangling the timeline of macrophage activation, the model identified distinct contributions of each activation mechanism, suggesting the CD40-CD40L axis as a major driver of cytokine release and a clinically feasible target to control the activation process and modulate cytokine peak height. Our multi-layer model provides a comprehensive framework for understanding the complex interactions between CAR-T cells, tumor cells, and macrophages during therapy.

CAR-T therapy dilemma and innovative design strategies for next generation

Chimeric antigen receptor (CAR)-T-cell therapy has shown remarkable curative effects on hematological tumors, driving the exponential growth in CAR-T-related research. Although CD19-targeting CAR-T-cell therapy has displayed remarkable promise in clinical trials, many obstacles are arising that limit its therapeutic efficacy in tumor immunotherapy. The "dilemma" of CAR-T cell-based tumor therapy includes lethal cytotoxicity, restricted trafficking, limited tumor infiltration, an immunosuppressive microenvironment, immune resistance and limited potency. The solution to CAR-T-cell therapy's dilemma requires interdisciplinary strategies, including synthetic biology-based ON/OFF switch, bioinstructive scaffolds, nanomaterials, oncolytic viruses, CRISPR screening, intestinal microbiota and its metabolites. In this review, we will introduce and summarize these interdisciplinary-based innovative technologies for the next generation CAR-T-cell design and delivery to overcome the key barriers of current CAR-T cells.

Mathematical Model of CAR T-Cell Therapy for a B-Cell Lymphoma Lymph Node

CAR T-cell therapies have demonstrated significant success in treating B-cell leukemia in children and young adults. However, their effectiveness in treating B-cell lymphomas has been limited in comparison to leukemia. In this paper we present a mathematical model that elucidates the dynamics of diffuse large B-cell lymphoma and CAR T-cells in a lymph node. The mathematical model aids in understanding the complex interplay between the cell populations involved and proposes ways to identify potential underlying dynamical causes of treatment failure. We also study the phenomenon of immunosuppression induced by tumor cells and theoretically demonstrate its impact on cell dynamics. Through the examination of various response scenarios, we underscore the significance of product characteristics in treatment outcomes.

CAR T-cell and oncolytic virus dynamics and determinants of combination therapy success for glioblastoma

Glioblastoma is a highly aggressive and treatment-resistant primary brain cancer. While chimeric antigen receptor (CAR) T-cell therapy has demonstrated promising results in targeting these tumors, it has not yet been curative. An innovative approach to improve CAR T-cell efficacy is to combine them with other immune modulating therapies. In this study, we investigate in vitro combination of IL-13Rα2 targeted CAR T-cells with an oncolytic virus (OV) and study the complex interplay between tumor cells, CAR T-cells, and OV dynamics with a novel mathematical model. We fit the model to data collected from experiments with each therapy individually and in combination to reveal determinants of therapy synergy and improved efficacy. Our analysis reveals that the virus bursting size is a critical parameter in determining the net tumor infection rate and overall combination treatment efficacy. Moreover, the model predicts that administering the oncolytic virus simultaneously with, or prior to, CAR T-cells could maximize therapeutic efficacy.

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.

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.

A war on many fronts: cross disciplinary approaches for novel cancer treatment strategies

Cancer is a disease characterized by uncontrolled cellular growth where cancer cells take advantage of surrounding cellular populations to obtain resources and promote invasion. Carcinomas are the most common type of cancer accounting for almost 90% of cancer cases. One of the major subtypes of carcinomas are adenocarcinomas, which originate from glandular cells that line certain internal organs. Cancers such as breast, prostate, lung, pancreas, colon, esophageal, kidney are often adenocarcinomas. Current treatment strategies include surgery, chemotherapy, radiation, targeted therapy, and more recently immunotherapy. However, patients with adenocarcinomas often develop resistance or recur after the first line of treatment. Understanding how networks of tumor cells interact with each other and the tumor microenvironment is crucial to avoid recurrence, resistance, and high-dose therapy toxicities. In this review, we explore how mathematical modeling tools from different disciplines can aid in the development of effective and personalized cancer treatment strategies. Here, we describe how concepts from the disciplines of ecology and evolution, economics, and control engineering have been applied to mathematically model cancer dynamics and enhance treatment strategies.

Mathematical modeling of hypoxia and adenosine to explore tumor escape mechanisms in DC-based immunotherapy

Identifying and controlling tumor escape mechanisms is crucial for improving cancer treatment effectiveness. Experimental studies reveal tumor hypoxia and adenosine as significant contributors to such mechanisms. Hypoxia exacerbates adenosine levels in the tumor microenvironment. Combining inhibition of these factors with dendritic cell (DC)-based immunotherapy promises improved clinical outcomes. However, challenges include understanding dynamics, optimal vaccine dosages, and timing. Mathematical models, including agent-based, diffusion, and ordinary differential equations, address these challenges. Here, we employ these models for the first time to elucidate how hypoxia and adenosine facilitate tumor escape in DC-based immunotherapy. After parameter estimation using experimental data, we optimize vaccination protocols to minimize tumor growth. Sensitivity analysis highlights adenosine's significant impact on immunotherapy efficacy. Its suppressive role impedes treatment success, but inhibiting adenosine could enhance therapy, as suggested by the model. Our findings shed light on hypoxia and adenosine-mediated tumor escape mechanisms, informing future treatment strategies. Additionally, identifiability analysis confirms accurate parameter determination using experimental data.

Making drugs from T cells: The quantitative pharmacology of engineered T cell therapeutics

Engineered T cells have emerged as highly effective treatments for hematological cancers. Hundreds of clinical programs are underway in efforts to expand the efficacy, safety, and applications of this immuno-therapeutic modality. A primary challenge in developing these "living drugs" is the complexity of their pharmacology, as the drug product proliferates, differentiates, traffics between tissues, and evolves through interactions with patient immune systems. Using publicly available clinical data from Chimeric Antigen Receptor (CAR) T cells, we demonstrate how mathematical models can be used to quantify the relationships between product characteristics, patient physiology, pharmacokinetics and clinical outcomes. As scientists work to develop next-generation cell therapy products, mathematical models will be integral for contextualizing data and facilitating the translation of product designs to clinical strategy.

A stochastic framework for evaluating CAR T cell therapy efficacy and variability

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy.

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.

Understanding the Interplay of CAR-NK Cells and Triple-Negative Breast Cancer: Insights from Computational Modeling

Chimeric antigen receptor (CAR)-engineered natural killer (NK) cells have recently emerged as a promising and safe alternative to CAR-T cells for targeting solid tumors. In the case of triple-negative breast cancer (TNBC), traditional cancer treatments and common immunotherapies have shown limited effectiveness. However, CAR-NK cells have been successfully employed to target epidermal growth factor receptor (EGFR) on TNBC cells, thereby enhancing the efficacy of immunotherapy. The effectiveness of CAR-NK-based immunotherapy is influenced by various factors, including the vaccination dose, vaccination pattern, and tumor immunosuppressive factors in the microenvironment. To gain insights into the dynamics and effects of CAR-NK-based immunotherapy, we propose a computational model based on experimental data and immunological theories. This model integrates an individual-based model that describes the interplay between the tumor and the immune system, along with an ordinary differential equation model that captures the variation of inflammatory cytokines. Computational results obtained from the proposed model shed light on the conditions necessary for initiating an effective anti-tumor response. Furthermore, global sensitivity analysis highlights the issue of low persistence of CAR-NK cells in vivo, which poses a significant challenge for the successful clinical application of these cells. Leveraging the model, we identify the optimal vaccination time, vaccination dose, and time interval between injections for maximizing therapeutic outcomes.

Deconvolution of clinical variance in CAR-T cell pharmacology and response

Chimeric antigen receptor T cell (CAR-T) expansion and persistence vary widely among patients and predict both efficacy and toxicity. However, the mechanisms underlying clinical outcomes and patient variability are poorly defined. In this study, we developed a mathematical description of T cell responses wherein transitions among memory, effector and exhausted T cell states are coordinately regulated by tumor antigen engagement. The model is trained using clinical data from CAR-T products in different hematological malignancies and identifies cell-intrinsic differences in the turnover rate of memory cells and cytotoxic potency of effectors as the primary determinants of clinical response. Using a machine learning workflow, we demonstrate that product-intrinsic differences can accurately predict patient outcomes based on pre-infusion transcriptomes, and additional pharmacological variance arises from cellular interactions with patient tumors. We found that transcriptional signatures outperform T cell immunophenotyping as predictive of clinical response for two CD19-targeted CAR-T products in three indications, enabling a new phase of predictive CAR-T product development.

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.

Mathematical modeling of radiotherapy: impact of model selection on estimating minimum radiation dose for tumor control

Introduction

Radiation therapy (RT) is one of the most common anticancer therapies. Yet, current radiation oncology practice does not adapt RT dose for individual patients, despite wide interpatient variability in radiosensitivity and accompanying treatment response. We have previously shown that mechanistic mathematical modeling of tumor volume dynamics can simulate volumetric response to RT for individual patients and estimation personalized RT dose for optimal tumor volume reduction. However, understanding the implications of the choice of the underlying RT response model is critical when calculating personalized RT dose.

Methods

In this study, we evaluate the mathematical implications and biological effects of 2 models of RT response on dose personalization: (1) cytotoxicity to cancer cells that lead to direct tumor volume reduction (DVR) and (2) radiation responses to the tumor microenvironment that lead to tumor carrying capacity reduction (CCR) and subsequent tumor shrinkage. Tumor growth was simulated as logistic growth with pre-treatment dynamics being described in the proliferation saturation index (PSI). The effect of RT was simulated according to each respective model for a standard schedule of fractionated RT with 2 Gy weekday fractions. Parameter sweeps were evaluated for the intrinsic tumor growth rate and the radiosensitivity parameter for both models to observe the qualitative impact of each model parameter. We then calculated the minimum RT dose required for locoregional tumor control (LRC) across all combinations of the full range of radiosensitvity and proliferation saturation values.

Results

Both models estimate that patients with higher radiosensitivity will require a lower RT dose to achieve LRC. However, the two models make opposite estimates on the impact of PSI on the minimum RT dose for LRC: the DVR model estimates that tumors with higher PSI values will require a higher RT dose to achieve LRC, while the CCR model estimates that higher PSI values will require a lower RT dose to achieve LRC.

Discussion

Ultimately, these results show the importance of understanding which model best describes tumor growth and treatment response in a particular setting, before using any such model to make estimates for personalized treatment recommendations.

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.

Modeling interaction of Glioma cells and CAR T-cells considering multiple CAR T-cells bindings

Chimeric antigen receptor (CAR) T-cell based immunotherapy has shown its potential in treating blood cancers, and its application to solid tumors is currently being extensively investigated. For glioma brain tumors, various CAR T-cell targets include IL13Rα2, EGFRvIII, HER2, EphA2, GD2, B7-H3, and chlorotoxin. In this work, we are interested in developing a mathematical model of IL13Rα2 targeting CAR T-cells for treating glioma. We focus on extending the work of Kuznetsov et al. (1994) by considering binding of multiple CAR T-cells to a single glioma cell, and the dynamics of these multi-cellular conjugates. Our model more accurately describes experimentally observed CAR T-cell killing assay data than the models which do not consider multi-cellular conjugates. Moreover, we derive conditions in the CAR T-cell expansion rate that determines treatment success or failure. Finally, we show that our model captures distinct CAR T-cell killing dynamics from low to high antigen receptor densities in patient-derived brain tumor cells.

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.

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.

Autocrine signaling can explain the emergence of Allee effects in cancer cell populations

In many human cancers, the rate of cell growth depends crucially on the size of the tumor cell population. Low, zero, or negative growth at low population densities is known as the Allee effect; this effect has been studied extensively in ecology, but so far lacks a good explanation in the cancer setting. Here, we formulate and analyze an individual-based model of cancer, in which cell division rates are increased by the local concentration of an autocrine growth factor produced by the cancer cells themselves. We show, analytically and by simulation, that autocrine signaling suffices to cause both strong and weak Allee effects. Whether low cell densities lead to negative (strong effect) or reduced (weak effect) growth rate depends directly on the ratio of cell death to proliferation, and indirectly on cellular dispersal. Our model is consistent with experimental observations from three patient-derived brain tumor cell lines grown at different densities. We propose that further studying and quantifying population-wide feedback, impacting cell growth, will be central for advancing our understanding of cancer dynamics and treatment, potentially exploiting Allee effects for therapy.

A common feature of tumor growth is the production, by the cancer cells themselves, of hormones known as growth factors that increase the rate of cell division. This type of signalling makes the growth rate of the tumor depend on the population size in a non-linear manner, and the growth rate might become low or negative for small population sizes. This is known as the Allee effect which has been studied extensively in ecology. We have developed a computational model that can explain the Allee effect in terms of growth factor signalling, and show by mathematical analysis of the model that the magnitude of the Allee effect depends on the ratio of cell death to proliferation, as well as the properties of the growth factor. In addition we show that the model is consistent with experimental observations from three different cell lines derived from the brain tumor glioblastoma. Our findings indicate that the Allee effect can be exploited in order to improve the treatment of glioblastoma patients.

Facing CAR T Cell Challenges on the Deadliest Paediatric Brain Tumours

Central nervous system (CNS) tumours comprise 25% of the paediatric cancer diagnoses and are the leading cause of cancer-related death in children. Current treatments for paediatric CNS tumours are far from optimal and fail for those that relapsed or are refractory to treatment. Besides, long-term sequelae in the developing brain make it mandatory to find new innovative approaches. Chimeric antigen receptor T cell (CAR T) therapy has increased survival in patients with B-cell malignancies, but the intrinsic biological characteristics of CNS tumours hamper their success. The location, heterogeneous antigen expression, limited infiltration of T cells into the tumour, the selective trafficking provided by the blood-brain barrier, and the immunosuppressive tumour microenvironment have emerged as the main hurdles that need to be overcome for the success of CAR T cell therapy. In this review, we will focus mainly on the characteristics of the deadliest high-grade CNS paediatric tumours (medulloblastoma, ependymoma, and high-grade gliomas) and the potential of CAR T cell therapy to increase survival and patients' quality of life.

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.