Chimeric Antigen Receptor T Cell Therapies: A Review of Cellular Kinetic-Pharmacodynamic Modeling Approaches

Mathematical modeling of endogenous and exogenously administered T cell recirculation in mouse and its application to pharmacokinetic studies of cell therapies

Introduction

In vivo T cell migration has been of interest to scientists for the past 60 years. T cell kinetics are important in the understanding of the immune response to infectious agents. More recently, adoptive T cell therapies have proven to be a most promising approach to treating a wide range of diseases, including autoimmune and cancer diseases, whereby the characterization of cellular kinetics represents an important step towards the prediction of therapeutic efficacy.

Methods

Here, we developed a physiologically-based pharmacokinetic (PBPK) model that describes endogenous T cell homeostasis and the kinetics of exogenously administered T cells in mouse. Parameter calibration was performed using a nonlinear fixed-effects modeling approach based on published data on T cell kinetics and steady-state levels in different tissues of mice. The Partial Rank Correlation Coefficient (PRCC) method was used to perform a global sensitivity assessment. To estimate the impact of kinetic parameters on exogenously administered T cell dynamics, a local sensitivity analysis was conducted.

Results

We simulated the model to analyze cellular kinetics following various T cell doses and frequencies of CCR7+ T cells in the population of infused lymphocytes. The model predicted the effects of T cell numbers and of population composition of infused T cells on the resultant concentration of T cells in various organs. For example, a higher percentage of CCR7+ T cells among exogenously administered T lymphocytes led to an augmented accumulation of T cells in the spleen. The model predicted a linear dependence of T cell dynamics on the dose of adoptively transferred T cells.

Discussion

The mathematical model of T cell migration presented here can be integrated into a multi-scale model of the immune system and be used in a preclinical setting for predicting the distribution of genetically modified T lymphocytes in various organs, following adoptive T cell therapies.

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.

Harnessing the Transcriptional Signatures of CAR-T-Cells and Leukemia/Lymphoma Using Single-Cell Sequencing Technologies

Chimeric antigen receptor (CAR)-T-cell therapy has greatly improved outcomes for patients with relapsed or refractory hematological malignancies. However, challenges such as treatment resistance, relapse, and severe toxicity still hinder its widespread clinical application. Traditional transcriptome analysis has provided limited insights into the complex transcriptional landscape of both leukemia cells and engineered CAR-T-cells, as well as their interactions within the tumor microenvironment. However, with the advent of single-cell sequencing techniques, a paradigm shift has occurred, providing robust tools to unravel the complexities of these factors. These techniques enable an unbiased analysis of cellular heterogeneity and molecular patterns. These insights are invaluable for precise receptor design, guiding gene-based T-cell modification, and optimizing manufacturing conditions. Consequently, this review utilizes modern single-cell sequencing techniques to clarify the transcriptional intricacies of leukemia cells and CAR-Ts. The aim of this manuscript is to discuss the potential mechanisms that contribute to the clinical failures of CAR-T immunotherapy. We examine the biological characteristics of CAR-Ts, the mechanisms that govern clinical responses, and the intricacies of adverse events. By exploring these aspects, we hope to gain a deeper understanding of CAR-T therapy, which will ultimately lead to improved clinical outcomes and broader therapeutic applications.

"Digital twins elucidate critical role of Tscm in clinical persistence of TCR-engineered cell therapy"

Despite recent progress in adoptive T cell therapy for cancer, understanding and predicting the kinetics of infused T cells remains a challenge. Multiple factors can impact the distribution, expansion, and decay or persistence of infused T cells in patients. We have developed a novel quantitative systems pharmacology (QSP) model of TCR-transgenic T cell therapy in patients with solid tumors to describe the kinetics of endogenous T cells and multiple memory subsets of engineered T cells after infusion. These T cells undergo lymphodepletion, proliferation, trafficking, differentiation, and apoptosis in blood, lymph nodes, tumor site, and other peripheral tissues. Using the model, we generated patient-matched digital twins that recapitulate the circulating T cell kinetics reported from a clinical trial of TCR-engineered T cells targeting E7 in patients with metastatic HPV-associated epithelial cancers. Analyses of key parameters influencing cell kinetics and differences among digital twins identify stem cell-like memory T cells (Tscm) cells as an important determinant of both expansion and persistence and suggest that Tscm-related differences contribute significantly to the observed variability in cellular kinetics among patients. We simulated in silico clinical trials using digital twins and predict that Tscm enrichment in the infused product improves persistence of the engineered T cells and could enable administration of a lower dose. Finally, we verified the broader relevance of the QSP model, the digital twins, and findings on the importance of Tscm enrichment by predicting kinetics for two patients with pancreatic cancer treated with KRAS G12D targeting T cell therapy. This work offers insight into the key role of Tscm biology on T cell kinetics and provides a quantitative framework to evaluate cellular kinetics for future efforts in the development and clinical application of TCR-engineered T cell therapies.

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.

PASCAR: a multiscale framework to explore the design space of constitutive and inducible CAR T cells

CAR T cells are engineered to bind and destroy tumor cells by targeting overexpressed surface antigens. However, healthy cells expressing lower abundances of these antigens can also be lysed by CAR T cells. Various CAR T cell designs increase tumor cell elimination, whereas reducing damage to healthy cells. However, these efforts are costly and labor-intensive, constraining systematic exploration of potential hypotheses. We develop a protein abundance structured population dynamic model for CAR T cells (PASCAR), a framework that combines multiscale population dynamic models and multi-objective optimization approaches with data from cytometry and cytotoxicity assays to systematically explore the design space of constitutive and tunable CAR T cells. PASCAR can quantitatively describe in vitro and in vivo results for constitutive and inducible CAR T cells and can successfully predict experiments outside the training data. Our exploration of the CAR design space reveals that optimal CAR affinities in the intermediate range of dissociation constants effectively reduce healthy cell lysis, whereas maintaining high tumor cell-killing rates. Furthermore, our modeling offers guidance for optimizing CAR expressions in synthetic notch CAR T cells. PASCAR can be extended to other CAR immune cells.

Development of a multiscale mechanistic modeling framework integrating differential cellular kinetics of CAR T-cell subsets and immunophenotypes in cancer patients

Chimeric antigen receptor (CAR) T-cell subsets and immunophenotypic composition of the pre-infusion product, as well as their longitudinal changes following infusion, are expected to affect CAR T-cell expansion, persistence, and clinical outcomes. Herein, we sequentially evolved our previously described cellular kinetic-pharmacodynamic (CK-PD) model to incorporate CAR T-cell product-associated attributes by utilizing published preclinical and clinical datasets from two affinity variants (FMC63 and CAT19 scFv) anti-CD19 CAR T-cells. In step 1, a unified cell-level PD model was used to simultaneously characterize the in vitro killing datasets of two CAR T-cells against CD19+ cell lines at varying effector:target ratios. In step 2, an augmented CK-PD model for anti-CD19 CAR T-cells was developed, by integrating CK dataset(s) from two bioanalytical measurements (quantitative polymerase chain reaction and flow cytometry) in patients with cancer. The model described the differential in vivo expansion properties of CAR T-cell subsets. The estimated expansion rate constant was ~1.12-fold higher for CAR+CD8+ cells in comparison to CAR+CD4+ T-cells. In step 3, the model was extended to characterize the disposition of four immunophenotypic populations of CAR T-cells, including stem-cell memory, central memory, effector memory, and effector cells. The model adequately characterized the longitudinal changes in immunophenotypes post anti-CD19 CAR T-cell infusion in pediatric patients with acute lymphocytic leukemia. Polyclonality in the pre-infusion product was identified as a categorical covariate influencing differentiation of immunophenotypes. In the future, this model could be leveraged a priori toward optimizing the composition of CAR T-cell infusion product, and further understand the CK-PD relationship in patients.

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 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.

Differential Response to Cytotoxic Drugs Explains the Dynamics of Leukemic Cell Death: Insights from Experiments and Mathematical Modeling

This study presents a framework whereby cancer chemotherapy could be improved through collaboration between mathematicians and experimentalists. Following on from our recently published model, we use A20 murine leukemic cells transfected with monomeric red fluorescent proteins cells (mCherry) to compare the simulated and experimental cytotoxicity of two Federal Drug Administration (FDA)-approved anticancer drugs, Cytarabine (Cyt) and Ibrutinib (Ibr) in an in vitro model system of Chronic Lymphocytic Leukemia (CLL). Maximum growth inhibition with Cyt (95%) was reached at an 8-fold lower drug concentration (6.25 μM) than for Ibr (97%, 50 μM). For the proposed ordinary differential equations (ODE) model, a multistep strategy was used to estimate the parameters relevant to the analysis of in vitro experiments testing the effects of different drug concentrations. The simulation results demonstrate that our model correctly predicts the effects of drugs on leukemic cells. To assess the closeness of the fit between the simulations and experimental data, RMSEs for both drugs were calculated (both RMSEs < 0.1). The numerical solutions of the model show a symmetrical dynamical evolution for two drugs with different modes of action. Simulations of the combinatorial effect of Cyt and Ibr showed that their synergism enhanced the cytotoxic effect by 40%. We suggest that this model could predict a more personalized drug dose based on the growth rate of an individual’s cancer cells.

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.

Peripheral leukemia burden at time of apheresis negatively affects the clinical efficacy of CART19 in refractory or relapsed B-ALL

Our previous clinical study achieved complete remission (CR) rates of >90% following chimeric antigen receptor T cells targeting CD19 (CART19) treatment of refractory/relapsed B cell acute lymphoblastic leukemia (r/r B-ALL); however, the influence of the leukemia burden in peripheral blood (PB) blasts remains unclear. Here, we retrospectively analyzed 143 patients treated with CART19 (including 36 patients with PB blasts) to evaluate the effect of peripheral leukemia burden at the time of apheresis. One hundred seventeen patients with high disease burdens achieved 91.5% CR or incomplete count recovery CR and 86.3% minimal residual disease-negative CR, and 26 patients with low disease burdens obtained 96.2% MRD⁻ CR. Collectively, 9 of 36 (25%) patients with PB blasts and 2 of 107 (1.87%) patients without PB blasts did not respond to CART19 therapy. The leukemia burden in PB negatively influenced ex vivo cell characteristics, including the transduction efficiency of CD3⁺ T cells and their fold expansion, and in vivo cell dynamics, including peak CART19 proportion and absolute count, fold expansion, and persistence duration. Further studies showed that these patients had higher programmed death-1 expression in CART19 products. Our data imply that PB blasts negatively affected CART19 production and the clinical efficacy of CART19 therapy in patients with r/r B-ALL.

A Mathematical Modeling Approach for Targeted Radionuclide and Chimeric Antigen Receptor T Cell Combination Therapy

Simple Summary

Targeted radionuclide therapy (TRT) and immunotherapy, an example being chimeric antigen receptor T cells (CAR-Ts), represent two potent means of eradicating systemic cancers. Although each one as a monotherapy might have a limited effect, the potency can be increased with a combination of the two therapies. The complications involved in the dosing and scheduling of these therapies make the mathematical modeling of these therapies a suitable solution for designing combination treatment approaches. Here, we investigate a mathematical model for TRT and CAR-T cell combination therapies. Through an analysis of the mathematical model, we find that the tumor proliferation rate is the most important factor affecting the scheduling of TRT and CAR-T cell treatments with faster proliferating tumors requiring a shorter interval between the two therapies.

Abstract

Targeted radionuclide therapy (TRT) has recently seen a surge in popularity with the use of radionuclides conjugated to small molecules and antibodies. Similarly, immunotherapy also has shown promising results, an example being chimeric antigen receptor T cell (CAR-T) therapy in hematologic malignancies. Moreover, TRT and CAR-T therapies possess unique features that require special consideration when determining how to dose as well as the timing and sequence of combination treatments including the distribution of the TRT dose in the body, the decay rate of the radionuclide, and the proliferation and persistence of the CAR-T cells. These characteristics complicate the additive or synergistic effects of combination therapies and warrant a mathematical treatment that includes these dynamics in relation to the proliferation and clearance rates of the target tumor cells. Here, we combine two previously published mathematical models to explore the effects of dose, timing, and sequencing of TRT and CAR-T cell-based therapies in a multiple myeloma setting. We find that, for a fixed TRT and CAR-T cell dose, the tumor proliferation rate is the most important parameter in determining the best timing of TRT and CAR-T therapies.

Potential of Immunotherapies in Treating Hematological Cancer-Infection Comorbidities-A Mathematical Modelling Approach

BACKGROUND

The immune system attacks threats like an emerging cancer or infections like COVID-19 but it also plays a role in dealing with autoimmune disease, e.g., inflammatory bowel diseases, and aging. Malignant cells may tend to be eradicated, to appraoch a dormant state or escape the immune system resulting in uncontrolled growth leading to cancer progression. If the immune system is busy fighting a cancer, a severe infection on top of it may compromise the immunoediting and the comorbidity may be too taxing for the immune system to control.

METHOD

A novel mechanism based computational model coupling a cancer-infection development to the adaptive immune system is presented and analyzed. The model maps the outcome to the underlying physiological mechanisms and agree with numerous evidence based medical observations.

RESULTS AND CONCLUSIONS

Progression of a cancer and the effect of treatments depend on the cancer size, the level of infection, and on the efficiency of the adaptive immune system. The model exhibits bi-stability, i.e., virtual patient trajectories gravitate towards one of two stable steady states: a dormant state or a full-blown cancer-infection disease state. An infectious threshold curve exists and if infection exceed this separatrix for sufficiently long time the cancer escapes. Thus, early treatment is vital for remission and severe infections may instigate cancer progression. CAR T-cell Immunotherapy may sufficiently control cancer progression back into a dormant state but the therapy significantly gains efficiency in combination with antibiotics or immunomodulation.

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.

Early Survival Prediction Framework in CD19-Specific CAR-T Cell Immunotherapy Using a Quantitative Systems Pharmacology Model

Chimeric antigen receptor (CAR)-T cell therapy has revolutionized treatment of relapsed/refractory non-Hodgkin lymphoma (NHL). However, since 36-60% of patients relapse, early response prediction is crucial. We present a novel population quantitative systems pharmacology model, integrating literature knowledge on physiology, immunology, and adoptive cell therapy together with 133 CAR-T cell phenotype, 1943 cytokine, and 48 metabolic tumor measurements. The model well described post-infusion concentrations of four CAR-T cell phenotypes and CD19+ metabolic tumor volume over 3 months after CAR-T cell infusion. Leveraging the model, we identified a low expansion subpopulation with significantly lower CAR-T cell expansion capacities amongst 19 NHL patients. Together with two patient-/therapy-related factors (autologous stem cell transplantation, CD4+/CD8+ T cells), the low expansion subpopulation explained 2/3 of the interindividual variability in the CAR-T cell expansion capacities. Moreover, the low expansion subpopulation had poor prognosis as only 1/4 of the low expansion subpopulation compared to 2/3 of the reference population were still alive after 24 months. We translated the expansion capacities into a clinical composite score (CCS) of 'Maximum naïve CAR-T cell concentrations/Baseline tumor burden' ratio and propose a CCSTN-value > 0.00136 (cells·µL-1·mL-1 as predictor for survival. Once validated in a larger cohort, the model will foster refining survival prediction and solutions to enhance NHL CAR-T cell therapy response.

A Systematic Review of the Efforts and Hindrances of Modeling and Simulation of CAR T-cell Therapy

Chimeric antigen receptor (CAR) T-cell therapy is an immunotherapy that has recently become highly instrumental in the fight against life-threatening diseases. A variety of modeling and computational simulation efforts have addressed different aspects of CAR T-cell therapy, including T-cell activation, T- and malignant cell population dynamics, therapeutic cost-effectiveness strategies, and patient survival. In this article, we present a systematic review of those efforts, including mathematical, statistical, and stochastic models employing a wide range of algorithms, from differential equations to machine learning. To the best of our knowledge, this is the first review of all such models studying CAR T-cell therapy. In this review, we provide a detailed summary of the strengths, limitations, methodology, data used, and data gap in currently published models. This information may help in designing and building better models for enhanced prediction and assessment of the benefit-risk balance associated with novel CAR T-cell therapies, as well as with the data need for building such models.

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

Chimeric antigen receptor (CAR) T cell therapy is a remarkably effective immunotherapy that relies on in vivo expansion of engineered CAR T cells, after lymphodepletion (LD) by chemotherapy. The quantitative laws underlying this expansion and subsequent tumour eradication remain unknown. We develop a mathematical model of T cell-tumour cell interactions and demonstrate that expansion can be explained by immune reconstitution dynamics after LD and competition among T cells. CAR T cells rapidly grow and engage tumour cells but experience an emerging growth rate disadvantage compared to normal T cells. Since tumour eradication is deterministically unstable in our model, we define cure as a stochastic event, which, even when likely, can occur at variable times. However, we show that variability in timing is largely determined by patient variability. While cure events impacted by these fluctuations occur early and are narrowly distributed, progression events occur late and are more widely distributed in time. We parameterized our model using population-level CAR T cell and tumour data over time and compare our predictions with progression-free survival rates. We find that therapy could be improved by optimizing the tumour-killing rate and the CAR T cells' ability to adapt, as quantified by their carrying capacity. Our tumour extinction model can be leveraged to examine why therapy works in some patients but not others, and to better understand the interplay of deterministic and stochastic effects on outcomes. For example, our model implies that LD before a second CAR T injection is necessary.