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

Mathematical Modeling Unveils Optimization Strategies for Targeted Radionuclide Therapy of Blood Cancers

Targeted radionuclide therapy is based on injections of cancer-specific molecules conjugated with radioactive nuclides. Despite the specificity of this treatment, it is not devoid of side-effects limiting its use and is especially harmful for rapidly proliferating organs well perfused by blood, like bone marrow. Optimization of radioconjugates administration accounting for toxicity constraints can increase treatment efficacy. Based on our experiments on disseminated multiple myeloma mouse model treated by 225Ac-DOTA-daratumumab, we developed a mathematical model which investigation highlighted the following principles for optimization of targeted radionuclide therapy. 1) Nuclide to antibody ratio importance. The density of radioconjugates on cancer cells determines the density of radiation energy deposited in them. Low labeling ratio as well as accumulation of unlabeled antibodies and antibodies attached to decay products in the bloodstream can mitigate cancer radiation damage due to excessive occupation of specific receptors by antibodies devoid of radioactive nuclides. 2) Cancer binding capacity-based dosing. The rate of binding of drug to cancer cells depends on the total number of their specific receptors, which therefore can be estimated from the pharmacokinetic curve of diagnostic radioconjugates. Injection of doses significantly exceeding cancer binding capacity should be avoided since radioconjugates remaining in the bloodstream have negligible efficacy to toxicity ratio. 3) Particle range-guided multi-dosing. The use of short-range particle emitters and high-affinity antibodies allows for robust treatment optimization via initial saturation of cancer binding capacity, enabling redistribution of further injected radioconjugates and deposited dose towards still viable cells that continue expressing specific receptors.

Designing combination therapies for cancer treatment: application of a mathematical framework combining CAR T-cell immunotherapy and targeted radionuclide therapy

Introduction

Cancer combination treatments involving immunotherapies with targeted radiation therapy are at the forefront of treating cancers. However, dosing and scheduling of these therapies pose a challenge. Mathematical models provide a unique way of optimizing these therapies.

Methods

Using a preclinical model of multiple myeloma as an example, we demonstrate the capability of a mathematical model to combine these therapies to achieve maximum response, defined as delay in tumor growth. Data from mice studies with targeted radionuclide therapy (TRT) and chimeric antigen receptor (CAR)-T cell monotherapies and combinations with different intervals between them was used to calibrate mathematical model parameters. The dependence of progression-free survival (PFS), overall survival (OS), and the time to minimum tumor burden on dosing and scheduling was evaluated. Different dosing and scheduling schemes were evaluated to maximize the PFS and optimize timings of TRT and CAR-T cell therapies.

Results

Therapy intervals that were too close or too far apart are shown to be detrimental to the therapeutic efficacy, as TRT too close to CAR-T cell therapy results in radiation related CAR-T cell killing while the therapies being too far apart result in tumor regrowth, negatively impacting tumor control and survival. We show that splitting a dose of TRT or CAR-T cells when administered in combination is advantageous only if the first therapy delivered can produce a significant benefit as a monotherapy.

Discussion

Mathematical models are crucial tools for optimizing the delivery of cancer combination therapy regimens with application along the lines of achieving cure, maximizing survival or minimizing toxicity.

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.

Sequential CAR T cell and targeted alpha immunotherapy in disseminated multiple myeloma

Multiple myeloma (MM) is still an incurable disorder despite improved antibody and cellular therapies against different MM antigens. Single targeted antigens have so far been ineffective against MM with most patients relapsing after initial response. Hence, sequential immunotherapies directed at different targets are expected to perform better than monotherapy alone. Here, we optimized and established in preclinical studies the therapeutic rationale of using targeted alpha therapy (TAT) directed against CD38 antigen (²²⁵Ac-DOTA-daratumumab) with CAR T cell therapy directed at CS1 antigen in a systemic MM model. The sequential therapies compared CAR T therapy followed by TAT to TAT followed by CAR T therapy. CAR T cell monotherapy increased median survival from 49 days (d) in untreated controls to 71d with a modest improvement to 89d for 3.7 kBq of TAT given 14d later. When CAR T was followed by 7.4 kBq of TAT 29d later, sequential therapy increased median survival from 47d in untreated controls to 106d, compared to 68d for CAR T monotherapy. When CAR T therapy was followed by untargeted alpha immunotherapy using 7.4 kBq of ²²⁵Ac-DOTA-trastuzumab (anti-HER2) antibody 29d later, there was only a slight improvement in response over CAR T monotherapy demonstrating the role of tumor targeting. TAT (7.4 kBq) followed by CAR T therapy was also effective when CAR T therapy was delayed for 21d vs 14d or 28d post TAT, highlighting the importance of timing sequential therapies. Sequential targeted therapies using CS1 CAR T or ²²⁵Ac-DOTA-CD38 TAT in either order shows promise over monotherapies alone.

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.

Mathematical modeling of cancer immunotherapy for personalized clinical translation

Encouraging advances are being made in cancer immunotherapy modeling, especially in the key areas of developing personalized treatment strategies based on individual patient parameters, predicting treatment outcomes and optimizing immunotherapy synergy when used in combination with other treatment approaches. Here we present a focused review of the most recent mathematical modeling work on cancer immunotherapy with a focus on clinical translatability. It can be seen that this field is transitioning from pure basic science to applications that can make impactful differences in patients' lives. We discuss how researchers are integrating experimental and clinical data to fully inform models so that they can be applied for clinical predictions, and present the challenges that remain to be overcome if widespread clinical adaptation is to be realized. Lastly, we discuss the most promising future applications and areas that are expected to be the focus of extensive upcoming modeling studies.

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.