Chemotherapy and external beam radiation therapy have been traditional approaches for treating hematological malignancies. External beam radiation therapy has typically been employed for treatment of solitary plasmacytomas and as a palliative measure for more widespread disease (1, 2). The primary disadvantage of external beam radiotherapy is the toxicity to normal cells present near malignant cells in the bone marrow. Thus, its role has been limited in the treatment of hematological malignancies. In contrast, immunotherapy-based approaches have been employed in standard regimens and have led to significant improvements in patient disease remission (3). The dysregulation of the immune system in multiple myeloma (MM) and its targeting by immunotherapies has been a key reason for immunotherapy success (4). In particular, Chimeric Antigen Receptor T cells (CAR-T cells) have recently come to the fore due to their efficacy against several hematological malignancies including MM, leukemia and B-cell malignancies (5). CAR-T cells are T cells that have been engineered to target a receptor on the tumor cells thus binding them to tumor cells for direct effect. B-Cell Maturation Antigen (BCMA) targeting CAR-T cells have recently been approved by the FDA for treatment of MM (6). While these novel immunotherapies have created a significant impact, most patients still experience relapse, leading to unsuccessful treatment (7), supporting the need to develop novel combinatorial approaches for complete disease eradication.

Targeted radionuclide therapy (TRT) is a form of radiation therapy in which a radionuclide delivering radiation is attached to an agent that targets tumor cells (8). The advantage of TRT is that it is both highly targeted and delivered systemically. In addition, the radionuclide can be chosen with a half-life that is appropriate for balancing efficacy and toxicity of the treatment. For example, we have shown that the targeted alpha particle therapy (TAT) with ²²⁵Ac conjugated to the CD38 receptor targeting antibody daratumumab demonstrated superior efficacy without added toxicity in treatment of disseminated multiple myeloma in a mouse model as compared to a beta particle emitter ¹⁷⁷Lu (9). The shorter range (< 100 μm) but higher potency (given by their high linear energy transfer) of alpha particles emitted from ²²⁵Ac and its daughters was crucial in targeting the cancer cells but sparing the normal tissue cells in the bone marrow. While TAT was associated with increased survival, it alone did not result in curative responses. To address this limitation of radionuclide therapies, we and others (10–12) have investigated the addition of immune-based therapies to TRT as a potentially curative combination therapy approach.

Selecting the dosing, timing, and sequencing of any combination therapy approach experimentally is challenging due to the number of possible combinations to be tested; therefore a more efficient method of experimental design to achieve optimal therapy regimens is useful and increasingly becoming essential (13). Fortunately, mathematical models aided by experimental data exemplify a way for achieving optimal combination of therapies. Combining multiple therapies can result in synergistic, additive or antagonistic effects. Methods have been proposed to quantify (14, 15) and optimize (16–18) these effects. Combination therapy optimization using mathematical models can be performed at several levels depending on our knowledge of the system parameters (19). Many types of therapy combinations have been investigated using mathematical models (20). In particular, mathematical models of tumor-immune system dynamics have been proposed to optimize and personalize immunotherapies (21–23) either on their own or in combination with chemotherapy (24). Additionally, mathematical modeling of radiation therapy using the linear-quadratic model (25) to optimize patient-specific treatment regimens has been investigated for decades (26, 27). The proposed radiobiological models have been used to study both tumor and normal tissue radiation dose-response effects (28–30). The modeling efforts using radiobiological models and their variations span both external beam, brachytherapy as well as targeted radionuclide radiotherapies (30–35). Recognizing the synergy between immunotherapies and radiation therapy, mathematical models utilizing the external beam radiation therapy and immunotherapies have been proposed (36, 37) in order to tailor the dose of external beam radiation therapy to elicit systemic immune response as well as to study the effect of radiation therapy on different immune populations (38, 39).

We recently proposed a mathematical model for optimization of targeted radionuclide therapy with CAR-T cell therapy (40). The model considered the tumor response to targeted radionuclide and CAR-T cell therapies as monotherapies and preclinical data from each set of monotherapy experiments was used to characterize the model. Different timing schedules of TAT and CAR-T cell therapies were tested in silico, and it was shown that the timing between the two therapies for maximizing the survival metrics was highly dependent on the tumor proliferation rate. Elucidating the mathematical parameters relevant for multiple therapies gives a novel way of investigating the dosing, timing, and the sequence of combination therapies and generate in silico therapeutic regimens that can then be tested in vivo.

Here we validate the mathematical model against experimental data where the timing of the CAR-T cell therapy is varied keeping the TAT dosage and timing constant. Model parameters are elucidated from the experimental data to optimize the timing of CAR-T cell therapy post-TAT by maximizing the progression-free survival. The effect of fractionated dosing of both TRT and CAR-T cell therapies on the survival metrics is also studied. In addition, multiple dosing strategies for TRT and CAR-T cell therapies are tested to analyze whether the splitting and scheduling of the doses result in improved tumor control or survival.

In this work we show a modeling framework of combined TRT and CAR-T cell therapy applied to experimental data. We have elucidated the parameters that are relevant for this combination in a murine model of multiple myeloma. We show that splitting of therapy doses is advantageous only if the first therapy can produce a significant benefit on its own. The model provides a quantitative framework to optimize the dosing of immunotherapies and targeted radionuclide therapies.

We optimized the TAT and CAR-T model parameters such that a single parameter set with 50% uncertainty can explain the differences in the tumor burden curves between individual mice. Such an approach can facilitate in silico optimization of the two therapies, where a single parameter set is associated with each of the therapies. While the introduction of uncertainties in the parameters results in better individual tumor curve fits, more information about CAR-T cell dynamics within the system can be highly informative regarding the model parameters. In particular, the value of CAR-T cell proliferation (k₂) was predicted to be small relative to other rate constants.

The optimized value of tumor proliferation rate (ρ = 0.21 day^-1) is smaller than the one calculated from untreated controls (ρ = 0.27 day^-1) which is used for BLI to tumor cell number conversion. There can be two reasons for this. First, the long-term growth of the tumor burden could be sigmoidal in nature instead of exponential as assumed in the model resulting in slowing down of the tumor growth at later stages as compared to the initial stages. Secondly, it could be that the post-treatment phenotype of the tumor cells could be more resistant and could grow slower in comparison to the pre-treatment phenotype. Such a scenario would also support the reduced effectiveness of CAR-T cell therapy when the interval between the therapies is increased ( Figure 3E ). The resistance of tumor cell population to therapy can be mitigated by combination therapy approaches targeting two different types of treatment sensitivities. Gatenby et al. (41) introduced the ecological evolutionary dynamics concept of ‘first strike-second strike’ approach (42) to strategically sequence therapies for tumor cure. The first strike reduces the size and heterogeneity of the tumor cell population while the second strike(s) pushes the population below a critical threshold that eventually results in tumor cell eradication. Relevant to the combinations used in this work, radiation therapy could be considered the tumor debulking treatment prior to CAR-T cell therapy (43).

Based on the mathematical model, it might be feasible to delay the delivery of the CAR-T cell dose post-TRT (CAR-T cells on day 25 vs 32), since the overall survival might increase. However, it comes at the cost of higher uncertainty in the PFS indicating that other factors that are not captured in the model might influence tumor growth that might let it escape treatment. Notably, the parameter evaluation for TRT + d32 CAR-T cell treatment indicates lower efficacy of CAR-T cells compared to other treatment combinations. This increased therapy interval can also potentially increase the mutational burden of the tumor and might lead to reduced therapy effectiveness.

In the current work, the optimization of multiple therapy combinations is done with the goal of maximizing PFS. Another strategy could be minimizing the tumor burden with the goal of curative response. For different therapy regimens, it could be tested whether tumor burden predicted by the model would be low enough for cure in contrast to a strategy for maximizing PFS, thus giving the model the flexibility to test different scenarios.

The mice experiments used in this work have been performed on immunocompromised mice. Thus, the effect of radiation on stimulating immune system is not present in this mouse model. This data presents a cleaner model system for elucidating the effect of CAR-T cells on the tumor volume by eradicating the influence of other immune system components that can affect tumor volume. The impact of radiation on the immune system will need to be incorporated for optimizing therapeutic regimens in humans.

Biological variability in both preclinical and clinical realms is a determinant of heterogeneous response to therapies both in terms of efficacy and toxicity. To this end, the model assumes that a set of model parameters is shared between the mice in the same group, albeit with some uncertainty. Here we have chosen the model parameters within a group to vary by 50% from the group mean. This uncertainty level was chosen to capture expected variation in mice groups based on our previous experience (40); and is enough to demonstrate the differences in mean response to therapy between the groups while at the same time accommodating qualitatively reasonable fits to individual mice. In patients, the model can be personalized better by delivering multiple cycles of therapy and evaluating the patient response to individual doses to tailor the next dose or therapy sequence. To this end clinical trials evaluating targeted radionuclide therapy using ²²⁵Ac-DOTA-Dara (Clinical trial identifier: NCT05363111) and CS1-CAR-T cell therapy (Clinical trial identifier: NCT03710421) as monotherapies in multiple myeloma patients are being evaluated to study patient response (toxicity and efficacy) to these agents. The combination of these therapies can bring synergistic effects and unique challenges. Radiation from TRT can give rise to non-specific immune response of CAR-T cells and might result in T-cell activation and priming. Abscopal effects of radiation that might be based on systemic responses can also result in increased efficacy compared to model predictions. A possible side effect especially relevant to targeted alpha particle therapies like ²²⁵Ac is the impact of these agents on the tumor vasculature. Depending on the specific tumor, its vasculature and the radiation dose delivered, a complex non-linear relationship might exist for vasculature killing that might impact the delivery of subsequent therapies. Studying the spatio-temporal nature of tumor response to different doses while at the same time imaging the accumulation of these agents in tumors (as being done in the ²²⁵Ac-Dara trial NCT05363111) can be key to develop more sophisticated mathematical models that can further optimize therapeutic regimen with targeted radionuclide therapies.

An obvious result is that higher dose of a therapy, the higher chance of cure; suggesting that the shorter the interval between two cycles of a therapy, the better the tumor reduction to the limit that CAR-T cells are not significantly damaged by the radiation. However, the interval between therapies cannot be shortened indefinitely. Reduced interval between TRT and CAR-T cell therapy results in death of CAR-T cells. On the other hand, reduced interval between two CAR-T cell doses or two TRT doses can be equivalent to a single high dose of that therapy. The radiation dose to organs at risk needs to be considered in a way that the rejuvenation of the organ at risk yields a therapeutic advantage when delivering a second cycle of the therapy. In the case of TAT, it could be the bone marrow while CAR-T cell toxicity can be in the form of cytokine release syndrome. Thus, a combination therapy where the two toxicity risks are unrelated to each other is seen to provide the best tumor control and delay tumor growth. Thus, the rationale for use of immunotherapies with TRT as part of a therapy regimen is strong and justifies its use for further investigation.

The data generated in this work are available in the article and the Supplemental File . The BLI data associated with the work is provided as another supplementary file. The associated code for analysis can be found at https://github.com/cohmathonc/TRT-and-CAR-T-cell-combination-therapy.git.

The animal study was approved by City of Hope Institutional Animal Care and Use Committee. The study was conducted in accordance with the local legislation and institutional requirements.

VA: Conceptualization, Formal analysis, Investigation, Methodology, Validation, Writing – original draft, Writing – review & editing. DA: Data curation, Formal analysis, Investigation, Validation, Writing – review & editing. EC: Data curation, Formal analysis, Investigation, Validation, Writing – review & editing. MM: Data curation, Formal analysis, Investigation, Validation, Writing – review & editing. MK: Formal analysis, Validation, Writing – review & editing. AK: Formal analysis, Validation, Writing – review & editing. JW: Formal analysis, Validation, Writing – review & editing. JS: Formal analysis, Funding acquisition, Investigation, Project administration, Supervision, Validation, Writing – review & editing. XW: Formal analysis, Funding acquisition, Investigation, Project administration, Resources, Supervision, Validation, Writing – review & editing. FP: Formal analysis, Funding acquisition, Investigation, Project administration, Supervision, Validation, Writing – review & editing. RR: Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Validation, Writing – original draft, Writing – review & editing.