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

Abstract

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.

Fig 1. Model schematic description. A Model for CAR-T cell therapy considering injected (CI), expander (CE), and persister (CP) CAR-T cells, and antigen-positive (Ag+) tumor cells (TP). The phenotypic differentiation of CAR-T cells is driven by antigen recognition on the surface of tumor cells (F(TP)). B The model is extended to describe patients who presented antigen-negative tumor relapses by including a compartment of antigen-negative (Ag-) tumor cells (TN). C The same model can be extended to describe macrophage-mediated cytokine release considering three different activation mechanisms: antigen-binding (upon antigen-recognition, activated CAR-T cells release inflammatory cytokines and molecules that activate naive macrophages, orange arrow); DAMPs-release (CAR-T-mediated killing of the tumor leads to the release of damage-associated molecular patterns (DAMPs) that promote macrophage activation, blue arrow); CD40-contact (in a contact-dependent manner, activated macrophages expressing CD40 bind to CD40 ligand expressed by CAR-T cells and promote further macrophage activation (pink arrow).

Fig 2. Model simulations. Model fits for selected patients that showed response to therapy (P01, G01, M57, and M68) or relapse either of antigen-positive tumor cells (L02, L04) or antigen-negative tumor cells (G02, and M44). See S1–S4 Figs for all 25 patients and Methods for details on parameter estimation. Although patients M57 and M68 were simulated until their PFS day, plots show their dynamics for 60 days for clarity. Tumor cell error bars represent the range of WBCs used in scaling while error bars for IL-6 in patients M44, M57, and M68 encompass the range reported in [32]. The CAR-T cell detection threshold of 2.5×105 cells is represented by the gray shaded area.

Fig 3. Identifying mechanisms driving therapy phases. A For each patient model fit, the distinct phases for CAR-T (green) and tumor (red) cell responses are identified and the characteristic slope is calculated and compared with the patient-specific mechanistic parameter driving the corresponding phase. B-H Comparison between the calculated slope and the mechanistic parameter for each phase and each patient. B Distribution phase: the calculated slope is the minimum (negative) slope of CAR-T cells, the mechanistic parameter is −μI. C Expansion phase: the calculated slope is the maximum (positive) slope of CAR-T cells, the mechanistic parameter is κ  −  μE. D Contraction phase: the calculated slope is the minimum (negative) slope of CAR-T cells, the mechanistic parameter is −μE. E Persistence phase: the calculated slope is the maximum (negative) slope of CAR-T cells, the mechanistic parameter is −μP. F Transient phase: the calculated slope is the maximum (positive) slope of tumor cells, the mechanistic parameter is ρ. G Shrinkage phase: the calculated slope is the minimum (negative) slope of tumor cells, the mechanistic parameter is ρ − γ. H Response phase: the calculated slope is the maximum (positive) slope of tumor cells for relapse patients only, the mechanistic parameter is ρ.

Fig 4. Mapping of mechanistic parameters on response characteristics. A qualitative sensitivity analysis identified a nonlinear mapping between ten different shape features of the model response (slopes mD,mE,mC,mP,mS,mP, CAR-T cell minimum, CAR-T cell peak concentration, minimum tumor load, and persistence level) to ten mechanistic parameters. This is illustrated by simulations for patient M44 (black) and alternative scenarios (blue and yellow) where one parameter is changed at a time. A-D The slopes in the distribution, expansion, and contraction phases are determined by the decay of injected CAR-T cells (μI), the net expansion rate of CAR-T expander cells (κ−μE), their death and exhaustion (μE), and the decay of CAR-T persister cells (μP). E The minimum level of CAR-T cells observed at the end of the distribution phase is determined by the activation rate of injected CAR-T cells (η). F,G The CAR-T cell peak depends on the saturation constants for the antigen binding (A) and tumor killing (B) functions. H The persistence level is mainly determined by the memory pool formation rate ϵ. I,J The slopes in the shrinkage and response phases of tumor dynamics are determined by CAR-T cell cytotoxicity (γ) and tumor growth rate (ρ), respectively. K,L The minimum tumor load is negatively correlated with the CAR-T cell peak and therefore is also determined by A and B. Although most of the response characteristics appear to have a first-order dependence on only one mechanistic parameter, this is not the case for the CAR-T cell peak and the minimum tumor burden, which also strongly depend on κ, μE, γ and ρ. See also S5 and S6 Figs.

Fig 5. Patient-specific pharmacological and clinical parameters evaluated from model fits. A–D Within the patient level, the fold change in IL-6 concentration (baseline to peak) cannot be predicted from a single indicator, such as total CAR-T dose, initial tumor burden, CAR-T cell fold change (dose to peak), or time of IL-6 peak. E However, for the majority of patients, the model predicts that the peak of CAR-T cells occurs between 0 and 5 days after the cytokine peak (gray area). F For all patients, the cytokine peak is predicted to occur between 0 and 2 days after the peak of activated macrophages (gray area). G,H The tumor burden at days 28 and 90 post-therapy initiation shows a weak negative correlation with CAR-T cell fold change (a value of 0.1 cells is assigned for cases where the model predicts zero tumor cells). I The model predicts a moderate correlation between tumor burden responses at days 28 and 90. In each panel, the best linear fit for the red points is shown in light red, and the corresponding correlation coefficient R2 and p-value are given.

Fig 6. Effect of simulating different dosing protocols on CAR-T cell dynamics, tumor response, and cytokine peak. To investigate the outcomes of a different CAR-T dose or change in the preconditioning or bridging therapy, we compared the standard scenario (Fit) with simulations starting with either a different CAR-T dose or initial tumor burden (10x and 100x smaller and higher). Assessed outcomes were: A number of CAR-T cells at peak (Cmax), B number of tumor cells at day 28, C number of persister CAR-T cells at day 28 D IL-6 fold change (baseline to peak), E day of CAR-T cell peak, F day of IL-6 peak. The number of tumor and CAR-T persister cells at day 90 were also assessed and did not present sensible differences (S7 Fig).

Fig 7. Dynamics of macrophage activation and IL-6 release. A Time course of patient M44, selectively activating DAMPs release, antigen-binding, and CD40 contact mechanisms one at a time. DAMPs-only activation leads to an IL-6 peak around day 3 during tumor shrinkage. Antigen-biding activation results in IL-6 increasing with CAR-T expansion, peaking around day 8. CD40-mediated activation alone maintains IL-6 at baseline, but when combined with small values for DAMPs and antigen-binding parameters, it produces an IL-6 peak around day 13, four days after the CAR-T cell peak. B Splitting the active macrophage population according to their source, i.e., activation mechanisms (see Methods), and reconstructing the timeline for each patient, we found that the peak of DAMP-activated macrophages takes place early, during the tumor shrinkage phase. The second subpopulation to present a peak is the antigen-binding-activated macrophages, which expand in parallel with CAR-T expansion. The last sub-population to peak are CD40-activated macrophages, which require the presence of previously activated macrophages. For 8 out of the 15 patients, the major source of activated macrophages was CD40 contact (pie charts), which was also the source of 62% of all activated macrophages when all patients are combined.

Fig 8. Blocking of macrophage activation and cytokine release. A Simulation results of interventions reducing mechanisms of macrophage activation one at a time, showing the reduction in IL-6 peak for each patient (gray curves) and mean effect (colored curves). For a simulated 50% reduction (dashed line, fourth panel) the overall reduction in IL-6 peak is indicated for each mechanism. B Simulation results of interventions blocking CD40 starting 0-10 days after CAR-T cell infusion, stopping -5, 0 and 5 days after CAR-T cell peak. The plots show the resulting reduction in IL-6 peak for each patient (gray curves) and the mean effect (colored curves).