Model‐Based Analysis with Mechanistic Insights to CAR‐T‐Cell Therapy Kinetics: Case Study with Axicabtagene Ciloleucel and Brexucabtagene Autoleucel

Abstract

Model‐informed drug development is increasingly used to support chimeric antigen receptor (CAR)‐T‐cell therapy programs. However, most population pharmacokinetic (PK) CAR‐T‐cell models available in literature are variations of an empirical piecewise‐linear model, which accurately describes the observed data but lacks a mechanistic foundation. This limits its use for simulations of scenarios beyond the observed data. This work presents a mechanism‐based population PK framework that aims to bridge existing empirical and mechanistic CAR‐T‐cell modeling approaches. The model was developed using a clinical database of 473 patients with various relapsed or refractory lymphomas (large B cell, follicular, marginal zone, or mantle cell) receiving axicabtagene ciloleucel or brexucabtagene autoleucel. The framework incorporates two CAR‐T‐cell compartments alongside a latent kinetic‐pharmacodynamic tumor compartment, utilizing a continuous, mechanistically‐driven approach to characterize the observed PK profiles. A covariate search identified five significant covariates impacting PK (P < 0.001). Among these, only product type/mantle cell lymphoma (MCL) disease type was deemed to have clinically relevant effects on exposure. Despite its mechanistic basis, the model remains parsimonious, requiring only seven structural parameters, and no additional data beyond post‐infusion CAR‐T‐cell peripheral blood concentrations and covariate information routinely collected in clinical trials. With its mechanistic foundation but parsimonious structure, this model balances data‐driven practicality with the integration of underlying biological processes. Its ability to identify relevant covariates could make it a valuable tool in supporting drug development decisions.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

Modeling and simulation can be used to support drug development decisions in CAR‐T‐cell programs. However, current pharmacokinetic (PK) models are mostly either highly empirical, limiting mechanistic interpretability and suitability for simulations, or highly mechanistic, making them less practical in late‐stage drug development with short development timelines.

• WHAT QUESTION DID THIS STUDY ADDRESS?

This study investigated whether a mechanism‐based population PK model could bridge existing empirical and mechanistic CAR‐T‐cell modeling approaches to better support drug development decisions in CAR‐T‐cell therapy programs.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

The developed population model provides a mechanism‐based framework for characterizing the PK of CAR‐T‐cell therapy. It was developed using data from 473 patients receiving either axi‐cel or brexu‐cel to treat large B cell, follicular, marginal zone, or mantle cell lymphoma (MCL). Identified significant covariates included product type/MCL disease type, the % of effector CAR‐T cells in the infusion product, prior bendamustine therapy, albumin, and body weight. However, only product type/MCL disease type was deemed to have a clinically relevant effect on the predicted CAR‐T‐cell exposure.

• HOW MIGHT THIS CHANGE CLINICAL PHARMACOLOGY OR TRANSLATIONAL SCIENCE?

Based on the generally conserved CAR‐T‐cell kinetics across products, the model can be used as a platform framework, as illustrated with axi‐cel and brexu‐cel in this case study. Its mechanistic background enables extrapolations and simulations of how factors like dose, patient characteristics, manufacturing conditions, and product characteristics impact CAR‐T‐cell exposure, supporting the framework's use in early‐ to late‐stage model‐informed drug development of CAR‐T‐cell therapy.

Chimeric antigen receptor (CAR)‐T‐cell therapy is a personalized anticancer treatment, in which T cells are genetically modified to eliminate cancer cells. Seven autologous CAR‐T‐cell products are currently approved for hematological cancers. Among these, axicabtagene ciloleucel (axi‐cel; Yescarta®) and brexucabtagene autoleucel (brexu‐cel; Tecartus®) share an identical CAR construct ¹ but differ in manufacturing attributes. ² , ³ In the pivotal trials, axi‐cel achieved an overall response rate (ORR) of 83% in relapsed/refractory (r/r) large B‐cell lymphoma (LBCL) (ZUMA‐1), ⁴ while brexu‐cel demonstrated an ORR of 85% in mantle cell lymphoma (MCL) (ZUMA‐2) ⁵ and 70% in B‐cell acute lymphoblastic leukemia (B‐ALL) (ZUMA‐3). ⁶ In the real world, similar efficacy outcomes were observed, ⁷ , ⁸ although disease relapse, serious adverse events, and financial burden remain a challenge. ⁹ , ¹⁰

With pronounced CAR‐T‐cell‐mediated efficacy after a single dose, maximum concentration (C _max) and area under the concentration‐time curve during the first 28 days (AUC_0–28d) are typically positively correlated with treatment response and toxicity. ² , ¹¹ , ¹² However, post‐infusion CAR‐T‐cell exposure is highly variable and largely unrelated to the administered dose. ¹¹ , ¹²

The models available to explore underlying sources of the pharmacokinetic (PK) variability tend to be either highly empirical ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ or mechanistic. ²⁰ , ²¹ , ²² Mechanistic models are particularly valuable in early drug development, yet they are time‐intensive to develop and their qualification and validation is complex, ²³ which makes them less practical in later‐stage drug development. Empirical piecewise‐linear CAR‐T‐cell PK models, ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ however, lack a mechanistic structure. Therefore, although they are useful for descriptive analyses or interpolations within observed data, their ability to support extrapolations or simulations of unobserved scenarios is limited.

In this work, we developed a mechanism‐based population PK model to bridge existing empirical and mechanistic approaches. This model can support drug‐development decisions in CAR‐T‐cell therapy by simulating CAR‐T‐cell exposure while exploring different doses or covariates. Data from 473 patients receiving axi‐cel or brexu‐cel were used to develop the model and to explore covariate‐parameter relationships.

MATERIALS AND METHODS

Clinical dataset

Data from 406 patients with r/r LBCL, FL, and marginal zone lymphoma, receiving axi‐cel in studies ZUMA‐1, ⁴ ZUMA‐5, ²⁴ and ZUMA‐7, ⁴ and data from 67 patients with MCL receiving brexu‐cel in study ZUMA‐2 ⁵ were used to develop the PK model. All study protocols were approved by the institutional review board or ethics committee at each investigational site, and the studies were conducted in accordance with Good Clinical Practice guidelines and adhered to the Declaration of Helsinki. All patients provided written informed consent. A summary of patient‐, disease‐, product‐, and treatment‐related patient characteristics is provided in Table 1 .

Table 1.

Number of patients in the full analysis set and their patient‐, disease‐, product‐, and treatment‐related characteristics that were considered for covariate testing, stratified by product and overall.

	Axi‐cel (n = 406)	Brexu‐cel (n = 67)	Overall (n = 473)
Number of patients
Study (n (%))
ZUMA‐1	99 (24.4%)	0 (0%)	99 (20.9%)
ZUMA‐2	0 (0%)	67 (100%)	67 (14.2%)
ZUMA‐5	146 (36.0%)	0 (0%)	146 (30.9%)
ZUMA‐7	161 (39.7%)	0 (0%)	161 (34.0%)
Patient‐related baseline characteristics
Sex (n (%))
Female	157 (38.7%)	11 (16.4%)	168 (35.5%)
Male	249 (61.3%)	56 (83.6%)	305 (64.5%)
Age (years)
Mean (SD)	58.0 (11.4)	63.1 (7.91)	58.7 (11.1)
Median [Min, Max]	59.5 [21.0, 80.0]	65.0 [38.0, 79.0]	60.0 [21.0, 80.0]
Body weight (kg)a
Mean (SD)	84.7 (20.4)	81.7 (16.8)	84.3 (19.9)
Median [Min, Max]	82.8 [43.1, 166]	80.9 [46.3, 140]	82.7 [43.1, 166]
Race (n (%))
Asian	15 (3.69%)	0 (0%)	15 (3.17%)
Black	18 (4.43%)	1 (1.49%)	19 (4.02%)
Native Hawaiianb	1 (0.246%)	1 (1.49%)	2 (0.423%)
Other	19 (4.68%)	4 (5.97%)	23 (4.86%)
White	353 (86.9%)	61 (91%)	414 (87.5%)
Disease‐related baseline characteristics
Baseline SPD (mm2)a
Mean (SD)	3,686 (3868)	3,280 (3582)	3,628 (3828)
Median [Min, Max]	2,342 [171,34,680]	2,158 [260,16,880]	2,244 [171,34,680]
Baseline ALT (U/L)a
Mean (SD)	23.1 (17.6)	32.1 (22.6)	24.4 (18.6)
Median [Min, Max]	19 [5,199]	26 [10,114]	20 [5,199]
Baseline LDH (U/L)a
Mean (SD)	353 (336)	386 (221)	358 (322)
Median [Min, Max]	241 [63,3,430]	310 [135,1,310]	247 [63,3,430]
Baseline ferritin (ng/mL)a
Mean (SD)	542 (963)	456 (642)	530 (924)
Median [Min, Max]	266 [0.0166, 10,600]	200 [0.781, 4,000]	258 [0.0166, 10,600]
Baseline CRP (mg/L)a
Mean (SD)	32.3 (65.4)	47.8 (93.6)	34.5 (70.2)
Median [Min, Max]	10.6 [2.76e‐05, 496]	13 [0.503, 496]	11.1 [2.76e‐05, 496]
Baseline albumin (g/L)
Mean (SD)	39.2 (5.12)	38 (5.67)	39 (5.21)
Median [Min, Max]	40 [19, 53]	40 [20, 47]	40 [19, 53]
Disease type (n (%))
DLBCL	191 (47.0%)	0 (0%)	191 (40.4%)
FL	124 (30.5%)	0 (0%)	124 (26.2%)
MZL	22 (5.42%)	0 (0%)	22 (4.65%)
PMBCLc	7 (1.72%)	0 (0%)	7 (1.48%)
TFL	16 (3.94%)	0 (0%)	16 (3.38%)
MCL	0 (0%)	67 (100%)	67 (14.2%)
Other	46 (11.3%)	0 (0%)	46 (9.73%)
Bone marrow involvement (n (%))
Bone marrow involvement	66 (16.3%)	36 (53.7%)	102 (21.6%)
No bone marrow involvement	333 (82.0%)	27 (40.3%)	360 (76.1%)
Missing	7 (1.72%)	4 (5.97%)	11 (2.33%)
Product‐related characteristics
CAR+ cells in infusion bag (106 cells)d
Mean (SD)	163 (31.7)	158 (29.8)	162 (31.5)
Median [Min, Max]	170 [58.0, 200]	160 [51.8, 201]	165 [51.8, 201]
Product TN a , e (% of viable CD3+ cells)
Mean (SD)	27.3 (17.8)	26.5 (17.6)	27.2 (17.8)
Median [Min, Max]	25.8 [0.060, 81.4]	24.9 [0.300, 80.7]	25.7 [0.060, 81.4]
Product TCM e (% of viable CD3+ cells)
Mean (SD)	20.9 (10.4)	16.4 (10.4)	20.2 (10.5)
Median [Min, Max]	19.2 [0, 71.7]	13.1 [2.3, 51.6]	18.0 [0, 71.7]
Product TEM e (% of viable CD3+ cells)
Mean (SD)	23.9 (15.3)	26.8 (16.3)	24.3 (15.4)
Median [Min, Max]	19.2 [0, 73.4]	23.6 [0.80, 70.3]	19.4 [0, 73.4]
Product TEFF e (% of viable CD3+ cells)
Mean (SD)	27.1 (14.9)	29.7 (13.4)	27.5 (14.7)
Median [Min, Max]	24.7 [1.30, 87.6]	28.2 [2.80, 65.2]	24.7 [1.30, 87.6]
Product (TN + TCM) a , e (% of viable CD3+ cells)
Mean (SD)	48.5 (18.5)	43.1 (20.6)	47.8 (18.9)
Median [Min, Max]	49.1 [7.59, 91.1]	40.4 [2.60, 88.8]	48.5 [2.60, 91.1]
Product (%TN + %TCM)/(%TEM + %TEFF)e
Mean (SD)	1.36 (1.42)	1.25 (1.63)	1.35 (1.45)
Median [Min, Max]	0.965 [0.0821, 10.2]	0.679 [0.0267, 8]	0.942 [0.0267, 10.2]
Product viability (%)f
Mean (SD)	93.0 (2.94)	89.4 (4.70)	92.5 (3.49)
Median [Min, Max]	94.0 [82.0, 98.0]	90.0 [73.0, 96.0]	93.0 [73.0, 98.0]
Product CD4/CD8 ratioa
Mean (SD)	1.34 (2.04)	0.864 (0.661)	1.27 (1.91)
Median [Min, Max]	0.859 [0.0277, 31.3]	0.728 [0.0372, 3.73]	0.859 [0.0277, 31.3]
IFNγ in the release assay (pg/mL)a
Mean (SD)	6,600 (3870)	6,620 (3650)	6,600 (3840)
Median [Min, Max]	5,840 [32.7, 18,800]	6,480 [424, 17,900]	6,060 [32.7, 18,800]
Treatment‐related characteristics
Number of prior lines of therapy
Mean (SD)	2.42 (1.67)	3.31 (1)	2.55 (1.62)
Median [Min, Max]	2.00 [1.00, 10.0]	3.00 [1.00, 5.00]	2.00 [1.00, 10.0]
Prior bendamustine treatment (n (%))
No prior bendamustine treatment	384 (94.6%)	31 (46.3%)	415 (87.7%)
Prior bendamustine treatment	22 (5.42%)	36 (53.7%)	58 (12.3%)
Co‐treatment with tocilizumab (n (%))g
No tocilizumab co‐treatment	179 (44.1%)	19 (28.4%)	198 (41.9%)
Tocilizumab co‐treatment	227 (55.9%)	48 (71.6%)	275 (58.1%)
Co‐treatment with corticosteroids (n (%))g
No corticosteroid co‐treatment	242 (59.6%)	28 (41.8%)	270 (57.1%)
Corticosteroid co‐treatment	164 (40.4%)	39 (58.2%)	203 (42.9%)
Infusion time of day category
Before 1 PMh	204 (50.2%)	–	204 (43.1%)
At or after 1PMh	202 (49.8%)	–	202 (42.7%)
Missing	0 (0%)	67 (100%)	67 (14.0%)

ALT, alanine aminotransferase; CRP, C‐reactive protein; DLBCL, diffuse large B‐cell lymphoma; FL, follicular lymphoma; IFNγ, Interferon gamma; LDH, lactate dehydrogenase; Max, maximum; MCL, mantle cell lymphoma; Min, minimum; MZL, marginal zone lymphoma; n (%), the number of patients in each category and corresponding percentage of total number of patients; specified in the column header; PMBCL, primary mediastinal B‐cell lymphoma; SD, standard deviation; SPD, sum of the product of diameters; TFL, transformed follicular lymphoma; T_CM, central memory T cells (CD45RA‐CCR7+); T_EFF, effector T cells (CD45RA+ CCR7‐); T_EM, effector memory T cells (CD45RA‐CCR7‐); T_N, naïve T cells (CD45RA+ CCR7+).

^a Log‐transformed during the covariate analysis.

^b Lumped with category White during the covariate analysis.

^c Lumped with category DLBCL during the covariate analysis.

^d Used as individual dose; not tested as covariate.

^e All phenotype‐related covariates were highly correlated. To avoid testing correlated covariates, all phenotype‐related covariates were tested on relevant model parameters in a single SCM forward step first, and only the respective phenotype‐related covariate resulting in the highest drop in the OFV for each parameter was considered in the search scope for the full covariate analysis.

^f Logit‐transformed during the covariate analysis.

^g Not tested as covariate due to graphical exploration suggesting correlative instead of causative relationship.

^h 1 PM was the median infusion time of day in ZUMA‐1, ZUMA‐5, and ZUMA‐7.

All patients received a single intravenous CAR‐T‐cell infusion at a target dose of 2 × 10⁶ CAR‐T‐cells/kg after lymphodepletion with cyclophosphamide and fludarabine. Cell viability was assessed at product release using validated flow cytometry‐based methods in accordance with Good Manufacturing Practice requirements, and all infused products met criteria for viable CAR‐positive T‐cells. The actual number of cells received (Table 1 ) was used as individual dose, assuming a 30 min infusion based on protocol information. PK samples were taken on days 7, 14, 28, and months 3, 6, 12, 18, 24 after infusion. In ZUMA‐7, additional samples were taken on days 1 and 3 (Figure S1 ). Axi‐cel's and brexu‐cel's PK and their relationship with efficacy have also been investigated in previous study‐specific publications. ⁴ , ⁵ , ²⁴ , ²⁵

Peripheral blood CAR‐T‐cell concentrations (n = 2,785) were quantified via real‐time quantitative polymerase chain reaction (qPCR) and translated into the unit of CAR‐T cells/μL based on the transduction frequency and the peripheral blood concentration of mononuclear cells. ¹⁹ , ²⁶ , ²⁷ , ²⁸ The lower limit of quantitation for the qPCR assay (1 CAR‐T‐cell/100,000 cells) was not applicable to the derived unit cells/μL. However, 14.6% of samples (408/2,785) were recorded as zero primarily late in the observation period, and these results were considered informative for the elimination phase. Consequently, the M3 method ²⁹ was used to censor concentrations reported as 0, and the lowest reported non‐zero concentration per study (ZUMA‐1: 0.00744 cells/μL; ZUMA‐2: 0.00612 cells/μL; ZUMA‐5: 0.00273273 cells/μL; ZUMA‐7: 0.0001624 cells/μL) was used as the censoring threshold (i.e., the assumed quantification limit, below which the model maximizes the likelihood that the true value lies between zero and this boundary). One patient for whom all post‐dose concentrations were below the censoring threshold was excluded.

Overview of model development

The analysis was performed in multiple steps: the initial structural and stochastic submodels were developed based on axi‐cel data. Next, the brexu‐cel data was included, and the base model was estimated. A covariate analysis was then performed for the base model. The model with the significant covariates included was finalized and used to illustrate the predicted covariate impact on C _max, AUC_0–28d, and the full PK profile.

Covariate analysis

The covariate analysis was performed using Stepwise Covariate Modeling (SCM) with adaptive scope reduction (ASR) (SCM+), ³⁰ employing significance levels α = 0.01 for the forward inclusion and ASR, and α = 0.001 for the backward elimination. Table 1 shows all evaluated covariates.

Continuous covariates were implemented using exponential models centered to the median. Categorical covariates were implemented as fractional change to the most common category. Infusion time of day was implemented as binary covariate (before vs. ≥1 PM). Categorical covariate levels with less than 10 patients were lumped with the most frequent category and covariates with more than two levels after lumping were binarized. Missing continuous covariate values (<8% of values for each continuous covariate) had been imputed with the median during the creation of the clinical database. Missing categorical covariate values were imputed with the most frequent category.

All patients receiving brexu‐cel had MCL disease type. Consequently, potential covariate effects for brexu‐cel product type and MCL disease type could not be disentangled and were evaluated as a single composite covariate. Furthermore, the product phenotype covariates (% naïve cells (T_N), % central memory T cells (T_CM), % effector memory T cells (T_EM), % effector T cells (T_EFF), % (T_N + T_CM), and (% T_N+ % T_CM)/(% T_EM + % T_EFF)) were highly correlated. To enable a data‐driven selection of the most relevant phenotype category, all phenotype‐related covariates were first tested in a separate SCM with a single forward step. The covariates resulting in the largest drop in the objective function value (OFV) for each parameter were then tested in the full SCM. No other covariates were highly correlated (all correlation coefficients <0.6).

Co‐treatment with tocilizumab or corticosteroids to manage adverse events were initially planned to be included in the covariate search due to their immunosuppressive effects, which could negatively affect CAR‐T‐cell expansion. ¹³ However, graphical explorations showed that expansion trended higher in patients who had received tocilizumab or corticosteroids compared to those who had not (Figure S2 ), suggesting that any covariate relationship would likely be due to a confounding factor, where patients with elevated PK and potential cytokine release syndrome and/or neurological events were managed and treated with tocilizumab or corticosteroids. This interpretation is consistent with a previous model‐based analysis of the axi‐cel data included in this analysis. ¹⁹ Retrospective knowledge of whether patients received tocilizumab or corticosteroids to manage adverse events associated with high expansion was not considered informative for predicting the PK of future patients, for whom such information would not be available. Consequently, neither covariate was included in the covariate search.

Illustration of covariate effects

The influence of covariates in the final model on C _max and AUC_0–28d was illustrated using Forest plots. ³¹ The Forest plots were generated using the final model, and the precision in the covariate effects was based on the 5^th and 95^th percentiles of the final output calculated based on 250 parameter vectors sampled from the NONMEM variance–covariance matrix.

Simulations

To illustrate the expected impact of different dose levels and covariates on the full PK profile, typical value simulations were performed. In these simulations, the dose, and covariate values were varied one at a time, with the others maintained at their reference values. Because more than 50% of patients in ZUMA‐2 had received prior bendamustine therapy (Table 1 ), and our analysis identified prior bendamustine therapy as a significant covariate consistent with prior clinical analyses, ³² separate simulations for brexu‐cel product type/MCL disease type with/without prior bendamustine therapy were performed.

Software

Modeling was performed using Importance Sampling (IMP) followed by an expectation only IMP step in NONMEM Version 7.5, facilitated by Perl‐speaks‐NONMEM (PsN). ³³ Standard errors were computed using the MATRIX = R option in the NONMEM $COV record. Pre‐ and post‐processing and generation of figures was performed in R/RStudio Version 4.2.2. ³⁴

Model evaluation and discrimination

Model evaluation was based on the inspection of relative standard errors, parameter estimates, condition number, prediction‐corrected visual predictive checks (pcVPCs), ³⁵ goodness of fit (GoF) plots, and changes in the OFV provided by NONMEM.

RESULTS

Model development

The structural model (Figure 1 ) consisted of a latent tumor burden compartment and two CAR‐T‐cell compartments. The peripheral CAR‐T‐cell compartment was included based on PK principles routinely applied to model biphasic disposition. Although the PK of CAR‐T‐cells differs from those of conventional drugs, the two compartments were applied in a similar manner to capture the multiple phases visible in CAR‐T‐cell PK profiles. The peripheral compartment empirically accounts for the kinetic effects of CAR‐T‐cell phenotypes with long life spans and/or CAR‐T‐cell distribution into deep tissues.

Figure 1.

Schematic representation of the mechanism‐based CAR‐T‐cell PK model. ρ, maximum expansion rate constant of CAR‐T cells; k ₁₂, rate constant for distribution from central to peripheral CAR‐T‐cell compartment; k ₂₁, rate constant for distribution from peripheral to central CAR‐T‐cell compartment; k _el, elimination rate constant; k _kill, tumor killing rate of CAR‐T‐cells; PK, pharmacokinetic; SPD, sum of the product of tumor diameters; SPD_BL, SPD at baseline; t _lag, lag time.

A patient's individual CAR‐T‐cell dose (unit: 10⁶ cells) was modeled to be intravenously infused into the central CAR‐T‐cell compartment. A latent kinetic‐pharmacodynamic approach was used to model the tumor burden over time, where the tumor burden compartment was initialized with a patient's observed baseline SPD. CAR‐T‐cells were assumed to undergo first‐order expansion with a rate constant dependent on the predicted current SPD relative to the observed SPD at baseline. A lag time before expansion was implemented to empirically account for initial distribution after infusion. The individual SPD was modeled to decline over time using a second‐order model dependent on the current number of CAR‐T‐cells in the central compartment and the predicted current SPD. As the predicted SPD decreased due to the modeled CAR‐T‐cell interaction, the predicted expansion rate of CAR‐T‐cells gradually declined. The amount in the central CAR‐T‐cell compartment was divided by an estimated scaling factor to link it to the observed unit of cells/μL.

The structural model was expressed in three differential equations:

$$\begin{array}{c}\frac{d}{\mathrm{d}t}\left(\mathit{CAR}-T_{\mathit{\text{central}}}\right)=\rho ·\mathit{CAR}-T_{\mathit{\text{central}}}·t_{\mathit{lag},\mathit{IND}}·\frac{\mathit{SPD}}{{\mathit{SPD}}_{\mathit{BL}}}\hfill \\ -k_{12}·\mathit{CAR}-T_{\mathit{\text{central}}}+k_{21}·\mathit{CAR}\hfill \\ -T_{\mathit{\text{peripheral}}}-k_{\mathit{el}}·\mathit{CAR}-T_{\mathit{\text{central}}}\hfill \end{array}$$ (1)

where $t_{\mathit{lag},\mathit{IND}}=0$ when $0\le t\le t_{\mathit{lag}}$ and $t_{\mathit{lag},\mathit{IND}}=1$ when $t>t_{\mathit{lag}}$

$$\frac{d}{\mathrm{d}t}\left(\mathit{CAR}-T_{\mathit{\text{peripheral}}}\right)=k_{12}·\mathit{CAR}-T_{\mathit{\text{central}}}-k_{21}·\mathit{CAR}-T_{\mathit{\text{peripheral}}}$$ (2)

$$\frac{d}{\mathrm{d}t}\left(\mathit{SPD}\right)=-k_{\mathit{\text{kill}}}·\mathit{CAR}-T_{\mathit{\text{central}}}·\mathit{SPD}$$ (3)

where ρ is the maximum expansion rate constant of CAR‐T‐cells, t _lag is the expansion lag time, t _lag,IND indicates whether the lag time has been exceeded, k ₁₂ is the rate constant for the distribution of CAR‐T‐cells from the central to the peripheral compartment, k ₂₁ is the rate constant for the distribution of CAR‐T‐cells from the peripheral to the central compartment, k _el is the elimination rate constant of CAR‐T‐cells, and k _kill is the tumor killing rate of CAR‐T‐cells.

Exponential interindividual variability (IIV) was included on ρ, k _el, k ₁₂, k ₂₁, and k _kill. Residual unexplained variability (RUV) was implemented as additive on the log scale with exponential IIV on the RUV parameter included.

Base model

The base model described the axi‐cel data well (Figure S3 ) and parameters were precisely estimated (Table S1 ). The concentrations for primary mediastinal B‐cell lymphoma (PMBCL) were underpredicted, likely due to the small number of patients with this disease type (n = 7). Additionally, the model underpredicted the observed concentrations in ZUMA‐2, especially the C _max. The predicted t_max for brexu‐cel product type/MCL disease type was also earlier than the observed t_max (Figure S3 ).

Covariate analysis based on pooled axi‐cel and brexu‐cel data

The covariates listed in Table 1 were evaluated on parameters ρ, k _el, and k _kill. In the initial SCM for the highly correlated covariates, %T_EFF resulted in the largest drop in the OFV for ρ (ΔOFV: −16.9), % (T_{N +} T_CM) resulted in the largest drop in the OFV for k _el (ΔOFV: −3.35), and %T_N resulted in the largest drop in the OFV for k _kill (ΔOFV: −5.79). Accordingly, these covariate‐parameter relationships were included in the full SCM.

The full covariate search revealed five significant covariates (α = 0.001): higher product %T_EFF and prior bendamustine exposure were negatively and baseline albumin was positively correlated with ρ. Baseline body weight was positively associated with k _el. Brexu‐cel product type/MCL disease type was associated with lower estimated k _kill compared to axi‐cel product type/non‐MCL disease type.

Final model

Including the significant covariate‐parameter relationships resolved the model misspecification for brexu‐cel product type/MCL disease type. During model finalization, an additional covariate effect for Study ZUMA‐7 on the RUV parameter was implemented to account for this study's higher unexplained residual variability. The final model's parameter estimates (Table 2 ) were determined with good precision and the condition number of 36 indicated a stable model with low collinearity. A pcVPC showed satisfactory predictive performance across studies and disease types (Figure 2 ). The interpretation of standard GoF plots was hampered by censored data, but with that taken into consideration, there was no indication of systematic model misspecification (Figures S4–S6). In general, the model adequately captured the observed C _max across studies, with population predictions already accounting for considerable variability (Figures S7, S8). Individual predictions showed a slight underprediction at the upper tail of observed C _max values. This deviation reflects the expected smoothing of time‐series data, as predictions are not intended to overfit extreme observations driven by RUV. A mirror plot (Figure S9 ), generated by simulating data from the final model and calculating the corresponding individual predictions, reproduced the observed trend, indicating no structural model misspecification. ³⁶ The pcVPC further supported this conclusion by demonstrating accurate prediction of C _max across studies. The population and individual predictions also captured individual concentration‐time profiles well (Figure 3 ).

Table 2.

Parameter estimates of the final axi‐cel and brexu‐cel PK model.

	Unit	Value	RSE (%)	SHR (%)
ρ	(day−1)	2.70	4.74
k el	(day−1)	0.120	8.06
k 12	(day−1)	0.0465	15.1
k 21	(day−1)	0.0108	15.4
k kill	((day·106 cells)−1)	1.33 × 10−6	16.9
t lag before expansion	(days)	2.47	5.24
Scaling factor	(L)	3.14 $\times$ 104	12.0
Baseline body weighta on k el		0.781	27.6
Product % TEFF on ρ		−0.00619	24.2
Prior bendamustine therapy on ρ		−0.241	18.7
Baseline albumin on ρ		0.0163	26.3
Brexu‐cel product type/MCL disease type on k kill		−0.617	12.3
Study ZUMA‐7 on RUV		0.719	18.1
IIV ρ	(CV)	0.264	15.3	43.6
IIV k el	(CV)	0.687	9.52	35.2
IIV k 12	(CV)	1.35	9.21	39.7
IIV k 21	(CV)	1.97	12.4	32.9
IIV k kill	(CV)	0.955	9.16	37.2
IIV RUV	(CV)	0.545	6.57	29.1
RUV	(CV)	0.969	4.94	22.0
OFV		6,263
Condition number		36

The RSE for IIV and RUV parameters are reported on the approximate SD scale.

ρ, maximum expansion rate constant of CAR‐T cells; IIV, interindividual variability; k ₁₂, rate constant for distribution from central to peripheral compartment; k ₂₁, rate constant for distribution from peripheral to central compartment; k _el, elimination rate constant; k _kill, tumor killing rate of CAR‐T cells, RSE, relative standard error; RUV, residual unexplained variability, SD, standard deviation; SHR, shrinkage; SPD, sum of the product of tumor diameters; T_EFF, effector T cells; t _lag, lag time.

^a Log‐transformed.

Figure 2.

Prediction‐corrected visual predictive check (pcVPC) of axi‐cel and brexu‐cel peripheral blood concentrations vs. time after dose, stratified by study and disease type, for the observations in the full analysis set, using the final axi‐cel and brexu‐cel PK model. Data were simulated 200 times using the study design, dosing, and covariate information for the patients in the full analysis set. Data are presented on a semi‐logarithmic scale. Timepoints associated with observations below the study‐specific censoring threshold (i.e., the assumed quantification limit, below which the model maximizes the likelihood that the true value lies between zero and this boundary) were included in the construction of the pcVPC. Observed and simulated observations below the study‐specific censoring threshold are censored prior to calculation of percentiles. The lower panel shows the observed and predicted fraction of censored observations vs. time after dose. DLBCL, diffuse large B‐cell lymphoma; FL, follicular lymphoma; MCL, mantle cell lymphoma; MZL, marginal zone lymphoma; PK, pharmacokinetics; PMBCL, primary mediastinal B‐scell lymphoma; TFL, transformed follicular lymphoma.

Figure 3.

Individual profiles of observed and predicted axi‐cel or brexu‐cel peripheral blood concentrations vs. time, using the final axi‐cel and brexu‐cel PK model, for 36 randomly selected patients. Observations are colored by study and shaped by censoring status. Data are presented on logarithmic scale. PK, pharmacokinetics.

Illustration of covariate effects

Forest plots illustrating the influence of significant covariates on C _max and AUC_0–28d are presented in Figure 4 . Compared to the reference patient, brexu‐cel product type/MCL disease type was predicted to be associated with 160% higher C _max and AUC_0–28d. The impact of the remaining significant covariates on exposure was small to moderate, with the 90% confidence intervals (CIs) of the effects within or crossing the bioequivalence reference area.

Figure 4.

Forest plots illustrating the effects of covariates on axi‐cel and brexu‐cel maximum concentration (C _max) and area under the concentration‐time curve during the first 28 days (AUC_0–28d) based on the final axi‐cel and brexu‐cel PK model. The covariate effects are based on an SCM analysis and the predictions are conditioned on a typical reference patient, assuming a baseline SPD of 2,244 mm² and a dose level of 2 $\times$ 10⁶ cells/kg. The covariate values on the y‐axis were used to generate the parameter predictions and represent the observed data either as the values of the categorical covariates or as the 5th and 95th percentiles of the continuous covariates. Closed dots represent the median of the predicted relative change from the reference patient. The 90% CIs associated with the medians are visualized by the error bars and include the uncertainty in the predictions for the reference patient. The specific values of the medians and 90% CIs are shown in the Statistics box on the right‐hand side of the parameter; these values are calculated based on 250 parameter vectors sampled from the variance–covariance matrix obtained from the $COV in NONMEM. The x‐axes are log‐transformed. The relative parameter values for a reference patient (for whom covariate characteristics are provided below the plot) are shown by the dotted vertical line; the shaded area indicates the 80%–125% margins relative to the reference patient, which are based on the standard bioequivalence limits.

Simulations

The simulations illustrated the model‐predicted impacts of different doses and covariate values on full CAR‐T‐cell PK profiles (Figure 5 ). The simulations for different dose levels replicated the frequently reported lack of an impact of the CAR‐T‐cell dose on peak expansion. ² , ¹¹ , ³⁷ Consistent with data for CD19‐targeted CAR‐T‐cell products ³⁸ , ³⁹ and other model‐based findings, ²⁰ t_max was predicted to shorten with increasing dose. The estimated 24.1% lower ρ associated with previous bendamustine exposure (Table 2 ) resulted in simulated delayed t_max and lower C _max, consistent with previously reported reduced expansion in patients receiving bendamustine ≤6 months before CAR‐T‐cell infusion. ³² Similarly, the estimated negative effect of product % T_EFF on ρ translated into decreasing predicted C _max with increasing % T_EFF. This is in line with clinical observations linking higher product frequencies of CAR‐T‐cells with naïve or central memory‐phenotype (negatively correlated with higher % T_EFF) to higher post‐infusion expansion. ²⁷ , ⁴⁰

Figure 5.

Simulations of the influence of different CAR‐T‐cell body weight‐normalized doses and covariate effects on the expected typical CAR‐T‐cell profile using the final axi‐cel and brexu‐cel PK model. The covariate effects are based on an SCM analysis, and the predictions are conditioned on a typical reference patient. Data are presented on logarithmic scales. The dose and covariate values for the reference patient were defined as follows: 2 $\times$ 10⁶ cells/kg dose, axi‐cel product type/non‐MCL disease type, 24.7% effector cells, no prior bendamustine, 82.7 kg body weight, 40 g/L baseline albumin.

DISCUSSION

This article presents a mechanism‐based modeling framework to characterize the kinetics of CAR‐T‐cell therapy products. In most piecewise‐linear models, the initial CAR‐T‐cell concentration is extrapolated from C _max, which is a primary PK parameter. ¹³ , ¹⁴ , ¹⁹ This approach contrasts with established PK principles, in which exposure is a function of dose, and C _max is a secondary PK parameter. Our presented model incorporates dosing events based on patients' individual CAR‐T‐cell doses and relates amounts in the central compartment to peripheral blood concentrations through a scaling factor, analogous to conventional PK models, in which the volume of distribution links amounts to concentrations.

Piecewise‐linear models also employ on/off switches to sequentially model kinetic processes, disregarding fundamental PK principles, which hold that they generally occur simultaneously. Similar to an extravascular two‐compartment model, in which absorption, distribution, and elimination are modeled as concurrent instead of sequential processes, the kinetic phases typical for CAR‐T‐cell therapy are modeled simultaneously in our framework. Expansion is driven by tumor burden, considering the observed baseline SPD and the predicted decline in SPD over time with respect to the baseline. As SPD decreases over time, the CAR‐T‐cell expansion signal declines, resulting in distribution and elimination driving the PK profile at later times. The linear killing term postulates rapid tumor clearance without saturation at high baseline tumor burden, consistent with the lack of an observed correlation between baseline SPD and C _max (Figure S10 ). For CAR‐T‐cell products showing such correlations, ¹⁴ , ¹⁷ , ¹⁸ , ³⁸ , ³⁹ , ⁴¹ an E_max killing term can be used. At sufficiently high observed baseline SPD relative to the estimated KM value, the predicted tumor elimination will then saturate, prolonging the phase where the tumor burden is high compared to its baseline, resulting in higher exposure.

The estimated minimum doubling time (T_DBL) of 0.257 days, calculated by log (2)/ρ, ⁴² is lower than the T_DBL for CAR‐T‐cell therapies estimated using piecewise‐linear models (0.534–0.78 days ¹³ , ¹⁴ , ¹⁹ ). This difference can be explained by the static nature of T_DBL over the expansion period in piecewise‐linear models. The T_DBL estimated here represents a minimum, with the current T_DBL increasing as tumor burden decreases. For all studies, there was a positive correlation between individual ρ estimates and the C _max/baseline SPD ratio (Figure S11 ), which has been proposed as a predictor of treatment outcomes. ²⁷ , ⁴³

Compared with piecewise‐linear models, the mechanistic basis of our model allows its use in extrapolations and simulations with fewer limitations. For example, the model could be used to explore the impact of patient characteristics, as well as actionable variables¹² on exposure. It can further serve as a platform framework for CAR‐T‐cell therapy, given that the typical PK profile is preserved across CAR‐T‐cell products, as illustrated in this case study with axi‐cel and brexu‐cel. If data from products with different tumor killing kinetics are to be modeled together, product‐ and/or tumor‐specific parameterizations can be used. Similarly, although developed based on PK data in the unit: cells/μL, the model is equally applicable to data quantified in the unit: copies/μg DNA, requiring only an adjustment of the scaling factor unit.

In this case study, several significant covariate‐parameter relationships were identified. The largest effect size was identified for product type/MCL disease type, which showed a 62% lower predicted k _kill for brexu‐cel product type/MCL disease type compared to axi‐cel product type/non‐MCL disease type (Table 2 ), resulting in later predicted t_max and 160% higher predicted C _max and AUC_0–28d. The effect could be explained with differences in the product related to the manufacturing process and/or the biological difference in tumor types for which axi‐cel and brexu‐cel are used. ³ Although the final model adequately described axi‐cel's kinetics in different LBCL disease types without inclusion of covariate effects (Figure 2 ), making a difference due to tumor type less likely, a previous study hypothesized that the stronger expansion of brexu‐cel in ZUMA‐2 could be attributed to higher expression of the CD19 protein in patients with MCL compared to patients with LBCL³. Concordant with the negative covariate effect on k _kill, the higher expansion could also result from a lower killing velocity of CAR‐T‐cells for MCL compared to other disease types, resulting in longer exposure of CAR‐T‐cells to antigen, and consequently, higher CAR‐T‐cell expansion.

The CAR‐T‐cell phenotype composition has been reported to influence exposure and response in several clinical studies. ²⁷ , ⁴⁰ , ⁴⁴ In this analysis, % T_CM, % T_EFF, % (T_N + T_CM), and (% T_N + % T_CM)/(% T_EM + % T_EFF) were significant covariates on ρ during the initial single forward step SCM. % T_EFF resulted in the largest reduction in the OFV and consequently, only % T_EFF was tested on ρ in the full SCM and remained a significant covariate in the final model (Table 2 ). However, its overall effect on exposure was not considered clinically relevant (Figure 4 ). No significant effects of CAR‐T‐cell phenotype‐related covariates were identified on k _el or k _kill during the covariate analysis. These findings suggest that product phenotype has a relevant impact on the initial expansion but not on the elimination of CAR‐T‐cells.

Body weight was identified as a covariate in a model‐based analysis for CAR‐T‐cell therapy for the first time, although a negative association between body weight and exposure has been reported for ide‐cel. ⁴⁵ Higher clearance with higher body weight is an established relationship for many conventional drugs; however, its impact in cell therapy is less clear. Even though the covariate effect was significant in this analysis, its impact on exposure was low (Figure 4 ).

A negative impact of recent prior bendamustine therapy on ρ was also identified (Table 2 ). When compared to the reference patient, prior bendamustine therapy was associated with a 29% lower predicted C _max and a 25% lower predicted AUC_0–28d (Figure 4 ). This covariate effect is in line with a previously reported negative impact of recent bendamustine co‐treatment on T‐cell fitness. ³²

A positive correlation between baseline albumin and ρ was observed. Despite statistical significance, the magnitude of the covariate effect was small (Figure 4 ). The 18% lower predicted C _max, relative to the reference patient, associated with low baseline albumin (5^th percentile; 30 g/L) may be attributed to a high inflammatory burden, which is often inversely related to albumin levels. High inflammatory factors have been negatively associated with the expansion of axi‐cel. ²⁷ This interpretation is supported by a negative relationship between baseline C‐reactive protein and ρ identified in the first step of the SCM forward search, which ultimately lost significance upon the inclusion of other covariates. Elevated baseline albumin levels may also be associated with improved immune recovery and lymphopoiesis, potentially mediated by reduced inflammatory signaling and by preserved amino‐acid and arginine metabolic availability that supports lymphocyte homeostasis. ⁴⁶ , ⁴⁷

Finally, a recent retrospective study linked early (<12:00 noon) CAR‐T‐cell infusions to higher expansion at Day 7, possibly due to chrono‐immunological effects. ⁴⁸ Conversely, our covariate analysis and graphical exploration (Figure S12 ) revealed no relevant relationship between infusion time (before vs. ≥ 1 PM) and PK. This discrepancy may be explained by the increased robustness of our methodology. By evaluating longitudinal PK profiles rather than single‐day observations, our approach provides a more comprehensive assessment of the potential impact of infusion time on the PK of CAR‐T‐cells.

The RUV estimate in the final model was relatively high, which likely results from using study‐specific LLOQs (0.0001624–0.00744 cells/μL) which were implemented to retain all observations quantifiable in the original assay unit. A sensitivity analysis showed that uniformly applying the highest LLOQ reduced η‐shrinkage for most parameters and eliminated the need for ZUMA‐7's additional RUV (Table S2 ). However, discarding bioanalytical data to lower the RUV and η‐shrinkage was deemed scientifically unjustified. Thus, our reported RUV and shrinkage remain conservative, yet data driven. To prevent η‐shrinkage from biasing the covariate analysis, SCM with ASR was utilized instead of Empirical Bayes Estimate‐based covariate screening. ⁴⁹ A recognized consequence of moderate‐to‐high shrinkage is that extreme individual exposure metrics may shrink toward the population mean, which could bias estimates in subsequent exposure‐response analyses.

Several limitations of this analysis should be highlighted: The tumor burden compartment in our framework aims to facilitate the accurate characterization of the observed PK profile. Since only baseline and no longitudinal tumor burden data are used for parameter estimation, the tumor compartment represents a simplification of the underlying biology and has not been validated for generating individual tumor burden predictions. The absence of detectable secondary expansion in our clinical dataset suggests that potential tumor re‐growth does not meaningfully impact the kinetic profiles of axi‐cel and brexu‐cel, supporting the appropriateness of this simplified approach. Nevertheless, the integration of longitudinal tumor burden measurements could extend the model into a PK‐tumor size dynamics framework. Another limitation is that other stimulants for CAR‐T‐cell expansion, such as CD19‐expressing healthy B cells, the immune microenvironment, and the impacts of variable CD19 expression in tumor tissue and lymphodepletion are not considered. While the presented model could adequately capture the observed data considering only SPD as a driver of expansion, the inclusion of additional CAR‐T‐cell‐stimulatory model components and consideration of target expression in tumor tissue could be investigated in the future.

FUNDING

This study was funded by Kite, A Gilead Company.

CONFLICT OF INTEREST

A. McL. is an employee of Pharmetheus AB. M.B. is an employee of Pharmetheus AB and holds stocks in the company. Support provided by A.McL. and M.B. at Pharmetheus AB was contracted and funded by Kite. A. R‐G. reports employment and leadership role with Gilead, and stock or other ownership in Gilead. R.S. reports employment and leadership role with Kite; stock or other ownership in Gilead; and patents, royalties, and other intellectual property from Kite. S.F. reports employment and leadership role with Kite; stock or other ownership in Gilead; and patents, royalties, and other intellectual property from Kite and Tusk Therapeutics.

AUTHOR CONTRIBUTIONS

A.McL: Wrote the manuscript, Designed the research, Performed the research, Analyzed the data. M.B.: Wrote the manuscript, Analyzed the data. A.R‐G: Wrote the manuscript, Analyzed the data. S.F.: Wrote the manuscript, Performed the research, Analyzed the data. R.S.: Wrote the manuscript, Designed the research, Performed the research, Analyzed the data.

Supporting information

Table S1.