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

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## Abstract

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## Simple Summary

## Abstract

^{+}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 CCS

_{TN}-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.

## 1. Introduction

^{+}/CD8

^{+}subset composition [12,13] in the infusion product, the tumor burden [10], the tumor microenvironment [14,15] and the dose and type of lymphodepleting chemotherapy [16,17]. Reported positive predictors for a long-term response are a high CAR-T cell maximum concentration (C

_{max}) [7,18,19], and a high area under the concentration–time curve in the first 28 days (AUC

_{0–28d}) [7]. Factors such as a high fraction of central memory T cells (T

_{CM}) or T memory stem cells (T

_{SCM}) in manufacturing and infusion product have been linked to a high expansion and persistence [11,20]. Yet there is still sizeable unexplained variability in expansion, persistence, and response amongst patients, i.e., interindividual variability [7].

^{+}metabolic tumor volume and the dynamics of their interactions. Combining top-down and bottom-up approaches, our population QSP model uses prior information on CAR-T cell physiology together with in vivo data to inform unknown model parameter values and their interindividual variability [26]. Leveraging the model, we aimed to quantify different levels of variability in a clinical cohort of 19 NHL patients and identify significant influential factors on CAR-T cell expansion and survival. Finally, we sought to translate the model-estimated T cell expansion capacity into a clinical composite score to propose a cut-off value that allows survival prediction leveraging but not requiring the use of the model.

## 2. Materials and Methods

#### 2.1. Patients and Treatment

^{−2}body surface area per day) and cyclophosphamide (500 mg·m

^{−2}body surface area per day) on days −5, −4, and −3. Further patient demographics and clinical characteristics prior to lymphodepleting chemotherapy are shown in detail in Supplementary Table S1. All patients received a single intravenous infusion of axicabtagene ciloleucel at a target dose of 2 × 10

^{6}CAR-T cell·kg

^{−1}body weight. Of the 24 patients, we excluded five patients for the model analysis. Amongst these, one patient had no active disease during the whole study, for two patients no baseline metabolic tumor volume measurement was available, and for two patients, the staining steps during flow cytometry to determine CAR-T cell concentrations failed.

#### 2.2. Tumor Size Measurements and Endpoint Assessment

#### 2.3. CAR-T Cell Sampling, Detection, and Quantification

#### 2.3.1. Sample Collection

#### 2.3.2. Cell-Free DNA Real-Time PCR

#### 2.3.3. Flow Cytometry

^{5}to 1 × 10

^{6}cells). We used a 12-color multiparametric approach using a 3-laser FACS Fortessa Cytometer (BD Biosciences, San Jose, CA, USA). We established a compensation matrix using the DiVa 6.1.1 software with the acquisition of single staining controls. We analyzed FCS files using FlowJo (BD Biosciences, San Jose, CA, USA). We plotted the total events on an SSC vs. FSC quadrant, and we excluded the doublets by gating out the cells on the periphery on the SSC vs. FSC plot (Supplementary Figure S1, top left). We excluded all dead cells by plotting SSC vs. Aqua (Supplementary Figure S1, top middle) and gated on the negative populations (live). We then re-plotted the live events using SSC vs. FSC and gated the lower and upper populations on the right (we did this because activated CAR-T cells appeared larger than normal lymphocytes) to select the lymphocyte populations (Supplementary Figure S1, top right). From the selected gate, we plotted SSC vs. CD3 (Supplementary Figure S1, bottom left); then, from the CD3

^{+}populations, we plotted CD3 vs. CAR-T to discriminate all CD3

^{+}CAR-T

^{−}from the CD3

^{+}CAR-T

^{+}cells (Supplementary Figure S1, bottom middle). Using the CD3

^{+}CAR-T

^{+}populations, we then plotted CD4 vs. CD8 to obtain single CD4

^{+}CAR-T

^{+}and CD8

^{+}CAR-T

^{+}populations (Supplementary Figure S1, bottom middle right). To define the phenotype, we plotted the CD4

^{+}and CD8

^{+}single-stained populations according to their level of expression of CD45RA vs. CCR7, thus, CD45RA

^{+}CCR7

^{−}(T

_{Eff}), CD45RA

^{+}CCR7

^{+}(T

_{N}), CD45RA

^{−}CCR7

^{+}(T

_{CM}), and CD45RA

^{−}CCR7

^{−}(T

_{EM}) (Supplementary Figure S1, bottom far right). We plotted each single subset vs. every single other marker included in each panel.

#### 2.3.4. Cytokine Measurements

#### 2.4. Development of the CD19-Specific CAR-T Cell Quantitative Systems Pharmacology Model

#### 2.4.1. Nonlinear Mixed-Effects Modeling

#### 2.4.2. Structural Submodel

#### 2.4.3. Statistical Submodel

#### 2.4.4. Covariate Submodel

#### 2.4.5. Model Estimation, Parameter Precision, and Software

^{®}Version 7.4.3 (ICON Development Solutions, Ellicott City, MD, USA ), called through Perl speaks NONMEM (PsN) Version 3.6.2 [37], using the modeling workbench Pirana Version 2.9.7 (Certara, Princeton, NJ, USA) [38]. For parameter estimation, First-Order Conditional Estimation with Interaction was used. Pre- and post-processing and model evaluation were performed using R Version 3.5.1 (https://www.R-project.org/ (accessed on 12 January 2021)) accessed through RStudio Version 1.2.1184 (http://www.rstudio.com/ (accessed on 12 January 2021)), using packages plyr, dplyr, Xpose4, ggplot2, and scales.

#### 2.5. Characterization of Patients in Different Model-Defined (Sub)Populations

_{max}), (ii) time at maximum concentration of all CAR-T cells (T

_{max}), (iii) area under the concentration–time curve from day 0 to day 28 (AUC

_{0–28d}) of all CAR-T cells, and (iv) the ratio of C

_{max}of all CAR-T cells over baseline metabolic tumor volume, as a possible predictor for a good prognosis [39], were compared between both subpopulations. To assess statistical significance of differences between continuous covariate or cell kinetic parameter values, two-sided non-parametric Wilcoxon tests (α = 0.05) using the function ‘compare_means’ of the R package ggpubr were performed. The results were visualized with box-whisker plots for continuous covariates and bar plots for categorical covariates using R package ggplot2.

#### 2.6. Clinical Endpoints in Patients of Different Model-Defined (Sub)Populations

_{max1}and clinical composite score (CCS) C

_{max}/baseline metabolic tumor volume was assessed for each CAR-T cell phenotype and the sum of CAR-T cell phenotypes (T

_{all}) using Pearson correlation tests through the ‘ggscatter’ function in the R package ggpubr. For the CAR-T cell phenotype for which the CCS showed the highest correlation with V

_{max1}, we assessed an optimal cut-off value of the CCS for detecting patients in the low expansion subpopulation, by performing a receiver operating characteristic (ROC) curve analysis using the R packages cutpointr and pROC [40]. Next, we performed univariate cox-proportional hazard analyses using the R package survival to assess if the identified CCS cut-off value for the chosen CAR-T cell phenotype was a significant predictor for survival. We tested and confirmed the proportional hazard assumption using the function ‘cox.zph’ in the R survival package. Finally, the correlation between the CCS using flow cytometry and the CCS using qPCR was quantified using a Pearson-correlation test. The CCS

_{qPCR}was compared between reference expansion population and low expansion subpopulation using a two-sided Wilcoxon test. Two additional previously digitized datasets [41], reporting C

_{max}(assessed by qPCR) and baseline tumor burden in CLL [42] and MM [43] patients, were digitized (Supplementary Figure S2). Next, CCS

_{qPCR}were computed and the differences between patients with CR/PR and PD/NR assessed using two-sided Wilcoxon tests.

## 3. Results

#### 3.1. The CD19-Specific CAR-T Cell Quantitative Systems Pharmacology Model

_{N}, T

_{CM}, T

_{EM}, and T

_{Eff}) as individual species. As a fifth species, we included CD19

^{+}metabolic tumor volume as a pharmacodynamic component and a key driver of CAR-T cell expansion. To jointly describe typical profiles of concentrations of CAR-T cell phenotypes and CD19

^{+}tumor volume across time and different layers of variability, we used nonlinear mixed-effects modeling.

#### 3.1.1. Structural Submodel

_{N}), central memory CAR-T cells (T

_{CM}), effector memory CAR-T cells (T

_{EM}), terminally differentiated effector CAR-T cells (T

_{Eff}), and CD19

^{+}metabolic tumor volume (CD19

^{+}) (Figure 1). For the nonlinear processes describing T cell expansion upon tumor contact and tumor killing upon CAR-T cell contact, different functional forms were explored. While the numerator always consisted of the product ${\mathrm{V}}_{\mathrm{max},\mathrm{x}}\xb7\mathrm{CD}{19}^{+}\xb7{\mathrm{T}}_{\mathrm{cell}}$, we tested three versions for the denominator, limiting the maximum expansion either by the respective T cell concentration, the metabolic tumor volume or both. For both terms, the form which described the data best was selected.

#### Central Memory CAR-T Cells (T_{CM})

_{N}, we modeled T

_{CM}to expand upon tumor contact with the same Michaelis–Menten parameters V

_{max1}and KM

_{1}and to undergo homeostatic proliferation with the rate constant kp

_{2}(0.007·day

^{−1}) [47]. Moreover, we described concentrations of T

_{CM}to increase by differentiation of T

_{N}with the rate constant k

_{12}. In line with the progressive differentiation model, concentrations of T

_{CM}were described to decrease due to differentiation into T

_{EM}with the rate constant k

_{23}(0.191·day

^{−1}, RSE: 11%) or apoptosis after a typical lifespan of 1/k

_{e2}(1/0.0104·day

^{−1}= 96 days, RSE: 13%) days. The resulting typical profile of T

_{CM}is given by Equation (6).

#### Effector Memory CAR-T Cells (T_{EM})

_{N}and T

_{CM}, we modeled T

_{EM}cells to expand upon tumor contact in a nonlinear process with the parameters V

_{max1}and KM

_{1}. In addition, T

_{EM}cells were described to undergo linear homeostatic proliferation with the rate constant kp

_{3}(0.007·day

^{−1}) [47] and to be formed via differentiation of T

_{CM}with the rate constant k

_{23}. Moreover, we described T

_{EM}to differentiate into T

_{Eff}with the rate constant k

_{34}(0.355·day

^{−1}, RSE: 13%) and to undergo apoptosis after a typical lifespan of 1/ke

_{3}(1/0.0104·day

^{−1}= 96 days, RSE: 13%) days. The resulting typical profile of T

_{EM}is given by Equation (7):

#### Terminally Differentiated Effector CAR-T Cells (T_{Eff})

_{Eff}cells unable to expand further in response to tumor contact or as homeostatic proliferation. We still considered them to be formed by differentiation of T

_{EM}with the rate constant k

_{34}. In line with previous findings [21,48], as shown in the high estimate for ke

_{4}, we approximated that a high fraction of T

_{Eff}will die each day (0.518·day

^{−1}, RSE: 13%). The resulting typical profile of T

_{Eff}is given by Equation (8).

#### CD19^{+} Metabolic Tumor Volume (CD19^{+})

^{+}metabolic tumor volume growth with a logistic growth function [28] with growth parameter k

_{5}(0.0023 day

^{−1}) and carrying capacity K

_{0}(5000 mL), which represents the highest metabolic tumor volume observable (Equation (9)). Tumor cell killing by the different CAR-T cell phenotypes was adapted from a previously published tumor immune reaction mathematical model [28] as a nonlinear process with maximum killing rate V

_{max5,x}(with x = 1−4 representing the four CAR-T cell phenotypes in the order naïve, central memory, effector memory and effector), and metabolic tumor volume at half-maximum killing rate KM

_{5}(276 mL, RSE: 33%). While for parameter V

_{max5,2}, the maximum killing rate for T

_{CM}was estimated (4.04 mL·day

^{−1}·(cells·µL

^{−1})

^{−1}, RSE: 39%), the maximum killing rates for the other T cell phenotypes were fixed based on the estimate for V

_{max5,2}and fractional changes in killing capacities extracted from a digitized plot showing in vitro killing capacities of different CAR-T cell phenotypes [49].

#### 3.1.2. Statistical Submodel

_{max1}(446% CV) and V

_{max5,2}(307% CV) using Equation (1)

_{.}The implementation of interindividual variability parameters on other structural submodel parameters was not supported by the dataset. Applying Equations (5)–(9) with the estimated parameter values to the measured concentrations of (i) the four CAR-T cell phenotypes and (ii) metabolic tumor volumes in our clinical dataset (n = 19 patients, Table S1), population and individual model predictions were in line with observed values for the majority of individuals. However, for some patients, typical predictions exceeded the measured T cell concentrations by up to 270-fold. A common feature of these patients was that T cells failed to expand as expected based on the high baseline tumor burden. Furthermore, we observed a bimodal distribution of individual V

_{max1.base}estimates. Based on this observation, we used a mixture model to investigate the presence of two subpopulations with separate estimates for V

_{max1,base}. We precisely estimated 20% (RSE: 11%) (n = 4) of patients to belong to a low expansion subpopulation with a significantly reduced (by 92%, p = 0.0043) typical value for V

_{max1,base}(V

_{max1,base,low}: 0.000700 (cells·µL

^{−1})·day

^{−1}·mL

^{−1}, RSE: 17%) compared to the reference population (V

_{max1,base,ref}: 0.00846 (cells·µ

^{−1})·day

^{−1}·mL

^{−1}, RSE: 36%). The mixture model’s implementation significantly improved and aligned typical and individual predictions for the low expansion subpopulation (Supplementary Figure S3).

#### 3.1.3. Covariate Submodel

^{+}to CD8

^{+}CAR-T cells on day seven and the concentrations of IL-2 and IL-15 for evaluation as covariates on model parameter V

_{max1,base}. Furthermore, we pre-selected tumor type and concentrations of Granzyme-B, TNFα, and IFN-γ on day seven for evaluation on model parameter V

_{max5,2}. Ratios of CD4

^{+}over CD8

^{+}CAR-T cells and cytokine concentrations were additionally available at baseline and on days four, nine, 14 and 28. However, measurements were not available for all patients at all time points. As measurements were available for 18 of 19 patients on day seven, we chose this time point for implementation.

_{max1,base,ref}and V

_{max1,base,low}. A previous ASCT was incorporated as dichotomous covariate (ASCT = 0: no previous ASCT, ASCT = 1: previous ASCT) and the change in V

_{max1,base}due to a previous ASCT was implemented using a fractional change model (ASCT

_{Vmax1}: 2.53, RSE: 31%, translating into a 3.53-fold higher V

_{max1,base}value in patients with a previous ASCT). Of note, the covariate effect for a previous ASCT was estimated for all patients simultaneously using their respective V

_{max1,base}value (V

_{max1,base,ref}or V

_{max1,base,low}) instead of estimating separate effects of a previous ASCT for V

_{max1,base,ref}and V

_{max1,base,low}. The second covariate, the ratio of CD4

^{+}/CD8

^{+}CAR-T cells at day seven (${\mathrm{CAR}}^{+}\mathrm{CD}4/\mathrm{CD}{8}_{\mathrm{day}7})$, was implemented on V

_{max1,base,ref}using a power function. An increasing ratio of CD4/CD8

^{+}CAR-T cells at day seven was associated with a moderate decrease in V

_{max1,base,ref}(CD4/CD8

_{exp}: −0.385, RSE: 45%). As for the low expansion subpopulation, an exploratory graphical analysis showed that only a previous ASCT but not the ratio of CD4

^{+}/CD8

^{+}CAR-T cells at day seven was influential on the baseline maximum expansion capacity V

_{max1,base,low}(Supplementary Figure S4) and only a previous ASCT remained as covariate on V

_{max1,base,low}. There was no significant relationship between other possible covariates and V

_{max1,base}. The final equations for V

_{max1}applicable to the reference and low expansion (sub)populations are shown in Equations (10) and (11), respectively. In these equations, V

_{max1,ref}and V

_{max1,low}are the maximum expansion rates per mL metabolic tumor volume in the reference and the low expansion (sub)population, respectively, based on (i) the typical maximum expansion rates per mL metabolic tumor volume in the reference population $\left({\mathrm{V}}_{\mathrm{max}1,\mathrm{base},\mathrm{ref}}\right)$ or the low expansion subpopulation $\left({\mathrm{V}}_{\mathrm{max}1,\mathrm{base},\mathrm{low}}\right)$, (ii) the fractional change in ${\mathrm{V}}_{\mathrm{max}1,\mathrm{base},\mathrm{ref}}$ or ${\mathrm{V}}_{\mathrm{max}1,\mathrm{base},\mathrm{low}}$ due to a previous ASCT (${\mathrm{ASCT}}_{\mathrm{Vmax}1}$), and (iii) for the reference population the change in ${\mathrm{V}}_{\mathrm{max}1,\mathrm{base},\mathrm{ref}}$ based on the measured ratio of CD4

^{+}/CD8

^{+}CAR-T cells on day 7 $({\mathrm{CAR}}^{+}\mathrm{CD}4/\mathrm{CD}{8}_{\mathrm{day}7}$) to the power of model-estimated exponent $\mathrm{CD}4/\mathrm{CD}{8}_{\mathrm{exp}}$.

_{max1,base,ref}was substantially reduced from 446% to 150% (RSE: 19%) CV. The interindividual variability in V

_{max1,base,low}was negligible and not included in the model. Final model predictions for concentration–time profiles of all T cell phenotypes and metabolic tumor volume corresponded well with the observations as shown in goodness of fit plots (Figure 2) and observations overlaid with model predictions (Figure 3).

_{N}, T

_{CM}, T

_{EM}, T

_{Eff}, and CD19

^{+}tumor, respectively).

#### 3.1.4. Model Estimation and Parameter Precision

^{−1}per phenotype as dose. It is plausible to observe this concentration after the initial distribution phase post-infusion. A subsequent sensitivity analysis showed that a ten-fold change of this value had a minor impact on the time of maximum T cell concentration but not on the maximum concentration itself (Supplementary Figure S5), which is in line with previously published data [13]. In addition, our model’s ability to describe the observed data well using the imputed doses supports previous findings of CAR-T cell doses not being predictive of expansion or response [3,18,41].

_{5}and K

_{0}, which describe undisturbed tumor growth and the largest tumor volume observable, were not identifiable and fixed to plausible values. Similarly, homeostatic proliferation rate constants were set to literature values [47] as we performed our CAR-T cell concentration measurements during the rapid expansion phase. As the proliferation in response to target engagement is much faster than homeostatic proliferation, homeostatic proliferation rate constants were unidentifiable. Finally, death rate constants for T

_{N}, T

_{CM}and T

_{EM}were unidentifiable and fixed based on the estimated death rate constant for T

_{Eff}and the relationship between death rate constants of short- and long-lived cells (2%), according to Stein et al. [21]. Final model parameter values are shown in Table 1.

#### 3.2. Characterization of Patients in Different Model-Defined (Sub)Populations

_{max}and AUC

_{0–28d}were similar in reference and low expansion (sub) populations, while T

_{max}were earlier in the reference compared to the low expansion (sub) population. When observed C

_{max}values were normalized to baseline metabolic tumor volumes, these ratios were significantly higher in the reference compared to the low expansion subpopulation (p = 0.024).

#### 3.3. Clinical Endpoints in Different Model-Defined Patient Subpopulations

_{max1}, allowed to identify a patient’s expansion (sub-)population, which was associated with survival; thus, we aimed to determine a cut-off value in this parameter, which would support survival prediction. Furthermore, we aimed to translate V

_{max1}into a predictor variable, which would be easily derivable in a clinical setting and leverage, but not require the use of the model. As a measurable clinical composite score (CCS) describing T cell expansion, inspired by a similar concept in anti-PD1 checkpoint blockade [39] and supported by a previous correlative analysis [50], the ratio of observed C

_{max}((cells·µL

^{−1}))/baseline metabolic tumor volume (mL), denoted in Equation (12), was positively correlated with V

_{max1}for all CAR-T cell phenotypes (T

_{N}: r = 0.98, T

_{CM}: r = 0.95, T

_{EM}: r = 0.94, T

_{EFF}: r = 0.86, T

_{all}: r = 0.94). As the highest correlation was observed for T

_{N}(Figure 9a), the CCS for T

_{N}(CCS

_{TN}) was taken forward as a possible predictor for survival.

_{TN}of 0.00136 (cells·µL

^{−1})·mL

^{−1}as cut-off value with optimal predictive capability for patients in the low expansion subpopulation (sensitivity: 75%, specificity: 100%; AUC: 91.7%) (Figure 9b and Supplementary Figure S6). The survival analysis, stratified for the proposed cut-off value, showed a clear superiority in survival in patients with a CCS

_{TN}≥ 0.00136 (cells·µL

^{−1})·mL

^{−1}compared to patients with a CCS below this value (median PFS: 11 months vs. 2 months (p = 0.014) and median OS: not reached vs. two months (p = 0.003)) (Figure 9c,d). Using a Cox-proportional hazard model, the estimated hazard ratios for PFS and OS in patients with a CCS

_{TN}above the proposed threshold were 0.17 (95% CI: 0.037–0.79) (p = 0.024) and 0.12 (95% CI: 0.025–0.63) (p = 0.012), respectively, suggesting that a CCS

_{TN}above the proposed threshold was associated with a 83% reduced risk of progression and a 88% reduced risk of death.

_{10}-transformed CCS using C

_{max}values for all CAR-T cells derived from flow cytometry were reasonably correlated with log-transformed CCS using C

_{max}values derived from cfDNA qPCR (r = 0.48, p = 0.037) and the CCS

_{qPCR}values were significantly higher in the reference expansion population compared to the low expansion subpopulation (median: 83.7 copies $\mu $g

^{−1}DNA·mL

^{−1}vs. median: 4.16 copies $\mu $g

^{−1}DNA·mL

^{−1}, p = 0.014) (Figure 10a,b). Furthermore, CCS

_{qPCR}values were significantly higher in patients with complete response/partial response vs. patients with progressive disease/no response in previously digitized data [41] of patients with multiple myeloma [43] (p = 0.017) and chronic lymphocytic lymphoma [42] (p = 0.0051) (Figure 10c,d), further supporting our clinical composite score framework.

## 4. Discussion

_{SCM}) over central memory cells, and over effector memory cells to short-lived effector cells. Although other lineage relationship models like the linear differentiation model [54] and the bifurcative differentiation model [55,56] have been proposed, the progressive differentiation model is most supported by experimental data [20,57,58,59,60,61]. Of note, our flow cytometry panel did not include the marker CD95 and thus did not support the detection of T

_{SCM}in the presence of T

_{N}. Thus, using an extended staining panel, future studies including cell concentration data of both T

_{N}and T

_{SCM}could extend our model, considering previous reports of the positive features of T

_{SCM}regarding CAR-T cell expansion and persistence. Additional flow cytometry markers such as TAM-3, LAG3, PD-1, and CD57 could further elucidate the state of the T cell with respect to exhaustion and senescence.

_{max,base}for each phenotype by estimating V

_{max,base}for T

_{N}and fractional changes in V

_{max,base}for the remaining three phenotypes. Point estimates of the fractional changes in V

_{max,base}for each phenotype were plausible (T

_{CM}: +24%; T

_{EM}: +14%, T

_{Eff}: −79%), however, with relative standard errors of 130–583%, the estimates were imprecise. We thus simplified the model by assuming the same V

_{max,base}for T

_{N}, T

_{CM}, and T

_{EM}and removing the respective expansion term for T

_{Eff}. Additional in vivo and in vitro data need to become available for precise estimation of V

_{max,base}parameter values for each CAR-T cell phenotype and for identification of the best CAR-T cell phenotype(s) for the strongest expansion.

_{max1,base}, namely the CD4

^{+}/CD8

^{+}CAR-T cell ratio at day seven and a previous ASCT. By additionally considering if patients showed a reference or low baseline expansion, we could substantially reduce the estimated interindividual variability on V

_{max1,base,ref}by two-thirds from 446% to 150% CV. We identified V

_{max1,base,ref}to moderately decrease with a higher ratio of CD4

^{+}to CD8

^{+}T cells at day seven. This means that we estimated CD8

^{+}T cells to have a higher expansion rate than CD4

^{+}T cells, as reported previously [64]. In contrast, we did not identify covariates that could explain parts of the large interindividual variability on CAR-T cells’ maximum tumor killing rate (V

_{max5}). While we did find a significant positive relationship between cytokine release syndrome grade ≥2 and maximum tumor killing rate by T

_{CM}(V

_{max5,2}), we think that this relationship is rather due to correlation than causation. A higher immune activation, leading to a higher grade of cytokine release syndrome, might be the reason for the increased killing rate. However, as we aimed for our model to be mechanistic and our data did not include the link (i.e., a biomarker) between cytokine release syndrome and V

_{max5,2}, we decided not to include cytokine release syndrome as a covariate on V

_{max5}. In general, the units of model parameters V

_{max1}, V

_{max5,2}, and the CCS could be further transformed by resolving the units, e.g., the different volume units (µL) and (mL). However, to ease interpretability and retain awareness for the different origins of the units ((µL) represents the distribution volume of the CAR-T cells and (mL) represents the metabolic tumor volume), the units of the parameters were kept in their original form.

^{+}/TNFα

_{lo}T cells in the manufacturing product and rapid expression of exhaustion markers after infusion. We hypothesize that the same pattern could have been observed in patients of our low expansion subpopulation. Unfortunately, no exhaustion markers were measured in our dataset, so we were not able to investigate this further, but the generated hypothesis should be tested in future. Furthermore, while we observed strong trends for differences in survival between the model-defined reference expansion and the low expansion (sub)population (PFS: 11 months vs. 2.5 months, OS: not reached vs. four months), the differences were not significant. Among the low expansion subpopulation, there was one individual with a previous ASCT, very high baseline metabolic tumor volume, and ~40-fold higher CAR-T cell C

_{max}compared to the mean C

_{max}in the other 18 patients. Interestingly, this individual’s survival was also much longer than the rest of the low expansion subpopulation (ongoing response at 16 months vs. median PFS and OS of 2 months). Had this patient been excluded from the analysis, the differences in PFS and OS between both (sub)populations would have been highly significant (p = 0.021 and 0.0049, respectively). Thus, future studies with a larger sample size to investigate the cell kinetic-independent impact of ASCT and other factors on survival and the model’s potential for response prediction are highly warranted. We subsequently translated our predictive model parameter V

_{max1}into clinical composite scores (CCS) of maximum CAR-T cell concentrations/baseline metabolic tumor burden, measurable in the clinic. The excellent correlations between V

_{max1}and the CCS for all CAR-T cell subpopulations (r ≥ 0.86) support our model. The highest concordance between the CCS for T

_{N}(r = 0.98) was supported by a previous correlative analysis [50] and allowed us to determine a CCS

_{TN}cut-off value for early response prediction.

## 5. Conclusions

## Supplementary Materials

^{+}and CD8

^{+}CAR-T cells from peripheral blood samples of patients at days 7, 14, and 28 after infusion and identification of the different phenotypes. Figure S2: Digitized data on C

_{max}and Baseline tumor burden in patients with MM and CLL. Figure S3: Measured concentrations and simulated typical and individual model predictions of different species after CAR-T-cell infusion for patients in the low expansion subpopulation before and after implementation of the mixture model. Figure S4: Estimated maximum expansion capacity upon tumor contact parameter Vmax

_{1}versus the CD4/CD8 CAR-T cell ratio at day seven. Figure S5: Simulated typical CAR-T cell concentration–time profiles using different initial CAR-T cell concentrations (0.1 cells µL

^{−1}as used in our model (light blue) and ten-fold lower (dark blue) or ten-fold higher (purple) and a baseline metabolic tumor volume of 85.7 mL (median baseline metabolic tumor volume in our dataset) (assuming reference covariate values of no previous autologous stem cell transplantation and a CD4/CD8 CAR-T cell ratio of 1).Figure S6: Receiver operating characteristic (ROC) curve for deriving an optimal cut-off value of the clinical composite score (CCS) Maximum CAR-T

_{N}cell concentrations (C

_{max})/Baseline metabolic tumor volume [(cells · µL

^{−1}) · mL

^{−1}] to determine if patients belong to low expansion subpopulation. Figure S7: Kaplan–Meier plots for and progression-free survival and overall survival in patients with high and low metabolic tumor volume in mL at baseline. Figure S8: Kaplan–Meier plots for progression-free survival and overall survival in patients with high (above median) and low (lower or equal to median) maximum CAR-T cell concentrations. Data points: measured concentrations. Figure S9: Kaplan–Meier plots for progression-free survival and overall survival in patients with high (above median) and low (lower or equal to median) AUC

_{0–28d}CAR-T cell concentrations. Figure S10: Measured CAR-T cell concentrations and predicted concentration–time profiles using base models with different forms of CAR-T cell expansion terms. Table S1: Patient characteristics. Table S2: Observed and predicted CAR-T cell kinetic parameters in the reference population and the low expansion subpopulation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic representation of the CD19-specific CAR-T cell population quantitative systems pharmacology model, describing kinetics and dynamics of the four CAR-T cell phenotypes and CD19

^{+}tumor metabolic tumor volume. Legend: Non-red arrows pointing to the right describe differentiation processes. Non-red downward arrows represent cell death processes. Circular arrows represent proliferation processes. The red arrow pointing to the right represents CD19

^{+}tumor death. Arrows pointing to parameter names indicate a positive impact on this parameter by the species of which the arrow is originating from. Abbreviations—T

_{N}: naïve CAR-T cells; T

_{CM}: central memory CAR-T cells; T

_{EM}: effector memory CAR-T cells; T

_{Eff}: effector CAR-T cells; CD19

^{+}: CD19

^{+}metabolic tumor volume; k

_{12}: rate constant for differentiation of T

_{N}to T

_{CM}; k

_{23}: rate constant for differentiation of T

_{CM}to T

_{EM}; k

_{34}: rate constant for differentiation of T

_{EM}to T

_{Eff}; ke

_{1}: death rate constant for T

_{N}; ke

_{2}: death rate constant for T

_{CM}; ke

_{3}: death rate constant for T

_{EM}; ke

_{4}: death rate constant for T

_{Eff}; kp

_{1}: homeostatic proliferation rate constant for T

_{N}; kp

_{2}: homeostatic proliferation rate constant for T

_{CM}; kp

_{3}: homeostatic proliferation rate constant for T

_{EM}; V

_{max1}: maximum expansion rate per mL tumor volume of T

_{N,}T

_{CM}and T

_{EM}upon tumor contact; KM

_{1}: T

_{N}, T

_{CM}and T

_{EM}concentration at half-maximum expansion of T

_{N}, T

_{CM}and T

_{EM}; V

_{max5,1}: maximum killing rate of metabolic tumor volume by T

_{N}; V

_{max5,2}maximum killing rate of metabolic tumor volume by T

_{CM}; V

_{max5,3}: maximum killing rate of metabolic tumor volume by T

_{EM}; V

_{max5,4}: maximum killing rate of metabolic tumor volume by T

_{Eff}; KM

_{5}: metabolic tumor volume at half-maximum killing rate; k

_{5}: proliferation rate constant of metabolic tumor volume; K

_{0}: maximum tumor volume observable (tumor carrying capacity).

**Figure 2.**Goodness of fit plots for the population quantitative systems pharmacology model using our clinical dataset of 19 patients. Legend: (

**a**) Typical predictions (not considering interindividual variability) vs. measured concentrations/volumes for all species; (

**b**) typical predictions (not considering interindividual variability) vs. measured concentrations/volumes, stratified for species; (

**c**) individual predictions vs. measured concentrations for all species; (

**d**) individual predictions vs. measured concentrations, stratified for species. Diagonal line: Line of identity. Tumor measurements marked as a complete response were set to a value of 0 mL and are not shown. Abbreviations—T

_{N}: naïve T cells, T

_{CM}: central memory T cells, T

_{EM}: effector memory T cells, T

_{Eff}: effector T cells, CD19

^{+}tumor: CD19

^{+}metabolic tumor volume.

**Figure 3.**Measured T cell concentrations/metabolic tumor volumes (data points) and simulated typical (dashed lines) and individual (solid lines) model predictions for individual patients 1–16, and 18–19 in panels a–e and, as concentrations/volumes of all species were significantly higher, for patient 17 in separate panel (

**f**). Legend: (

**a**) Naïve CAR-T cells; (

**b**) Central memory CAR-T cells; (

**c**) Effector memory CAR-T cells; (

**d**) Effector CAR-T cells; (

**e**) CD19

^{+}metabolic tumor volume; (

**f**) Concentrations of naive, central memory, effector memory, and effector CAR-T cells as well as CD19

^{+}metabolic tumor volume for patient 17. Abbreviations—T

_{N}: naïve CAR-T cells, T

_{CM}: central memory CAR-T cells, T

_{EM}: effector memory CAR-T cells, T

_{Eff}: effector CAR-T cells, CD19

^{+}tumor: CD19

^{+}metabolic tumor volume.

**Figure 4.**Patient characteristics in the reference expansion population and the low expansion subpopulation. Legend: (

**a**) Baseline metabolic tumor volume (mL) in the reference expansion population and the low expansion subpopulation. (

**b**) Patient age in the reference expansion population and the low expansion subpopulation. Boxes: interquartile range (IQR) including median; whiskers: range from hinge to lowest/highest value within 1.5 IQR; points: data outside whisker. (

**c**) Frequency of patients in the reference expansion population and the low expansion subpopulation, stratified for disease type. (

**d**) Frequency of patients in the reference expansion population and the low expansion subpopulation, stratified for a previous ASCT. Abbreviations—ASCT: autologous stem cell transplantation, DLBCL: diffuse large B cell lymphoma, PMBCL: primary mediastinal B cell lymphoma, TFL: transformed follicular lymphoma, *: p ≤ 0.05, ns: p > 0.05.

**Figure 5.**Observed (light blue boxes) and model predicted (dark blue boxes) CAR-T cell kinetic parameters for the sum of all CAR-T cell populations. (

**a**) Maximum cell concentration (Cmax). (

**b**) Area under the concentration–time curve from day 0–28 (AUC

_{0–28d}). (

**c**) Time at maximum concentration (days); data points of differences sizes mark the number of observations/predictions at different time points. (

**d**) Cmax/Baseline metabolic tumor volume (cells µL

^{−1}mL

^{−1}). Legend—Boxes: interquartile range (IQR) including median; whiskers: range from hinge to lowest/highest value within 1.5 IQR; points: data outside whisker. Abbreviations—Tmax: time at maximum CAR-T cell concentration; AUC 0–28d: area under the concentration–time curve from days 0–28, Cmax: maximum CAR-T cell concentration.

**Figure 6.**Kaplan–Meier plots for (

**a**) progression-free survival and (

**b**) overall survival in the reference T cell expansion population (green) and the low expansion subpopulation (orange); log-rank tests.

**Figure 7.**Kaplan–Meier plots for (

**a**) progression-free survival and (

**b**) overall survival in patients having undergone (magenta) or having or not undergone (blue) a previous ASCT; log-rank tests. Abbreviations—ASCT: autologous stem cell transplantation.

**Figure 8.**Kaplan–Meier plots for (

**a**) progression-free survival and (

**b**) overall survival in patients with different combinations of T cell expansion and previous ASCT group; log-rank tests. Pairwise comparisons were performed to assess between which curves there was a significant difference (

**a**): significant difference between Reference/Yes and Low/No, p = 0.019, (

**b**): significant difference between Reference/Yes and Low/No, p = 0.026). Legend—Magenta curve: Patients in the low expansion subpopulation who did not undergo a previous ASCT; orange curve: patients in the normal expansion subpopulation who did not undergo a previous ASCT; purple curve: patients in the low expansion subpopulation who underwent a previous ASCT, blue curve: patients in the reference expansion population who underwent a previous ASCT. Abbreviations—ASCT: autologous stem cell transplantation.

**Figure 9.**Determination of a clinical composite score (CCS) cut-off value for early response-prediction. (

**a**) Correlation between model parameter V

_{max1}((cells·µL

^{−1})·day

^{−1}·mL

^{−1}) and CCS Maximum naïve CAR-T cell concentration/Metabolic tumor volume at baseline ((cells·µL

^{−1}) ·mL

^{−1}). (

**b**) Correlation plot as

**A**but on a log-log scale and different labeling of the T cell expansion subpopulation. The dashed horizontal line marks the CCS cut-off value most predictive for allocation to the low expansion subpopulation, as determined using ROC analysis. (

**c**) Kaplan–Meier probabilities for progression-free survival in patients below or exceeding the determined CCS

_{TN}cut-off value. (

**d**) Kaplan–Meier plots for overall survival in patients below or exceeding the determined CCS

_{TN}cut-off value. Abbreviations—CCS

_{TN}: clinical composite score for naïve CAR-T cells.

**Figure 10.**(

**a**) Correlation for the clinical composite score for T

_{all}using flow cytometry or qPCR and comparisons of the CCS using qPCR between (

**b**) reference expansion population and low expansion subpopulation in our clinical dataset, (

**c**) CR/PR and PD/NR in CLL patients (n = 12) and (

**d**) CR/PR and PD/NR in MM patients (n = 19). Abbreviations—CLL: chronic lymphocytic leukemia; CR: complete response; MM: multiple myeloma; NR: no response; PR: partial response; qPCR: quantitative polymerase chain reaction; T

_{all}: the sum of all measured CAR-T cell phenotypes. *: p ≤ 0.05, **: p ≤ 0.01.

**Table 1.**Final parameter estimates for the CD19-specific CAR-T cell quantitative systems pharmacology model.

Parameter (Unit) | Description | Estimate | RSE or Literature Source |
---|---|---|---|

V_{max1,base,ref}[(cells·µL ^{−1}) ·day^{−1}·mL^{−1}] | Maximum expansion rate per mL tumor volume of T_{N}, T_{CM}, and T_{EM} for the reference expansion population without previous ASCT and a CD4^{+}/CD8^{+} CAR-T cell ratio at day seven of 1 | 0.00846 | 36% |

V_{max1,base,low}[(cells·µL ^{−1}) ·day^{−1}·mL^{−1}] | Maximum expansion rate per mL tumor volume of T_{N}, T_{CM}, and T_{EM} for the low expansion subpopulation without previous ASCT | 0.000700 | 17% |

ASCT_{Vmax1} §(−) | Fractional change in V_{max1,base,ref} or V_{max1,base,low} due to a previous ASCT | 2.53 | 31% |

CD4/CD8_{exp} †(−) | Fractional change in V_{max1,base,ref} due to a change of the CD4^{+}/CD8^{+} CAR-T cell ratio on day seven from a value of 1 | −0.385 | 45% |

KM_{1}(cells·µL ^{−1}) | T_{N}, T_{CM}, or T_{EM} concentration at half-maximum expansion of T_{N}, T_{CM}, or T_{EM} | 1.13 | 22% |

kp_{1} (day^{−1}) | Homeostatic proliferation rate constant for T_{N} | 0.0005 | [47] |

kp_{2} (day^{−1}) | Homeostatic proliferation rate constant for T_{CM} | 0.007 | [47] |

kp_{3} (day^{−1}) | Homeostatic proliferation rate constant for T_{EM} | 0.007 | [47] |

k_{12} (day^{−1}) | Rate constant for differentiation of T_{N} to T_{CM} | 0.140 | 9% |

k_{23} (day^{−1}) | Rate constant for differentiation of T_{CM} to T_{EM} | 0.191 | 11% |

k_{34} (day^{−1}) | Rate constant for differentiation of T_{EM} to T_{Eff} | 0.355 | 13% |

ke_{1} (day^{−1}) | Death rate constant for T_{N} | 0.0104 ‡ | 13% |

ke_{2} (day^{−1}) | Death rate constant for T_{CM} | 0.0104 ‡ | 13% |

ke_{3} (day^{−1}) | Death rate constant for T_{EM} | 0.0104 ‡ | 13% |

ke_{4} (day^{−1}) | Death rate constant for T_{Eff} | 0.518 | 13% |

V_{max 5,1} [mL·day^{−1} ·(cells·µL^{−1})^{−1}] | Maximum killing rate of metabolic tumor volume by T_{N} | 2.57 * | 39% |

V_{max 5,2} [mL·day^{−1} ·(cells·µL^{−1})^{−1}] | Maximum killing rate of metabolic tumor volume by T_{CM} | 4.04 | 39% |

V_{max 5,3} [mL·day^{−1} ·(cells·µL^{−1})^{−1}] | Maximum killing rate of metabolic tumor volume by T_{EM} | 3.78 * | 39% |

V_{max 5,4} [mL· day^{−1} ·(cells·µL^{−1})^{−1}] | Maximum killing rate of metabolic tumor volume by T_{Eff} | 4.24 * | 39% |

KM_{5} (mL) | Metabolic tumor volume at half-maximum killing rate | 276 | 33% |

K_{0} (mL) | Maximum tumor volume observable (tumor carrying capacity) | 5000 | - |

k_{5} (day^{−1}) | Proliferation rate constant of metabolic tumor volume | 0.0023 | - |

MIXP (−) | Estimated proportion of patients in the reference population using the mixture model | 0.803 | 11% |

IIV V_{max1,base,ref} | Interindividual variability in V_{max1,base,,ref} | 150% CV | 19% |

IIV V_{max 5,2} | Interindividual variability in V_{max 5,2} | 307% CV | 19% |

RUV T_{N} | Residual unexplained variability in observed T_{N} concentrations | 59.1% CV | 11% |

RUV T_{CM} | Residual unexplained variability in observed T_{CM} concentrations | 85.9% CV | 9% |

RUV T_{EM} | Residual unexplained variability in observed T_{EM} concentrations | 120% CV | 9% |

RUV T_{Eff} | Residual unexplained variability in observed T_{Eff} concentrations | 70.6%CV | 10% |

RUV CD19^{+}tumor | Residual unexplained variability in observed metabolic tumor volumes | 115% CV | 12% |

`·`100; §: implemented as fractional change covariate model, †: implemented as power covariate model; ‡ derived using the estimated death rate constant for effector T cells ke

_{4}and the relationship between death rate constants of short- and long-lived T cells in the publication by Stein et al. [21]; * derived using the estimated maximum killing rate of metabolic tumor volume by T

_{CM}and the digitized relationships of tumor cell killing rates in the publication by Schmueck-Henneresse et al. [49].

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Mueller-Schoell, A.; Puebla-Osorio, N.; Michelet, R.; Green, M.R.; Künkele, A.; Huisinga, W.; Strati, P.; Chasen, B.; Neelapu, S.S.; Yee, C.;
et al. Early Survival Prediction Framework in CD19-Specific CAR-T Cell Immunotherapy Using a Quantitative Systems Pharmacology Model. *Cancers* **2021**, *13*, 2782.
https://doi.org/10.3390/cancers13112782

**AMA Style**

Mueller-Schoell A, Puebla-Osorio N, Michelet R, Green MR, Künkele A, Huisinga W, Strati P, Chasen B, Neelapu SS, Yee C,
et al. Early Survival Prediction Framework in CD19-Specific CAR-T Cell Immunotherapy Using a Quantitative Systems Pharmacology Model. *Cancers*. 2021; 13(11):2782.
https://doi.org/10.3390/cancers13112782

**Chicago/Turabian Style**

Mueller-Schoell, Anna, Nahum Puebla-Osorio, Robin Michelet, Michael R. Green, Annette Künkele, Wilhelm Huisinga, Paolo Strati, Beth Chasen, Sattva S. Neelapu, Cassian Yee,
and et al. 2021. "Early Survival Prediction Framework in CD19-Specific CAR-T Cell Immunotherapy Using a Quantitative Systems Pharmacology Model" *Cancers* 13, no. 11: 2782.
https://doi.org/10.3390/cancers13112782