Modeling Patient-Specific CAR-T Cell Dynamics: Multiphasic Kinetics via Phenotypic Differentiation

Abstract

Chimeric Antigen Receptor (CAR)-T cell immunotherapy revolutionized cancer treatment and consists of the genetic modification of T lymphocytes with a CAR gene, aiming to increase their ability to recognize and kill antigen-specific tumor cells. The dynamics of CAR-T cell responses in patients present multiphasic kinetics with distribution, expansion, contraction, and persistence phases. The characteristics and duration of each phase depend on the tumor type, the infused product, and patient-specific characteristics. We present a mathematical model that describes the multiphasic CAR-T cell dynamics resulting from the interplay between CAR-T and tumor cells, considering patient and product heterogeneities. The CAR-T cell population is divided into functional (distributed and effector), memory, and exhausted CAR-T cell phenotypes. The model is able to describe the diversity of CAR-T cell dynamical behaviors in different patients and hematological cancers as well as their therapy outcomes. Our results indicate that the joint assessment of the area under the concentration-time curve in the first 28 days and the corresponding fraction of non-exhausted CAR-T cells may be considered a potential marker to classify therapy responses. Overall, the analysis of different CAR-T cell phenotypes can be a key aspect for a better understanding of the whole CAR-T cell dynamics.

Keywords: CAR-T cell exhaustion; antigen dependent CAR-T expansion; functional CAR-T cells; hematological malignancies; memory pool; treatment outcomes.

Figure 1

Multiphasic CAR-T cell dynamics. (a) Schematic representation of the multiphasic response to CAR-T cell therapy as described by the model. After CAR-T infusion, the typical response profile shows a rapid and usually undetectable decline of circulating CAR-T cells, featuring the distribution phase. The expansion phase is characterized by the antigen-mediated proliferation of engrafted CAR-T cells and reaches its peak about two weeks after starting treatment. Over time, effector cells contribute to the formation of the memory cells but also lose proliferative and cytotoxic capacities, becoming exhausted CAR-T cells. The expansion peak is followed by a contraction phase, marked by a sharp decay of CAR-T cells. The longer lifespan of memory cells leads to a long period of smooth decline, which characterizes the persistence phase. (b) Schematic description of the CAR-T immunotherapy model in patients. The CAR-T cells infused into the patient undergo a rapid distribution phase ($C_D$). Part of these cells undergoes engraftment and settles in the blood and tumor niche. Engrafted cells are called effector CAR-T cells ($C_T$) and expand upon antigen contact, differentiate into memory CAR-T cells ($C_M$), become exhausted ($C_E$), and die naturally or are targeted by tumor immunosuppressive mechanisms. Both $C_T$ and $C_D$ populations present cytotoxic effects and, therefore, are named functional CAR-T cells. Memory CAR-T cells die naturally but are readily responsive to antigen-positive cells. When they interact with tumor cells, they differentiate back into effector CAR-T cells, producing a rapid immune response against the tumor. Over time, effector CAR-T cells become exhausted and are eliminated. Tumor cells (T), which express the specific target antigen, grow depending on the resources available in the microenvironment and are killed by functional CAR-T cells. The net growth of tumor cells results from the balance between their proliferation and natural death. (c) Illustrative patient profiles of the function $\kappa \left(t\right)$, describing the antigen-mediated and time-dependent expansion rate of engrafted CAR-T cells. Individual characteristics and heterogeneity of the infused product ultimately define the strength and duration of each phase of the CAR-T cell dynamics.

Figure 2

Schematic description of the strategy used to assess the dominant mechanisms underlying the multiphasic CAR-T cell dynamics. (a) Experimental data () of CAR-T cell kinetics from a representative patient profile were split among the four phases of CAR-T cell dynamics to which lines in the logplot of the CAR-T cell population along time were fitted. The corresponding (growth or decline) rates are denoted by $m_d,m_e,m_c$, and $m_p$, associated with the distribution, expansion, contraction, and persistence phases, respectively. These rates are used as first approximations to the parameters of the leading mechanism(s) of each phase. Specifically, the distribution phase is mainly driven by the reduction rate of the injected CAR-T cells so that $m_d\approx \beta$; the expansion phase is driven by the combined effect between the $C_T$ expansion ($p_1+r_{min}$) and mortality ($\xi$), leading to $m_e\approx p_1+r_{min}-\xi$; the contraction and persistence phases are mainly driven by the mortality of exhausted and memory CAR-T cells, respectively, which yield $m_c\approx \delta$ and $m_p\approx \mu$. (b) The per capita rate of the total CAR-T cell population ($C_D+C_T+C_E+C_M$) is displayed over time after infusion together with the calibrated values of $\beta$, $p_1+r_{min}-\xi$, $\delta$, and $\mu$.

Figure 3

Model simulations fitted to the experimental data () from [22]. Each column corresponds to the dynamics of the total CAR-T cell population () for different diseases (DLBCL, pediatric and adult ALL, and CLL) and different patients. The total CAR-T cell population is divided into effector ($C_T$), memory ($C_M$), and exhausted ($C_E$) phenotypes, shown in continuous, dashed, and dotted green, respectively. The mean dose value of $1.0\times {10}^8$ cells () presented in [21] is used as a surrogate for the actual doses when not reported for patients with ALL. The gray region represents the undetectable levels (below the threshold of $5.0\times {10}^6$ cells to DLBCL and pediatric ALL, $1.0\times {10}^6$ cells to adult ALL, and $2.5\times {10}^6$ cells to CLL [22]). Data points in this region () were not used for calibration and error calculation due to their high uncertainties. The bottom row presents the time-dependent expansion rate function ($\kappa \left(t\right)$) for each patient.

Figure 4

Model simulations fitted to the experimental data () from [37,38]. Each column corresponds to the dynamics of the total CAR-T cell population () for different therapy responses at the last follow-up (interval from infusion to the last follow-up in days) (CR—complete response, PR—partial response, and SD—stable disease) and different patients. The total CAR-T cell population is divided into effector ($C_T$), memory ($C_M$), and exhausted ($C_E$) phenotypes, shown in continuous, dashed, and dotted green, respectively. The gray region represents the undetectable level. Data points () may assume any value in this region, but some () were not used for calibration and error calculation of the model due to their greater uncertainty. The bottom row presents the time-dependent expansion rate function ($\kappa \left(t\right)$) for each patient.

Figure 5

CAR-T therapy outcomes for different patients (one in each column) with ALL, CLL, MCL, or DLBCL with different therapy responses (CR—complete response, PR—partial response, and SD—stable disease). Pie charts display the fractions of functional, memory, and exhausted cells composing the area under the curve of the entire CAR-T population during the first 28 (first row), 60 (second row), and 90 (third row) days after infusion; absolute values of AUC are indicated by the radii of the pies. The bar plot in the fourth row shows the ratio between the CAR-T cell peak value and the infused dose (in black), along with the quantity of each CAR-T cell subpopulation (green tones) on the day when the subpopulation is at the peak time. The bar plot at the bottom presents the time of the theoretical relapse ($t_{TR}$, gray) and the corresponding CAR-T cell subpopulations (green tones). NA (not applicable) indicates no theoretical relapse due to: (a) the occurrence of the limit cycle at undetectable levels; (b) no tumor recurrence within 20,000 days.

Figure 6

Summary of patient outcomes with respect to kinetic parameters in appropriate units. Panel (a) highlights the importance of the fraction of non-exhausted cells ($C_D+C_T+C_M$) in the first 28 days after infusion together with AUC0-28. Patient outcomes are concentrated in three distinct regions. Fully responsive patients (CR) have high fractions of non-exhausted cells while patients who achieved stable disease (SD) have small AUC0-28 values with fractions of non-exhausted CAR-T cells below 0.8. Of the three patients who achieved partial response (PR), patient P12 displays a moderate value of AUC and a high percentage of exhausted cells. Patients P22 and B11 also have moderate AUC values but a small fraction of exhausted cells. Of note, there is no information on the cause of patient B11 relapse but patient P22 (marked with ▵) underwent mutation with CD19-dim cells. The relationships between AUC0-28 and $C\left(t_{peak}\right)$ (b), and $C\left(t_{peak}\right)$/dose and fractions of $C_D+C_T+C_M$ (c) are also considered but do not provide clear separation among the response groups.