Delay Differential Equation (DDE) Modeling of CAR-T Cellular Kinetics: Application to BCMA-Targeted (Ide-cel, Orva-cel) and CD19-Targeted (Liso-cel) Therapies

Abstract

Chimeric antigen receptor (CAR) T-cell therapies undergo rapid in vivo expansion followed by contraction and variable long-term persistence after a single infusion, yielding cellular kinetic (CK) profiles that differ fundamentally from conventional small-molecule and biologic pharmacokinetics. Piecewise, phase-based CK models are widely used, but discontinuous switching and constant expansion assumptions can create numerical instability around the transition window and bias the characterization of early expansion and near-peak behavior. Building on our prior saturable expansion framework (Vmax/Km), we advanced CAR-T CK modeling by introducing (i) smooth S-shaped gating to replace discontinuous phase switching and enable continuous time-varying expansion dynamics, and (ii) delay differential equation (DDE) components to evaluate whether longitudinal data support explicit lags in downstream biological processes. Data were pooled from three CAR-T trials (TRANSCEND, KarMMa-3, and EVOLVE) spanning two BCMA-targeted products (ide-cel, orva-cel) and one CD19-targeted product (liso-cel). Models were estimated in Monolix using SAEM with importance sampling for final likelihood evaluation. Model selection relied on likelihood-based criteria (AIC, BIC, and Monolix BICc) and diagnostic assessments. Relative to a constant-expansion baseline, saturable expansion improved fit and reduced systematic model misspecification at high transgene levels (e.g., qPCR transgene copies/{micro}g). Among multiple DDE placements evaluated, the data most strongly supported a delay on effector-to-memory conversion; delays in effector-like and/or memory-like decay were not favored. Simulations indicated that the conversion delay primarily modulated the timing and magnitude of the memory-like trajectory, with minimal impact on total-cell trajectories during the expansion phase at the evaluated scale. In a shared covariate framework with product as a categorical effect, BCMA-targeted products exhibited higher baseline levels and expansion capacity than liso-cel, with stronger evidence for slower effector-like decay for orva-cel than ide-cel. Overall, smooth-gated saturable expansion with DDE-based delayed conversion provides a parsimonious, biologically motivated framework for CAR-T CK and supports cross-product comparisons under harmonized structural assumptions.