A Regime-Switching Dynamic Reserve Model Linking Relative Dose Intensity and Functional Recovery During First-Line Diffuse Large B-Cell Lymphoma Therapy

Abstract

Relative dose intensity (RDI) summarizes treatment delivery in diffuse large B-cell lymphoma (DLBCL), but it cannot show when declining reserve changes a patient from treatment-tolerant to treatment-limited. We developed a theoretical regime-switching model linking lymphoma burden, hematologic reserve, functional reserve, comorbidity pressure, and delivered RDI across first-line therapy. Four normalized states represented lymphoma burden, hematologic reserve H(t), functional reserve, and cumulative delivered intensity. A Dynamic Treatment Reserve Index, governed preserved-reserve, compensated-vulnerability, and treatment-intolerance regimes with illustrative dose multipliers of 1.00, 0.75, and 0.55. Literature informed variable selection and plausible ranges; no patient-level fitting was performed. We examined existence, uniqueness, positivity, boundedness, regime-specific equilibria, Jacobian stability, switching boundaries, and basin behavior. Six-cycle Runge-Kutta simulations, two-dimensional continuation, 500-set Latin hypercube sampling, PRCC, stochastic parameter perturbation, and solver-tolerance checks assessed robustness. In the reference scenario, modeled RDI was 0.674, lymphoma burden fell from 0.750 to 0.149, while DTRI moved from 0.549 to 0.397. High initial reserve increased RDI to 0.785 and reduced final burden to 0.103. Low reserve reduced RDI to 0.553 and left burden at 0.211, severe constraint remained treatment-intolerant for 100.0% of simulated time. Continuation located an illustrative boundary near equal baseline reserves of 0.745. The 90% uncertainty interval was 0.567-0.753 for RDI and 0.081-0.288 for final burden. Dominant RDI determinants included baseline hematologic reserve (PRCC 0.859), functional reserve (0.872), hematologic toxicity (-0.653), functional toxicity (-0.694), and comorbidity pressure (-0.769). Parameter refinement and biological calibration are ongoing. This mechanistic proof-of-concept provides a mathematically testable framework for locating treatment-tolerance windows that conventional association analyses may not reveal. Its intended uses are serial-variable selection, dose-delivery hypothesis development, and retrospective or prospective validation with lymphoma teams. The expected benefit is earlier recognition of reserve collapse; its research advantages are transparent transitions, reproducible counterfactuals, explicit uncertainty, and separation of simulated thresholds from clinical recommendations.