The Third Dimension of Pharmacokinetic–Pharmacodynamic Theory: Adaptive Rate Capacity as a Conserved Constraint on Biological Tolerability

Pharmacokinetic–pharmacodynamic theory describes drug action in two dimensions, magnitude and time, yet rate-dependent toxicity recurs across unrelated therapies without a unifying principle. We propose the Human Adaptive Rate Limit (HARL): every physiological system tolerates a maximum velocity of state change, |dS/dt|max = σmax/τ, set by its reserve σ and adaptation time τ. We show that nifedipine, erythropoiesis-stimulating agents, radiation, vancomycin and CAR T-cell therapy obey one velocity boundary spanning minutes to weeks. Reanalysing the 202-patient CAR-T cohort of Wei et al., a dual-velocity classifier (ferritin and D-dimer rate of rise) predicted severe cytokine release syndrome with 100% sensitivity and a median 4-day lead time before clinical onset. Velocity is a third, governable dimension of tolerability; a dynamic maximum tolerated rate should complement the maximum tolerated dose in drug development.