Topological Pharmacokinetics: Reading the Shape of Drug Disposition from Data

Pharmacokinetic analysis has spent half a century compressing drug concentration-time curves into scalar summaries--AUC, Cmax, clearance--discarding the shape information that encodes mechanistic fingerprints of the underlying physiology. We introduce Topological Pharmacokinetics (TPK), a framework that reads the shape of pharmacokinetic trajectories directly from data without prior commitment to a compartmental model. TPK uses delay embedding to reconstruct the pharmacokinetic attractor from the concentration-time curve, and persistent homology to extract its topological invariants--connected components and loops--as a Pharmacokinetic Topological Invariant (PTI) vector. We validate TPK across three levels: linear systems (negative control), nonlinear saturable elimination (detection of the N_PTP +1 rule and a nonlinear diagnostic triad), and endogenous circadian rhythms (contrastive detection of rhythmic interference via Dev specificity and Decouple Collapse). The PTI vector provides a model-agnostic shape fingerprint that, in simulation, demonstrates the diagnostic potential of shape-based analysis; validation on experimental data is required to assess whether this potential generalizes to real pharmacokinetic data. All findings are demonstrated as proof of concept on simulated data; validation on experimentally measured concentration-time curves is the essential next step.