The Patch as a Spatial Dose-Segregation Device: Free Local Drug Concentration as the Primary Efficacy Variable for Skin-Targeted JAK Inhibition, with a Transparent Depth Bounding Model for Tofacitinib

Hypothesis-and-theory preprint (v2). A transdermal patch built for a skin-target drug is reframed not as a pump aimed at the bloodstream but as a spatial dose-segregation device: it builds a high local drug compartment in the skin while holding systemic plasma exposure low. For a drug whose target lives in the skin and whose systemic exposure is the liability, the governing efficacy variable is the free drug concentration in the target tissue compartment measured against the cellular IC50, not plasma pharmacokinetics. The lens is worked through tofacitinib (JAK1/3 inhibitor; pSTAT IC50 ≈ 15–60 nM). A transparent one-dimensional steady-state model (Fickian diffusion against a vascular clearance sink, parameterized entirely from published values) bounds the depth profile and shows the superficial-versus-follicular split is a steep geometric cliff, with passive delivery to the 4–5 mm scalp hair bulb at or beyond physical reach. The single experiment that would settle the question is a depth-resolved, stratified measurement of free (and total) drug concentration across stratum corneum, viable epidermis, dermis, and hair follicle from a real patch, benchmarked against an approved comparator and paired with a skin pharmacodynamic readout. Central claim: local free concentration and plasma concentration are spatially distinct and can diverge by orders of magnitude under topical delivery. The dose is not a number; it is a field. Contents: manuscript (PDF + LaTeX source), Figure 5 (depth bounding model), and bounding-model.py (the one-dimensional steady-state skin PK bounding model, NumPy). Scope: hypothesis-tier; AI-assistance is disclosed in the manuscript. Theoretical/educational — not a clinical claim, not medical advice, and not a dosing recommendation.