Conditions for Pharmacological Sanctuaries in Perivascular Tumour Cords: A Reaction–Diffusion Analysis, a Regrowth-Kinetics Identity, and a Descriptive Survival Analysis of Histologic Subtype in Resected Lung Adenocarcinoma

Abstract Background: Adjuvant osimertinib markedly improves disease-free survival in resected EGFR-mutated non-small-cell lung cancer (NSCLC). However, extended follow-up in the ADAURA trial revealed that among patients who experienced disease recurrence, the majority of relapses manifested after planned treatment cessation at year 3, frequently without acquired secondary genomic resistance mutations. We examined whether biophysical drug transport limitations could establish tissue sanctuaries that shelter drug-sensitive tumor cells. Methods: We analyzed steady-state reaction–diffusion transport in two canonical tumor micro-architectures: out-ward perivascular cords (divergent cylindrical geometry, modified Bessel 𝐾0 ) and inward avascular nests (convergent cylindrical geometry, modified Bessel 𝐼0 ). We derived an exact algebraic identity governing post-cessation exponential regrowth from molecular residual disease (ctDNA, 107 cells) to radiologic detection (CT, 109 cells). We evaluated the clinical prognostic relevance of histologic architecture in 604 resected lung adenocarcinoma patients from Memorial Sloan Kettering Cancer Center (MSKCC 2020). Results: In perivascular cords, outward radial diffusion of osimertinib (𝜆 = 627.6 𝜇m) produces a steep concentration drop beneath the IC50 threshold (𝜃 = 0.35, corresponding to unbound 𝐶0 ≈ 40 nM and IC50 ≈ 14 nM) at 𝑟crit = 165.9 𝜇m. Depending on physiological oxygenation limits, a viable pharmacological sanctuary shell of width Δ𝑟 = 34.1 𝜇m (for 𝑟ox = 200 𝜇m) or Δ𝑟 = 14.1 𝜇m (for 𝑟ox = 180 𝜇m) can persist. Under an assumed sigmoidal dose-response (ℎ = 1.5), residual drug exposure in the shell (𝐶 ≈ 0.31–0.35 𝐶0 ) maintains partial target inhibition (~45–50%), sufficient under physiological baseline apoptosis to induce near-zero net growth (cytostasis). Conversely, in inward avascular nests, convergent geometry maintains osimertinib at 90.6%–99.4% of boundary levels throughout viable regions (𝑅 ≤ 160–200 𝜇m), precluding small-molecule sanctuaries. For macromolecular antibody–drug conjugates (ADCs, 𝜆 = 77.5 𝜇m), central concentration drops below 𝜃 = 0.35 only for nest radii 𝑅 > 180 𝜇m, an architectural domain typically constrained by hypoxia and necrosis. In Monte Carlo parameter sampling (𝑁 = 10, 000 draws, log-normal priors, seed = 2), an outward perivascular sanctuary shell existed in 46.1% of parameter draws (62.8% when 𝑟ox = 200 𝜇m is fixed). The diagnostic lead time Δ𝑡 = 𝑇𝑠 ⋅ log2 (100) = 5.46 months (for doubling time 𝑇𝑠 = 25 days) is an analytical property of exponential expansion and assay thresholds, rather than an empirical confirmation of sanctuary existence. In the MSKCC cohort (reverse Kaplan–Meier median follow-up 23.8 months, IQR: 13.3–31.8 months), lepidic architecture was consistent with a substantially lower hazard of recurrence (4.55%, stage-adjusted 𝐻𝑅 = 0.25, 95% CI ∶ 0.09–0.70, 𝑝 = 0.0084 vs acinar). In 10-fold Holm-adjusted pairwise comparisons, lepidic recurrence was significantly lower than solid (𝑝adj = 0.0026) and papillary (𝑝adj = 0.0203), whereas differences vs acinar (𝑝adj = 0.0703) and micropapillary (𝑝adj = 0.3911, unadjusted 𝑝 = 0.0559) did not achieve significanceunder family-wise error control. Grouping solid and micropapillary patterns yielded an exploratory contrast of 𝐻𝑅 = 6.75 (95% CI ∶ 2.28–19.97; Firth penalized shrinkage 𝐻𝑅 = 2.60–3.42) against lepidic, based on 4 lepidic events, whereas across the unselected cohort the hazard ratio was 1.32 (𝑝 = 0.239). Conclusions: Small-molecule pharmacological sanctuaries are geometrically restricted to outward perivascular cords and do not occur in avascular nests. Clinical cohort data demonstrate baseline protection associated with lepidic growth rather than an escalating risk across compact patterns. Surveillance strategies based on molecular lead time must be evaluated in prospective trials to rule out lead-time bias.