A Multiscale Biophysical Reaction-Diffusion Framework Coupling Histological Architecture, Interstitial Transport, and Inflammatory Tension in Solid Tumors: An Exploratory In Silico and Retrospective Multi-Cohort Analysis

Background In solid oncology, anatomical TNM staging and somatic mutational profiling provide the cornerstone of clinical risk stratification. Nevertheless, substantial clinical heterogeneity remains unexplained: curatively resected (R0) tumors frequently recur, and targeted adjuvant therapies—such as 36-month adjuvant osimertinib in the landmark ADAURA trial—exhibit a post-discontinuation recurrence rebound where 67.9% of all relapse events occur after planned treatment cessation. Similarly, in desmoplastic colorectal cancer (CMS4 subtype), cytotoxic chemotherapy de-escalation/escalation strategies (investigated in trials such as PEGASUS) confront persistent micrometastatic reservoirs that evade clearance. We hypothesized that post-resection persistence and delayed relapse are modulated by the biophysical coupling between epithelial polarity integrity (“The Seed”) and microenvironmental inflammatory-transport resistance (“The Soil”). Methods We established a multiscale biophysical reaction-diffusion continuum model integrating: 1. Spatial drug penetration across microvascular cords governed by modified cylindrical Bessel functions of the second kind (K0); 2. Interstitial transport limitations driven by elevated interstitial fluid pressure ( I F P ≈ 20 – 35 mmHg) and absent functional lymphatic drainage (Δ P ≈ 0); 3. Plastic drug-tolerant persister (DTP) cell transitions within viable, sub-therapeutic annular niches (p O2 ≥ 1 – 2 mmHg); 4. A hereditary Volterra memory functional of residual cytotoxic immune surveillance (Eimm ( t ) = E0 e− γ ∫ Φ d τ) formalizing cumulative inflammatory damage; 5. An exploratory translational metric—the Host-Tumor Biophysical Index (HTBI)—integrating histopathological polarity, stromal desmoplasia, and systemic inflammatory blood parameters (neutrophil-to-lymphocyte ratio [NLR] and C-reactive protein [CRP]). In accordance with REMARK reporting recommendations, the framework was evaluated across 3,461 curatively treated cancer patients with clinically indexed records across 11 cohorts (with 3,425 complete matched multi-omic and blood profiles analyzed, strictly excluding 36 TCGA cases lacking paired RNA-seq matrices and 274 incomplete blood records): - Discovery Cohort: 604 curatively resected lung adenocarcinoma patients from Memorial Sloan Kettering Cancer Center (MSKCC 2020); - Raw Blood Chemistry Cohort: 1,056 curatively resected surgical patients evaluated via strict complete-case analysis with raw pre-operative complete blood counts (NLR) and serum CRP/Albumin (PLOS ONE open data); - Multi-Cohort Solid Epithelial Cohorts (N = 986 matched RNA-seq / N =1 ,222 clinical): Colorectal (TCGA-COADREAD, N =592), Pancreatic (TCGA-PAAD, N =177), Esophageal (TCGA-ESCA, N =181), Cholangiocarcinoma (TCGA-CHOL, N =36), and External Lung (GSE31210, N = 226); - Inherited Cholangiopathy Model: 18 clinically annotated biliary cases (JAG1, NOTCH2, PKHD1, TJP2); - Proof-by-Contradiction Falsification Controls (N =535): Acute Myeloid Leukemia (TCGA-LAML, N =149), Testicular Germ Cell (TCGA-TGCT, N =133), and Soft-Tissue Sarcoma (TCGA-SARC, N = 253); - External Clinical Trial Anchor: The landmark double-blind randomized CANTOS trial (The Lancet 2017, N =10 ,061). Findings In the complete-case raw laboratory cohort (N =1 ,056), pre-operative biophysical inflammatory tier stratified 5-year overall survival from 69.4% (Low HTBI) to 56.7% (High HTBI) (p =3.81×10−7), maintaining independent prognostic association in multivariable Cox proportional hazards regression adjusting for Pathologic TNM Stage and Histological Grade (Hazard Ratio H R =1.43, 95 %CI:1.14 – 1.81 , p = 0.0022; continuous multivariable H R = 2.20, p = 0.00041). In the MSKCC lung adenocarcinoma discovery cohort (N = 604 , 98 recurrences), continuous decoupled HTBI conferred an adjusted H R = 2.49 ( 95 %CI:1.00 – 6.18 , p = 0.050) (binary adjusted H R =1.89, p = 0.029) after controlling for Pathologic TNM Stage (H R = 2.53 , p < 0.0005), patient sex, and somatic EGFR mutations. Schoenfeld residuals confirmed proportional hazards ( χ2 =3.82 , p = 0.431). 500-fold bootstrap cross-validation showed an incremental discrimination gain (ΔC -index =+ 0.050 , p = 0.044; 2-year A U C = 0.794). In competing risks analysis (Aalen-Johansen cumulative incidence function), HTBI specifically stratified cancer-related recurrence ( p = 0.029), while remaining unstratified for non-cancer competing mortality ( p = 0.680). In proof-by-contradiction negative controls evaluated with genuine empirical RNA-seq expression z-scores lacking solid epithelial boundaries, the model was statistically non-significant as predicted: liquid tumors (TCGA-LAML, N =149 , H R =1.28 , p = 0.246), non-epithelial germline tumors (TCGA-TGCT, N =133 , H R = 2.33 , p = 0.471), and mesenchymal sarcomas (TCGA-SARC, N = 253 , H R = 0.85 , p = 0.413). The continuum model analytically reproduced the empirical 5.46-month median ctDNA-to-imaging lead time (transition from 106 to 108 cells with doubling time T d = 24.6 days), and simulated anti-inflammatory microenvironmental stabilization aligned with the biological feasibility demonstrated in published systemic IL-1β neutralization trials (CANTOS, H R = 0.23 , p = 0.0002). Interpretation The Host-Tumor Biophysical Index demonstrates that combining routine surgical histopathology and standard laboratory inflammatory markers with physical transport mechanics provides independent prognostic stratification in retrospective cohorts. This exploratory framework offers a mechanistic hypothesis for residual tumor dormancy and a quantitative foundation for evaluating microenvironmental decompression and host anti-inflammatory strategies in prospective research settings.