The Spatial-Genomic Oncology Continuum

A Biophysical Reaction-Diffusion Theory of Pharmacological Sanctuaries, the Post-ADAURA Cessation Dilemma, and the Bedside Composite Resistance Index (CRI)

Author: Luca Celebrano, MD Candidate
Affiliation: Department of Clinical Medicine and Surgery, School of Medicine, Università degli Studi di Napoli Federico II, Naples, Italy
Correspondence: l.celebrano@studenti.unina.it

---

🚀 Interactive Clinical Web App Available: Test the real-time Bedside CRI Decision Engine and Bessel $K_0$ reaction-diffusion sanctuary simulator directly in your browser:
👉 https://lukecele.github.io/spatial-continuum-oncology/
🎮 60 FPS Live Digital Twin & 5-Year Trial Simulator:
👉 https://lukecele.github.io/spatial-continuum-oncology/simulator.html

⭐️ Support Open-Science Oncology: If you find this framework, biophysical model, or web simulator useful, please consider giving the repository a star on GitHub — it directly aids community discovery and open-science adoption!

---

📌 Executive Summary

In early-stage EGFR-mutated non-small cell lung cancer (NSCLC), 36 months of adjuvant osimertinib significantly extends disease-free survival (ADAURA trial). However, longitudinal molecular residual disease (MRD) monitoring (Herbst et al., Nature Medicine 2025) reveals an alarming paradox:

• $67.9%$ of all recurrence events occur after the planned 36-month discontinuation.
• $57.9%$ of post-cessation relapses cluster within the first 12 months post-discontinuation.
• $75\text{--}80%$ of relapsing patients do NOT harbor secondary pocket mutations (such as EGFR C797S), and 4th-generation allosteric inhibitors fail to prevent relapse.

This repository provides the complete, mathematically closed, and empirical literature-validated computational framework resolving this dilemma from first physical principles.

    Microvascular Reaction-Diffusion Cord & Pharmacological Sanctuary:
    Capillary (r0 = 10 um)        Sterilized Cuff                Cytostatic Sanctuary Cuff             Necrotic Core
    [ C0 = 28.6 nM ] ======> [ C(r) > IC50 (10 nM) ] ======> [ 2 nM < C(r) < 10 nM (G0/G1) ] ======> [ Hypoxia / Necrosis ]
    |------------------------ 0 to 165.9 um ----------------|--- 165.9 um to 200.0 um (31.3% Vol) ---|---- r > 200 um ----|

---

🔬 Core Biophysical Equations

1. Starling-Darcy Convective Shutdown ($Pe < 0.1$)

In solid lung adenocarcinoma, elevated Interstitial Fluid Pressure ($\text{IFP} = 9.8 \pm 6.8\ \text{mmHg}$, Mori et al. 2015) equilibrates with microvascular pressure ($P_v \approx 15\text{--}20\ \text{mmHg}$), collapsing the transvascular hydrostatic pressure gradient: $$\Delta P = P_v - \text{IFP} \le 10\ \text{mmHg} \implies \mathbf{v}{\text{fluid}} < 0.05\ \mu\text{m/s}$$ $$Pe = \frac{v{\text{fluid}} \cdot L}{D_{\text{eff}}} < 0.1$$ Convective filtration ceases, establishing 100% diffusion-dominated transport.

2. Cylindrical Bessel $K_0$ Reaction-Diffusion Concentration Profile

Steady-state radial concentration from a cylindrical microvessel is governed by the modified Bessel function of the second kind of order zero: $$C(r) = C_0 \cdot \frac{K_0(r/\lambda)}{K_0(r_0/\lambda)}$$ where:

• $r_0 = 10.0\ \mu\text{m}$ (capillary radius)
• $D_{\text{eff}} = 59.29\ \mu\text{m}^2/\text{s}$ (interstitial diffusivity)
• $k = 1.5052 \times 10^{-4}\ \text{s}^{-1}$ (tissue clearance rate constant)
• $\lambda = \sqrt{D_{\text{eff}} / k} = 627.6\ \mu\text{m}$ (characteristic penetration length)
• $\theta = \frac{\text{IC}{50}}{C{0,\text{free}}} = \frac{10.0\ \text{nM}}{28.62\ \text{nM}} = 0.349$

The critical radius at which $C(r_{\text{crit}}) = \text{IC}{50}$ is: $$r{\text{crit}} = \mathbf{165.89\ \mu\text{m}}$$

Because the empirical oxygen viability boundary in human lung carcinoma extends to $r_{\text{ox}} = 200.0\ \mu\text{m}$ (Thomlinson & Gray, Br J Cancer 1955), a mandatory sub-therapeutic pharmacological sanctuary exists: $$\Delta r = r_{\text{ox}} - r_{\text{crit}} = 200.0 - 165.89 = \mathbf{34.11\ \mu\text{m}}$$ $$f_{\text{vol}} = \frac{r_{\text{ox}}^2 - r_{\text{crit}}^2}{r_{\text{ox}}^2 - r_0^2} = \frac{200^2 - 165.89^2}{200^2 - 10^2} = \mathbf{31.28%}$$

---

📊 Longitudinal ctDNA Mathematical Lead Time Identity

During active therapy, sanctuary cells ($2\text{--}8\ \text{nM}$) remain trapped in cytostatic $G_0/G_1$ dormancy. Upon drug withdrawal at Month 36 ($C \to 0$), persister cells awaken into exponential clonal expansion ($T_d = 24.6\ \text{days}$): $$\Delta t_{\text{lead}} = T_d \cdot \log_2(100) = 6.644 \cdot 24.6\ \text{days} = 163.4\ \text{days} = \mathbf{5.37\ \text{months}}$$

• Clinical Trial Observation (Herbst et al., Nat Med 2025): Median $4.7\ \text{months}$ ($95%,\text{CI}: 2.2\text{--}5.6\ \text{months}$).
• Concordance: Our derived analytical lead time falls strictly inside the human clinical $95%,\text{CI}$.

---

🏆 Head-to-Head Clinical Superiority Benchmark: SG-ADAURA vs. Standard of Care

To address whether our spatial-continuum framework provides superior clinical outcomes compared to current standard-of-care guidelines (36-month fixed adjuvant osimertinib discontinuation), we conducted a rigorous in silico trial ($N = 500$ virtual patients, 5 treatment arms, followed across 1,825 days / 5 years post-resection).

Full study: 📄 11_STUDIO_SUPERIORITA_CLINICA_E_BENCHMARK_SOC_ADAURA.md
Live Portal Audit: 🌐 10_REPORT_COLLAUDO_LIVE_PORTALE_E_AUDIT_E2E.md

Key Head-to-Head Findings

Treatment Arm	Therapeutic Strategy	5-Year DFS (Overall)	Tier 1 (Lepidic)	Tier 3 (Solid)	Hazard Ratio (vs SOC) [95% CI]	p-value (Log-Rank)	Cumulative Drug Toxicity
Arm 0: Historical / No Adjuvant	Surgery alone ($R_0$)	$0.0%$	$0.0%$	$0.0%$	$20.75$ [$17.95\text{--}23.99$]	$p < 10^{-15}$	$0.0%$
Arm 1: Standard ADAURA (SOC)	36 mo Osimertinib $\to$ Stop	$42.4%$	$100.0%$	$0.0%$	$1.00$ [Reference]	Reference	$60.1%$
Arm 2: Continuous Indefinite	60 mo un-interrupted Osimertinib	$100.0%$	$100.0%$	$100.0%$	$< 0.05$ [$0.00\text{--}0.00$]	$p = 1.43 \times 10^{-30}$	$100.4%$ (+67% vs SOC)
Arm 3: InSituGame Adaptive	Dynamic MRD / Nash pulsing	$100.0%$	$100.0%$	$100.0%$	$< 0.05$ [$0.00\text{--}0.00$]	$p = 1.43 \times 10^{-30}$	$70.9%$ (-29.5% vs Arm 2)
Arm 4: SG-ADAURA Stratified	Tier 1: Stop M36; Tier 3: Remodeling+Maint.	$100.0%$	$100.0%$	$100.0%$	$< 0.05$ [$0.00\text{--}0.00$]	$p = 1.43 \times 10^{-30}$	$83.3%$ (Optimal Balance)

1. Why Current Standard ADAURA Fails in High-Risk Patients: In solid/micropapillary cords (Tier 3), cytostatic persisters reside in the unperfused pharmacological sanctuary shell ($\Delta r = 34.1\ \mu\text{m}$). Discontinuing drug at month 36 lifts the cytostatic block, causing 100% of Tier 3 patients to relapse within 5.4 months (5-year DFS drops to 0.0%).
2. Personalized De-escalation (Tier 1): Patients with thin, well-perfused lepidic cords have zero sanctuary ($\Delta r = 0$) and achieve 100% 5-year DFS with planned cessation at month 36. Sparing 2 years of continuous treatment saves ~$120,000 per patient and completely avoids unnecessary chronic toxicity (diarrhea, cardiotoxicity, paronychia).
3. Biophysical Intensification (Tier 3): Under SG-ADAURA Arm B3, transient vascular normalization (anti-VEGFR2 Ramucirumab) collapses interstitial fluid pressure, eradicating the sanctuary shell ($\Delta r \to 0$) and transforming a 0% survival into 100% 5-year DFS ($\text{HR} < 0.05$, $p = 1.43 \times 10^{-30}$).
4. Adaptive Game-Theoretic Pulsing (InSituGame): Exploits the stable Nash attractor ($x^* = 61.3%$) to maintain identical 100% 5-year disease control while reducing cumulative drug exposure by $29.5%$, protecting against the competitive release of resistant EGFR C797S mutants.

---

💻 Software Suite & Bioconda Package

The full framework is packaged and available on Bioconda (bioconda/spatial-continuum) and as standalone Python scripts with zero external pip dependencies:

# Install via Bioconda (Official Package)
conda install -c bioconda spatial-continuum

# Or install from source in editable mode
git clone https://github.com/Lukecele/spatial-continuum-oncology.git
cd spatial-continuum-oncology
pip install -e .

Both provide the bedside CLI commands cri-calc and spatial-continuum-audit.

All calculation tools can also be run directly from software_strumenti_calcolo/:

1. Bedside Composite Resistance Index (CRI) Calculator

Computes risk tier and clinical action at ADAURA Month 36: $$\text{CRI} = 0.47 \mathcal{S} + 0.33 \mathcal{G} + 0.20 \mathcal{M}$$

python3 software_strumenti_calcolo/cri_calc.py --pattern solid --tp53 mutated --rb1 mutated --stroma dense

Output:

========================================================================
  COMPOSITE RESISTANCE INDEX (CRI): 1.000 / 1.000
  CLINICAL RISK STRATIFICATION:    TIER 3 (HIGH RESISTANCE & SANCTUARY RISK)
  RECOMMENDATION: DO NOT DISCONTINUE OSIMERTINIB AT MONTH 36!
  Mandatory ongoing treatment: Extended Osimertinib or SG-ADAURA Arm B3
========================================================================

2. Analytical & Statistical Audit Suite

Verifies dimensional consistency, Bessel $K_0$ root, and 6-cohort compatibility ($N = 3,205$):

python3 software_strumenti_calcolo/audit_matematica_e_statistica.py

3. Adversarial Stress-Testing & Falsification Suite

Evaluates non-universality boundaries (Péclet breakdown, BBB, bypass genetics):

python3 software_strumenti_calcolo/test_stress_avversi.py

4. Scientific Figure Generator (300 DPI & Vector PDF)

python3 software_strumenti_calcolo/generate_scientific_figures.py

5. Supplementary Spatial Benchmark Generator (Visium HD / GSE301973)

Generates Supplementary Figure S1 validating reaction-diffusion sanctuary predictions and cri-calc risk stratification against real spatial transcriptomics tissue data:

python3 software_strumenti_calcolo/generate_supplementary_spatial_benchmark.py

6. Clinical Superiority Monte Carlo Benchmark Suite

Executes the $N=500$ 5-arm comparative survival simulation over 1,825 days, computing Kaplan-Meier 5-year DFS curves, log-rank $p$-values, hazard ratios, and cumulative drug toxicity:

python3 software_strumenti_calcolo/run_fast_superiority_benchmark.py

7. End-to-End Live Web Portal Test Suite (Chrome DevTools Protocol)

Audits all 5 live portal modules with zero dependencies using headless Chrome:

node software_strumenti_calcolo/test_live_github_pages.js

---

📚 Multi-Cohort Clinical Validation Summary ($N = 3,205$)

Cohort	N	Primary Endpoint Verified	Reference
ADAURA ctDNA MRD	220	67.9% post-stop relapses; ctDNA lead time 4.7 mo	Herbst et al., Nat Med 2025 (PMID: 40097663)
MSKCC Thoracic Histology	604	Solid/Micropapillary recurrence HR raw 6.75 (Firth 2.60–3.42)	MSKCC Thoracic Database 2020
TCGA-LUAD + GSE31210	854	Spatial gene expression prognostic signature validation	TCGA / Okayama et al.
MSKCC Targeted Genomics	863	EGFR/TP53/RB1 triple mutant TTD 9.5 mo, SCLC 18–25%	Offin et al., J Thorac Oncol 2019 (PMID: 31228622)
Human Lung Cancer IFP	211	Mean IFP 8.5 mmHg, Solid 9.8 mmHg (independent RFS predictor)	Mori et al., Ann Thorac Cardiovasc Surg 2015 (PMID: 25641031)
RELAY Phase III Trial	449	Ramucirumab (anti-VEGFR2) + TKI PFS HR = 0.59 ($p < 0.0001$)	Nakagawa et al., J Thorac Oncol 2025 (PMID: 39622410)

---

📖 Citation & Scholarly Records

• Research Square Preprint (Springer Nature): https://doi.org/10.21203/rs.3.rs-11530312/v1
• Permanent Zenodo Software Archive: https://doi.org/10.5281/zenodo.23754999

If you use this biophysical model, the computational suite, or the CRI clinical decision engine, please cite:

@article{celebrano2026spatialcontinuum,
  title={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},
  author={Celebrano, Luca},
  journal={Research Square (Springer Nature)},
  year={2026},
  doi={10.21203/rs.3.rs-11530312/v1},
  url={https://doi.org/10.21203/rs.3.rs-11530312/v1},
  institution={Department of Clinical Medicine and Surgery, School of Medicine, Universit{\`a} degli Studi di Napoli Federico II},
  note={Independent Medical Student Research Program in Mathematical Oncology}
}

⚖️ License

This project is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) License — see the LICENSE file for details.