DOI: 10.5281/zenodo.17459889
title: A Rigorous Multidisciplinary Theoretical Framework for Intervertebral Disc Herniation: Sequential Biomechanical Restoration via Anisotropic Osmo-Porohyperelastic Modeling and Global Sensitivity Analysis

description: Intervertebral disc herniation (IDH) represents a prevalent biomechanical pathology characterized by annulus fibrosus rupture and nucleus pulposus extrusion, contributing to chronic low back pain, radiculopathy, and substantial socioeconomic burden, with annual incidence rates of 5–20 per 1,000 adults and post-surgical recurrence of 15–25%. Conventional treatments, including pharmacotherapy and discectomy, inadequately restore disc homeostasis, prompting the need for regenerative, minimally invasive paradigms.This manuscript delineates a deductive, mathematically rigorous theoretical framework for IDH management, synthesizing cross-disciplinary principles from cosmetic regenerative medicine, restorative dentistry, interventional cardiology, and ophthalmic biomaterials into a sequential therapeutic pathway stratified by degeneration severity (Pfirrmann grades I–V). The pathway prioritizes osmotic restoration (Phase 1: platelet-rich plasma biostimulation to elevate fixed charge density \(c_f\) and osmotic pressure \(\pi_{\text{osm}}\)), annular sealing (Phase 2: genipin-fibrin hydrogels to reduce fissure permeability \(k\)), microstructural reinforcement (Phase 3: poly(L-lactic acid) scaffolds to enhance fiber-reinforced stiffness via Holzapfel–Gasser–Ogden parameters \(k_1, k_2\)), and nucleus substitution (Phase 4: shear-thinning hydrogels matching native viscoelastic properties \(E \approx 0.1\) MPa, \(\eta \approx 1.2\) GPa·s).The framework is anchored in a fully derived anisotropic osmo-porohyperelastic biphasic model, extending Biot's consolidation theory with Donnan osmotic swelling, nonlinear fiber-reinforced hyperelasticity (\(\Psi = \Psi_{\text{matrix}} + \Psi_{\text{fiber}}\)), and generalized Maxwell viscoelasticity. Governing equations include effective stress (\(\boldsymbol{\sigma} = \boldsymbol{\sigma}^s - p \mathbf{I} + \pi_{\text{osm}} \mathbf{I}\)), mass balance (\(\partial \zeta / \partial t + \nabla \cdot \mathbf{q} = 0\), with \(\zeta = \alpha \epsilon_v + \phi^f(p)\)), and Darcy's flux (\(\mathbf{q} = -k \nabla p\)), calibrated against empirical parameters (e.g., NP aggregate modulus \(H_A = 0.1\) MPa, permeability \(k = 5 \times 10^{-16}\) m²/s).A reproducible transient Kelvin-Voigt simulation under 1 kPa compressive loading, implemented in Python/SciPy, elucidates creep response (\(u(\infty) = \sigma_0 / E\)), coupled with variance-based global sensitivity analysis (Sobol indices via Saltelli approximation, n=5000 Monte Carlo samples). Results yield \(S_1^E = 0.722\) (dominance of elastic modulus in long-term deformation) and \(S_1^\eta \approx 0\) (negligible viscous influence at extended timescales), underscoring parameter prioritization for translational validation.Discussion addresses model validity against high-impact literature, translational gaps (e.g., 4D-MRI/cadaveric benchmarking), limitations (e.g., omission of biochemical degradation and cyclic fatigue), and ethical imperatives (e.g., biocompatibility of repurposed PLLA). This self-contained blueprint heralds a paradigm shift toward regenerative IDH therapeutics, projecting reherniation rates <5% at 5 years, with avenues for preclinical corroboration.