Influence of disc height and strain-dependent solute diffusivity on metabolic transport in patient-personalized...

Intervertebral disc (IVD) degeneration is a primary contributor to low back pain, with nutritional stress due to the IVD's avascularity recognized as a key factor. Solute transport within the disc relies predominantly on diffusion, which is governed by tissue morphology and mechanical deformation. However, the interplay between disc geometry, poro-mechanical strain, diffusion, and degeneration remains incompletely characterized. Previous specimen-specific models have captured inter-subject variability in metabolite transport, but the isolated effects of disc height and degeneration-dependent material composition have not been systematically assessed. Moreover, although strain-dependent diffusion coefficients are commonly modeled as porosity functions, the role of intra-element diffusivity gradients $\left(\nabla D\right)$ , arising under large deformation, has been largely overlooked.

The present study focuses on poro-mechanical finite element (FE) models of three patient-personalized L4-L5 lumbar IVD geometries, representing varying heights categorized as thin, medium, and tall IVDs. Three days of physiological mechanical load cycles, comprising 8 hours of rest and 16 hours of activity, were simulated, under both 'healthy' (Pfirrmann grade 1) and degenerated (Pfirrmann grade 3) tissue conditions.

Simulation outcomes demonstrated that a one-third reduction in disc height (relative to medium height) led to $>30\%$ increases in oxygen and glucose concentrations and $\ge 20\%$ decreases in lactate levels, particularly in the nucleus and anterior regions. Conversely, a one-third height increase resulted in $>30\%$ reductions in oxygen and glucose and a corresponding rise in lactate levels. These deviations were more pronounced in degenerated tissues, highlighting the synergistic role of morphology and matrix integrity in determining metabolic homeostasis. Importantly, the inclusion of $\nabla D$ in the diffusion-reaction model produced negligible changes in solute concentration profiles.

These findings underscore the predominant influence of disc geometry and matrix composition on IVD metabolic homeostasis, suggesting limited relevance of the $\left(\nabla D\right)$ term in practical simulations. Simplified diffusion models, without $\left(\nabla D\right)$ , may be sufficient for future IVD mechano-transport FE modeling.