Novel finite element fully coupled multi-species mechano-transport simulations approach of the Intervertebral Disc

Intervertebral disc (IVD) degeneration (IDD) is closely linked to impaired nutrient transport within the avascular disc, critically affecting cell viability and tissue health. Finite element (FE) modeling of mechano-metabolic-transport phenomena is widely used to explore disc nutrition, degeneration, and metabolic stress. However, traditional sequential coupling approaches remain limited by reduced accuracy, long runtimes, and implementation complexity. This study aimed to develop and validate an efficient and accurate multi-species transport simulation method integrated within mechanical analyses, thereby overcoming existing limitations for large-scale patient-personalized (PP) cohort simulations.

We developed a multi-species diffusion-reaction User ELement (UEL) subroutine in Abaqus that simultaneously simulates oxygen, glucose, and lactate transport coupled with mechanical deformation within a single stiffness matrix. This UEL was integrated with mechanical models through submodeling, allowing for independent time stepping and consistent mechanical baselines. Accuracy and efficiency were validated against sequential Abaqus User THermal MATerial (UMATHT) simulations using a symmetric diffusion chamber with four cell density groups (2, 4, 8, and 16 million ×10^-3 cells/mm³) and a PP FE IVD model. Parameters influencing cell viability - glucose decay rate, glucose threshold, and pH-induced cell decay - were optimized for each group.

UEL and UMATHT methods yielded nearly identical solute concentration predictions, with normalized root mean square error (NRMSE) of 0.2% and maximum relative error of 1%. Our UEL reduced computational time by over 60% (from >30 to ∼11 h). Cell viability model optimization improved the accuracy for the four cell density groups by 20.8%, 16.4%, 5.4%, and 25.0%, respectively. UEL also provided smoother and more accurate solute concentration fields by utilizing all the 20 nodes of second-order elements, surpassing UMATHT's first-order corner-node limitation.

The proposed UEL significantly improves computational efficiency and accuracy in multi-species nutrient transport simulations. Its integration with mechanical analyses and submodeling technique enables large-scale, standardized, patient-specific studies. By openly sharing our validated Mechano-Transport subroutines (GitHub: https://github.com/bmmbUPF/abaqusIVD) and compatible FE meshes (SpineView Repository: https://ivd.spineview.upf.edu/), we support reproducibility, facilitating automated simulations using clinical magnetic resonance imaging, and promoting standardized methodologies across diverse research initiatives. Ultimately, these contributions advance patient stratification and personalized spine care.