A porohyperelastic scheme targeted at High-Performance Computing frameworks for the simulation of the intervertebral disc.

Background and objective: The finite element method is widely used for studying the intervertebral disc at the organ level due to its ability to model complex geometries. An indispensable requirement for proper modelling of the intervertebral disc is a reliable porohyperelastic framework that captures the elaborate underlying mechanics. The increased complexity of such models requires significant computational power that is available within high-performance computing systems. The objective of this study is to present such a framework, validated both against literature and experiments, aiming to enable intervertebral disc research to benefit from state-of-the-art computational resources.

Methods: In the context of this work, we implement a biphasic model that captures the mechanical response of the intricate, tissue-dependent models of the solid phase along with the hydrostatic pressure effects of the fluid phase. The tissue-dependent models involve the hyperelastic ground substance, fibrillar reinforcement, and osmotic swelling. The derived porohyperelastic, staggered scheme is implemented in Alya, a finite element code targeted at high-performance computing applications. The formulation is subsequently verified and validated by comparing the results of consolidation simulations with literature data for simulations and experiments using either generic or patient-specific geometries. Additionally, in-house experiments are replicated, evaluating the model's ability to simulate alternating loading. Finally, the implementation's circadian response is compared to previous implementation of similar material models in commercial software.

Results: Results align well with experimental and literature findings in terms of disc height reduction (4% error), intradiscal pressure (14% error) and disc bulging. Validating the patient-specific geometry results in 4% and 7% deviation in measuring height loss. Simulations show excellent agreement with in-house experimental results, with less than 1% error regarding height reduction. Finally, the comparison to similar, published, earlier implementation in commercial software unveils excellent agreement of less than 1% error for the water content during circadian simulations. Simulation times are reported at 4 min per circadian cycle in the supercomputer Marenostrum V.

Conclusions: This work presents a clear and validated formulation for simulating porohyperelastic materials based on assumptions that comply with the non-linear elasticity theory. The implementation in Alya enables intervertebral disc research to benefit from high-performance computing systems.