Effect of Mechanical Loading on the Calcification of Intervertebral Discs：Quantitative Analysis

Mechanical loading was associated with IVD calcifications, however how mechanical loading affects calcium (Ca ²⁺ ) and phosphate (Pi) concentration were unknown yet. This study aims to investigate the effects of mechanical loading on the change of calcium and phosphate concentrations in the human intervertebral disc (IVD) with a modeling approach. A finite element model was adopted and extended based on the triphasic continuum mixture theory. The disc was modeled as an inhomogeneous, porous, mixture consisting of a negatively charged solid phase, a fluid phase, and the solute phase (e.g., Na ⁺ , Cl ⁻ , Ca ²⁺ , Pi). The material properties of fixed charge density, hydraulic permeability, and solute diffusivities were nonlinearly coupled with tissue deformation. The interactions among tissue deformation, electrical charge, fluid, and solute transport were considered. We found that average calcium concentration increased 30% in cartilaginous endplate, 18% in nucleus pulposus, 25% in annulus fibrosus, while the phosphate concentration decreased 17% in cartilaginous endplate, 20% in nucleus pulposus, and 11% in annulus fibrosus, when the load on the disc increased from 0.5 MPa to 1.0 MPa. The difference in the trend between [Ca ²⁺ ] and [Pi] is mainly caused by the Donnan effects due to the existence of the fixed charge density in the IVDs. Higher mechanical loading increases the fixed charge density (due to deformation) and thus leads to even larger Donnan effects. Our results indicate that large mechanical loading may increase the risk potential of IVD calcification. This study is important for understanding the mechanisms of mechanical loading related IVD calcification.