Multiscale dynamics analysis of lumbar vertebral cortical bone based on the Abaqus submodel finite element method

The direct effect of macroscopic loads on the microstructure of bone tissue in a vibration environment is not yet known. Therefore, this study aims to investigate the macro- and micro-biomechanical properties of the lumbar spine system under dynamic loading in such an environment. We analyzed the dynamic characteristics of osteon by establishing a macro- and micro-scale model of the lumbar spine, using a submodel-specific boundary displacement method based on St. Venant's principle. Utilizing the results from the transient dynamic analysis of the entire lumbar spine as boundary conditions, this study simulates the dynamic behavior of osteon in each segment of the spine on a microscopic scale. The macroscopic results of the transient dynamic analysis showed that the rates of change in dynamic displacement amplitude relative to static displacement amplitude for the L1-L5 vertebrae were 212.60%, 242.11%, 314.80%, 1.17%, and 3.75%, respectively. The change in displacement amplitude under dynamic load relative to static load was highest for the L3 vertebra, as observed in the macroscopic model. The stress and strain values in the microscopic osteon of each lumbar spine segment under sinusoidal periodic loading were higher than those in the macroscopic osteon. In the microscopic bone unit, the maximum stress occurred at the cement line during the peak stress moment, while the minimum stress was observed at the innermost bone plate during the moment of minimum stress. Under dynamic loading, the microscopic bone osteon demonstrated a cyclic stress and strain response, with variations observed in different components of the osteon. These findings provide new insights into the biomechanical behavior of the lumbar spine in a vibration environment.