Influence of different frequencies of axial cyclic loading on time-domain vibration response of the lumbar spine: A finite element study

Very few studies have quantitatively analyzed influence of the loading frequency on time-domain vibration response of the whole lumbar spine in the presence of a physiologic compressive preload. In this study, a three-dimensional non-linear finite element model of ligamentous L1-S1 segment was developed to predict time domain dynamic response of the whole lumbar spine to axial cyclic loading with different frequencies. A compressive follower preload of 400 N was applied to the model to simulate the physiologic compressive load. Modal analysis was initially performed to extract axial resonant frequency of the model under a 40 kg upper body mass and the 400 N preload. The result showed that the axial resonant frequency was 7.77 Hz. Subsequently, transient dynamic analyses were performed on the model under a sinusoidal axial load of +/- 40 N at frequencies of 3, 5, 7, 9, 11, 13 and 15 Hz with the 400 N preload and 40 kg mass. The computational results (strains and stresses in the spinal components) were collected and plotted as a function of time. These predicted results were found to be frequency-dependent and consistent with the notion in engineering dynamics texts that the closer the loading frequency approaches the resonant frequency, the larger the response is. For example, the results for 5 Hz load compared to 3 Hz load showed a 68.6-111.5% increase in peak-to-bottom variations of the predicted response parameters, and the results for 13 Hz load compared to 11 Hz load showed a 26.4-37.8% decrease in these variations.