Concept of mathematical modeling of lumbar and thoracic spine based on elastic beam theory

Abstract

Modeling of the human spine is important for establishing quantitative assessment methods of low back pain (LBP) caused by manual material handling (MMH). This study developed mathematical models of the lumbar and thoracic spine based on the elastic beam theory. Two types of models, uniform and non-uniform, were derived. First, to simplify the Bernoulli-Euler beam theory, three assumptions were introduced for the uniform beam model: (i) the vertebrae and intervertebral disc were considered as a composite material, (ii) constant crosssectional area, and (iii) conversion of muscular strength to bending moment. However, on fitting to the actual spine position data from the literature, the uniform beam model was found to be unable to reproduce the spine shape, particularly in the lumbar region. Therefore, the non-uniform beam model was derived by removing assumption (ii), which does not agree with the actual human spine profile. Consequently, the spine was modeled as a trapezoid from around S1 to C7 in the sagittal plane, by adjusting the proportionality factor of trapezoid via tapering or widening, and the non-uniform beam model was found to better reproduce the spine shape, including the lumbar region. The model has practicability, such as estimation of spine shape; however, the proportionality factor that was used to reproduce the spine shape did not agree with the actual human spine profile; further theoretical development has been left as future work.

Posture and Mechanical Load Assessment During Patient Transfers

“…We used a segmented model to approximate the spine from L5 to C7 and to calculated the upper body postures. More complex segmented models and musculoskeletal models have been presented in literature [44,45] as well as modeling the spine as an elastic beam [46] to derive lumbar compressive forces. Further work is needed to link the body postures to the loads.…”