Abstract
Spine structure is mainly constructed of many vertebrae and flexible intervertebral disks, and it is unstable by itself under standing condition. Supporting by erector muscles and ligaments keep the spine standing condition, so that boundary condition of each vertebra depend on the muscle and ligament forces. Moment applied to vertebra by intervertebral disk deformation also has to be considered for the boundary condition of vertebra Biomechanical simulation of musculoskeletal model taking account of muscle and ligament forces and intervertebral joint moments is necessary to determine the boundary condition of vertebral analysis. In this study, a musculoskeletal model around lumber vertebrae was developed, and loading condition of each vertebra was analyzed considering muscle and ligament forces and joint moments. Number of unknown variables, which were muscle and ligament forces and intervertebral joint moments, was greater than number of the equilibrium equations. That is, the problem to solve the force and moment was higher order indeterminate problem. In order to solve the problem, an optimization problem has to be formulated. We considered an objective function corresponds to work done by muscle force and intervertebral joint moment This is a typical quadratic programming problem, so the optimization problem was solved by quadratic programming method. Muscle forces and intervertebral joint moments were evaluated varying flexion or extension angle, and efficiency of the musculoskeletal model and proposed method to obtain the muscle forces and intervertebral joint moments was discussed.
