On Application of Optimization to the Validation of a Follower Load in Spine Biomechanics

1. Abstract A 2-dimensional lumbar spine is modeled with 64 back muscles and the static behavior of the model is predicted using an optimization technique. The goal of this study was to investigate if a follower load can be produced by the back muscles for enhancing the mechanical stability of the lumbar spine in a quiet standing posture. Recent studies demonstrated that the stability of the lumbar spine can be greatly increased with the maintenance of reasonable flexibility when the resultant force of the spinal muscle forces, body weight and external loads is directed along the spinal axis (tangent to the spinal curve). This follower load is suggested as a normal physiological load in the spine based on these findings. However, the roles of back muscles in producing the follower load in the lumbar spine have not been well understood yet. Two-dimensional optimization problem was formulated to investigate the muscle forces required for producing the follower load in the lumbar spine in quiet standing posture. Upper trunk (350N), 5 lumbar vertebrae, sacrum and pelvis connected by 64 muscle fascicles (22 long and 42 short) were simulated. Summation of joint follower forces and joint moments were minimized to determine the muscle forces. A parametric study was also performed to obtain the optimum follower load path. The effect of increasing external force or the external moment on the follower load was also investigated with the follower load path fixed at the optimum location. Minimum follower forces were predicted when the follower load path was followed the points 7 mm posterior to geometrical centers of each vertebra. Results of this study showed that the back muscles, particularly short segmental muscles, are able to control the stability of the spine in a static posture by producing the follower load with no joint reaction moments. The fact that no joint reaction moment in the lumbar spine is found under the follower load suggests that the major biomechanical role of short segmental back muscles is to create the follower load for achieving the maximum stability, which may be critically related to the segmental instability.