Development of a static optimization method for musculoskeletal modelling of kinematic-coupled lumbar spine and its application to alpine skiing

The accurate quantification of trunk muscle biomechanics during alpine skiing remains challenging, primarily owing to the inconsistent validation of core muscle activation patterns in existing musculoskeletal models under three-dimensional dynamic conditions. Therefore, we developed a static optimization with summed equilibrium equation (SO-SEE) algorithm for a kinematic-coupled lumbar spine musculoskeletal model and applied it to alpine skiing. The algorithm consolidated individual intervertebral joint equilibrium equations into three kinematic-coupled constraints, thereby resolving the kinematic redundancy induced by the lumbopelvic rhythm. The model comprised a rigid pelvis and sacrum, five lumbar vertebrae and a rigid torso. Eight major muscle groups around the spine, covering the rectus abdominis, external obliques, internal obliques and erector spinae of both sides, were modelled using a Hill-type muscle model. Validation of SO-SEE using kinematic and surface electromyography data during three-dimensional spinal motions revealed that it more accurately predicted muscle activation (R = 0.73; RMSE = 0.087) than did traditional static optimization (R = 0.32; RMSE = 0.117). We further applied the SO-SEE algorithm to evaluate trunk muscle function in one elite and one amateur skier. The simulated data successfully quantified biomechanical differences in core muscle activation patterns during ski turning, providing valuable insights for performance optimization.