Computational modeling of spine and trunk muscles subjected to follower force

Recently, the follower force concept was introduced in the field of biomechanics to elucidate how the stability of the human spine could be maintained under substantial compressive loads. However, it has been controversial if the follower load concept is feasible to maintain the spinal stability by coordinating the appropriate trunk muscles. The purpose of this paper is to propose a computational model of the human spine and trunk muscles based on finite element method combining with an optimization formulation subjected to the follower force constraint in order to confirm that the follower force is related to the spinal stability and can be generated by the activation of trunk muscles. Spinal motion segments were modeled as linear elastic beam elements and trunk muscles were assumed to be static. In the optimization formulation, the muscle forces, the follower forces and shear forces, and the deformed shape of the spine model were investigated minimizing the sum of the magnitudes of follower forces under the constraints for the equilibrium equations, the directions of resultant forces, and the physiological bounds of muscle forces. Through a numerical example, it was confirmed that there was a combination of muscle activations transmitting external forces and moments along the follower force direction and the spinal stability was maintained with little change of spinal shape.