Modélisation de la colonne vertébrale par la méthode des éléments finis basée sur la cinématique incluant le critère de la stabilité

The objective of this work is to develop an optimization algorithm for estimating the abdominal muscle forces (while acting antagonistically) that maximizes the trunk stability and minimizes the risk of back pain, either separately or both together. This algorithm is based on the kinematics-driven finite element method, Lagrangian optimization and regression method.

A non-linear sagittaly-symmetric finite element model based on the kinematics-driven algorithm and Lagrangian optimization was used to resolve the redundancy of equilibrium equations of the spine in upright standing posture during lifting tasks. This model consists of six deformable beams representing the intervertebral discs at T12-S1 and rigid elements that represent the T1-S1 vertebrae. The muscular architecture includes 46 local muscle fascicles joining the lumbar vertebrae to the pelvis with the exception of the iliopsoas muscle which originates from the femur, and 10 global muscle fascicles that connect the ribs to pelvis. The mechanical properties and anatomy of the spine are taken from the literature. Small intersegmental rotations associated with the standing upright posture calculated by optimization have been incorporated in this finite element model.

To calculate the compressive and shear forces, global and local muscle forces have been estimated by Lagrangian optimization and, subsequently, were applied as external loads acting on the intervertebral discs. After reaching equilibrium, stability analysis is performed to calculate the critical buckling force P_cr.

In the current study, we proposed two methods B and D based on Lagrangian optimization method to calculate the muscle forces and subsequently the compressive force F_C at the center of the L5-S1 disk and critical buckling forces P_cr.

The empirical expression of the critical buckling force P _cr and the compressive force F_C were obtained by regression as functions of input variables. The analysis of regression coefficients showed that the P_cr and F_C forces adequately represented the results of the finite element method and that their terms were significant in the response of the spine.

Empirical expressions obtained from the approach B and the regression method were optimized predicting the optimal abdominal muscle forces that minimize the objective function F_obj = α*F_C – β*P_cr. If we set α = 1 and β = 0, minimization of the objective function F_obj can predict the minimum compressive force and in this case, IO muscle is the most efficient muscle. However, if we set α = 0 and β = 1, minimizing F_obj then maximizes the critical buckling force P_cr. For large abdominal muscle coactivities, EO muscle is the most efficient muscle by maximizing the trunk stability.

Method D directly calculates the abdominal muscle forces by fixing sum of the abdominal muscles moments a priori in the Lagrangian optimization procedure that simultaneously minimizes sum of extensor muscle stresses cubed and maximizes sum of abdominal muscle stresses cubed. The predicted abdominal muscles forces depend neither on M nor on muscle rigidity coefficient q. The IO muscle is the most effective muscle in maximizing the stability of trunk P _cr and minimizing the compression force F^C. (Abstract shortened by UMI.)