Optimization of rib surgery parameters for the correction of scoliotic deformities using approximation models

Background. As opposed to thoracoplasty (a cosmetic surgical intervention used to reduce the rib hump associated with scoliosis), experimental scoliosis has been produced or reversed on animals by rib shortening or lengthening. In a prior work (J. Orthop. Res., 20, pp. 1121-1128), a finite element modeling (FEM) of rib surgeries was developed to study the biomechanics of their correction mechanisms. Our aims in the present study were to investigate the influence of the rib surgery parameters and to identify optimal configurations. Hence, a specific objective of this study was to develop a method to find surgical parameters maximizing the correction by addressing the issue of high computational cost associated with FEM. Method of Approach. Different configurations of rib shortening or lengthening were simulated using a FEM of the complete torso adapted to the geometry of six patients. Each configuration was assessed using objective functions that represent different correction objectives. Their value was evaluated using the rib surgery simulation for sample locations in the design space specified by an experimental design. Dual kriging (interpolation technique) was used to fit the data from the computer experiment. The resulting approximation model was used to locate parameters minimizing the objective function. Results. The overall coverage of the design space and the use of an approximation model ensured that the optimization algorithm had not found a local minimum but a global optimal correction. The interventions generally produced slight immediate modifications with final geometry presenting between 95-120 % of the initial deformation in about 50 % of the tested cases. But in optimal cases, important loads (500-2000 N mm) were generated on vertebral endplates in the apical region, which could potentially produce the long-term correction of vertebral wedging by modulating growth. Optimal parameters varied among patients and for different correction objectives. Conclusions. Approximation models make it possible to study and find optimal rib surgery parameters while reducing computational cost.