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TECHNICAL PAPERS: Joint/Whole Body

# Optimization of Rib Surgery Parameters For the Correction of Scoliotic Deformities Using Approximation Models

[+] Author and Article Information
J. Carrier

Biomedical Engineering Institute, Ecole Polytechnique de Montreal, P.O. Box 6079, Station Centre-ville, Montreal (Quebec), H3C 3A7 CanadaBiomechanical Modeling & Computer Assisted Surgery Laboratory, Research Center,  Ste-Justine Hospital 3175, Côte Sainte-Catherine Rd, Montreal (Quebec), H3T 1C5 Canada

C.-E. Aubin1

Department of Mechanical Engineering,  Ecole Polytechnique de Montreal, P.O. Box 6079, Station Centre-ville, Montreal (Quebec), H3C 3A7 CanadaBiomechanical Modeling & Computer Assisted Surgery Laboratory, Research Center,  Ste-Justine Hospital 3175, Côte Sainte-Catherine Rd, Montreal (Quebec), H3T 1C5 Canada

F. Trochu

Department of Mechanical Engineering,  Ecole Polytechnique de Montreal, P.O. Box 6079, Station Centre-ville, Montreal (Quebec), H3C 3A7 Canada

H. Labelle

Research Center,  Ste-Justine Hospital 3175, Cote Sainte-Catherine, Montreal (Quebec), H3T 1C5 Canada

1

Address for notification: Carl-Éric Aubin, Ph.D., Canada Research Chair “CAD Innovations in Orthopedic Engineering,” Department of Mechanical Engineering, Ecole Polytechnique de Montreal, P.O. Box 6079, Station Centre-ville, Montreal (Quebec), H3C 3A7 Canada. Telephone: (514) 340-4711; ext. 4437; fax: (514) 340-5867; e-mail: carl-eric.aubin@polymtl.ca

J Biomech Eng 127(4), 680-691 (Mar 17, 2005) (12 pages) doi:10.1115/1.1933879 History: Received June 05, 2003; Revised March 17, 2005

## Abstract

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 $(500–2000Nmm)$ 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.

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## Figures

Figure 2

Schematic representation of the geometric configuration of the six patients: In the frontal and lateral planes, and in the transverse plane for the apical level (dark grey)

Figure 3

Desired moments on the vertebral endplates. The sign convention was chosen so that desired moments minimized the objective function (for a positive wedging difference the desired moments were negative).

Figure 4

For the case used in the first accuracy study, approximation models built with N=30 samples whose locations were specified by a uniform design (+) and with Nerror=500 samples used to validate, for the three objective functions: (a) φG1(x), (b) φG2(x), and (c) φM(x). The x and y axis represent the surgery parameters and the grey value corresponds to the objective function value as presented in the scales at the bottom.

Figure 5

For patients 1 to 6, clinical indices computed for the initial geometry and for the geometries obtained from simulations with optimal parameters found for the three objective functions: φG1(x), φG2(x), and φM(x)

Figure 6

For patients 1 to 6, vertebral wedging and moments transmitted to vertebrae in the frontal plane (average between superior and inferior endplates) for the simulations with optimal parameters found for the three objective functions: φG1(x), φG2(x), and φM(x)

Figure 1

Finite element model of the trunk: (a) posteroanterior view (spinal axis system); (b) details of a typical functional unit with an adjacent pair of ribs, lateral view (vertebra axis system)

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