Simulation de mouvements du rachis avec ajustement continu suivant des courbes expérimentales de comportement force-déplacement

In adolescent idiopathic scoliosis, surgical treatment strategy is determined from flexibility tests (e.g. lateral bending, traction, suspension...). These tests evaluate the reduction in spine curvature and are also used to identify the levels to be instrumented. However, conventional tests do not assess the real spine flexibility since they do not consider forces needed to modify the spine's curvature.

Personalization methods used in current biomechanical models generally determine flexibility in a manner that is dependent on the modelling technique used. Thus, the flexibility calculated from this personalization process is normally not the same. Since the simulation results are influenced by the calculated flexibility, an attempt to compare the results obtained from different models will be misleading.

The goal of this project was to create an interactive side-bending test simulator of scoliotic spine where the personalization process is not influenced by the modelling technique used. This simulator used force-displacement behavioural curves deduced from experiments. It was hypothesized that the maximum side-bending test simulation of a scoliosis patient can predict the movement of the spine when the model includes direct spinal behaviour from experimental curves. The secondary objective was to evaluate the system accuracy by performing maximum side-bending simulations on a set of scoliosis patients.

To achieve these objectives, a personalized 3D spine reconstruction (T1-L5) of the patient was created from biplanar x-ray images. Then, the spine midline and Cobb angles in the upright posture and at maximum right and left side-bending were measured directly on radiographs. This information was used to measure the system accuracy during side-bending test simulations.

The simulator used these personalized 3D spine reconstructions by specifying a spherical joint constraint between each vertebra. Using the experimental force-displacement curves, three torques were applied to each vertebra in a functional unit. These torques were determined throughout the simulation by the angle between the vertebral bodies. The spine shape in maximum side-bending taken from the radiographs was reproduced by gradually applying a torque on T1 vertebra and by fixing all degrees of freedom of L5. The resulting torque was the one that gives the lowest error between the simulated spine displacement and the real values obtained from lateral bending test.

This project also experimented an interactive rigid body simulation system in which each joint was treated locally thus reducing the solving complexity of the constraint system. This approach was based on the assumption that the joint effect is localized for small time steps and thus its effect can be calculated without considering other joints within the system.

The simulations were able to reproduce more than 94% of the spinal displacement produced during the side-bending test for the 10 scoliosis patients. The average error on the position of the vertebrae was 5mm ± 3mm and the variation of the Cobb angle was 50 ± 3°. These values were obtained for 95% of cases. It was also possible to assess the torques needed to reproduce the side-bending test, ranging from 2.8Nm to 17.5Nm. In addition, all simulations were carried out in real time. These results confirm the hypothesis and demonstrate the feasibility of simulating maximum side-bending test in an interactive way with a simplified spine model.

The simulation method used in this project is a first step in developing real-time systems that are more adapted to the clinical environment. And because of its execution time, it offers more opportunities to be used.