Design methodology and numerical optimization of ultrasonic transducers for spinal surgery

Nowadays, the general trend towards to minimally invasive interventions is present in all the medical domains. For the surgical intervertebral spinal disc cutting or removal domain, it is particularly a necessity because the manual methods currently employed are tedious, time consuming and taxing on the hands of the practitioner. In that context, new devices that are small enough to pass through a small opening in the skin or through a small portal are required. A detailed analysis of current cutting methods that are or could be used for disc and disc nucleus removal provided that ultrasonics technology should be investigated as a possible solution. The study of ultrasonics technology to fulfil the overall cutting function needed for spinal annulus and nucleus disc material removal is based on a design methodology that breaks down the overall cutting function in many partial functions. The applied design methodology consists in drawing a complete catalogue of solutions for each partial function. Based on a predetermined choice of criteria for each partial function, the evaluation and the classification of each solution allows determination of the best solutions for each partial function. A new ultrasonic transducer designed device composed of a piezoelectric stack for the source of energy and movement, a transmission partial function with rods or discs, an amplification partial function with exponential horns and the cutting partial function solutions is detailed. Existing analytical methods for the design of ultrasonic transducers are mostly based on quarter wavelength segments used to build the transducer. The modeling of that transducers with a finite element method (FEM) avoids building the prototypes and constitutes progress. Analytical models different from the quarter wavelength approach have already been developed and are very useful when used in an optimization process. Furthermore, when the geometry of the analyzed model is not straightforward, a FEM optimization approach to solve that kind of problems can be a valid solution too. Some existing optimization algorithms and other already developed pseudo-gradient methods applied to optimize the analytical models of the ultrasonic transducers are not valid for numerical optimizations where the computing time is a key factor. This leads to the development a new genetic algorithm (GA) optimization methods. One advantage being that the number of parameters to be optimized does not change the complexity of the algorithm unlike other algorithms. Three GAs with improvements done on different parts are discussed, implemented and tested. One GA is chosen to optimize the transducer model with numerical methods. As the main drawback with FE optimizations is the amount of computation time spent for each simulation, this creates a need to develop numerical 2D models that can be quickly simulated but with accurate results. Ultrasonic transducer prototypes are also built and measured. As the prototype has to be used for the cutting or the removal of spinal disc material, the cutting effect of the prototypes has been tested and evaluated.

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