This thesis is part of the long-term development of an ultrasonic device of prediction of the fracture risk of the hip. We hypothesize that estimations of the thickness and elastic properties of the cortical shell could enhance the prediction of the risk. Analysis of the waves guided by the shell could yield these estimates. A method, in non-destructive testing, based on the decomposition of the time reversal operator (DORT) was developed to characterize empty metallic tubes. The goal of this thesis is to adapt this method to the specific features of the femoral neck. Several phantoms were built in order to decouple the problems due to the bone characteristics. First, an empty bone phantom of circular cross-section was used to optimize the experimental conditions to measure circumferential guided wave backscattered signals despite adverse material properties of bone. Second, the simulation study of bone phantoms of circular cross section filled with a marrow-mimicking fluid led to the development of a filtering method to eliminate contributions of reflections on the cavity walls. Finally, the analysis of the radiated guided waves enables us to extend the method to shells of any shape, in particular to an elliptical shell. These thesis works result in several tools to characterize waveguides of any shape, with constant thickness, the cavity being empty or filled with a fluid. This represents a significant step towards the ultrasonic characterization of the femoral neck.
