Numerical estimation of femoral neck cortical bone thickness based on time domain topological energy and sparse signal approximation

Osteoporosis is a frequent bone disease that mainly affects women after menopause. It is characterized by a decrease in bone mass and a deterioration of the micro-architecture which can lead to an increased risk of fracture. Ultrasound technologies provide an affordable mean to implement non invasive solutions to diagnostically assess the characteristics of the bone structure. In this work, we are interested in the evaluation of the thickness of cortical bone using the topological energy method, in conjunction with a sparse signal approximation. The method has been adapted to the inspection of the femoral neck in a numerical simulation study. Through a 2D numerical experiment, we show that it is possible to obtain an image of the external and internal interfaces of the bone, as well as a local estimation of the i cortical thickness. These two properties are important to interpret the measurements of guided waves dispersion curves. To the best of our knowledge, this work represents the first ultrasound application of the topological energy method in the medical field.