Model to estimate the sound velocity in a circular wave guide in a through transmission measurement setup from multiple receivers

Quantitative ultrasound (QUS) at the femoral neck has to be conducted in a through transmission measurement setup. In this context, the Time Of Flight of the First Arriving Signal (TOFFAS) results from a wave being guided along the cortical shell and is supposed to be influenced by the elastic properties of the femoral neck cortex. In such a contact free measurement setup, the TOFFAS results from a combination of pathways through water and bone of unknown portions. It would be beneficial to estimate the Speed of Sound (SOS) in the wave guide from TOFFAS measurements without knowing the geometry of the wave guide. We developed a simple model based on a circular wave guide with unknown radius, location and SOS, but known positions of emitter and receiver array. An optimization routine was implemented to find the SOS in the circular wave guide from 24 TOFFAS obtained from the receiver array starting from an initial guess. A first test at different working points revealed that the outcome of the optimization routine did not depend on the initial guess at hand. Furthermore, noisy input led to acceptable errors in SOS. For the application on non-circular wave guides it is necessary to improve the model.