A survey of time-of-flight algorithms to determine bone positions in movement

In biomechanical applications where an ultrasound signal is used to determine the position of a specific organ or tissue, like for example a bone, a so-called A-mode ultrasonog- raphy is used. A ultrasonic pulse is generated by a transducer, injected in the tissue to be examined, and then the echoes are received and processed. Echoes are generated by changes in acoustic impedance in the medium, like for example a change of tissue from muscle to bone. To determine the position of the reflecting interface, the time-of-flight is measured and, utilizing well-know values for the transmission speed, the distance or depth is computed. If the localization device is to be designed to be small, wearable, and low-power, it is expected that the signal will be of worse quality with respect to traditional ultrasonography systems, especially under the point of view of signal-to-noise ratio. In these conditions, the reliability of the algorithm that implement the time-of-flight calculation is of paramount importance. In this paper, a simulated soft tissue bone interface (implemented with an ultrasound gel-pad) has been measured with intentionally low excitation signals and with the presence of imperfections similar to those expected in a physiological system. Several classic algorithms have been tested and benchmarked in this condition, and a new method with better reliability and repeatability is proposed.