Signal analysis of quantitative ultrasound measurements at the proximal femur

For the prediction of osteoporotic fracture risk quantitative Ultrasound (QUS) is an alternative to techniques like X-ray absorptiometry or magnetic resonance tomography. In QUS measurements short pulses with center frequencies of 0.5 – 1 MHz are transmitted through bone. From the received signals characteristic transfer parameters associated with mechanical bone properties are determined. Within two research projects a device has been developed to transfer this technique from peripheral sites like the heel to the proximal femur, which is a main fracture site. In doing so, the conventional signal processing techniques for the calculation of the standard QUS parameters frequently failed due to multipath transmission of sound waves in bone. Therefore, the aim of this work is the development of a signal analysis which allows for characterizing sound paths separately. Based on theoretical considerations regarding sound propagation in bone and the introduction of the standard QUS parameters, the impact of multipath transmission to the calculation of these parameters is discussed. Analytically and with simulations errors are illustrated which arise from disregarding the existence of multiple sound paths. Furthermore, the ex vivo and in vivo measurement setups are shortly presented. Main focus of this work is put on the signal analysis. For the separation of superimposed signal components from different sound paths a model-based signal analysis is adapted from the area of nondestructive material testing to this specific task, at first. This algorithm is based on the analytical description of the received US pulses in the time domain as a superposition of several Gaussianmodulated cosines with additive white noise. Applying nonlinear optimization procedures using leastsquares fits which are integrated in an iterative Space Alternating Generalized Expectationmaximization algorithm (SAGE) the difference between measured and modelled signal is minimized and, thus, the model parameters of each signal component are determined. Then, the transfer parameters are calculated from the shift of these parameters compared to a reference signal. However, this algorithm is limited to signals, which can be described as Gaussian modulated cosines in the time domain.