B-mode ultrasound has long been a first-line examination tool for the diagnosis of many musculoskeletal diseases in children. Due to the high acoustic impedance contrast between echogenic bone structures and adjacent soft tissue, B-mode ultrasound can only see the outer surface of bone structures, not what lies inside. In this context, linear ultrasound computed tomography can visualize the different morphologies of small organs (bone structures and adjacent soft tissues), but does not provide quantitative, parametric images. This article proposes a nonlinear approach to ultrasound computed tomography using a full waveform inversion algorithm, based on a complete numerical modeling of wave propagation in media and on the minimization, in the L 2 -norm sense, of a functional based on the iterative solution of the inverse problem. Our study was performed in two dimensions, as justified by current conventional experimental setups in medical imaging. We used an acoustic modeling for simplification and computational cost reduction. The inverse problem was solved iteratively using a quasi-Newton method known as the memory-limited Broyden-Fletcher-Goldfarb-Shanno method. The gradient of the misfit function was obtained based on the adjoint state method, which required only two simulations of the wave propagation problem per source at each iteration. Experiments were conducted on a newborn arm phantom containing the humerus, radius and ulna, deep radial and ulnar veins, embedded in homogeneous adipose tissue. We show the images obtained for different configurations of initialization and a priori information on the medium: without any a priori information on the medium, a priori information on the initial map of mass densities, and ultrasonic wave velocities.

Convergences were of the order of 10 iterations in practice for each frequency band used, typically 150 kHz to 600 kHz. The normalized error was limited to less than 11%.