Time-domain formulation for coherent plane wave compounding in horizontally layered media

Abstract

The locations of origin of ultrasonic echoes from soft tissue in conventional ultrasound beamforming are based on measured time of flight. For simplicity it is usually assumed that the region of interest is homogeneous with a constant sound speed, but in many in vivo and benchtop applications the imaging region is composed of horizontal layers, each with a distinct sound speed. In addition to time-of-flight complications, sound speed differences between the layers result in refraction through the interface of both the transmitted pulse and those reflected from the tissue, further influencing the fidelity of beamforming for target localization or other quantitative ultrasound metrics. A formulation is presented for delay-and-sum coherent Plane Wave Compounding (PWC) that accounts for variation in sound speed and refraction of ultrasound pulses in a region with two horizontal layers. The algorithm is formulated completely in the time domain, enabling simple implementation or extension of existing homogeneous PWC algorithms. Simulated and experimental images are investigated for a typical two-layer benchtop configuration, where the sound speeds in the upper and lower layers are relatively slow (water or gel) and fast (muscle), respectively. Extension of the formulation to a medium with N distinct layers is discussed.