Tomoelastography by multifrequency wave number recovery from time-harmonic propagating shear waves

Palpation is one of the most sensitive, effective diagnostic practices, motivating the quantitative and spatially resolved determination of soft tissue elasticity parameters by medical ultrasound or MRI. However, this so-called elastography often suffers from limited anatomical resolution due to noise and insufficient elastic deformation, currently precluding its use as a tomographic modality on its own. We here introduce an efficient way of processing wave images acquired by multifrequency magnetic resonance elastography (MMRE), which relies on wave number reconstruction at different harmonic frequencies followed by their amplitude-weighted averaging prior to inversion. This results in compound maps of wave speed, which reveal variations in tissue elasticity in a tomographic fashion, i.e. an unmasked, slice-wise display of anatomical details at pixel-wise resolution. The method is demonstrated using MMRE data from the literature including abdominal and pelvic organs such as the liver, spleen, uterus body and uterus cervix. Even in small regions with low wave amplitudes, such as nucleus pulposus and spinal cord, elastic parameters consistent with literature values were obtained. Overall, the proposed method provides a simple and noise-robust strategy of in-plane wave analysis of MMRE data, with a pixel-wise resolution producing superior detail to MRE direct inversion methods.