Transient high-order ultrasonic scattering

Abstract

To improve the reliability of diagnosis of tissue pathologies (e.g., cancers) based on ultrasonic imaging, quantitative images of physiological parameters such as speed of sound and/or absorption coefficient can in theory be obtained by inverse scattering procedures. Previous studies [Cavicchi et al., IEEE Trans. Ultrason. Ferroelec. Freq. Control UFFC-35, 22–33 (1988)] employed a moment-method matrix formulation under a monofrequency assumption. Periodicities of the field phasors caused a uniqueness problem in the inverse scattering solution for scatterers with phase shift magnitudes greater than π; in practical medical imaging, the phase shift would be hundreds of π. A reformulation of the method in the time domain appears more promising because the phase shifts are now merely time delays. The moment-method formulation is presented for forward scattering. A preliminary numerical study has verified the expansion using the moment-method equation and the internal field calculated by the inverse discrete Fourier transform of the well-known monofrequency solution solved at many frequencies. Future studies will address the more difficult problems of time-domain field inversion and inverse scattering.