A model for estimating ultrasound attenuation along the propagation path to the fetus from backscattered waveforms

Abstract

Accurate estimates of the ultrasound pressure and/or intensity incident on the developing fetus on a patient-specific basis could improve the diagnostic potential of medical ultrasound by allowing the clinician to increase the transmit power while still avoiding the potential for harmful bioeffects. Neglecting nonlinear effects, the pressure/intensity can be estimated if an accurate estimate of the attenuation along the propagation path (i.e., total attenuation) can be obtained. Herein, a method for determining the total attenuation from the backscattered power spectrum from the developing fetus is proposed. The boundaries between amnion and either the fetus' skull or soft tissue are each modeled as planar impedance boundaries at an unknown orientation with respect to the sound beam. A mathematical analysis demonstrates that the normalized returned voltage spectrum from this model is independent of the planes orientation. Hence, the total attenuation can be estimated by comparing the location of the spectral peak in the reflection from the fetus to the location of the spectral peak in a reflection obtained from a rigid plane in a water bath. The independence of the attenuation estimate and plane orientation is then demonstrated experimentally using a Plexiglas plate, a rat's skull, and a tissue-mimicking phantom. LIST OF SYMBOLSf = frequency f peak = frequency corresponding to the spectral peak at each inclination angle (i.e., ). g(r⃗ d , r⃗ ′) = effective Green's function valid from the scattering region to the detector G o = geometric gain value for velocity potential field at focus when W source is approximated by a Gaussian (m) G T = dimensionless aperture gain function that accounts for the focusing of the ultrasound source H = dimensionless filtering characteristics for the ultrasound source k = effective wave number along the propagation path k̃ = effective complex wave number along the propagation path (i.e., k̃ = k + iα) K uV = conversion constant relating voltage to particle velocity for ultrasound source (m/s V

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