Ultrasound attenuation estimation using backscattered echoes from multiple sources

Abstract

The objective of this study was to devise an algorithm that can accurately estimate the attenuation along the propagation path ͑i.e., the total attenuation͒ from backscattered echoes. It was shown that the downshift in the center frequency of the backscattered ultrasound echoes compared to echoes obtained in a water bath was calculated to have the form ⌬f = mf o + b after normalizing with respect to the source bandwidth where m depends on the correlation length, b depends on the total attenuation, and f o is the center frequency of the source as measured from a reference echo. Therefore, the total attenuation can be determined independent of the scatterer correlation length by measuring the downshift in center frequency from multiple sources ͑i.e., different f o ͒ and fitting a line to the measured shifts versus f o . The intercept of the line gives the total attenuation along the propagation path. The calculations were verified using computer simulations of five spherically focused sources with 50% bandwidths and center frequencies of 6, 8, 10, 12, and 14 MHz. The simulated tissue had Gaussian scattering structures with effective radii of 25 m placed at a density of 250/ mm 3 . The attenuation of the tissue was varied from 0.1 to 0.9 dB/ cm-MHz. The error in the attenuation along the propagation path ranged from −3.5Ϯ 14.7% for a tissue attenuation of 0.1 dB/ cm-MHz to −7.0Ϯ 3.1% for a tissue attenuation of 0.9 dB/ cm-MHz demonstrating that the attenuation along the propagation path could be accurately determined using backscattered echoes from multiple sources using the derived algorithm.

Estimating the total ultrasound attenuation along the propagation path by applying multiple filters to backscattered echoes from a single spherically focused source

“…F ( ω,a eff ) has been shown to be approximately proportional to exp(− Af n ) for most scattering models where A ~ (2 πa eff / c ) n with a eff being the effective radius of the tissue microstructure, c being the speed of sound in the tissue, and n ≅ 2 [17]. Therefore, as was shown in [16], [17], ${\tilde{f}}_o^{″}$ and ${\tilde{\sigma }}_{\omega }^2$ are given by $$\begin{array}{cc}right& left{\tilde{f}}_o^{″}\cong f_o-4z_T{\alpha }_o{\tilde{\sigma }}_{\omega }^2-{\tilde{\sigma }}_{\omega }^{2}An{f}_o\\ right& left{\tilde{\sigma }}_{\omega }^2\cong \frac{{\sigma }_{\omega }^2}{1+An{\sigma }_{\omega }^2}.\end{array}$$ Hence, ${\tilde{f}}_o^{″}$ depends on both the attenuation along the propagation path and the frequency dependence of the backscatter, whereas ${\tilde{\sigma }}_{\omega }^2$ only depends on the scattering.…”

“…Previously, we derived an algorithm for estimating the slope of the total attenuation along the propagation path assuming a linear dependence on frequency and demonstrated that the algorithm yielded accurate results in computer simulations [16], [17]. One difficulty in implementing the algorithm, however, is that it requires scanning the same tissue region with multiple single-element spherically focused sources.…”

“…Therefore, after correcting for local attenuation and diffraction effects in the scattering region, the backscattered power spectrum would be given by [16], [17] $$\begin{array}{cc}right\mathrm{E}& left{true[{\mid V_{\mathrm{scat}\left(f\right)}\mid }^{2}true]}_{\text{Compensated}}\\ right& left\propto k^4{\mid V_{\text{plane}}\left(f\right)\mid }^2\exp (-4z_T{\alpha }_{o}f)F_{\gamma }(f,a_{\mathrm{eff}})\\ right& left\propto \exp \left(-\frac{{(f-{\tilde{f}}_o^{″})}^2}{2{\tilde{\sigma }}_{\omega }^2}\right),\end{array}$$ where ${\tilde{f}}_o^{″}$ is the expected spectral peak frequency and ${\tilde{\sigma }}_{\omega }^2$ is the bandwidth of the backscattered spectrum. In this equation, k is the wave number, α o is the effective attenuation coefficient for the intervening tissue layers between the ultrasound source and the ROI, and z T is the distance between the aperture plane of the source and the ROI.…”

“…Recently, a new algorithm [16], [17] was developed that estimated the total attenuation along the propagation path by processing echoes from multiple sources used to scan the same tissue region. The algorithm only needed echoes from a single ROI to obtain an estimate of the total attenuation between the source and the ROI, even though the algorithm did not assume that the tissue was homogeneous between the source and the ROI.…”

Performance evaluation of an automatic controlled sonoporation therapy device

“…Unfortunately, this approach requires MB destruction, which is related to increased cell death. An estimation of tissue attenuation can be determined from backscattered high frequency image data of a tissue region, as presented by Bigelow [9] and Labyed [10]. In this setup, that algorithm allows to determine the total attenuation of overlaying tissue layers, when analyzing the phantom region just above the MB channel, as displayed in Fig.…”