Lower Bound on Estimation Variance of the Ultrasonic Attenuation Coefficient Using the Spectral-Difference Reference-phantom Method

Abstract

Ultrasonic attenuation is one of the primary parameters of interest in Quantitative Ultrasound (QUS). Non-invasive monitoring of tissue attenuation can provide valuable diagnostic and prognostic information to the physician. The Reference Phantom Method (RPM) was introduced as a way of mitigating some of the system-related effects and biases to facilitate clinical QUS applications. In this paper, under the assumption of diffuse scattering, a probabilistic model of the backscattered signal spectrum is used to derive a theoretical lower bound on the estimation variance of the attenuation coefficient using the Spectral-Difference RPM. The theoretical lower bound is compared to simulated and experimental attenuation estimation statistics in tissue-mimicking (TM) phantoms. Estimation standard deviation (STD) of the sample attenuation in a region of interest (ROI) of the TM phantom is measured for various combinations of processing parameters, including Radio-Frequency (RF) data block length (i.e., window length) from 3 to 17 mm, RF data block width from 10 to 100 A-lines, and number of RF data blocks per attenuation estimation ROI from 3 to 10. In addition to the Spectral-Difference RPM, local attenuation estimation for simulated and experimental data sets was also performed using a modified implementation of the Spectral Fit Method (SFM). Estimation statistics of the SFM are compared to theoretical variance predictions from the literature.1 Measured STD curves are observed to lie above the theoretical lower bound curves, thus experimentally verifying the validity of the derived bounds. This theoretical framework benefits tissue characterization efforts by isolating processing parameter ranges that could provide required precision levels in estimation of the ultrasonic attenuation coefficient using Spectral Difference methods.