Accuracy of backscatter coefficient estimation using highly focused transducers

Backscatter coefficients (BSCs) have been proposed for decades for tissue characterization. The availability of formulations based on weakly focusing conditions has resulted in a widespread use of large focal number (f/#) transducers for BSC estimation. The use of highly focused transducers (HFTs) offers the possibility of improving the spatial resolution of BSC based imaging. The model by Chen et al. [1] was developed for estimating BSCs using transducers of arbitrary f/#. However, to this date only preliminary experimental validation of this method has been performed. The goal of the present study is to analyze for the first time the accuracy of Chen's method when estimating BSC vs. frequency curves with HFTs through both simulations and experiments. In simulations, BSC estimates were obtained using synthetic data produced with FIELD II, thereby including frequencydependent diffraction effects, from a simulated phantom containing 41 μm diameter solid spheres. The bandwidths of the simulated transducers ranged from 6-21 MHz with f/#s between 1.5 and 3. In physical experiments, radio frequency (rf) data were obtained with 15 MHz, f/1.5 and 10 MHz, f/2 transducers from a physical phantom containing glass beads of 41+/-5 μm diameter. BSC estimates were produced using two methods: Chen's model (CM) and Chen's approximate model for weakly focusing conditions (CAM). Accuracy was quantified using the mean fractional error (MFE) between the estimated and theoretical BSC curves. BSCs were estimated using gate lengths (Δz) between 15λ and 30λ. In simulations, the MFE using the CAM ranged from 30.6%56.7%, 11.8%-32.3%, and 4.8%-9.3% for an f/1.5, f/2, and f/3 transducers, respectively. The MFEs were reduced to 8.5%9.3%, 7%-7.4%, and 3.9%-4.1%, respectively when using the CM. In experiments, the MFE using the CAM ranged from 22.6%-43.3% and 6%-20.7% with the f/1.5 and f/2 transducers, respectively. The MFEs were reduced to 13.2%-26.7% and 5.9%7.8% respectively when using the CM. These results suggest that significant improvements in the accuracy of BSC estimation with highly focused transducers can be achieved by using Chen's general model instead of weakly focused transducer formulations.