Trade-offs in data acquisition and processing parameters for backscatter and scatterer size estimations

Abstract

By analyzing backscattered echo signal power spectra and thereby obtaining backscatter coefficient vs. frequency data, the size of sub-resolution scatterers contributing to echo signals can be estimated.Here we investigate tradeoffs in data acquisition and processing parameters for reference phantom based backscatter and scatterer size estimations. RF echo data from a tissue-mimicking test phantom were acquired using a clinical scanner equipped with linear array transducers. One array has a nominal frequency bandwidth of 5-13 MHz and the other 4-9 MHz. Comparison of spectral estimation methods showed that the Welch method provided spectra yielding more accurate and precise backscatter coefficient and scatterer size estimations than spectra computed by applying rectangular, Hanning, or Hamming windows and much reduced computational load than if using the multitaper method. For small echo signal data block sizes, moderate improvements in scatterer size estimations were obtained using a multitaper method but this significantly increases the computational burden.It is critical to average power spectra from lateral A-lines for the improvement of scatterer size estimation. Averaging approximately 10 independent A-lines laterally, with an axial window length 10 times the center frequency wavelength optimized tradeoffs between spatial resolution and the variance of scatterer size estimates. Applying the concept of a time-bandwidth product this suggests using analysis blocks that contain at least 30 independent samples of the echo signal.The estimation accuracy and precision depend on the ka range where k is the wave number and a is the effective scatterer size. This introduces an ROI depth dependency to the accuracy and precision because of preferential attenuation of higher frequency sound waves in tissue-like media. With the 5-13 MHz transducer ka ranged from 0.5 -1.6 for scatterers in the test phantom, which is a favorable range, and the accuracy and precision of scatterer size estimations were both within ~5% using optimal analysis block dimensions. When the 4-9 MHz transducer was used, the ka value ranged from 0.3 to 0.8 -1.1 for the experimental conditions, and the accuracy and precision were found to be ~10% and 10% -25%, respectively. Although the experiments were done with two specific models of transducers on the test phantom, the results can be generalized to similar clinical arrays available from a variety of manufacturers and/or for different size of scatterers with similar ka range.

Toward 3-D Echocardiographic Determination of Regional Myofiber Structure

“…Spatial averaging serves to reduce the potential consequences of speckle on estimates of fiber orientation. (Baldwin et al 2005; Liu and Zagzebski 2010) Although this spatial averaging reduces the effective resolution of our method, results seen in Figures 2 through 8 clearly indicate the gradation of fiber orientation, as expected. In addition, a single transmit focus was utilized for these studies.…”

Task-Oriented Comparison of Power Spectral Density Estimation Methods for Quantifying Acoustic Attenuation in Diagnostic Ultrasound Using a Reference Phantom Method

“…This is within the range of 7-15 pulse lengths that is frequently presented as the window length offering the best tradeoff between spatial resolution, accuracy and precision when estimating attenuation and effective scatterer size. 20,24-26,31,36,64-69 Tapering functions such as the Hann or Hamming, commonly used in QUS, 14,15,24,25,36,62,67,70 were found to increase the bias and standard deviation of the attenuation estimates. This indicates a less important role of side-lobe reduction in the accuracy and precision of the estimated parameters than the frequency resolution and SNR of the power spectral density estimate.…”

“…These results agree with previous findings that the total area spanned by the parameter estimation region would be limited by errors caused by its axial length rather than those caused by its lateral width. 26,27,63 …”

“…For this purpose we computed the separation between the two closest axial samples and closest lateral samples considered to be uncorrelated. 20,26,50-53 For segments including m axial samples of RF echo signals from N adjacent acoustic scanlines, the lateral correlation coefficient is defined as: 26 $${\rho }_L\left(\Delta \right)=\frac{1}{N}\sum _{j=1}^N\frac{\sum _{i=1}^m\left[(X_{j,i}-\overline{X_j})(X_{j+\Delta ,i}-\overline{X_{j+\Delta }})\right]}{\sqrt{\sum _{i=1}^m\left[{(X_{j,i}-\overline{X_j})}^2{(X_{j+\Delta ,i}-\overline{X_{j+\Delta }})}^2\right]}}$$ where X j,i is the i th ( i =1,.., m ) axial sample of the segment of the j th ( j =1,..., N ) acoustic scanline. The upper bar indicates averaging of all the axial samples within the segment of a particular acoustic scanline signal.…”

“…The resulting NW value is consistent with common values used to estimate smooth spectra. 26,29 Further optimization of the NW value for the reduction of coherent noise is the subject of ongoing studies.…”