Signal processing strategies that improve performance and understanding of the quantitative ultrasound SPECTRAL FIT algorithm

Attenuation Compensation and Estimation

Estimating the loss of ultrasound signal with propagation depth as a function of frequency is essential for quantifying tissue properties. Specifically, ultrasound attenuation is used to correct for spectral distortion prior to estimating quantitative ultrasound parameters to assess the tissue. Ultrasound attenuation can also be used independently to characterize the tissue. In this chapter, we review the primary algorithms for estimating both the local attenuation within a region of interest as well as the total attenuation between a region of interest and an ultrasound source. The strengths and weaknesses of each algorithm are also discussed.

Low Variance Estimation of Backscatter Quantitative Ultrasound Parameters Using Dynamic Programming

One of the main limitations of ultrasound imaging is that image quality and interpretation depend on the skill of the user and the experience of the clinician. Quantitative ultrasound (QUS) methods provide objective, system-independent estimates of tissue properties, such as acoustic attenuation and backscattering properties of tissue, which are valuable as objective tools for both diagnosis and intervention. Accurate and precise estimation of these properties requires correct compensation for intervening tissue attenuation. Prior attempts to estimate intervening-tissue attenuation based on minimizing cost functions that compared backscattered echo data to models have resulted in limited precision and accuracy. To overcome these limitations, in this paper, we incorporate the prior information of piecewise continuity of QUS parameters as a regularization term into our cost function. We further propose to calculate this cost function using dynamic programming (DP), a computationally efficient optimization algorithm that finds the global optimum. Our results on tissue-mimicking phantoms show that DP substantially outperforms a published least squares method in terms of both estimation bias and variance.

Review of Quantitative Ultrasound: Envelope Statistics and Backscatter Coefficient Imaging and Contributions to Diagnostic Ultrasound

Conventional medical imaging technologies, including ultrasound, have continued to improve over the years. For example, in oncology, medical imaging is characterized by high sensitivity, i.e., the ability to detect anomalous tissue features, but the ability to classify these tissue features from images often lacks specificity. As a result, a large number of biopsies of tissues with suspicious image findings are performed each year with a vast majority of these biopsies resulting in a negative finding. To improve specificity of cancer imaging, quantitative imaging techniques can play an important role. Conventional ultrasound B-mode imaging is mainly qualitative in nature. However, quantitative ultrasound (QUS) imaging can provide specific numbers related to tissue features that can increase the specificity of image findings leading to improvements in diagnostic ultrasound. QUS imaging can encompass a wide variety of techniques including spectral-based parameterization, elastography, shear wave imaging, flow estimation, and envelope statistics. Currently, spectral-based parameterization and envelope statistics are not available on most conventional clinical ultrasound machines. However, in recent years, QUS techniques involving spectral-based parameterization and envelope statistics have demonstrated success in many applications, providing additional diagnostic capabilities. Spectral-based techniques include the estimation of the backscatter coefficient (BSC), estimation of attenuation, and estimation of scatterer properties such as the correlation length associated with an effective scatterer diameter (ESD) and the effective acoustic concentration (EAC) of scatterers. Envelope statistics include the estimation of the number density of scatterers and quantification of coherent to incoherent signals produced from the tissue. Challenges for clinical application include correctly accounting for attenuation effects and transmission losses and implementation of QUS on clinical devices. Successful clinical and preclinical applications demonstrating the ability of QUS to improve medical diagnostics include characterization of the myocardium during the cardiac cycle, cancer detection, classification of solid tumors and lymph nodes, detection and quantification of fatty liver disease, and monitoring and assessment of therapy.

Improved algorithm for estimation of attenuation along propagation path using backscattered echoes from multiple sources

Accurately determining the attenuation along the propagation path leading to a region of interest could significantly improve diagnostic ultrasound tissue characterization since tissue characterization requires exact compensation for the frequency-dependent attenuation along the propagation path. In a previous study (JASA, 124:1367, 2008), it was shown that the total attenuation can be determined by using the backscattered echoes from multiple sources. The preliminary computer simulation results, had an average error between -0.3 and +0.2dB/MHz for the cases tested with a trend towards increasing error with increasing correlation length (i.e., characteristic size of the tissue microstructure of the scattering medium) and attenuation along the propagation path. Therefore, the goal of this study was to improve the accuracy of previously derived algorithm and reduce the dependence of the algorithm on correlation length and attenuation. In this study, the previous derivations were redone and the assumptions made by the algorithm regarding the scattering properties of the medium and the shape of the backscattered power spectrum were relaxed. The revised algorithm was then verified using computer simulations of five sources (6, 8, 10, 12, and 14MHz, 50% bandwidth) exposing a homogeneous tissue region. The simulated tissue had microstructure following a Gaussian spatial correlation function (i.e., exp(-0.827(ka(eff))(2)) where k is the wavenumber) with effective radii, a(eff), of 5-55microm (one size per simulated case) placed at a density of 250/mm(3) ( approximately 5 scatterers/resolution cell for 14MHz transducer). The attenuation of the tissue was also varied from 0.1 to 0.9dB/cm-MHz. The computer simulations demonstrated that the modifications significantly improved the accuracy of the algorithm resulting in average errors between -0.04 and 0.1dB/MHz which is three times better than the error performance of the original algorithm.

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

Quantifying the correlation length of the tissue microstructure has shown potential for differentiating between benign and malignant tumors. To implement these advances in the clinic, the total frequency-dependent attenuation along the propagation path must be determined on a patient specific basis. Previously, an algorithm was developed to estimate this attenuation using echoes from multiple sources. In this study, the developed algorithm was extended to echoes from a single source by filtering the echoed signal into multiple frequency bands. This step was needed because it would be challenging to scan exactly the same tissue region using multiple sources in the clinic. Computer simulations and phantom experiments were conducted to verify the attenuation could be determined by filtering the echoes from a single source. The simulations utilized a spherically focused single-element source (5 cm focal length, f/4, 14 MHz center frequency, 50% bandwidth) exposing a homogeneous tissue region (Gaussian scattering structures with effective radii of 5 to 55 mum at a density of 250/mm(3), attenuation of 0.1 to 0.9 dB/cm.MHz). The phantom experiments utilized a spherically focused single-element source (5.08 cm focal length, f/4, 7.5 MHz center frequency) exposing a 0.5 dB/cm.MHz homogeneous glass bead phantom. The computer simulations and phantom experiment confirmed that the total attenuation along the propagation path can be determined by appropriately applying multiple filters to the backscattered echoes from a single source.

Ultrasound characterization of red blood cell aggregation with intervening attenuating tissue-mimicking phantoms

The analysis of the ultrasonic frequency-dependent backscatter coefficient of aggregating red blood cells reveals information about blood structural properties. The difficulty in applying this technique in vivo is due to the frequency-dependent attenuation caused by intervening tissue layers that distorts the spectral content of signals backscattered by blood. An optimization method is proposed to simultaneously estimate tissue attenuation and blood structure properties, and was termed the structure factor size and attenuation estimator (SFSAE). An ultrasound scanner equipped with a wide-band 25 MHz probe was used to insonify porcine blood sheared in both Couette and tubular flow devices. Since skin is one of the most attenuating tissue layers during in vivo scanning, four skin-mimicking phantoms with different attenuation coefficients were introduced between the transducer and the blood flow. The SFSAE gave estimates with relative errors below 25% for attenuations between 0.115 and 0.411 dBMHz and kR<2.08 (k being the wave number and R the aggregate radius). The SFSAE can be useful to examine in vivo and in situ abnormal blood conditions suspected to promote pathophysiological cardiovascular consequences.

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

By analyzing backscattered echo signal power spectra and thereby obtaining backscatter coefficient vs. frequency data, the size of subresolution scatterers contributing to echo signals can be estimated. Here we investigate trade-offs 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 to 13 MHz and the other 4 to 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 trade-offs 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 a region-of-interest depth dependency to the accuracy and precision because of preferential attenuation of higher frequency sound waves in tissuelike media. With the 5 to 13 MHz, transducer ka ranged from 0.5 to 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 approximately 5% using optimal analysis block dimensions. When the 4- to 9-MHz transducer was used, the ka value ranged from 0.3 to 0.8 to 1.1 for the experimental conditions, and the accuracy and precision were found to be approximately 10% and 10% to 25%, respectively. Although the experiments were done with 2 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.

Ultrasound attenuation estimation using backscattered echoes from multiple sources

The objective of this study was to devise an algorithm that can accurately estimate the attenuation along the propagation path (i.e., the total attenuation) 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 Deltaf=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 mum 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 -3.5+/-14.7% for a tissue attenuation of 0.1 dB / cm-MHz to -7.0+/-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.

Impact of local attenuation approximations when estimating correlation length from backscattered ultrasound echoes

Estimating the characteristic correlation length of tissue microstructure from the backscattered power spectrum could improve the diagnostic capability of medical ultrasound. Previously, size estimates were obtained after compensating for source focusing, the frequency-dependent attenuation along the propagation path (total attenuation), and the frequency-dependent attenuation in the scattering region (local attenuation). In this study, the impact of approximations of the local attenuation on the scatterer size estimate was determined using computer simulations and theoretical analysis. The simulations used Gaussian impedance distributions with an effective radius of 25 microm randomly positioned in a homogeneous half-space sonified by a spherically focused source (f/1 to f/4). The approximations of the local attenuation that were assessed neglected local attenuation (i.e., assume 0 dB/cm-MHz) neglected frequency dependence of the local attenuation, and assumed a finite frequency dependence (i.e., 0.5 dB/cm-MHz) independent of the true attenuation of the medium. Errors in the scatterer size estimate due to the local attenuation approximations increased with increasing window length, increasing true local attenuation and increasing f number. The most robust estimates were obtained when the local attenuation was approximated by a tissue-independent attenuation value that was greater than 70% of the largest attenuation expected in the tissue region of interest.

Evaluation of the spectral fit algorithm as functions of frequency range and deltakaeff

Considerable effort has been directed at quantifying the properties of the tissue microstructure (i.e., scatterer correlation length) to diagnose disease and monitor treatment. In vivo assessments have had limited success due to frequency-dependent attenuation along the propagation path (i.e., total attenuation) masking the frequency dependence of the scattering from the tissue microstructure. Previously, both total attenuation and scatterer correlation length, given by the effective radius, were solved simultaneously by a two-parameter minimization of the mean squared error between a reference spectrum, modified by the attenuation and scatterer effective radius, and the backscattered waveforms using an algorithm termed the spectral fit algorithm. Herein, the impact of frequency range (largest frequency minus smallest frequency) and deltakaeff (largest kaeff value minus smallest kaeff value; k is wave number and aeff is scatterer effective radius) used by the spectral fit algorithm on estimating the scatterer effective radius, and total attenuation was assessed by computer simulations while excluding frequencies of the backscattered power spectrum dominated by electronic noise. The simulations varied the effective radius of the scatterers (5 microm to 150 microm), the attenuation of the region (0 to 1 dB/cm-MHz), the bandwidth of the source, and the amount of electronic noise added to the radio frequency (rf) waveforms. The center frequency of the source was maintained at 8 MHz. Comparable accuracy and precision of the scatterer effective radius were obtained for all the simulations whenever the same deltakaeff was used to obtain the estimates. A deltakaeff of 1 gave an accuracy and precision of approximately 15% +/- 35%, and a width of 1.5 gave an accuracy and precision of approximately 5% +/- 15% consistently for all of the simulations. Similarly, the accuracy and precision of the total attenuation estimate were improved by increasing the frequency range used by the spectral fit algorithm.