Method for estimating total attenuation from a spatial map of attenuation slope for quantitative ultrasound imaging

In Vivo Validation of an In Situ Calibration Bead as a Reference for Backscatter Coefficient Calculation

OBJECTIVE

The study described here was aimed at assessing the capability of quantitative ultrasound (QUS) based on the backscatter coefficient (BSC) for classifying disease states, such as breast cancer response to neoadjuvant chemotherapy and quantification of fatty liver disease. We evaluated the effectiveness of an in situ titanium (Ti) bead as a reference target in calibrating the system and mitigating attenuation and transmission loss effects on BSC estimation.

METHODS

Traditional BSC estimation methods require external references for calibration, which do not account for ultrasound attenuation or transmission losses through tissues. To address this issue, we used an in situ Ti bead as a reference target, because it can be used to calibrate the system and mitigate the attenuation and transmission loss effects on estimation of the BSC. The capabilities of the in situ calibration approach were assessed by quantifying consistency of BSC estimates from rabbit mammary tumors (N = 21). Specifically, mammary tumors were grown in rabbits and when a tumor reached ≥1 cm in size, a 2 mm Ti bead was implanted in the tumor as a radiological marker and a calibration source for ultrasound. Three days later, the tumors were scanned with an L-14/5 38 array transducer connected to a SonixOne scanner with and without a slab of pork belly placed on top of the tumors. The pork belly acted as an additional source of attenuation and transmission loss. QUS parameters, specifically effective scatterer diameter (ESD) and effective acoustic concentration (EAC), were calculated using calibration spectra from both an external reference phantom and the Ti bead.

RESULTS

For ESD estimation, the 95% confidence interval between measurements with and without the pork belly layer was 6.0, 27.4 using the in situ bead and 114, 135.1 with the external reference phantom. For EAC estimation, the 95% confidence intervals were -8.1, 0.5 for the bead and -41.5, -32.2 for the phantom. These results indicate that the in situ bead method has reduced bias in QUS estimates because of intervening tissue losses.

CONCLUSION

The use of an in situ Ti bead as a radiological marker not only serves its traditional role but also effectively acts as a calibration target for QUS methods. This approach accounts for attenuation and transmission losses in tissue, resulting in more accurate QUS estimates and offering a promising method for enhanced disease state classification in clinical settings.

Pulse-echo ultrasound attenuation tomography

Objective.We present the first fully two-dimensional attenuation imaging technique developed for pulse-echo ultrasound systems. Unlike state-of-the-art techniques, which use line-by-line acquisitions, our method uses steered emissions to constrain attenuation values at each location with multiple crossing wave paths, essential to resolve the spatial variations of this tissue property.Approach.At every location, we compute normalized cross-correlations between the beamformed images that are obtained from emissions at different steering angles. We demonstrate that their log-amplitudes provide the changes between attenuation-induced amplitude losses undergone by the different incident waves. This allows us to formulate a linear tomographic problem, which we efficiently solve via a Tikhonov-regularized least-squares approach.Main results.The performance of our tomography technique is first validated in numerical examples and then experimentally demonstrated in custom-made tissue-mimicking phantoms with inclusions of varying size, echogenicity, and attenuation. We show that this technique is particularly good at resolving lateral variations in tissue attenuation and remains accurate in media with varying echogenicity.Significance.Based on a similar principle, this method can be easily combined with computed ultrasound tomography in echo mode for speed-of-sound imaging, paving the way towards a multi-modal ultrasound tomography framework characterizing multiple acoustic tissue properties simultaneously.

In vivo validation of an in situ calibration bead as a reference for backscatter coefficient calculation

Objectives

The study aims to assess the capability of Quantitative Ultrasound (QUS) based on the backscatter coefficient (BSC) for classifying disease states, such as breast cancer response to neoadjuvant chemotherapy and quantifying fatty liver disease. We evaluate the effectiveness of an in situ titanium (Ti) bead as a reference target in calibrating the system and mitigating attenuation and transmission loss effects on BSC estimation.

Methods

Traditional BSC estimation methods require external references for calibration, which do not account for ultrasound attenuation or transmission losses through tissues. To address this issue, we use an in situ titanium (Ti) bead as a reference target, because it can be used to calibrate the system and mitigate the attenuation and transmission loss effects on estimation of the BSC. The capabilities of the in situ calibration approach were assessed by quantifying consistency of BSC estimates from rabbit mammary tumors (N = 21 ). Specifically, mammary tumors were grown in rabbits and when a tumor reached 1 cm or greater in size, a 2-mm Ti bead was implanted into the tumor as a radiological marker and a calibration source for ultrasound. Three days later, the tumors were scanned with a L-14/5 38 array transducer connected to a SonixOne scanner with and without a slab of pork belly placed on top of the tumors. The pork belly acted as an additional source of attenuation and transmission loss. QUS parameters, specifically effective scatterer diameter (ESD) and effective acoustic concentration (EAC), were calculated using calibration spectra from both an external reference phantom and the Ti bead.

Results

For ESD estimation, the 95% confidence interval between measurements with and without the pork belly layer was (6.0,27.4) using the in situ bead and (114, 135.1) with the external reference phantom. For EAC estimation, the 95% confidence interval were (-8.1, 0.5) for the bead and (-41.5, -32.2) for the phantom. These results indicate that the in situ bead method shows reduced bias in QUS estimates due to intervening tissue losses.

Conclusions

The use of an in situ Ti bead as a radiological marker not only serves its traditional role but also effectively acts as a calibration target for QUS methods. This approach accounts for attenuation and transmission losses in tissue, resulting in more accurate QUS estimates and offering a promising method for enhanced disease state classification in clinical settings.

Regularized Ultrasound Phantom-Free Local Attenuation Coefficient Slope (ACS) Imaging in Homogeneous and Heterogeneous Tissues

Attenuation maps or measurements based on the local attenuation coefficient slope (ACS) in quantitative ultrasound (QUS) have shown potential for the diagnosis of liver steatosis. In liver cancers, tissue abnormalities and tumors detected using ACS are also of interest to provide new image contrast to clinicians. Current phantom-based approaches have the limitation of assuming a comparable speed of sound between the reference phantom and insonified tissues. Moreover, these methods present the inconvenience for operators to acquire data on phantoms and patients. The main goal was to alleviate these drawbacks by proposing a methodology for constructing phantom-free regularized (PF-R) local ACS maps and investigate the performance in both homogeneous and heterogeneous media. The proposed method was tested on two tissue-mimicking media with different ACS constructed as homogeneous phantoms, side-by-side and top-to-bottom phantoms, and inclusion phantoms with different attenuations. Moreover, an in vivo proof-of-concept was performed on healthy, steatotic, and cancerous human liver datasets. Modifications brought to previous works include: 1) a linear interpolation of the power spectrum in the log scale; 2) the relaxation of the underlying hypothesis on the diffraction factor; 3) a generalization to nonhomogeneous local ACS; and 4) an adaptive restriction of frequencies to a more reliable range than the usable frequency range. Regularization was formulated as a generalized least absolute shrinkage and selection operator (LASSO), and a variant of the Bayesian information criterion (BIC) was applied to estimate the Lagrangian multiplier on the LASSO constraint. In addition, we evaluated the proposed algorithm when applying median filtering before and after regularization. Tests conducted showed that the PF-R yielded robust results in all tested conditions, suggesting potential for additional validation as a diagnosis method.

Multiplexed Ultrasound Imaging Using Spectral Analysis on Gas Vesicles

Current advances in ultrasound imaging techniques combined with the next generation contrast agents such as gas vesicles (GV) revolutionize the visualization of biological tissues with spatiotemporal precision. In optics, fluorescent proteins enable understanding of molecular and cellular functions in biological systems due to their multiplexed imaging capability. Here, a panel of GVs is investigated using mid-band fit (MBF) spectral imaging to realize multiplexed ultrasound imaging to uniquely visualize locations of different types of stationary GVs. The MBF spectral imaging technique demonstrates that stationary clustered GVs are efficiently localized and distinguished from unclustered GVs in agarose gel phantom and 3D vessel structures are visualized in ex vivo mouse liver specimens. Mouse macrophages serve as carriers of clustered and unclustered GVs and multiplexing beacons to report cells' spatial locations by emitting distinct spectral signals. 2D MBF spectral images are reconstructed, and pixels in these images are classified depending on MBF values by comparing predetermined filters that predict the existence of cells with clustered and unclustered GVs. This pseudo-coloring scheme clearly distinguishes the locations of two classes of cells like pseudo-color images in fluorescence microscopy.

Identifying and overcoming limitations with in situ calibration beads for quantitative ultrasound

Ensuring the consistency of spectral-based quantitative ultrasound estimates in vivo necessitates accounting for diffraction, system effects, and propagation losses encountered in the tissue. Accounting for diffraction and system effects is typically achieved through planar reflector or reference phantom methods; however, neither of these is able to account for the tissue losses present in vivo between the ultrasound probe and the region of interest. In previous work, the feasibility of small titanium beads as in situ calibration targets (0.5-2 mm in diameter) was investigated. In this study, the importance of bead size for the calibration signal, the role of multiple echoes coming from the calibration bead, and sampling of the bead signal laterally through beam translation were examined. This work demonstrates that although the titanium beads naturally produce multiple reverberant echoes, time-windowing of the first echo provides the smoothest calibration spectrum for backscatter coefficient calculation. When translating the beam across the bead, the amplitude of the echo decreases rapidly as the beam moves across and past the bead. Therefore, to obtain consistent calibration signals from the bead, lateral interpolation is needed to approximate signals coming from the center of the bead with respect to the beam.

A multiparametric volumetric quantitative ultrasound imaging technique for soft tissue characterization

Quantitative ultrasound (QUS) offers a non-invasive and objective way to quantify tissue health. We recently presented a spatially adaptive regularization method for reconstruction of a single QUS parameter, limited to a two dimensional region. That proof-of-concept study showed that regularization using homogeneity prior improves the fundamental precision-resolution trade-off in QUS estimation. Based on the weighted regularization scheme, we now present a multiparametric 3D weighted QUS (3D QUS) method, involving the reconstruction of three QUS parameters: attenuation coefficient estimate (ACE), integrated backscatter coefficient (IBC) and effective scatterer diameter (ESD). With the phantom studies, we demonstrate that our proposed method accurately reconstructs QUS parameters, resulting in high reconstruction contrast and therefore improved diagnostic utility. Additionally, the proposed method offers the ability to analyze the spatial distribution of QUS parameters in 3D, which allows for superior tissue characterization. We apply a three-dimensional total variation regularization method for the volumetric QUS reconstruction. The 3D regularization involving N planes results in a high QUS estimation precision, with an improvement of standard deviation over the theoretical 1/N rate achievable by compounding N independent realizations. In the in vivo liver study, we demonstrate the advantage of adopting a multiparametric approach over the single parametric counterpart, where a simple quadratic discriminant classifier using feature combination of three QUS parameters was able to attain a perfect classification performance to distinguish between normal and fatty liver cases.

Total attenuation compensation for backscatter coefficient estimation using full angular spatial compounding

The backscatter coefficient (BSC) quantifies the frequency-dependent reflectivity of tissues. Accurate estimation of the BSC is only possible with the knowledge of the attenuation coefficient slope (ACS) of the tissues under examination. In this study, the use of attenuation maps constructed using full angular spatial compounding (FASC) is proposed for attenuation compensation when imaging integrated BSCs. Experimental validation of the proposed approach was obtained using two cylindrical physical phantoms with off-centered inclusions having different ACS and BSC values than the background, and in a phantom containing an ex vivo chicken breast sample embedded in an agar matrix. With the phantom data, three different ACS maps were employed for attenuation compensation: (1) a ground truth ACS map constructed using insertion loss techniques, (2) the estimated ACS map using FASC attenuation imaging, and (3) a uniform ACS map with a value of 0.5 dBcm^{\protect \relax \special {t4ht=-}1}MHz^{\protect \relax \special {t4ht=-}1}, which is commonly used to represent attenuation in soft tissues. Comparable results were obtained when using the ground truth and FASC-estimated ACS maps in term of inclusion detectability and estimation accuracy, with averaged fractional error below 2.8 dB in both phantoms. Conversely, the use of the homogeneous ACS map resulted in higher levels of fractional error (>10 dB), which demonstrates the importance of an accurate attenuation compensation. The results with the ex vivo tissue sample were consistent with the observations using the physical phantoms, with the FASC-derived ACS map providing comparable BSC images to those formed using the ground truth ACS map and more accurate than those BSC images formed using a uniform ACS. These results suggest that BSCs can be reliably estimated using FASC when a self-consistent attenuation compensation stemming from prior estimation of an accurate ACS map is used.

Estimation of Tissue Attenuation from Ultrasonic B-Mode Images-Spectral-Log-Difference and Method-of-Moments Algorithms Compared

We report on results from the comparison of two algorithms designed to estimate the attenuation coefficient from ultrasonic B-mode scans obtained from a numerical phantom simulating an ultrasound breast scan. It is well documented that this parameter significantly diverges between normal tissue and malignant lesions. To improve the diagnostic accuracy it is of great importance to devise and test algorithms that facilitate the accurate, low variance and spatially resolved estimation of the tissue’s attenuation properties. A numerical phantom is realized using k-Wave, which is an open source Matlab toolbox for the time-domain simulation of acoustic wave fields that facilitates both linear and nonlinear wave propagation in homogeneous and heterogeneous tissue, as compared to strictly linear ultrasound simulation tools like Field II. k-Wave allows to simulate arbitrary distributions, resolved down to single voxel sizes, of parameters including the speed of sound, mass density, scattering strength and to include power law acoustic absorption necessary for simulation tasks in medical diagnostic ultrasound. We analyze the properties and the attainable accuracy of both the spectral-log-difference technique, and a statistical moments based approach and compare the results to known reference values from the sound field simulation.

Estimation of Backscatter Coefficients Using an In Situ Calibration Source

The objective of this article is to demonstrate the feasibility of estimating the backscatter coefficient (BSC) using an in situ calibration source. Traditional methods of estimating the BSC in vivo using a reference phantom technique do not account for transmission losses due to intervening layers between the ultrasonic source and the tissue region to be interrogated, leading to increases in bias and variance of BSC-based estimates. To account for transmission losses, an in situ calibration approach is proposed. The in situ calibration technique employs a titanium sphere that is well-characterized ultrasonically, biocompatible, and embedded inside the sample. A set of experiments was conducted to evaluate the embedded titanium spheres as in situ calibration targets for BSC estimation. The first experiment quantified the backscattered signal strength from titanium spheres of three sizes: 0.5, 1, and 2 mm in diameter. The second set of experiments assessed the repeatability of BSC estimates from the titanium spheres and compared these BSCs to theory. The third set of experiments quantified the ability of the titanium bead to provide an in situ reference spectrum in the presence of a lossy layer on top of the sample. The final set of experiments quantified the ability of the bead to provide a calibration spectrum over multiple depths in the sample. All experiments were conducted using an L9-4/38 linear array connected to a SonixOne system. The strongest signal was observed from the 2-mm titanium bead with the signal-to-noise ratio (SNR) of 11.6 dB with respect to the background speckle. Using an analysis bandwidth of 2.5-5.5 MHz, the mean differences between the experimentally derived BSCs and BSCs derived from the Faran theory were 0.54 and 0.76 dB using the array and a single-element transducer, respectively. The BSCs estimated using the in situ calibration approach without the layer and with the layer and using the reference phantom approach with the layer were compared to the reference phantom approach without the layer present. The mean differences in BSCs were 0.15, 0.73, and -9.69 dB, respectively. The mean differences of the BSCs calculated from data blocks located at depths that were either 30 pulse lengths above or below the actual bead depth compared to the BSC calculated at bead depth were -1.55 and -1.48 dB, respectively. The results indicate that an in situ calibration target can account for overlaying tissue losses, thereby improving the robustness of BSC-based estimates.

Ultrasound-Based Regularized Log Spectral Difference Method For Monitoring Microwave Hyperthermia

The feasibility of using normalized cumulative difference attenuation (NCDA) map for tracking the spatial and temporal evolution of temperature during microwave hyperthermia experiment on in-vitro phantoms is explored in this study. The NCDA maps were estimated from the beamformed ultrasound radio frequency (RF) data using a regularized log spectral difference (RLSD) technique. The NCDA maps were estimated at different time instants for the entire period of the experiment. The contour maps of the NCDA and the ground truth temperature map, obtained using an infra-red(IR) thermal camera corresponding to the ultrasound imaging plane, showed that NCDA was able to locate the axial and lateral co-ordinates of the hotspot with the error of <; 1.5 mm axially and <; 0.1 mm laterally. The error in the estimated hotspot area was less than 8 %. This preliminary in-vitro study suggests that NCDA maps estimated using RLSD may have potential in evaluating the spatio-temporal evolution of temperature and may help in the development of ultrasound-based image-guided temperature monitoring system for microwave hyperthermia.

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.

Far-field scattering model for wave propagation in random media

A simple approximate model is developed for ultrasonic wave propagation in a random elastic medium. The model includes second order multiple scattering and is applicable in all frequency ranges including geometric. It is based on the far field approximation of the reference medium Green's function and simplifications of the mass operator in addition to those of the first smooth approximation. In this approximation, the dispersion equation for the perturbed wave number is obtained; its solution yields the dispersive ultrasonic velocity and attenuation coefficients. The approximate solution is general and is suitable for nonequiaxed grains with arbitrary elastic symmetry. For equiaxed cubic grains, the solution is compared with the existing second order models and with the Born approximation. The comparison shows that the obtained solution has smaller error than the Born approximation and shows reasonably well the onset of multiple scattering and the applicability limit of the Born approximation at high frequency. The perturbed wave number in the developed model does not depend explicitly on the crystallite elastic properties even for arbitrary crystallographic symmetry; it depends on two nondimensional scattering elastic parameters and the macroscopic ultrasonic velocity (those are dependent on the crystallite moduli). This provides an advantage for potential schemes for inversion from attenuation to material microstructure.

Performance evaluation of the spectral centroid downshift method for attenuation estimation

Estimation of frequency-dependent ultrasonic attenuation is an important aspect of tissue characterization. Along with other acoustic parameters studied in quantitative ultrasound, the attenuation coefficient can be used to differentiate normal and pathological tissue. The spectral centroid downshift (CDS) method is one the most common frequencydomain approaches applied to this problem. In this study, a statistical analysis of this method's performance was carried out based on a parametric model of the signal power spectrum in the presence of electronic noise. The parametric model used for the power spectrum of received RF data assumes a Gaussian spectral profile for the transmit pulse, and incorporates effects of attenuation, windowing, and electronic noise. Spectral moments were calculated and used to estimate second-order centroid statistics. A theoretical expression for the variance of a maximum likelihood estimator of attenuation coefficient was derived in terms of the centroid statistics and other model parameters, such as transmit pulse center frequency and bandwidth, RF data window length, SNR, and number of regression points. Theoretically predicted estimation variances were compared with experimentally estimated variances on RF data sets from both computer-simulated and physical tissue-mimicking phantoms. Scan parameter ranges for this study were electronic SNR from 10 to 70 dB, transmit pulse standard deviation from 0.5 to 4.1 MHz, transmit pulse center frequency from 2 to 8 MHz, and data window length from 3 to 17 mm. Acceptable agreement was observed between theoretical predictions and experimentally estimated values with differences smaller than 0.05 dB/cm/MHz across the parameter ranges investigated. This model helps predict the best attenuation estimation variance achievable with the CDS method, in terms of said scan parameters.

Window-modulated compounding Nakagami imaging for ultrasound tissue characterization

Ultrasound Nakagami parametric imaging is a useful tool for tissue characterization. Previous literature has suggested using a square with side lengths corresponding to 3 times the transducer pulse length as the minimum window for constructing the Nakagami image. This criterion does not produce sufficiently smooth images for the Nakagami image to characterize homogeneous tissues. To improve image smoothness, we proposed window-modulated compounding (WMC) Nakagami imaging based on summing and averaging the Nakagami images formed using sliding windows with varying window side lengths from 1 to N times the transducer pulse length in 1 pulse length step. Simulations (the number densities of scatterers: 2-16 scatterers/mm(2)) and experiments on fully developed speckle phantoms (the scatterer diameters: 20-106 μm) were conducted to suggest an appropriate number of frames N and to evaluate the image smoothness and resolution by analyzing the full width at half maximum (FWHM) of the parameter distribution and the widths of the image autocorrelation function (ACF), respectively. In vivo ultrasound measurements on rat livers without and with cirrhosis were performed to validate the practical performance of the WMC Nakagami image in tissue characterization. The simulation results showed that using a range of N from 7 to 10 as the number of frames for image compounding reduces the estimation error to less than 5%. Based on this criterion, the Nakagami parameter obtained from the WMC Nakagami image increased from 0.45 to 0.95 after increasing the number densities of scatterers from 2 to 16 scatterers/mm(2). The FWHM of the parameter distribution (bins=40) was 13.5±1.4 for the Nakagami image and 9.1±1.43 for the WMC Nakagami image, respectively (p-value<.05). The widths of the ACF for the Nakagami and WMC Nakagami images were 454±5.36 and 458±4.33, respectively (p-value>.05). In the phantom experiments, we also found that the FWHM of the parameter distribution for the WMC Nakagami image was smaller than that of the conventional Nakagami image (p-value<.05), and there was no significant difference of the ACF width between the Nakagami and WMC Nakagami images (p-value>.05). In the animal experiments, the Nakagami parameters obtained from the WMC Nakagami image for normal and cirrhotic rat livers were 0.62±0.08 and 0.92±0.07, respectively (p-value<.05). The results demonstrated that the WMC technique significantly improved the image smoothness of Nakagami imaging without resolution degradation, giving Nakagami model-based imaging the ability to visualize scatterer properties with enhanced image quality.