Power-Doppler Ultrasonic Imaging of Peripheral Perfusion in Diabetic Mice.

OBJECTIVE: We explored the capabilities of power-Doppler ultrasonic (PD-US) imaging without contrast enhancement for monitoring changes in muscle perfusion over time. METHODS: Ischemic recovery was observed in healthy and type II diabetic male and female mice with and without exercise. In separate studies, perfusion was measured during and after 5-min ischemic periods and during four-week recovery periods following irreversible femoral ligation. A goal was to assess how well PD-US estimates tracked the diabetic-related changes in endothelial function that influenced perfusion. RESULTS: The average perfusion recovery time following femoral ligation increased 47% in diabetic males and 74% in diabetic females compared with non-diabetic mice. Flow-mediated dilation in conduit arteries and the reactive hyperemia index in resistive vessels each declined by one half in sedentary diabetic mice compared with sedentary non-diabetic mice. We found that exercise reduced the loss of endothelial function from diabetes in both sexes. The reproducibility of perfusion measurements was limited primarily by our ability to select the same region in muscle and to effectively filter tissue clutter. CONCLUSIONS/SIGNIFICANCE: PD-US measurements can precisely follow site-specific changes in skeletal muscle perfusion related to diabetes over time, which fills the need for techniques capable of regularly monitoring atherosclerotic changes leading to ischemic vascular pathologies.

Deep Q-learning to globally optimize a k-D parameter search for medical imaging.

Background: Estimation of the global optima of multiple model parameters is valuable for precisely extracting parameters that characterize a physical environment. This is especially useful for imaging purposes, to form reliable, meaningful physical images with good reproducibility. However, it is challenging to avoid different local minima when the objective function is nonconvex. The problem of global searching of multiple parameters was formulated to be a k-D move in the parameter space and the parameter updating scheme was converted to be a state-action decision-making problem. Methods: We proposed a novel Deep Q-learning of Model Parameters (DQMP) method for global optimization which updated the parameter configurations through actions that maximized the Q-value and employed a Deep Reward Network (DRN) designed to learn global reward values from both visible fitting errors and hidden parameter errors. The DRN was constructed with Long Short-Term Memory (LSTM) layers followed by fully connected layers and a rectified linear unit (ReLU) nonlinearity. The depth of the DRN depended on the number of parameters. Through DQMP, the k-D parameter search in each step resembled the decision-making of action selections from 3k configurations in a k-D board game. Results: The DQMP method was evaluated by widely used general functions that can express a variety of experimental data and further validated on imaging applications. The convergence of the proposed DRN was evaluated, which showed that the loss values of six general functions all converged after 12 epochs. The parameters estimated by the DQMP method had relative errors of less than 4% for all cases, whereas the relative errors achieved by Q-learning (QL) and the Least Squares Method (LSM) were 17% and 21%, respectively. Furthermore, the imaging experiments demonstrated that the imaging of the parameters estimated by the proposed DQMP method were the closest to the ground truth simulation images when compared to other methods. Conclusions: The proposed DQMP method was able to achieve global optima, thus yielding accurate model parameter estimates. DQMP is promising for estimating multiple high-dimensional parameters and can be generalized to global optimization for many other complex nonconvex functions and imaging of physical parameters.

Monitoring Muscle Perfusion in Rodents During Short-Term Ischemia Using Power Doppler Ultrasound.

OBJECTIVE: The aim of this work was to evaluate the reliability of power Doppler ultrasound (PD-US) measurements made without contrast enhancement to monitor temporal changes in peripheral blood perfusion. METHODS: On the basis of pre-clinical rodent studies, we found that combinations of spatial registration and clutter filtering techniques applied to PD-US signals reproducibly tracked blood perfusion in skeletal muscle. Perfusion is monitored while modulating hindlimb blood flow. First, in invasive studies, PD-US measurements in deep muscle with laser speckle contrast imaging (LSCI) of superficial tissues made before, during and after short-term arterial clamping were compared. Then, in non-invasive studies, a pressure cuff was employed to generate longer-duration hindlimb ischemia. Here, B-mode imaging was also applied to measure flow-mediated dilation of the femoral artery while, simultaneously, PD-US was used to monitor downstream muscle perfusion to quantify reactive hyperemia. Measurements in adult male and female mice and rats, some with exercise conditioning, were included to explore biological variables. RESULTS: PD-US methods are validated through comparisons with LSCI measurements. As expected, no significant differences were found between sexes or fitness levels in flow-mediated dilation or reactive hyperemia estimates, although post-ischemic perfusion was enhanced with exercise conditioning, suggesting there could be differences between the hyperemic responses of conduit and resistive vessels. CONCLUSION: Overall, we found non-contrast PD-US imaging can reliably monitor relative spatiotemporal changes in muscle perfusion. This study supports the development of PD-US methods for monitoring perfusion changes in patients at risk for peripheral artery disease.

Combining Spatial Registration With Clutter Filtering for Power-Doppler Imaging in Peripheral Perfusion Applications.

Power-Doppler ultrasonic (PD-US) imaging is sensitive to echoes from blood cell motion in the microvasculature but generally nonspecific because of difficulties with filtering nonblood-echo sources. We are studying the potential for using PD-US imaging for routine assessments of peripheral blood perfusion without contrast media. The strategy developed is based on an experimentally verified computational model of tissue perfusion that simulates typical in vivo conditions. The model considers directed and diffuse blood perfusion states in a field of moving clutter and noise. A spatial registration method is applied to minimize tissue motion prior to clutter and noise filtering. The results show that in-plane clutter motion is effectively minimized. While out-of-plane motion remains a strong source of clutter-filter leakage, those registration errors are readily minimized by straightforward modification of scanning techniques and spatial averaging.

A data-driven approach to characterizing nonlinear elastic behavior of soft materials.

The Autoprogressive (AutoP) method is a data-driven inverse method that leverages finite element analysis (FEA) and machine learning (ML) techniques to build constitutive relationships from measured force and displacement data. Previous applications of AutoP in tissue-like media have focused on linear elastic mechanical behavior as the target object is infinitesimally compressed. In this study, we extended the application of AutoP in characterizing nonlinear elastic mechanical behavior as the target object undergoes finite compressive deformation. Guided by the prior of nonlinear media, we modified the training data generated by AutoP to speed its ability to learn to model deformations. AutoP training was validated using both synthetic and experimental data recorded from 3D objects. Force-displacement measurements were obtained using ultrasonic imaging from heterogeneous agar-gelatin phantoms. Measurement on samples of phantom components were analyzed to obtain independent measurements of material properties. Comparisons validated the material properties found from neural network constitutive models (NNCMs) trained using AutoP. Results were found to be robust to measurement errors and spatial variations in material properties.

Multi-parameter Sub-Hertz Analysis of Viscoelasticity With a Quality Metric for Differentiation of Breast Masses.

We applied sub-Hertz analysis of viscoelasticity (SAVE) to differentiate breast masses in pre-biopsy patients. Tissue response during external ramp-and-hold stress was ultrasonically detected. Displacements were used to acquire tissue viscoelastic parameters. The fast instantaneous response and slow creep-like deformations were modeled as the response of a linear standard solid from which viscoelastic parameters were estimated. These parameters were used in a multi-variable classification framework to differentiate malignant from benign masses identified by pathology. When employing all viscoelasticity parameters, SAVE resulted in 71.43% accuracy in differentiating lesions. When combined with ultrasound features and lesion size, accuracy was 82.24%. Adding a quality metric based on uniaxial motion increased the accuracy to 81.25%. When all three were combined with SAVE, accuracy was 91.3%. These results confirm the utility of SAVE as a robust ultrasound-based diagnostic tool for non-invasive differentiation of breast masses when used as stand-alone biomarkers or in conjunction with ultrasonic features.

Fluidity and elasticity form a concise set of viscoelastic biomarkers for breast cancer diagnosis based on Kelvin-Voigt fractional derivative modeling.

Cancer progression involves biomechanical changes within transformed cells and the surrounding extracellular matrix (ECM). The viscoelastic features of fluidity and elasticity that are based on a novel Kelvin-Voigt fractional derivative (KVFD) model were found capable of discriminating normal, benign and malignant breast biopsy tissues on the cellular scale. The improved specificity of KVFD model parameters derives from greater accuracy of fitting the entire approaching force-indentation measurement curve ([Formula: see text] > 0.99) compared with traditional elastic models ([Formula: see text] < 0.86). Moreover, model parameters can be interpreted in terms of histopathological features. First, statistical comparisons reveal there are significant differences (p < 0.001) in elasticity E0, fluidity [Formula: see text], and viscosity [Formula: see text] among healthy, benign, and malignant groups. Malignant breast tissues show low-value, broad-distributions in E0 and with high fluidity [Formula: see text] as compared with healthy and benign tissues. Second, histograms of E0 and [Formula: see text] provide distinctive features by fitting to Gaussian mixture (GM) models. The histograms of E0 and [Formula: see text] are best fit by two kernels GM for malignant tissues, indicating that the cells are soft but with high fluidity and the ECM is stiff but with low fluidity. However, the data suggest one-kernel GM model for benign tissue and a patched uniform distribution for healthy tissue. Third, using fluidity [Formula: see text] as the test statistic, the area under the receiver operator characteristic curve (AUC) is 0.701 ± 0.012 (p < 0.0001) for control versus malignant and 0.706 ± 0.013 (p < 0.0001) for benign versus malignant group. Variations in tissue fluidity and elasticity offer a concise set of viscoelastic biomarkers that correlate well with histopathological features.

Experimental Validation of Perfusion Imaging With HOSVD Clutter Filters.

Novel pulsed-Doppler methods for perfusion imaging are validated using dialysis cartridges as perfusion phantoms. Techniques that were demonstrated qualitatively at 24 MHz, in vivo, are here examined quantitatively at 5 and 12.5 MHz using phantoms with the blood-mimicking fluid flow within cellulose microfibers. One goal is to explore a variety of flow states to optimize measurement sensitivity and flow accuracy. The results show that 2-3-s echo acquisitions at roughly 10 frames/s yield the highest sensitivity to flows of 1-4 mL/min. A second goal is to examine methods for setting the parameters of higher order singular value decomposition (HOSVD) clutter filters. For stationary or moving clutter, the velocity of the blood-mimicking fluid in the microfibers is consistently estimated within measurement uncertainty (mean coefficient of variation = 0.26). Power Doppler signals were equivalent for stationary and moving clutter after clutter filtering, increasing approximately 3 dB/mL/min of blood-mimicking fluid flow for 0 ≤ q ≤ 4 mL/min. Comparisons between phantom and preclinical images show that peripheral perfusion imaging can be reliably achieved without contrast enhancement.

Imaging the Landmarks of Vascular Recovery.

Background: Peripheral arterial disease (PAD) is a major worldwide health concern. Since the late 1990s therapeutic angiogenesis has been investigated as an alternative to traditional PAD treatments. Although positive preclinical results abound in the literature, the outcomes of human clinical trials have been discouraging. Among the challenges the field has faced has been a lack of standardization of the timings and measures used to validate new treatment approaches. Methods: In order to study the spatiotemporal dynamics of both perfusion and neovascularization in mice subjected to surgically-induced hindlimb ischemia (n= 30), we employed three label-free imaging modalities (a novel high-sensitivity ultrasonic Power Doppler methodology, laser speckle contrast, and photoacoustic imaging), as well as a tandem of radio-labeled molecular probes, 99mTc-NC100692 and 99mTc-BRU-5921 respectively, designed to detect two key modulators of angiogenic activity, αVß3 and HIF-1α , via scintigraphic imaging. Results: The multimodal imaging strategy reveals a set of "landmarks"-key physiological and molecular events in the healing process-that can serve as a standardized framework for describing the impact of emerging PAD treatments. These landmarks span the entire process of neovascularization, beginning with the rapid decreases in perfusion and oxygenation associated with ligation surgery, extending through pro-angiogenic changes in gene expression driven by the master regulator HIF-1α , and ultimately leading to complete functional revascularization of the affected tissues. Conclusions: This study represents an important step in the development of multimodal non-invasive imaging strategies for vascular research; the combined results offer more insight than can be gleaned through any of the individual imaging methods alone. Researchers adopting similar imaging strategies and will be better able to describe changes in the onset, duration, and strength of each of the landmarks of vascular recovery, yielding greater biological insight, and enabling more comprehensive cross-study comparisons. Perhaps most important, this study paves the road for more efficient translation of PAD research; emerging experimental treatments can be more effectively assessed and refined at the preclinical stage, ultimately leading to better next-generation therapies.

Physics-guided machine learning for 3-D quantitative quasi-static elasticity imaging.

We present a 3D extension of the Autoprogressive Method (AutoP) for quantitative quasi-static ultrasonic elastography (QUSE) based on sparse sampling of force-displacement measurements. Compared to current model-based inverse methods, our approach requires neither geometric nor constitutive model assumptions. We build upon our previous report for 2D QUSE and demonstrate the feasibility of recovering the 3D linear-elastic material property distribution of gelatin phantoms under compressive loads. Measurements of boundary geometry, applied surface forces, and axial displacements enter into AutoP where a Cartesian neural network constitutive model (CaNNCM) interacts with finite element analyses to learn physically consistent material properties with no prior constitutive model assumption. We introduce a new regularization term uniquely suited to AutoP that improves the ability of CaNNCMs to extract information about spatial stress distributions from measurement data. Results of our study demonstrate that acquiring multiple sets of force-displacement measurements by moving the US probe to different locations on the phantom surface not only provides AutoP with the necessary information for a CaNNCM to learn the 3D material property distribution, but may significantly improve the accuracy of the Young's modulus estimates. Furthermore, we investigate the trade-offs of decreasing the contact area between the US transducer and phantom surface in an effort to increase sensitivity to surface force variations without additional instrumentation. Each of these modifications improves the ability of CaNNCMs trained in AutoP to learn the spatial distribution of Young's modulus from force-displacement measurements.

Data-Driven Elasticity Imaging Using Cartesian Neural Network Constitutive Models and the Autoprogressive Method.

Quasi-static elasticity imaging techniques rely on model-based mathematical inverse methods to estimate mechanical parameters from force-displacement measurements. These techniques introduce simplifying assumptions that preclude exploration of unknown mechanical properties with potential diagnostic value. We previously reported a data-driven approach to elasticity imaging using artificial neural networks (NNs) that circumvents limitations associated with model-based inverse methods. NN constitutive models can learn stress-strain behavior from force-displacement measurements using the autoprogressive (AutoP) method without prior assumptions of the underlying constitutive model. However, information about internal structure was required. We invented Cartesian NN constitutive models (CaNNCMs) that learn the spatial variations of material properties. We are presenting the first implementation of CaNNCMs trained with AutoP to develop data-driven models of 2-D linear-elastic materials. Both simulated and experimental force-displacement data were used as input to AutoP to show that CaNNCMs are able to model both continuous and discrete material property distributions with no prior information of internal object structure. Furthermore, we demonstrate that CaNNCMs are robust to measurement noise and can reconstruct reasonably accurate Young's modulus images from a sparse sampling of measurement data. CaNNCMs are an important step toward clinical use of data-driven elasticity imaging using AutoP.

Modeling Ramp-hold Indentation Measurements based on Kelvin-Voigt Fractional Derivative Model.

Interpretation of experimental data from micro- and nano-scale indentation testing is highly dependent on the constitutive model selected to relate measurements to mechanical properties. The Kelvin-Voigt Fractional Derivative model (KVFD) offers a compact set of viscoelastic features appropriate for characterizing soft biological materials. This paper provides a set of KVFD solutions for converting indentation testing data acquired for different geometries and scales into viscoelastic properties of soft materials. These solutions, which are mostly in closed-form, apply to ramp-hold relaxation, load-unload and ramp-load creep-testing protocols. We report on applications of these model solutions to macro- and nano-indentation testing of hydrogels, gastric cancer cells and ex vivo breast tissue samples using an Atomic Force Microscope (AFM). We also applied KVFD models to clinical ultrasonic breast data using a compression plate as required for elasticity imaging. Together the results show that KVFD models fit a broad range of experimental data with a correlation coefficient typically R2 > 0.99. For hydrogel samples, estimation of KVFD model parameters from test data using spherical indentation versus plate compression as well as ramp relaxation versus load-unload compression all agree within one standard deviation. Results from measurements made using macro- and nano-scale indentation agree in trend. For gastric cell and ex vivo breast tissue measurements, KVFD moduli are, respectively, 1/3 - 1/2 and 1/6 of the elasticity modulus found from the Sneddon model. In vivo breast tissue measurements yield model parameters consistent with literature results. The consistency of results found for a broad range of experimental parameters suggest the KVFD model is a reliable tool for exploring intrinsic features of the cell/tissue microenvironments.

Multidimensional Clutter Filter Optimization for Ultrasonic Perfusion Imaging.

Combinations of novel pulse-echo acquisitions and clutter filtering techniques can improve the sensitivity and the specificity of power Doppler (PD) images, thus reducing the need for exogenous contrast enhancement. We acquire echoes following bursts of Doppler pulse transmissions sparsely applied in regular patterns over long durations. The goal is to increase the sensitivity of the acquisition to slow disorganized patterns of motion from the peripheral blood perfusion. To counter a concomitant increase in clutter signal power, we arrange the temporal echo acquisitions into two data-array axes, combine them with a spatial axis for the tissue region of interest, and apply 3-D singular-value decomposition (SVD) clutter filtering. Successful separation of blood echoes from other echo signal sources requires that we partition the 3-D SVD core tensor. Unfortunately, the clutter and blood subspaces do not completely uncouple in all situations, so we developed a statistical classifier that identifies the core tensor subspace dominated by tissue clutter power. This paper describes an approach to subspace partitioning as required for optimizing PD imaging of peripheral perfusion. The technique is validated using echo simulation, flow-phantom data, and in vivo data from a murine melanoma model. We find that for narrow eigen-bandwidth clutter signals, we can routinely map phantom flows and tumor perfusion signals at speeds less than 3 mL/min. The proposed method is well suited to peripheral perfusion imaging applications.

Method for Recovering Lost Ultrasonic Information Using the Echo-intensity Mean.

The axial resolution of a B-mode (or intensity) image is limited by the bandwidth of the pulse envelope. In this report, we investigate the source of this limitation by examining the transfer of high-resolution information from the tissue impedance variance throughout the imaging process. For that purpose, we express the mean and variance of the echo-intensity signal as a linear system to track the flow of object information along the image-formation chain. The results reveal how demodulation influences the available information by discarding high spatial-frequency information. This analysis further points to a simple way to recover lost information with only a minor addition to signal processing. Software phantoms are used to show that under ideal conditions, information from small-scale high-contrast reflectors, such as microcalcifications, can be significantly enhanced with this simple change to echo processing.

Improvements to ultrasonic beamformer design and implementation derived from the task-based analytical framework.

The task-based framework, previously developed for beamformer comparison [Nguyen, Prager, and Insana, J. Acoust. Soc. Am. 140, 1048-1059 (2016)], is extended to design a new beamformer with potential applications in breast cancer diagnosis. The beamformer is based on a better approximation of the Bayesian strategy. It is a combination of the Wiener-filtered beamformer and an iterative process that adapts the generated image to specific features of the object. Through numerical studies, the new method is shown to outperform other beamformers drawn from the framework, but at an increase in computational cost. It requires a preprocessing step where the scattering field is segmented into regions with distinct statistical properties. Segmentation errors become a major limitation to the beamformer performance. All the beamformers under investigation are tested using data obtained from an instrumented ultrasound machine. They are implemented using a new time delay calculation, recently developed in the pixel-based beamforming studies presented here, which helps to overcome the challenge posed by the shift-variant nature of the imaging system. The efficacy of each beamformer is evaluated based on the quality of generated images in the context of the task-based framework. The in vitro results confirm the conclusions drawn from the simulations.

Expanding Acquisition and Clutter Filter Dimensions for Improved Perfusion Sensitivity.

A method is explored for increasing the sensitivity of power-Doppler imaging without contrast enhancement. We acquire 1-10 s of echo signals and arrange it into a 3-D spatiotemporal data array. An eigenfilter developed to preserve all three dimensions of the array yields power estimates for blood flow and perfusion that are well separated from tissue clutter. This method is applied at high frequency (24-MHz pulses) to a murine model of an ischemic hindlimb. We demonstrate enhancements to tissue perfusion maps in normal and ischemic tissues. The method can be applied to data from any ultrasonic instrument that provides beamformed RF echo data.

Assessing composition and structure of soft biphasic media from Kelvin-Voigt fractional derivative model parameters.

Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques - ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulus E0 closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material's fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, EA . The slope of EA versus η is determined by α and the applied indentation ramp time Tr. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the η - EA relation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties.

Linear System Models for Ultrasonic Imaging: Intensity Signal Statistics.

Despite a great deal of work characterizing the statistical properties of radio frequency backscattered ultrasound signals, less is known about the statistical properties of demodulated intensity signals. Analysis of intensity is made more difficult by a strong nonlinearity that arises in the process of demodulation. This limits our ability to characterize the spatial resolution and noise properties of B-mode ultrasound images. In this paper, we generalize earlier results on two-point intensity covariance using a multivariate systems approach. We derive the mean and autocovariance function of the intensity signal under Gaussian assumptions on both the object scattering function and acquisition noise, and with the assumption of a locally shift-invariant pulse-echo system function. We investigate the limiting cases of point statistics and a uniform scattering field with a stationary distribution. Results from validation studies using simulation and data from a real system applied to a uniform scattering phantom are presented. In the simulation studies, we find errors less than 10% between the theoretical mean and variance, and sample estimates of these quantities. Prediction of the intensity power spectrum (PS) in the real system exhibits good qualitative agreement (errors less than 3.5 dB for frequencies between 0.1 and 10 cyc/mm, but with somewhat higher error outside this range that may be due to the use of a window in the PS estimation procedure). We also replicate the common finding that the intensity mean is equal to its standard deviation (i.e., signal-to-noise ratio = 1) for fully developed speckle. We show how the derived statistical properties can be used to characterize the quality of an ultrasound linear array for low-contrast patterns using generalized noise-equivalent quanta directly on the intensity signal.

Limitations on estimation of effective scatterer diameters.

The influence of spatial diversity in acoustic scattering properties on estimates of the effective scatterer diameter (ESD) applied to soft biological tissues is investigated. This study is based on two-dimensional simulations of scattering media, beginning with random distributions of simple disk structures where all scattering features are known exactly. It concludes with an analysis of histology maps from healthy and fatty rabbit liver. Further, the liver histology is decomposed using an orthonormal basis to separate acoustic scattering at various spatial scales and observe how it influences ESD estimates. Overall, the goal is to quantitatively interpret ESD results for diagnostic assessments despite wide variations in tissue scatterer properties.

An information-based machine learning approach to elasticity imaging.

An information-based technique is described for applications in mechanical property imaging of soft biological media under quasi-static loads. We adapted the Autoprogressive method that was originally developed for civil engineering applications for this purpose. The Autoprogressive method is a computational technique that combines knowledge of object shape and a sparse distribution of force and displacement measurements with finite-element analyses and artificial neural networks to estimate a complete set of stress and strain vectors. Elasticity imaging parameters are then computed from estimated stresses and strains. We introduce the technique using ultrasonic pulse-echo measurements in simple gelatin imaging phantoms having linear-elastic properties so that conventional finite-element modeling can be used to validate results. The Autoprogressive algorithm does not require any assumptions about the material properties and can, in principle, be used to image media with arbitrary properties. We show that by selecting a few well-chosen force-displacement measurements that are appropriately applied during training and establish convergence, we can estimate all nontrivial stress and strain vectors throughout an object and accurately estimate an elastic modulus at high spatial resolution. This new method of modeling the mechanical properties of tissue-like materials introduces a unique method of solving the inverse problem and is the first technique for imaging stress without assuming the underlying constitutive model.