Patent Publication Number: US-2022211350-A1

Title: Methods, systems, and computer readable media for generating images of microvasculature using ultrasound

Description:
PRIORITY APPLICATION 
     This application claims the priority benefit of U.S. Provisional Patent Application Ser. No. 62/846,133, filed May 10, 2019, the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     GOVERNMENT INTEREST 
     This invention was made with government support under Grant Numbers CA220681 and CA189479 awarded by the National Institutes of Health. The government has certain rights in the invention. 
    
    
     TECHNICAL FIELD 
     The subject matter described herein relates to generating images of the microvasculature. More particularly, the subject matter described herein relates to methods, systems, and computer readable media for generating images of the microvasculature using ultrasound. 
     BACKGROUND 
     Traditional ultrasound imaging, with or without contrast agents, is ‘diffraction limited’. This means that the best case resolution of the imaging system is dictated by the frequency of the ultrasound wave, the pulse length, and the beam diameter. The beam diameter is also a function of the aperture (aperture is the size—i.e., the diameter, if the transducer is circular) of the transducer and the distance of the transducer to the target (focal length). These constraints are for circular transducers, but the physics is similar for rectangular transducers. That means, for example, that the best case axial resolution is one half of the pulse length, i.e., the spatial extent of the acoustic pulse. For clinical ultrasound systems that operate between 2-10 MHz, for example, the best resolution is on the order of a few hundred microns. If you have two 50 micron vessels 50 microns apart, they will be blurred into one vessel. 
     Accordingly, in light of these difficulties, there exists a need for improved methods, systems and computer readable media for generating images of the microvasculature using ultrasound. 
     SUMMARY 
     A method for producing an image of at least one vessel with ultrasound includes administering a contrast agent particle into the at least one vessel, and delivering an ultrasound pulse having a first frequency range to the at least one vessel. The method further includes detecting ultrasound energy scattered from the contrast agent particle at a second frequency range that is different from the first frequency range, converting the scattered ultrasound energy into an electronic radio frequency signal, and using an algorithm to determine a spatial location of the contrast agent particle based on extraction of a specific feature of the radio frequency signal. The method further includes generating an image by displaying a marker of the spatial location of the contrast agent particle with a resolution that is finer than a pulse length of the ultrasound pulse and repeating the detecting, converting, using, and generating for a plurality of contrast agent particles until sufficient markers have been accumulated to reconstruct a pattern of the at least one vessel; wherein the pattern is an image of the at least one vessel. 
     According to one aspect of the subject matter described herein, a resolution of the image is at least twice as fine as the pulse length of the ultrasound pulse. 
     According to another aspect of the subject matter described herein, the at least one vessel comprises a blood vessel, a lymphatic vessel, or part of a venous or capillary network in a human body. 
     According to yet another aspect of the subject matter described herein, endothelial cells within the at least one vessel express a biomarker which causes the contrast agent particles to adhere to a wall of the at least one vessel. 
     According to yet another aspect of the subject matter described herein, the particles are stationary within the at least one vessel. 
     According to yet another aspect of the subject matter described herein, the pattern is an image of contrast agent particle distribution within vessels of tissue, an organ, or a tumor. 
     According to yet another aspect of the subject matter described herein, the contrast agent particle is first detected by detecting ultrasound energy scattered from the contrast agent particle after exciting the contrast agent particle with ultrasound energy in the first frequency range with a single pulse. 
     According to yet another aspect of the subject matter described herein, the mean or the median of the second frequency range detected is at least double or at least triple the mean or the median of the first frequency range. 
     According to yet another aspect of the subject matter described herein, detecting the ultrasound energy scattered from the contrast agent particle utilizes transmitting and receiving ultrasound transducers having at least one of non-overlapping −6 dB bandwidths and non-overlapping −12 dB bandwidths. 
     According to yet another aspect of the subject matter described herein, the contrast agent particles include at least one of microbubbles and nanobubbles. 
     According to yet another aspect of the subject matter described herein, the contrast agent particles include phase-change agents each comprising a liquid perfluorocarbon core prior to ultrasound exposure. 
     According to yet another aspect of the subject matter described herein, the algorithm includes high pass filtering followed by a thresholding operation. 
     According to yet another aspect of the subject matter described herein, the algorithm includes using a centroid of the radio frequency signal to estimate a location of the contrast agent particle. 
     According to yet another aspect of the subject matter described herein, the algorithm includes using an onset of the radio frequency signal to estimate the location of the contrast agent particle. 
     According to yet another aspect of the subject matter described herein, the algorithm allows calculation of a velocity and a direction of the contrast agent particle. 
     According to yet another aspect of the subject matter described herein, the algorithm determines the spatial location of the contrast agent particle without using a singular value decomposition filter. 
     According to another aspect of the subject matter described herein, the ultrasound pulse having a first frequency range is transmitted with zero phase delay across a plurality of elements of a transmitting ultrasound transducer to emit a plane wave into the at least one vessel. 
     According to yet another aspect of the subject matter described herein, the system of claim  20  wherein the first frequency range is between 0.5 and 5 MHz, and the second frequency range is between 5 and 50 MHz. 
     According to yet another aspect of the subject matter described herein, a system for producing an image of at least one vessel using ultrasound is provided. The system includes at least one ultrasound transducer for delivering an ultrasound pulse having a first frequency range to at least one vessel infused with a contrast agent particle, for detecting ultrasound energy scattered from the contrast agent particle at a second frequency range that is different from the first frequency range, and for converting the scattered ultrasound energy into an electronic radio frequency signal. The system further includes a super-resolution processor for using an algorithm to determine a spatial location of the contrast agent particle based on extraction of a specific feature of the radio frequency signal, generating an image by displaying a marker of the spatial location of the contrast agent particle with a resolution that is finer than a pulse length of the ultrasound pulse, and repeating the detecting, converting, using, and generating for a plurality of contrast agent particles until sufficient markers have been accumulated to reconstruct a pattern of the at least one vessel; wherein the pattern is an image of the at least one vessel. 
     According to yet another aspect of the subject matter described herein, a non-transitory computer readable medium having stored thereon executable instructions that when executed by a processor of a computer control the computer to perform steps is provided. The steps include controlling at least one ultrasound transducer for delivering an ultrasound pulse having a first frequency range to at least one vessel infused with a contrast agent, detecting ultrasound energy scattered from the contrast agent particle at a second frequency range that is different from the first frequency range, and converting the scattered ultrasound energy into an electronic radio frequency signal. The steps further include using an algorithm to determine a spatial location of the contrast agent particle based on extraction of a specific feature of the radio frequency signal. The steps further include generating an image by displaying a marker of the spatial location of the contrast agent particle with a resolution that is finer than a pulse length of the ultrasound pulse. The steps further include repeating the detecting, converting, using, and generating for a plurality of contrast agent particles until sufficient markers have been accumulated to reconstruct a pattern of the at least one vessel; wherein the pattern is an image of the at least one vessel. 
     The subject matter described herein may be implemented in hardware, software, firmware, or any combination thereof. As such, the terms “function,” “node,” or “module” as used herein refer to hardware, which may also include software and/or firmware components, for implementing the feature being described. In one exemplary implementation, the subject matter described herein may be implemented using a computer readable medium having stored thereon computer executable instructions that when executed by the processor of a computer control the computer to perform steps. Exemplary computer readable media suitable for implementing the subject matter described herein include non-transitory computer-readable media, such as disk memory devices, chip memory devices, programmable logic devices, and application specific integrated circuits. In addition, a computer readable medium that implements the subject matter described herein may be located on a single device or computing platform or may be distributed across multiple devices or computing platforms. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The subject matter described herein will now be explained with reference to the accompanying drawings of which: 
         FIG. 1  is a block diagram of a test setup for evaluating the imaging capabilities of dual-frequency mode microvasculature imaging; 
         FIG. 2  is a block diagram of a system for imaging the microvasculature using dual-frequency ultrasound imaging; 
         FIGS. 3A and 3B  are a flow chart illustrating an exemplary process for imaging the microvasculature using dual-frequency ultrasound imaging; 
         FIG. 4A  is a schematic diagram of the elevation cross section of the dual frequency (DF) assembly with low frequency (LF) transducers (outer two transducers) and high frequency (HF) array (center transducer). W=2.9 mm, α=27°, (y c , z c )=(8.45 mm, 0.73 mm); 
         FIG. 4B  is an image of the DF probe used in experiments, illustrating the 1.7 MHz LF transducers running parallel to the 21-MHz HF transducer array on the front face; 
         FIG. 4C  is Hydrophone measurement of the LF beam pattern in the elevational-axial plane. The −6-dB contour of the beam is marked with a dashed line. The axial dimension is measured relative to the face of the HF array,  FIGS. 4A and 4B  are reproduced from Cherin et al. with permission [26]; 
         FIGS. 5A-5C  illustrate an overview of data collection and processing for superharmonic ULM.  FIG. 5A  illustrates an imaging sequence used for this study. Chunks of 100 DF frames collected at a frame rate of 500 Hz are separated by b-mode frames for motion tracking. RF data are saved after 1000 DF frames. In  FIG. 5B , speckle tracking is performed between a manually selected reference frame and each b-mode frame to estimate the non-rigid deformation of the kidney during imaging. In  FIG. 5C , DF images are processed using a threshold and peak detector to localize MBs. These positions are then corrected according to the displacements estimated from speckle tracking or thrown out if the parent b-mode patch is not well correlated with the reference patch; 
         FIGS. 6A-6C  illustrate a comparison of super harmonic imaging—ultrasound localization microscopy (SHI-ULM) and acoustic angiography (AA), which is a superharmonic imaging technique, using a pair of 46-μm tubes in a water bath. The scale bars in the upper left-hand corners of  FIGS. 6A and 6B  are 500 μm.  FIG. 6A  is a SHI-ULM image generated from 25000 frames.  FIG. 6B  is a maximum intensity projection (MIP) of the super harmonic imaging (SHI) frames used to generate the image in  FIG. 6A .  FIG. 6C  is a graph of average profiles within the regions of interest from  FIGS. 6A and 6B . In  FIG. 6C , the inner (narrower) peak is for SHI-ULM. The outer or wider profile peak is for dual-frequency MIP. The full width at half maximum (FWHM) values of the acoustic angiography (AA) and SHI-ULM profiles are 113 and 44 μm, respectively; demonstrating that SHI-ULM can resolve the true tube diameter, even though superharmonic imaging cannot. 
         FIGS. 7A and 7B  are velocity maps of crossed 46-μm tubes in a water bath. The scale bars in the top left hand corners of  FIGS. 7A and 7B  are 500 μm.  FIG. 7A  is a direction map with flow direction indicated by the color wheel.  FIG. 7B  is a map of the average speed for each pixel. 
         FIGS. 8A-8D  are MIPs for singular value decomposition (SVD)-filtered and superharmonic images of a 200-μm tube in different flow regimes. All images are displayed on a 25-dB dynamic range for comparison.  FIG. 8A  is a MIP of superharmonic images collected at 0.25 μL/min.  FIG. 8B  is a MIP of superharmonic images collected at 15.0 μL/min.  FIG. 8C  is a MIP of SVD-filtered images collected at 0.25 μL/min.  FIG. 8D  is a MIP of SVD-filtered images collected at 15.0 μL/min; 
         FIG. 9  is a graph of SNR versus flow rate for DF and SVD-filtered images. The upper plot in  FIG. 9  is for DF-filtered images, and the lower plot in  FIG. 9  is for SVD-filtered images. DF imaging results in an average improvement of 10.3 dB over SVD imaging, even at slow flow rates below 5 microns/frame; 
         FIGS. 10A-10C  illustrate examples of SHI-ULM applied to a rodent kidney with motion correction.  FIG. 10A  is a b-mode scan of the kidney used as a reference for motion correction.  FIG. 10B  is a MIP of superharmonic images used to generate the SHI-ULM image (frames with motion discarded).  FIG. 10C  is a SHI-ULM image generated from 25000 frames with motion correction applied; 
         FIGS. 11A-11C  illustrate selected vessels from the rodent kidney 3-D data set. More particularly,  FIGS. 11A-11C  illustrate example vessels cropped from SHI-ULM images.  FIG. 11D  is a graph illustrating average profiles of the vessels in  FIGS. 11A-11C  with FWHM values of 20.9, 17.2, and 29.1 μm, respectively; 
         FIGS. 12A and 12B  illustrate a comparison of SHI-ULM with and without motion correction based on sparsely interleaved b-mode frames.  FIG. 12A  illustrates rodent kidney vessels are smeared out by respiratory and cardiac motion artifacts.  FIG. 12B  illustrates fine detail of the vessel structure is recovered by a combination of removal of decorrelated frames and using speckle tracking to estimate nonrigid displacements; 
         FIGS. 13A and 13B  are velocity maps tracking bubbles in vivo allows for the mapping of blood velocity in a rodent kidney.  FIG. 13A  illustrates the average direction of MBs for the SHI-ULM image in  FIG. 10C .  FIG. 13B  illustrated the magnitude of the velocity for the same data set; 
         FIG. 14  is an example of a 3-D SHI-ULM by mechanically scanning the transducer in the elevational dimension. This image was generated with 17 slices spaced at 500 μm and contains vessels on the order of 20 μm; and 
         FIGS. 15A and 15B  illustrate examples of super-resolution molecular imaging in-vivo in a rodent tumor model. The scale bar on the lower left hand corner of  FIG. 15B  is 1 mm.  FIG. 15A  is a b-mode image from the center slice of the tumor.  FIG. 15B  is a SHI-ULM vascular image shown in grayscale overlaid with localizations of VEGFR2-targeted microbubbles (small dots in image). The ULM image is a maximum intensity projection from 5 slices spaced by 1 mm. 
     
    
    
     DETAILED DESCRIPTION 
     In order to address the resolution issues with diffraction limited ultrasound, the subject matter described herein utilizes a technique called ultrasound localization microscopy, or super-resolution imaging, which allows you to image vessels below the diffraction limit. Microbubble contrast agents are injected into vessels, detected, and then used to create images of vessels with resolution as small as 20 microns, or smaller, whereas diffraction limited ultrasound resolution would be approximately 10× worse. However, these techniques involve detecting the presence of microbubbles either by their movement (usually through a singular value decomposition filter or similar technique). The subject matter described herein includes improvements to super-resolution imaging by providing a mechanism for detecting these microbubbles using a difference in the frequency of ultrasound that the microbubbles scatter, compared to the frequency of ultrasound that is sent into the sample volume. Specifically, this frequency difference is quite large, ideally receiving above the third harmonic of the transmitted frequency. In one exemplary implementation, we transmit with a 2 MHz transmitter and receive with a 20 MHz receiver. Because we are using a very wideband transducer, and we are listening to frequencies of ultrasound far above what is transmitted, the bubbles can be detected with good sensitivity and there is a very low noise background from tissue, which otherwise confounds bubble detection. The result is that the bubbles do not need to be moving to be detected, or they can be detected even when moving very slowly. After this detection of bubbles using the frequency difference, we can perform some of the analysis steps of super-resolution imaging to make images of vessels with a resolution finer than that using diffraction limited ultrasound imaging. 
     The following steps illustrate an example of data acquisition for producing an image of a vessel using ultrasound.
     1.) A contrast agent is administered to a subject, preferably into a blood vessel or lymphatic vessel. The subject may be a human patient, a non-human animal, or in an in-vitro vessel. The contrast agent may be a microbubble, a nanobubble, or a phase change liquid perfluorocarbon nanodroplet.   2.) A low-frequency pulse generated by a wide-bandwidth ultrasonic transducer is transmitted into the subject, causing the contrast agent to change diameter, typically in an oscillatory fashion. As the contrast agent oscillates, the contrast agent scatters ultrasound of many different frequencies. In one implementation, an ultrasound transducer with separate transmit and receive arrays or elements which provide a very wide bandwidth can be used to transmit the ultrasound pulse into the subject. In an alternate implementation, a CMUT (capacitive micromachined ultrasonic transducer), which has a wide bandwidth, may be used to transmit and detect the ultrasound energy.   3.) The echoes scattered by the contrast agent are detected by an ultrasound transducer (either the transmitting transducer or a separate transducer).   4.) One aspect of the subject matter described herein is the combination of ultrasound imaging where the frequency content of the scattered echoes received is higher than that of the low-frequency pulse transmitted into the subject with super-resolution imaging. One example of an ultrasound imaging technique suitable for use with the subject matter described herein is described in U.S. Pat. No. 9,553,769, the disclosure of which is incorporated herein by reference in its entirety.   5.) The above process is repeated successive times to gather many hundreds of samples of the same volume.   

     Once the scattered ultrasound energy measurements are collected, the measurements are used to generate a super-resolution image of the vessel. The following are exemplary steps for vessel image formation.
     1.) Radio frequency (RF) echo data are filtered to isolate the contrast agent acoustic response from that of the tissue. Typically, a high-pass filter would be applied to the received echoes, so that only the echoes returning from the contrast agent, and not any low frequency echoes scattered from tissue, would be preserved.   2.) Dynamic receive beamforming is used to generate a stack of b-mode images from the RF data.   3.) A threshold is applied to each b-mode image. Each pixel in the resulting image is equal to the original image value if the reference pixel value is greater than or equal to the threshold, and zero otherwise.   4.) A mechanism is used to estimate the location of the contrast agent. One mechanism would be to use a Gaussian kernel with a root mean squared (RMS) width equal to that of the point-spread function (PSF) of the imaging system, which is convolved over the stack of images generated in step 3. Contrast agent centroids are estimated using either center-of-mass for each connected component or by using a simple peak detection (slightly faster).   5.) In one implementation, particle tracking is performed on each stack of centroid images and line segments are drawn between particles that appear in adjacent frames.   6.) Contrast agent locations from the centroid (step 4) or line segments (step 5) are accumulated over many frames to generate a super-resolved image of the vessels in the sample volume.   

     Additional examples of super-resolution processing techniques suitable for use with the subject matter described herein are provided in Couture, et al., Ultrasound Location Microscopy and Super Resolution: A State of the Art, IEEE Transaction on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 65, No. 8, August 2018 and Christensen-Jeffries et al., Microbubble Axial Localization Errors in Ultrasound Super-Resolution Imaging, the disclosures of which are incorporated herein by reference in their entireties. 
       FIG. 1  is a block diagram of a test system used to evaluate the vessel imaging methodology described herein. Referring to  FIG. 1 , simulated vessels  100  and  102  are suspended in a water tank  104 . Each simulated vessel is infused with a contrast agent, such as microbubbles, nanobubbles, or a phase change agent that forms microbubbles or nanobubbles when exposed to ultrasound energy. The infusion is controlled by infusion pumps  106  and  108 . A dual-frequency ultrasound transducer array  110  is at least partially immersed in water tank  104 . A low frequency ultrasound system  112  generates low frequency ultrasound energy and delivers the energy to a transducer array  110 . Transducer array  110  transmits the low frequency ultrasound energy into simulated vessels  100  and  102  where the energy is scattered by contrast agent particles. 
     Transducer array  110  detects the scattered ultrasound energy at a frequency higher than the transmitted ultrasound energy and converts the scattered ultrasound signal into a radio frequency signal. A super-resolution processor  114  associated with a high frequency ultrasound system  116  detects a spatial location of a contrast agent particle in simulated vessels  100  and  102  using an algorithm to determine spatial locations of contrast agent particles based on extraction of a specific feature of the radio frequency signal. Super-resolution processor  114  generates an image of the simulated vessels by displaying a marker of the spatial location of a contrast agent particle with a resolution that is finer than the pulse length of the ultrasound pulse and repeating the detecting, converting, using, and generating for a plurality of contrast agent particles until sufficient markers have been accumulated to reconstruct a pattern of the vessel; where the pattern is an image of the at least one vessel. 
       FIG. 2  is a block diagram of a system for imaging a vessel using ultrasound. In  FIG. 2 , one or more ultrasound transducers  110  delivers ultrasound energy into at least one vessel of a subject  200 , where the vessel or vessels are infused with an ultrasound enhancing contrast agent delivered by one or more contrast agent infusion devices  202 . Contrast agent infusion devices  202  may be infusion pumps, syringes, or other devices capable of delivering a contrast agent into a vessel of a subject. Subject  200  may be a human, a non-human animal, or an in-vitro vessel. The vessels being imaged may be blood vessels, lymphatic vessels, or part of a venous or capillary network in a human body. In another example, endothelial cells within the vessel express a biomarker which causes the contrast agent particles to adhere to the walls of the vessel. Unlike conventional super-resolution imaging, using the system illustrated in  FIG. 2 , the contrast agent and the corresponding vessel structure can be imaged even when the contrast agent is not moving or moving very slowly. The contrast agent may be least one of microbubbles, nanobubbles, and are phase-change agents comprising a liquid perfluorocarbon core prior to ultrasound exposure. 
     The ultrasound energy delivered by ultrasound transducers  110  is scattered by the contrast agent and by structures within subject  200 . However, the system illustrated in  FIG. 2  can differentiate between energy scattered by the contrast agent and by other structures, in part, by transmitting an ultrasound pulse having a first frequency range and detecting scattered ultrasound energy on a second frequency range that is different from the first frequency range. In one example, the −6 dB bandwidths of the receiving and transmitting ultrasound transducers do not overlap. In another example, the −12 dB bandwidths of the receiving and transmitting ultrasound transducers do not overlap. In one example, the mean and/or the median of the second frequency range detected is at least double or at least triple the mean and/or the median of the first frequency range. In one example, ultrasound transducers  110  may deliver a single pulse of ultrasound energy to subject  200 , and the scattered ultrasound energy may be first detected after transmission of the single pulse. 
     Ultrasound transducers  110  convert the scattered ultrasound energy into a radio frequency signal and provides the radio frequency signal to super-resolution processor  114 . Super-resolution processor  114  uses an algorithm to determine a spatial location of the contrast agent particle based on extraction of a specific feature of the radio frequency signal, generates an image by displaying a marker of the spatial location of the contrast agent particle with a resolution that is finer than a pulse length of the ultrasound pulse, and repeats the processes of detecting, converting, using, and generating for a plurality of contrast agent particles until sufficient markers have been accumulated to reconstruct a pattern of the at least one vessel; wherein the pattern is an image of the at least one vessel. In one example, the resolution of the image generated by super-resolution processor  114  is at least twice as fine as the pulse length of the ultrasound pulse. For example, if the transmitted ultrasound frequency is 2 MHz, the transmitted pulse has a wavelength of 0.77 mm in soft tissue. The resolution of the resulting reconstructed image will be at least 0.335 mm. The pattern generated by super-resolution processor  114  may be an image of contrast agent particle distribution within vessels of tissue, an organ, or a tumor. 
     The algorithm used by super-resolution processor  114  to determine the spatial locations of contrast agent particles may include high pass filtering followed by a thresholding operation. The algorithm may utilize a centroid of the radio frequency signal produced by ultrasound transducers  110  to estimate a location of the contrast agent particle. The algorithm may include using an onset of the radio frequency signal to estimate the location of the contrast agent particle. The algorithm may also provide for computing velocity and direction of movement of the ultrasound particles. In one example, the algorithm determines the spatial location of the contrast agent particle without using a singular value decomposition filter. 
     Super-resolution processor  114  may output the pattern as display data to a display device  204 . Display device  204  may be a display that is integrated with the ultrasound transducer or a separate display. The resulting displayed image may be similar to the image in  FIG. 6A . The resolution of the displayed image may be at least twice as fine as the pulse length of the ultrasound pulse transmitted into the vessel or vessels. 
       FIGS. 3A and 3B  are a flow chart illustrating an exemplary process for imaging a vessel using ultrasound. Referring to  FIG. 3A , in step  300 , the process includes administering a contrast agent particle into the at least one vessel. For example, at least one microbubble, nanobubble, or phase change agent that comprises a perfluorocarbon having a liquid core prior to exposure to ultrasound may be infused, injected, or otherwise placed into the vessel of a subject. 
     In step  302 , the process includes delivering an ultrasound pulse having a first frequency range to the at least one vessel. In one example, the ultrasound pulse may be a single pulse having a frequency range that is centered at 2 MHz. The first frequency range may be between 0.5 and 5 MHz. The ultrasound pulse may be transmitted simultaneously (with zero phase delay) across plural elements of the transmitting transducer to emit a plane wave into the at least one vessel. 
     In step  304 , the process includes detecting ultrasound energy scattered from the contrast agent particle at a second frequency range that is different from the first frequency range. In one example, the second frequency range may be centered at 20 MHz. The second frequency range may be between 5 and 50 MHz. As indicated above, the first and second frequency ranges may have non-overlapping −6 dB bandwidths, −12 dB bandwidths, or both. 
     In step  306 , the process includes converting the scattered ultrasound energy into an electronic radio frequency signal. This operation may be performed by the circuitry associated with the ultrasound transducer. 
     Referring to  FIG. 3B , in step  308 , the process includes using an algorithm to determine a spatial location of the contrast agent particle based on extraction of a specific feature of the radio frequency signal. In one example, super-resolution processor  114  may perform steps (4)-(6) above to determine the locations of contrast agent particles. 
     In step  310 , the process includes generating an image by displaying a marker of the spatial location of the contrast agent particle with a resolution that is finer than the pulse length of the ultrasound pulse. For example, each tracked particle location may be displayed as a pixel or pixels in image data that is generated to be sent to a display device. 
     In step  312 , the process includes repeating the detecting, converting, using, and generating for a plurality of contrast agent particles until sufficient markers have been accumulated to reconstruct a pattern of the vessel; where the pattern is an image of the vessel. For example, once a predetermined percentage of particles present in the vessel have been located, it may be determined that there is sufficient data for displaying an image of the vessel. When this occurs, the particle tracking may cease, and the final image may be displayed. The displayed image may be similar to that illustrated in  FIG. 6A . 
     The following section illustrates a study where super-harmonic imaging is used in combination with super-resolution imaging to image tubes in vitro, contrast agent flowing through the tubes, and rodent vessels in vivo. 
     Superharmonic Ultrasound for Motion-Independent Localization Microscopy: Applications to Microvascular Imaging From Low to High Flow Rates 
     Recent advances in high frame rate biomedical ultrasound have led to the development of ultrasound localization microscopy (ULM), a method of imaging 
     microbubble (MB) contrast agents beyond the diffraction limit of conventional coherent imaging techniques. By localizing and tracking the positions of thousands of individual MBs, ultrahigh resolution vascular maps are generated which can be further analyzed to study disease. Isolating bubble echoes from tissue signal is a key requirement for super-resolution imaging which relies on the spatiotemporal separability and localization of the bubble signals. To date, this has been accomplished either during acquisition using contrast imaging sequences or post-beamforming by applying a spatiotemporal filter to the b-mode images. Superharmonic imaging (SHI) is another contrast imaging method that separates bubbles from tissue based on their strongly nonlinear acoustic properties. This approach is highly sensitive, and, unlike spatiotemporal filters, it does not require decorrelation of contrast agent signals. Since this superharmonic method does not rely on bubble velocity, it can detect completely stationary and moving bubbles alike. In this work, we apply SHI to ULM and demonstrate an average improvement in SNR of 10.3-dB in vitro when compared with the standard singular value decomposition filter approach and an increase in SNR at low flow (0.27 μm/frame) from 5 to 16.5 dB. Additionally, we apply this method to imaging a rodent kidney in vivo and measure vessels as small as 20 μm in diameter after motion correction. 
     I. INTRODUCTION 
     Recently, super-resolution imaging with ultrasound localization microscopy (ULM) has attracted attention because it resolves blood vessels on the order of a few microns in diameter at centimeters in depth in vivo [1], [2]. A model relating the spatial localization error of microbubble (MB) contrast agents to arrival time estimation error predicts that for certain in vivo scenarios, such as human breast imaging, ULM will achieve resolutions on the order of 1 μm [3]. It has long been known that abnormal angiogenesis and vascular morphology are biomarkers for different diseases, including diabetes, inflammatory conditions, and cancer [4], [5]. Recently, imaging abnormal angiogenesis with ultrasound microvascular imaging techniques has been proposed as a method of identifying malignancies [6]-[8]. In this context, ULM has shown diagnostic potential by measuring tortuosity of blood vessel structure in subcutaneous tumors in a rodent model [9]. In addition to providing morphological data, ULM is also able to provide accurate quantification of blood flow velocity, which can be combined with other metrics, such as vessel distances, to create a rich characterization of the imaging target [10]. 
     Many different approaches to ULM are present in the literature, although the method for generating a super-resolved image with ultrasound can be described by three general components [11]. First, MB contrast agents are administered intravenously, and a series of frames is acquired (normally hundreds to hundreds of thousands). While some groups have reported success with clinical scanners constrained to lower frame rates (&lt;100 Hz) [2], [10], generally a high frame rate on the order of 1-10 kHz is used to perform accurate velocimetry after target localization. Second, the data set is processed to separate MB and tissue signals, which overlap in conventional ultrasound imaging. Popular approaches to this step will be subsequently discussed in this section. Finally, MBs are localized in each frame with subwavelength accuracy, and the positions are accumulated on a high-resolution grid. The bubble positions are typically tracked between frames to also create high-resolution blood velocity maps [2]. 
     As mentioned previously, a crucial step to the process of generating a ULM image is the separation of MB signals from background tissue signal. The most popular method of suppressing tissue speckle prior to localization is a filter based on singular value decomposition (SVD). The SVD filter isolates MBs by taking advantage of the different spatiotemporal coherences of tissue speckle and contrast agents [12], [13]. Although the MBs and tissue may be moving with the same velocity magnitude, the fact that the MBs are localized in space implies that they have far smaller spatial coherence lengths in the beamformed images. When tissue is relatively static within an ultrafast ensemble, its features tend to be represented in the first singular vectors, where the right singular vectors (also called temporal singular vectors in this context) have most of their energy near 0 Hz [12], [14]. Blood, on the other hand, flows at a range of velocities, and its scatterers decorrelate at varying rates over the course of an acquisition. Crucially, these scatterers decorrelate in spatially localized regions of the image. The energy from these scatterers, thus, tends to occupy a subspace of higher singular vectors in which the spatiotemporal vectors are higher frequency than those corresponding to tissue. As long as there is sufficient separation between the vector subspaces occupied by tissue and blood flow, a data set can be filtered to remove the tissue. 
     However, in the slow-flow regime, the tissue and blood singular vector subspaces significantly overlap, especially since the bubble signal can be orders of magnitude smaller than the tissue signal. Due to this low contrast, they can be 
     impossible to tease apart. In [13], it was demonstrated that SVD filtering of an ultrafast ensemble of b-mode images using a commercially available contrast agent in a flow phantom resulted in contrast-to-tissue ratios (CTRs) of 11 and 25 dB for flow rates of 2 and 20 mm/s, respectively, when imaging at 3000 frames/s. Furthermore, [14] has documented the difficulty in determining an appropriate singular vector threshold for the SVD filter in vivo. In their study, the most successful of 13 different threshold estimators was able to achieve a CTR within 10% of the maximum CTR for only 74% of in vivo data sets. The results are even worse for their manual threshold selection, where a relative CTR difference of 10% or less was achieved for only 13% of data sets. Although SVD-based processing has produced many impressive ULM images ([1], [9]), the results of [14] suggest that the performance of such a filter may suffer when applied to the smallest of capillaries where peak blood velocity ranges between 0.2 and 1.7 mm/s [15], [16]. Furthermore, SVD may not be appropriate for new applications, such as super resolution molecular imaging, in which bubbles would exhibit no motion relative to the tissue. 
     Another approach to contrast enhancement that has been used for ULM is nonlinear imaging [2], [17]. While spatiotemporal processing methods rely on the motion of contrast agents relative to tissue in slow time, nonlinear imaging sequences rely on the fact that MB contrast agents generate significantly more harmonic energy than tissue under most circumstances. For example, one study reports that imaging at 1.7-MHz center frequency results in a second harmonic that is 24-dB down compared with the fundamental for tissue and around 9-dB down for MBs [18]. To date, methods such as pulse inversion [19], amplitude modulation [20], [21], and more sophisticated combinations of phase and amplitude modulation [22] have achieved CTR on the order of 50 dB with commercially available contrast agents. 
     Superharmonic imaging (SHI) is a method of contrast-enhanced ultrasound that reconstructs images using the third- and higher order harmonics of the fundamental frequency of the transmit waveform [18]. The advantage of SHI is an improvement in CTR compared with fundamental and second harmonic imaging (40-dB increase reported in [18]), along with an increased resolution from the higher frequencies and reduced sidelobes [23]. These improvements come at the cost of decreased imaging performance at depth because of the rapid attenuation of high-frequency (HF) waves in tissue. SHI is extensively used for vascular imaging with an approach called acoustic angiography (AA) [24]. In the 
     previously mentioned study, an AA image is generated by receiving from the third to approximately the tenth harmonic of the MB frequency response by using an ultrawideband dual-frequency (DF) transducer (transmit center frequency: 4 MHz, receive center frequency: 30 MHz, both roughly 100% relative bandwidth), producing images of blood vessels with a resolution of approximately 150 μm. It has been shown that AA is able to resolve microvasculature in vivo with high CTR in both rodents and humans [24], [25], although this technique remains fundamentally diffraction limited. 
     Thus, in this document, we report a combination of SHI and super-resolution processing without the SVD filter. In this manner, we eliminate the need to detect MBs through their spatiotemporal coherence, and we also overcome the diffraction limitation of SHI. In this article, superharmonic ULM is performed using a novel DF array system with transmission at 1.7 MHz and a receive bandwidth centered at 20 MHz [26]. In vitro, we image a 46-μm inner diameter tube and compare the sensitivities of SHI- and SVD-based approaches to ULM with respect to flow velocity. In vivo, we target the rodent kidney and discuss strategies for motion correction in a DF imaging scheme. For both in vitro and in vivo studies, we compare the resolution of the images to AA maximum intensity projections (MIPs). Finally, we discuss the strengths and weaknesses of SHI for ULM along with areas of future work. 
     II. MATERIALS AND METHODS 
     A. Experimental Setup 
     1) Contrast Agent Preparation: MBs were prepared in-house according to [27]. Briefly, a 1-mM lipid solution comprising 90 mole % 1, 2-distearoyl-sn-glycero-3-phosphocholine and 10 mole % 1, 2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy(polyethylene glycol)-2000] was formulated in phosphate-buffered saline containing 15% (v/v) propylene glycol and 5% (v/v) glycerol. Aseptic lipid solution was packaged into 3-mL glass vials, and the air headspace was exchanged with decafluorobutane (C 4 F 10 ) prior to creating the MB emulsion by shaking in a VialMix (Lantheus Medical Imaging, N. Billerica, Mass.). Concentration and size distribution of the MB contrast agent were measured using an Accusizer 780 AD (Entegris, Billerica, Mass.); typical concentration was 3E10 MB/mL with an average diameter of 0.97 μm±0.51 μm (mode=0.6 μm, median=0.9 μm). 
     2) DF Transducer: A custom DF probe described in [26] was used for all imaging in this study (see  FIG. 4A ). Briefly, it consists of a commercial 256-element linear array transducer (MS250, VisualSonics, Toronto, Canada) outfitted with two low-frequency (LF) elements. The LF transmit beam has a depth of field of 11 mm with peak pressure at 20 mm in the axial dimension. The HF array has a center frequency measured at 18 MHz and relative bandwidth of 70%, while the LF elements have a center frequency of 1.7 MHz and relative bandwidth of 78%. This transducer can be operated in DF mode by transmitting with the LF elements and receiving with the HF array and in conventional mode by transmitting and receiving with the HF array. When operating in the DF mode, the transmit pulse is a single-cycle, cosine-windowed sine wave with a center frequency of 1.7 MHz [28]. The LF elements are driven by an arbitrary waveform generator (AWG 2021, Tektronix, Beaverton, Oreg., USA) connected to a 50-dB radio frequency (RF) power amplifier (240 L, ENI, Rochester, N.Y., USA). Receiving with the HF array is controlled by a Vantage 256 scanner (HF configuration, Verasonics, Kirkland, Wash.). 
     B. ULM Imaging Scheme 
     All ULM images illustrated in the accompanying figures were generated using the DF mode with a pulse repetition frequency (PRF) of 500 Hz at a mechanical index (MI) of 0.24 for a total of 25000 frames. RF data were beamformed offline on a 10-μm grid and thresholded to remove background noise (threshold empirically determined). Bubbles were localized using peak detection with an isotropic Gaussian aperture with an RMS width of 100 μm and tracked between frames using a nearest neighbors approach with a maximum linking distance of 100 μm between frames. For comparison, a superharmonic MIP was generated from the stack of DF images used to create the ULM image. 
     C. Tube Imaging In Vitro 
     A resolution phantom was made using two microtubes made of fluorinated ethylene propylene, each with an inner diameter of 46 μm (measured optically with a calibrated microscope). The phantom was submerged in a water bath, and the tubes crossed in an “X” configuration at a depth of approximately 20 mm. A dilution of MBs in saline with a concentration of 1E7 MB/mL was prepared and infused through both tubes in opposite directions at 10 μL/min using an infusion pump (Harvard Apparatus, Holliston, Mass.). The tubes were imaged according to the protocol described in Section II-B, and the average tube profiles were measured within the same ROI for ULM and AA images for comparison. 
     D. Flow Study In Vitro 
     A cellulose tube with an inner diameter of 200 μm was suspended in a water bath at a depth of 20 mm. A dilution of MB in saline with concentration 1E7 MB/mL was infused through the tube at volume flow rates ranging between 0.25 and 15.0 μL/min using an infusion pump (Harvard Apparatus, Holliston, Mass.). These flow rates correspond to the mean displacements of 0.27 and 15.90 μm/frame. Before collecting data for each trial, the tube was flushed with air and water and reinfused with a newly prepared dilution of contrast agent. Infusion was allowed to proceed for a minimum of 3 min before imaging to ensure that the velocity of the contrast agent in the tube had reached steady state. For each trial, 
     1000 frames were acquired, and three trials for each modality per flow rate were performed. DF frames were collected according to Section II-B, while b-mode frames were collected at an MI of 0.11 (center frequency=15.6 MHz) and a PRF 
     of 500 Hz. 
     Each batch of b-mode images was SVD filtered as follows: 
     1) arranged the beamformed RF data into the Casorati matrix in which columns are vectorized b-mode frames; 2) performed an SVD on this matrix; 3) zeroed all singular values for the first 15 singular vectors (empirically determined); and 4) reconstructed the b-mode frames with the new set of singular values. Each set of 1000 frames was then used to generate an MIP, which was normalized and converted to decibels. A reference b-mode frame was used to draw a pair of ROIs corresponding to the tube and the background. SNR in this experiment is defined as the difference between the maximum value of the tube ROI and the average magnitude within the background ROI. This definition has been chosen to account for the sparse number of bubbles present in each MIP for the slower flow rates because averaging within a tube ROI artificially lowers the SNR for each trial by including gaps between bubbles in the average calculation. 
     E. Kidney Imaging In Vivo 
     In vivo imaging was performed in healthy female Fischer 344 rats (Charles River Laboratories, Durham, N.C.) according to a protocol approved by the Institutional Animal Care and Use committee at the University of North Carolina at Chapel Hill. A polydisperse population of MB contrast agent (mean=0.97 μm, standard deviation=0.51 μm) was diluted to 1E9 MB/mL and administered via a catheter placed in the tail vein at 25 μL/min using a syringe pump (Harvard Apparatus, Holliston, Mass.). Infusion was allowed to proceed for 3 min prior to any imaging to allow the concentration of contrast in circulation to approach steady state. DF images were collected and processed according to the parameters in Section II-B. To estimate physiological motion, b-mode frames were interleaved between every 100 DF acquisitions [see  FIG. 5A ]. 2-D speckle tracking was performed on adjacent b-mode frames according to [29] with a square 2-mm kernel (approximately 20 HF wavelengths in either dimension), ±150-μm search window with 1-pixel step size, and 50-μm steps between adjacent kernels [see  FIG. 5B ]. The displacement grid for each time step was spatially interpolated to match the 10-μm pixel size of the original image. 
     To estimate the tissue displacement for a given DF image [see  FIG. 5C ], linear interpolation is performed through the slow time dimension between consecutive displacement arrays. Then, for each DF image, detected bubble locations are adjusted based on the estimated deformation of the tissue at that time point. Bubble localizations are also weighted in the final image according to the peak correlation coefficient associated with the bubble&#39;s parent patch during motion estimation. For example, if the correlation search is able to find a perfect match, the bubble&#39;s localization is given a value of 1, whereas a poor match might result in the bubble being weighted at 0.5. Bubbles below a correlation threshold of 0.3 are completely filtered from the analysis. The accuracy of the speckle tracking depends partially on how much the target decorrelates as a result of motion [30]. Therefore, contributions to the final ULM image were weighted by the correlation coefficient from the speckle tracking in order to minimize the effect of inaccurate displacement estimation on image quality. The correlation threshold of 0.3 for completely removing a localization was empirically determined. Between frames, MB centroids are linked using the nearest neighbor approach, and these line segments are drawn to create the final image. The diameters of selected vessels in ULM images were determined by taking the average of multiple full-width at half-maximum (FWHM) measurements along the axis of each vessel. 
     Three-dimensional imaging was accomplished by using a linear motion stage (XSlide, Velmex, Inc., N.Y., USA) controlled by a custom LabVIEW program (National Instruments, Tex., USA) to mechanically sweep the ultrasound transducer in the elevational dimension. A total of 25 000 DF frames were acquired at each position, and each position was spaced by 500 μm. 
     III. RESULTS 
     A. Tube Imaging In Vitro 
     A ULM image was generated with 25000 frames using a 1.7-MHz plane wave transmission and a receive center frequency of 15.6 MHz [see  FIG. 6A ]. The average FWHM values measured within the regions of interest shown in  FIGS. 6A and 6B  were 44 μm for the ULM image and 113 μm for the superharmonic MIP [see  FIG. 6B ]. These average profiles are overlaid for comparison in  FIG. 6C . Maps of velocity direction [see  FIG. 7A ] and magnitude [see  FIG. 7B ] were also created. From  FIG. 7A , the mean angles of flow for these tubes were measured to be 3.0° and 169.3°, which correspond with the tubes  700  and  702 , respectively. From  FIG. 7B , the average velocity magnitude within the tubes was measured to be 67.5 mm/s. For a 46-μm tube, a volume flow rate of 10 μL/min corresponds to an average velocity of 100.3 mm/s through a cross section of the tube. Applying a ⅔ correction factor to account for integrating through elevation [31] predicts the average velocity measured in the ULM imaging plane to be 66.9 mm/s, which agrees well with the measurement; 
     B. Flow Study In Vitro 
     MIPs for all the flow rates and trials were created, and examples of slow- and fast-flow MIPs are provided in  FIGS. 8A-8D . The MIPs were generated by envelope detecting the beamformed RF data and taking the maximum through time for each pixel. 
     When infusing a 200-μm tube at 0.25 μL/min and imaging at 500 frames/s, SHI produces an average SNR of 16.5 dB over three trials [see  FIG. 8A ]. Increasing the volume flow rate to 15 μL/min and holding frame rate constant increases the SNR to 27.4 dB [see  FIG. 8B ]. SVD filtering produces SNR values of 5.1 dB [see  FIG. 8C ] and 18.3 dB [see  FIG. 8D ] for the slow- and fast-flow conditions, respectively. Across all flow rates, SHI produces an average improvement in SNR of 10.3 dB compared with SVD filtering (see  FIG. 9 ). 
     C. Kidney Imaging In Vivo 
     A superharmonic ULM image of a rodent kidney was generated from 25000 DF frames (500-Hz PRF and MI of 0.24) and shows the ability to resolve vessels on the order of 20 μm in diameter (see  FIGS. 10A-10C ). For comparison, a conventional b-mode frame [see  FIG. 10A ] and a superharmonic MIP [(see  FIG. 10B )] are provided. Selected vessels from this ULM data set have average FWHM values of 20.9, 17.2, and 29.1 μm [see  FIGS. 11A-11C ]. The average profiles are provided for comparison in  FIG. 11D . A ULM image was created from the same data set without applying motion correction to demonstrate the effects of large magnitude respiratory and cardiac artifacts on image quality [see  FIG. 12A ]. A qualitative visualization of the performance of the motion correction based on sparsely interleaved b-mode frames and speckle tracking is provided in  FIG. 12B .  FIGS. 13A and 13B  contain the velocity maps corresponding to the motion-corrected ULM frame shown in  FIG. 10C . By mechanically scanning the imaging probe in the elevational dimension, three-dimensional ULM data sets were acquired.  FIG. 14  shows an MIP for a rodent kidney data set (rendered using 3-D Slicer 4.10.2, Kitware, Clifton Park, N.Y.). This volume was generated from 17 slices spaced by 500 μm with 25000 DF frames per slice. 
     IV. DISCUSSION 
     A new approach to ULM using SHI has been demonstrated both in vitro and in vivo, resolving vessels on the order of 20 μm in diameter in a rodent kidney. SHI offers greater CTR than traditional contrast pulse sequences or SVD filtering while still allowing for motion correction by sparsely interleaving HF b-mode frames into the imaging sequence (1-100 ratio). With a DF arrangement, it is also possible to image slowly moving contrast agents in a cellulose tube in a water bath with much higher SNR than an SVD-based approach. This improvement in SNR may decrease the variance in spatial localizations of slow MB contrast agents, which has been modeled as a linear function of the Cramer-Rao lower bound (CRLB) for time delay estimates [3], [30]. The CRLB itself increases strongly as SNR decreases below 10 dB, holding other parameters constant. For applications such as molecular imaging, for which the aim is to image stationary bubbles, ULM with SVD filtering may prove challenging even in the absence of physiological motion, assuming that MB contrast agents do not decorrelate through slow time. 
     Interestingly, the results of this flow study revealed a dependence of SNR on flow rate in SHI. It is possible that this phenomenon is related to the polydispersity of the contrast agent dilution. The majority of the MBs used in this study are around 1 μm in diameter, which have resonance frequencies higher than the 1.7-MHz transmit pulse [32], [33]. For higher flow rates, there is an increased probability that a large bubble with a resonant frequency closer to the LF element center frequency will pass through the field of view during the 1000-frame acquisition. For slower flow rates, bubbles do not traverse the full length of the tube during a 1000-frame acquisition [see  FIG. 8A ]. This means that if a large bubble is not present at the onset of data collection, it is unlikely that one will appear in the tube before all the frames for that particular trial have been collected. A monodisperse population of bubbles may flatten the SNR versus flow rate curve for SHI, though this was not investigated. 
     The study of SNR versus flow rate suffers from some drawbacks, however, such as the relatively low number of trials for each set of parameters (n=3), which may affect the results shown in  FIGS. 8A-8D and 9 . Even with its limitations, the results of this study suggest that DF imaging outperforms SVD filtering in terms of SNR for all the flow rates tested between 0.27 and 15.90 μm/frame and that SHI is better suited for imaging slowly moving contrast agents in a tube when imaging at 500 frames/s. It is important to consider that the performance of the SVD filter depends on both particle speed and frame rate; hence, we report the results as SNR versus microns per frame. 
     In vitro images of a 46-μm tube resulted in an average FWHM measurement of 44 μm, an error of 4.3%. In vivo, it is quite difficult to assess the accuracy of the ULM imaging without ground truth information regarding the diameter of individual vessels. However, we believe that given the theoretical resolution limit of this system derived in [3] along with the measured error reported earlier, we are justified in assuming the diameters of the selected vessels shown in  FIGS. 11A-11C  to be on the order of 20-30 μm, if not smaller. If we assume the resolution error of this system is a fixed 2-μm bias rather than 4.3% of the real value, then the vessels shown in  11 A- 11 C would measure 22.9, 19.2, and 31.1 μm. In any case, these measurements are well below the diffraction-limited resolution of the HF array and were collected in a freely breathing rodent without physical constraints. 
     One limitation of SHI-ULM is the shallow depth of penetration based on the high center frequency of the receiving transducer. This configuration is well suited for many preclinical scenarios and superficial clinical targets and less so for larger animals and the majority of human organs. However, prior clinical studies have demonstrated SHI of microvasculature in the human breast at 25 MHz at less than 2 cm, and we have demonstrated the ability to image microvasculature as deep as 4 cm at 20 MHz in a rodent cancer model [34]. 
     Thus, we hypothesize that SHI-ULM will be relevant for transcutaneous assessment of abnormal angiogenesis or other vascular pathologies in the breast, prostate, thyroid, or other shallow organs and could be used for deeper organs endoscopically. 
     Although this study was limited to small animal imaging and in vitro experiments, the probe used in this work shows an improvement over previous state of the art devices in SHI in terms of imaging depth, depth of field, and frame rate. For translation to a clinical population, further study is needed regarding optimal transducer design parameters for an appropriate balance between CTR and imaging depth for DF ultrasonic imaging. 
     Another limitation unique to SHI for ULM is the MI (&gt;0.2) necessary to achieve adequate CTR. In these studies, we utilized MIs up to 0.24. While we expect these parameters to be safe based on [35]-[37], this MI is partially destructive to bubbles over repeated pulsing. This might be especially problematic for imaging small capillaries, in which MBs may require time scales on the order of minutes to traverse the entire path length of an individual capillary [38]. For this reason, it may provide additional benefit in the future to explore optimization of experimental parameters including frame rate, MI, MB formulation and stability, MB concentration, infusion rate, and others in an effort to realize the full potential of the SHI approach for ULM. 
     Another challenge associated with this imaging method is the unique point spread function produced by SHI. Under the right circumstances, a single contrast agent will exhibit a point spread function which is multimodal in the axial dimension due to the strongly nonlinear vibrations of the bubble shell. The presence of such an artifact has a negative impact on the final image quality if not accounted for because current popular localization methods were not designed with such a phenomenon in mind [39]. In order to control this issue, we have tuned the transmit pressure to attain sufficient CTR for accurate localization while minimizing the multimodal artifact. This approach, combined with noise thresholding, proved sufficient to mitigate the deleterious effects of the superharmonic artifact. Another approach that can be explored in the future is designing a localization process tailored to the presence of this artifact such that higher MI pulses can be employed to further improve CTR. 
     It should be noted that the results of this study are strongly independent on the characteristics of the contrast agent used during imaging. Recent work has examined the relationship between MB parameters and their influence on superharmonic response [40]. One critical parameter is the resonance frequency of the contrast agent, which is largely determined by its diameter [33]. Driving bubbles at or near their resonance frequency leads to strongly nonlinear oscillations of the shell and hence contributes to generating higher harmonics. The results of [40] demonstrate that the in-house bubbles used for this study are comparable to commercially available contrast agents, such as Definity and Micromarker, in terms of superharmonic backscatter. This finding suggests that the imaging methods described in this work can be replicated in clinical or preclinical settings using commercial bubbles. 
     One subject that is not studied in this work is the effect of the transducer geometry on ULM image quality. It is certain that the “X” configuration of the LF elements results in appreciable transmit pressures away from the HF array&#39;s imaging plane [see  FIG. 1( c ) ]. While off-target bubbles are sonicated on transmit, hydrophone measurements show the elevational beamwidth of the HF transducer ranges between 0.5 and 1.0 mm over the main lobe of the LF transmission. It follows that this system is not sensitive to contrast agents that are more than 0.5 mm out of plane. However, we must consider the depth-dependent response of the system imposed by the broadening HF beamwidth. Precisely controlling the contrast concentration in the blood pool ensures that we retain a sparse group of bubbles in each frame even as we receive with a thicker beam at greater depths. Another source of depth dependence that is not directly accounted for in this study is the variable amplitude of the transmitted pressure in the axial dimension which is given by the degree of overlap between the crossed LF beams. It should be noted, however, that these specific limitations are unique to this sort of transducer design and are not necessarily associated with DF imaging in general. 
     As mentioned previously, the current system is suitable for imaging preclinical models, such as rodents, but is not flexible enough for interrogating targets located beyond the mechanically fixed beam pattern. Perhaps, future research will focus on the continued development of confocal DF probes, such as that demonstrated by van Neer et al. [23], to further improve this imaging method. A fully confocal array design would significantly improve the limited depth of field of a cross-beam transducer (11 mm in this study), allowing for interrogation of larger targets. It is also possible that using DF transducers with transmit/receive frequencies lower than the 1.7/20 MHz used in this study will allow for deeper SHI. While lower frequencies will result in a larger diffraction limited resolution, we expect to recover resolution with ULM. Another area that requires further exploration is the parameter space for motion correction based on sparsely interleaved b-mode acquisitions. 
       FIGS. 12A and 12B  show an example of the improvement in image quality provided by this algorithm, though we believe that most of the improvement in image quality is derived from simply discarding batches of frames associated with large physiological motions. It is possible that moving to a smaller ratio of SHI to b-mode frames will allow for higher fidelity speckle tracking based on the smaller decorrelation between b-mode frames of neighboring acquisitions. The in vivo images shown in this article were produced with a 100-to-1 ratio in which b-mode frames were separated temporally by 200 ms. This b-mode frame rate is sufficient for tracking respiratory motion but must be increased to fully sample the cardiac motion of the rodent model. It is difficult to quantify the performance of this motion correction approach in vivo because we lack ground truth information. Further studies may focus on characterizing this approach via simulations and in vitro. 
     This study also accomplished three-dimensional ULM in a similar fashion to the methods used by Lin et al. [9]. However, because of time constraints during imaging, a relatively large step size of 500 μm was used, which means the elevational resolution was orders of magnitude worse than the axial or lateral resolution. This sort of volume might be useful for evaluating metrics such as vascular density but will likely fall short for accurately assessing features such as tortuosity. However, this study highlights the potential of utilizing ULM for imaging whole organs in preclinical targets. Improvements in transducer technology might one day lead to fully sampled matrix arrays capable of ultrafast SHI for ULM. 
     V. CONCLUSION 
     SHI improves SNR by more than 10-dB in vitro compared with SVD filtering for average flow rates between 0.3 and 15.9 μm/frame. Since the method does not rely on motion to discriminate contrast from background signal, we expect SHI to work well even when MBs are stationary relative to tissue. Furthermore, SHI operates without the need to tune the singular vector threshold for each data set, which can be a cumbersome manual process. Baranger et al. [14] demonstrated that the most successful automatic threshold estimator for SVD filtering achieves optimal CTR for only roughly 60% of in vivo data sets. SHI, on the other hand, is a robust imaging scheme that requires a simple background noise threshold to produce images suitable for ULM processing. Furthermore, a relatively simple speckle-tracking scheme based on [29] applied over sparsely interleaved b-mode frames provides a framework for nonrigid displacement corrections without the need for optimizing a nonrigid transformation estimator such as [41]. SHI, therefore, offers a straightforward approach to bubble detection for ULM, even for challenging imaging scenarios, such as in the presence of slow flow or physiological motion. 
     The following section illustrates the use of superharmonic imaging to image a molecularly targeted contrast agent bound to a target molecule in vivo. 
     Super-Resolution Mapping of Molecularly Targeted Ultrasound Contrast Bound in vivo using Superharmonic Imaging 
     In vivo biomarker expression can be measured with ultrasound molecular imaging and targeted microbubbles (MB). Conventional molecular imaging is constrained by diffraction-limited resolution. Our objective was to create super-resolution maps of targeted MB bound within blood vessels in vivo. 
     Statement of Contribution/Methods 
     Rodents were implanted with a subcutaneous fibrosarcoma tumor model. Images were acquired using a dual-frequency array transducer containing a 20 MHz high-frequency (HF) linear array outfitted with two 1.7 MHz elements that generated a low-frequency (LF) plane wave. Superharmonic (SH) imaging was accomplished by transmitting and receiving with the LF and HF elements, respectively. b-mode images were collected using the HF probe. 
     Animals received a bolus injection of 1E8 MB targeted to VEGFR2 by a heptapeptide. MB circulated for 5 minutes, then 1,000 SH frames were captured at 100 fps. Images were thresholded at 5 times the noise floor and convolved with a Laplacian of Gaussian kernel calibrated to the point spread function. The MB signal to noise floor ratio was 42 dB. MB were localized using a center of mass estimation and considered bound if they persisted for at least 30 consecutive frames without moving more than 2 microns. After the molecular imaging acquisition, conventional ultrasound localization microscopy (ULM) was performed via an infusion of non-targeted MB. 25,000 SH frames were captured at 500 fps. In both acquisitions, b-mode frames were interleaved for motion compensation. Rigid motion was estimated using the normalized correlation coefficient between each b-mode image and a reference frame; images with a correlation coefficient less than 0.9 were discarded. 3D scanning for data acquisition was achieved by translating the probe in elevation on a linear motion stage (4 mm scan, 1 mm step size). 
     Results/Discussion 
     Molecular targeting ( FIG. 15B ) was confined almost exclusively within the anatomical boundaries of the tumor ( FIG. 15A ). SH imaging was sensitive to bound MB because of its excellent CTR across all flow rates (42 dB in this experiment). This study provided proof-of-concept that targeted MB can be localized with superharmonic super-resolution imaging and was the first report of super-resolution ultrasound molecular imaging. 
     The disclosure of each of the following references is hereby incorporated herein by reference in its entirety 
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     It will be understood that various details of the presently disclosed subject matter may be changed without departing from the scope of the presently disclosed subject matter. Furthermore, the foregoing description is for the purpose of illustration only, and not for the purpose of limitation.