Contrast-enhanced ultrasound imaging using capacitive micromachined ultrasonic transducers.

Capacitive micromachined ultrasonic transducers (CMUTs) have a nonlinear relationship between the applied voltage and the emitted signal, which is detrimental to conventional contrast enhanced ultrasound (CEUS) techniques. Instead, a three-pulse amplitude modulation (AM) sequence has been proposed, which is not adversely affected by the nonlinearly emitted harmonics. In this paper, this is shown theoretically, and the performance of the sequence is verified using a 4.8 MHz linear capacitive micromachined ultrasonic transducer (CMUT) array, and a comparable lead zirconate titanate (PZT) array, across 6-60 V applied alternating current (AC) voltage. CEUS images of the contrast agent SonoVue flowing through a 3D printed hydrogel phantom showed an average enhancement in contrast-to-tissue ratio (CTR) between B-mode and CEUS images of 49.9 and 37.4 dB for the PZT array and CMUT, respectively. Furthermore, hydrophone recordings of the emitted signals showed that the nonlinear emissions from the CMUT did not significantly degrade the cancellation in the compounded AM signal, leaving an average of 2% of the emitted power between 26 and 60 V of AC. Thus, it is demonstrated that CMUTs are capable of CEUS imaging independent of the applied excitation voltage when using a three-pulse AM sequence.

Vector Flow Imaging Compared with Conventional Doppler Ultrasound and Thermodilution for Estimation of Blood Flow in the Ascending Aorta.

Transverse oscillation (TO) is a real-time ultrasound vector flow method implemented on a commercial scanner. The TO setup was examined on a flowrig with constant and pulsatile flow. Subsequently, 25 patients undergoing cardiac bypass surgery were scanned intraoperatively with TO on the ascending aorta and compared to transesophageal echocardiography (TEE) and pulmonary artery catheter thermodilution (PACTD). On the flowrig, TO had a precision of 5.5%, 9.4% and 14.7%, a percentage error of 18.2%, 14.6% and 40.7%, and a mean bias of 0.4 cm/s, 36.8 ml/min and 32.4 ml/min for velocity and flow rate (constant and pulsatile) estimation. The correlation coefficients for all flowrig evaluations were 0.99 indicating systematic bias. After bias correction, the percentage error was reduced to 11.5%, 12.6% and 15.9% for velocity and flow rate (constant and pulsatile) estimation. In the in vivo setup, TO, TEE, and PACTD had a precision of 21.9%, 13.7%, and 12.0%. TO compared with TEE and PACTD had a mean bias of 12.6 cm/s and -0.08 l/min, and a percentage error of 23.4%, and 36.7%, respectively. The percentage error was reduced to 22.9% for the TEE comparison, but increased to 43.8% for the PACTD comparison, after correction for the systematic bias found in the flowrig. TO is a reliable and precise method for velocity and flow rate estimation on a flowrig. However, TO with the present setup, is not interchangeable with PACTD for cardiac volume flow estimation, but is a reliable and precise angle-independent ultrasound alternative for velocity estimation of cardiac flow.

Tissue harmonic synthetic aperture ultrasound imaging.

Synthetic aperture sequential beamforming (SASB) and tissue harmonic imaging (THI) are combined to improve the image quality of medical ultrasound imaging. The technique is evaluated in a comparative study against dynamic receive focusing (DRF). The objective is to investigate if SASB combined with THI improves the image quality compared to DRF-THI. The major benefit of SASB is a reduced bandwidth between the probe and processing unit. A BK Medical 2202 Ultraview ultrasound scanner was used to acquire beamformed RF data for offline evaluation. The acquisition was made interleaved between methods, and data were recorded with and without pulse inversion for tissue harmonic imaging. Data were acquired using a Sound Technology 192 element convex array transducer from both a wire phantom and a tissue mimicking phantom to investigate spatial resolution and penetration. In vivo scans were also performed for a visual comparison. The spatial resolution for SASB-THI is on average 19% better than DRI-THI, and the investigation of penetration showed equally good signal-to-noise ratio. In vivo B-mode scans were made and compared. The comparison showed that SASB-THI reduces the artifact and noise interference and improves image contrast and spatial resolution.

Modal radiation patterns of baffled circular plates and membranes.

The far field velocity potential and radiation pattern of baffled circular plates and membranes are found analytically using the full set of modal velocity profiles derived from the corresponding equation of motion. The derivation is valid for a plate or membrane subjected to an external excitation force, which is used as a sound receiver in any medium or as a sound transmitter in a gaseous medium. A general, concise expression is given for the radiation pattern of any mode of the membrane and the plate with arbitrary boundary conditions. Specific solutions are given for the four special cases of a plate with clamped, simply supported, and free edge boundary conditions as well as for the membrane. For all non-axisymmetric modes, the velocity potential along the axis of the radiator is found to be strictly zero. In the long wavelength limit, the radiation pattern of all axisymmetric modes approaches that of a monopole, while the non-axisymmetric modes exhibit multipole behavior. Numerical results are also given, demonstrating the implications of having non-axisymmetric excitation using both a point excitation with varying eccentricity and a homogeneous excitation acting on half of the circular radiator.

Diverging Polymer Acoustic Lens Design for High-Resolution Row-Column Array Ultrasound Transducers.

Spherical diverging acoustic lenses mounted on flat 2-D row-column-addressed (RCA) ultrasound transducers have shown the potential to extend the field of view (FOV) from a rectilinear to a curvilinear volume region and, thereby, enable 3-D imaging of large organs. Such lenses are usually designed for small aperture low-frequency transducers, which have limited resolution. Moreover, they are made of off-the-shelf pieces of materials, which leaves no room for optimization. We hypothesize that acoustic lenses can be designed to fit high-resolution transducers, and they can be fabricated in a fast, cost-effective, and flexible manner using a combination of 3-D printing and casting or computer numerical control (CNC) machining techniques. These lenses should increase the FOV of the array while preserving the image quality. In this work, such lenses are made in concave, convex, and compound spherical shapes and from thermoplastics and thermosetting polymers. Polymethylpentene (TPX), polystyrene (PS), polypropylene (PP), polymethyl methacrylate (PMMA), polydimethylsiloxane (PDMS), and room-temperature-vulcanizing (RTV) silicone diverging lenses have been fabricated and mounted on a 128 + 128 6-MHz RCA transducer. The performances of the lenses have been assessed and compared in terms of FOV, signal-to-noise ratio (SNR), bandwidth, and potential artifacts. The largest FOV (24.0.) is obtained with a 42.64-mm radius PMMA-RTV compound lens, which maintains a decent fractional bandwidth (53%) and SNR at 6 MHz (.9.1-dB amplitude drop compared with the unlensed transducer). The simple PMMA TPX, PS, PP, PDMS, and RTV lenses provide an FOV of 12.2°, 6.3°, 8.1°, 11.7°, 0.6°, and 10.4°; a fractional bandwidth of 97%, 46%, 103%, 46%, 97%, 53%, and 49%; and an amplitude drop of -5.2, -4.4, -2.8, -15.4, -6.0, and -1.8 dB, respectively. This work demonstrates that thermoplastics are suitable materials for fabricating low-attenuation convex diverging lenses for large-aperture, high-frequency 2-D transducers. This is highly desired to achieve high-resolution volumetric imaging of large organs.

Underestimation of Flow Velocity in 2-D Super-Resolution Ultrasound Imaging.

Velocity estimation in ultrasound imaging is a technique to measure the speed and direction of blood flow. The flow velocity in small blood vessels, i.e., arterioles, venules, and capillaries, can be estimated using super-resolution ultrasound imaging (SRUS). However, the vessel width in SRUS is relatively small compared with the full-width-half-maximum of the ultrasound beam in the elevation direction (FWHMy), which directly impacts the velocity estimation. By taking into consideration the small vessel widths in SRUS, it is hypothesized that the velocity is underestimated in 2-D super-resolution ultrasound imaging when the vessel diameter is smaller than the FWHMy. A theoretical model is introduced to show that the velocity of a 3-D parabolic velocity profile is underestimated by up to 33% in 2-D SRUS, if the width of the vessel is smaller than the FWHMy. This model was tested using Field II simulations and 3-D printed micro-flow hydrogel phantom measurements. A Verasonics Vantage 256™ scanner and a GE L8-18i-D linear array transducer with FWHMy of approximately 770 µm at the elevation focus were used in the simulations and measurements. Simulations of different parabolic velocity profiles showed that the velocity underestimation was 36.8%±1.5% (mean±standard deviation). The measurements showed that the velocity was underestimated by 30%±6.9%. Moreover, the results of vessel diameters, ranging from 0.125×FWHMy to 3×FWHMy, indicate that velocities are estimated according to the theoretical model. The theoretical model can, therefore, be used for the compensation of velocity estimates under these circumstances.

Investigating the importance of left atrial compliance on fluid dynamics in a novel mock circulatory loop.

The left atrium (LA) hemodynamic indices hold prognostic value in various cardiac diseases and disorders. To understand the mechanisms of these conditions and to assess the performance of cardiac devices and interventions, in vitro models can be used to replicate the complex physiological interplay between the pulmonary veins, LA, and left ventricle. In this study, a comprehensive and adaptable in vitro model was created. The model includes a flexible LA made from silicone and allows distinct control over the systolic and diastolic functions of both the LA and left ventricle. The LA was mechanically matched with porcine LAs through expansion tests. Fluid dynamic measures were validated against the literature and pulmonary venous flows recorded on five healthy individuals using magnetic resonance flow imaging. Furthermore, the fluid dynamic measures were also used to construct LA pressure-volume loops. The in vitro pressure and flow recordings expressed a high resemblance to physiological waveforms. By decreasing the compliance of the LA, the model behaved realistically, elevating the a- and v-wave peaks of the LA pressure from 12 to 19 mmHg and 22 to 26 mmHg, respectively, while reducing the S/D ratio of the pulmonary venous flowrate from 1.5 to 0.3. This model provides a realistic platform and framework for developing and evaluating left heart procedures and interventions.

Super-Resolution Ultrasound Imaging Using the Erythrocytes-Part II: Velocity Images.

Super-resolution ultrasound imaging using the erythrocytes (SURE) has recently been introduced. The method uses erythrocytes as targets instead of fragile microbubbles (MBs). The abundance of erythrocyte scatterers makes it possible to acquire SURE data in just a few seconds compared with several minutes in ultrasound localization microscopy (ULM) using MBs. A high number of scatterers can reduce the acquisition time; however, the tracking of uncorrelated and high-density scatterers is quite challenging. This article hypothesizes that it is possible to detect and track erythrocytes as targets to obtain vascular flow images. A SURE tracking pipeline is used with modules for beamforming, recursive synthetic aperture (SA) imaging, motion estimation, echo canceling, peak detection, and recursive nearest-neighbor (NN) tracker. The SURE tracking pipeline is capable of distinguishing the flow direction and separating tubes of a simulated Field II phantom with 125-25- [Formula: see text] wall-to-wall tube distances, as well as a 3-D printed hydrogel micr-flow phantom with 100-60- [Formula: see text] wall-to-wall channel distances. The comparison of an in vivo SURE scan of a Sprague-Dawley rat kidney with ULM and micro-computed tomography (CT) scans with voxel sizes of 26.5 and [Formula: see text] demonstrated consistent findings. A microvascular structure composed of 16 vessels exhibited similarities across all imaging modalities. The flow direction and velocity profiles in the SURE scan were found to be concordant with those from ULM.

ULTRA-SR Challenge: Assessment of Ultrasound Localization and TRacking Algorithms for Super-Resolution Imaging.

With the widespread interest and uptake of super-resolution ultrasound (SRUS) through localization and tracking of microbubbles, also known as ultrasound localization microscopy (ULM), many localization and tracking algorithms have been developed. ULM can image many centimeters into tissue in-vivo and track microvascular flow non-invasively with sub-diffraction resolution. In a significant community effort, we organized a challenge, Ultrasound Localization and TRacking Algorithms for Super-Resolution (ULTRA-SR). The aims of this paper are threefold: to describe the challenge organization, data generation, and winning algorithms; to present the metrics and methods for evaluating challenge entrants; and to report results and findings of the evaluation. Realistic ultrasound datasets containing microvascular flow for different clinical ultrasound frequencies were simulated, using vascular flow physics, acoustic field simulation and nonlinear bubble dynamics simulation. Based on these datasets, 38 submissions from 24 research groups were evaluated against ground truth using an evaluation framework with six metrics, three for localization and three for tracking. In-vivo mouse brain and human lymph node data were also provided, and performance assessed by an expert panel. Winning algorithms are described and discussed. The publicly available data with ground truth and the defined metrics for both localization and tracking present a valuable resource for researchers to benchmark algorithms and software, identify optimized methods/software for their data, and provide insight into the current limits of the field. In conclusion, Ultra-SR challenge has provided benchmarking data and tools as well as direct comparison and insights for a number of the state-of-the art localization and tracking algorithms.

Synthetic aperture flow imaging using dual stage beamforming: simulations and experiments.

A method for synthetic aperture flow imaging using dual stage beamforming has been developed. The main motivation is to increase the frame rate and still maintain a beamforming quality sufficient for flow estimation that is possible to implement in a commercial scanner. This method can generate continuous high frame rate flow images with lower calculation demands than the full synthetic aperture flow imaging. The performance of the approach was investigated using Field II simulations and measurements with the experimental scanner SARUS. A laminar flow with a parabolic profile was generated by a flow rig system. The flow data were acquired by a commercial 7 MHz linear array transducer. Four emissions were transmitted sequentially and repeated 12 times corresponding to 48 emissions. Flow with a peak velocity of 0.12 m/s was measured, the relative standard deviation was 6.4%, and the bias was 7.6% (2.1% and 3.2% for the simulations). A parameter study revealed that emission spacing, number of cross-correlation functions used for averaging, and the length of the velocity searching range influence the performance. Compared to the full synthetic aperture flow imaging the total number of beamformed samples are reduced by a factor of 64 times, and the frame rate is much higher than the conventional method for the same velocity estimation accuracy.

Intraoperative cardiac ultrasound examination using vector flow imaging.

Conventional ultrasound (US) methods for blood velocity estimation only provide one-dimensional and angle-dependent velocity estimates; thus, the complexity of cardiac flow has been difficult to measure. To circumvent these limitations, the Transverse Oscillation (TO) vector flow method has been proposed. The vector flow method implemented on a commercial scanner provided real-time, angle-independent estimates of cardiac blood flow. Epicardiac and epiaortic, intraoperative US examinations were performed on three patients with stenosed coronary arteries scheduled for bypass surgery. Repeating cyclic beat-to-beat flow patterns were seen in the ascending aorta and pulmonary artery of each patient, but these patterns varied between patients. Early systolic retrograde flow filling the aortic sinuses was seen in the ascending aorta as well as early systolic retrograde flow in the pulmonary artery. In diastole, stable vortices in aortic sinuses of the ascending aorta created central antegrade flow. A stable vortex in the right atrium was seen during the entire heart cycle. The measurements were compared with estimates obtained intraoperatively with conventional spectral Doppler US using a transesophageal and an epiaortic approach. Mean differences in peak systole velocity of 11% and 26% were observed when TO was compared with transesophageal echocardiography and epiaortic US, respectively. In one patient, the cardiac output derived from vector velocities was compared with pulmonary artery catheter thermodilution technique and showed a difference of 16%. Vector flow provides real-time, angle-independent vector velocities of cardiac blood flow. The technique can potentially reveal new information of cardiovascular physiology and give insight into blood flow dynamics.

Transverse oscillation tensor velocity imaging using a row-column addressed array: Experimental validation.

Tensor velocity imaging (TVI) performance with a row-column probe was assessed for constant flow in a straight vessel phantom and pulsatile flow in a carotid artery phantom. TVI, i.e., estimating the 3-D velocity vector as a function of time and spatial position, was performed using the transverse oscillation cross-correlation estimator, and the flow was acquired with a Vermon 128+128 row-column array probe connected to a Verasonics 256 research scanner. The emission sequence used 16 emissions per image, and a TVI volume rate of 234 Hz was obtained for a pulse repetition frequency (fprf) of 15 kHz. The TVI was validated by comparing estimates of the flow rate through several cross-sections with the flow rate set by the pump. For the constant 8 mL/s flow in the straight vessel phantom with relative estimator bias (RB) and standards deviation (RSD) was found in the range of -2.18% to 0.55% and 4.58% to 2.48% in measurements performed with an fprf of 15, 10, 8, and 5 kHz. The pulsatile flow in the carotid artery phantom the was set to an average flow rate of 2.44 mL/s, and the flow was acquired with an fprf of 15, 10, and 8 kHz. The pulsatile flow was estimated from two measurement sites: one at a straight section of the artery and one at the bifurcation. In the straight section, the estimator predicted the average flow rate with an RB value ranging from -7.99% to 0.10% and an RSD value ranging from 10.76% to 6.97%. At the bifurcation, RB and RSD values were between -7.47% to 2.02% and 14.46% to 8.89%. This demonstrates that an RCA with 128 receive elements can accurately capture the flow rate through any cross-section at a high sampling rate.

Intra-Cardiac Flow from Geometry Prescribed Computational Fluid Dynamics: Comparison with Ultrasound Vector Flow Imaging.

PURPOSE: This paper investigates the accuracy of blood flow velocities simulated from a geometry prescribed computational fluid dynamics (CFD) pipeline by applying it to a dynamic heart phantom. The CFD flow patterns are compared to a direct flow measurement by ultrasound vector flow imaging (VFI). The hypothesis is that the simulated velocity magnitudes are within one standard deviation of the measured velocities. METHODS: The CFD pipeline uses computed tomography angiography (CTA) images with 20 volumes per cardiac cycle as geometry input. Fluid domain movement is prescribed from volumetric image registration using the CTA image data. Inlet and outlet conditions are defined by the experimental setup. VFI is systematically measured in parallel planes, and compared to the corresponding planes in the simulated time dependent three dimensional fluid velocity field. RESULTS: The measured VFI and simulated CFD have similar flow patterns when compared qualitatively. A quantitative comparison of the velocity magnitude is also performed at specific regions of interest. These are evaluated at 11 non-overlapping time bins and compared by linear regression giving R2 = 0.809, SD = 0.060 m/s, intercept = - 0.039 m/s, and slope = 1.09. Excluding an outlier at the inlet, the correspondence between CFD and VFI improves to: R2 = 0.823, SD = 0.048 m/s, intercept = -0.030 m/s, and slope = 1.01. CONCLUSION: The direct comparison of flow patterns shows that the proposed CFD pipeline provide realistic flow patterns in a well-controlled experimental setup. The demanded accuracy is obtained close to the inlet and outlet, but not in locations far from these.

Row-Column Beamformer for Fast Volumetric Imaging.

This work presents a beamforming procedure that significantly reduces the number of operations when performing volumetric synthetic aperture imaging with row-column addressed arrays (RCAs). The proposed beamformer uses that the image values along the elevation direction of the low-resolution volume (LRV) are approximately constant. It is thus hypothesized that the entire LRV could be reconstructed from a single 2-D cross section of the LRV. The presented method contains two stages. The first stage beamforms, for each emission, a cross section using the conventional RCA beamformer. The second stage extrapolates the rest of the image points in the volume from the 2-D cross sections. Assuming the image volume is covered by 3-D grid coordinates with a size of Nw×Nw ×Nz , i.e., Nw samples along the x - and y -axis and Nz samples along the z -axis, the proposed beamformer reduces the number of mathematical operations by a factor of approximately NNw/(NS+Nw) . Here, S is the ratio between the first- and second-stage axial sampling rates, and N is the receiving aperture's number of channels. Beamforming a 128×128×1024 volume from data acquired with N = 128 receiving channel can thus be achieved with 25.6 times fewer operations, when S = 4. A 9.23 times increase in the beamforming rate for a 100×100×200 volume was demonstrated on complex data from a 128 + 128 Vermon RCA probe. Real-time volumetric beamformation can, with this increase, be performed with a pulse repetition frequency of up to 1804.80 Hz. The proposed and conventional beamformer's output was visually indistinguishable, and the full width at half maximum (FWHM) and full width at tenth maximum (FWTM) were at most 1.19% larger with the proposed approach. The proposed beamformer can thus perform volumetric imaging significantly faster than the current approach, with a negligible difference in image quality.

Universal Synthetic Aperture Sequence for Anatomic, Functional, and Super Resolution Imaging.

Synthetic aperture (SA) can be used for both anatomic and functional imaging, where tissue motion and blood velocity are revealed. Often, sequences optimized for anatomic B-mode imaging are different from functional sequences, as the best distribution and number of emissions are different. B-mode sequences demand many emissions for a high contrast, whereas flow sequences demand short sequences for high correlations yielding accurate velocity estimates. This article hypothesizes that a single, universal sequence can be developed for linear array SA imaging. This sequence yields high-quality linear and nonlinear B-mode images as well as accurate motion and flow estimates for high and low blood velocities and super-resolution images. Interleaved sequences with positive and negative pulse emissions for the same spherical virtual source were used to enable flow estimation for high velocities and make continuous long acquisitions for low-velocity estimation. An optimized pulse inversion (PI) sequence with 2 ×12 virtual sources was implemented for four different linear array probes connected to either a Verasonics Vantage 256 scanner or the SARUS experimental scanner. The virtual sources were evenly distributed over the whole aperture and permuted in emission order for making flow estimation possible using 4, 8, or 12 virtual sources. The frame rate was 208 Hz for fully independent images for a pulse repetition frequency of 5 kHz, and recursive imaging yielded 5000 images per second. Data were acquired from a phantom mimicking the carotid artery with pulsating flow and the kidney of a Sprague-Dawley rat. Examples include anatomic high contrast B-mode, non-linear B-mode, tissue motion, power Doppler, color flow mapping (CFM), vector velocity imaging, and super-resolution imaging (SRI) derived from the same dataset and demonstrate that all imaging modes can be shown retrospectively and quantitative data derived from it.

Precise Estimation of Intravascular Pressure Gradients.

This study presents a method for noninvasive pressure gradient estimation, which allows the detection of small pressure differences with higher precision compared to invasive catheters. It combines a new method for estimating the temporal acceleration of the flowing blood with the Navier-Stokes equation. The acceleration estimation is based on a double cross-correlation approach, which is hypothesized to minimize the influence of noise. Data are acquired using a 256-element, 6.5-MHz GE L3-12-D linear array transducer connected to a Verasonics research scanner. A synthetic aperture (SA) interleaved sequence with 2 ×12 virtual sources evenly distributed over the aperture and permuted in emission order is used in combination with recursive imaging. This enables a temporal resolution between correlation frames equal to the pulse repetition time at a frame rate of half the pulse repetition frequency. The accuracy of the method is evaluated against a computational fluid dynamic simulation. Here, the estimated total pressure difference complies with the CFD reference pressure difference, which yields an R -square of 0.985 and an RMSE of 3.03 Pa. The precision of the method is tested on experimental data, measured on a carotid phantom of the common carotid artery. The volume profile used during measurement was set to mimic flow in the carotid artery with a peak flow rate of 12.9 mL/s. The experimental setup showed that the measured pressure difference changes from -59.4 to 31 Pa throughout a single pulse cycle. This was estimated with a precision of 5.44% (3.22 Pa) across ten pulse cycles. The method was also compared to invasive catheter measurements in a phantom with a 60% cross-sectional area reduction. The ultrasound method detected a maximum pressure difference of 72.3 Pa with a precision of 3.3% (2.22 Pa). The catheters measured a maximum pressure difference of 105 Pa with a precision of 11.2% (11.4 Pa). This was measured over the same constriction and with a peak flow rate of 12.9 mL/s. The double cross-correlation approach revealed no improvement compared to a normal differential operator. The method's strength, thus, lies primarily in the ultrasound sequence, which allows precise and accurate velocity estimations, at which acceleration and pressure differences can be acquired.

Super-Resolution Ultrasound Imaging of Renal Vascular Alterations in Zucker Diabetic Fatty Rats during the Development of Diabetic Kidney Disease.

Individuals with diabetes at risk of developing diabetic kidney disease (DKD) are challenging to identify using currently available clinical methods. Prognostic accuracy and initiation of treatment could be improved by a quantification of the renal microvascular rarefaction and the increased vascular tortuosity during the development of DKD. Super-resolution ultrasound (SRUS) imaging is an in vivo technique capable of visualizing blood vessels at sizes below 75 µm. This preclinical study aimed to investigate the alterations in renal blood vessels' density and tortuosity in a type 2 diabetes rat model, Zucker diabetic fatty (ZDF) rats, as a prediction of DKD. Lean age-matched Zucker rats were used as controls. A total of 36 rats were studied, subdivided into ages of 12, 22, and 40 weeks. Measured albuminuria indicated the early stage of DKD, and the SRUS was compared with the ex vivo micro-computed tomography (µCT) of the same kidneys. Assessed using the SRUS imaging, a significantly decreased cortical vascular density was detected in the ZDF rats from 22 weeks of age compared to the healthy controls, concomitant with a significantly increased albuminuria. Already by week 12, a trend towards a decreased cortical vascular density was found prior to the increased albuminuria. The quantified vascular density in µCT corresponded with the in vivo SRUS imaging, presenting a consistently lower vascular density in the ZDF rats. Regarding vessel tortuosity, an overall trend towards an increased tortuosity was present in the ZDF rats. SRUS shows promise for becoming an additional tool for monitoring and prognosing DKD. In the future, large-scale animal studies and human trials are needed for confirmation.

̀Spatial impulse response of a rectangular double curved transducer.

Calculation of the pressure field from transducers with both a convex and a concave surface geometry is a complicated assignment that often is accomplished by subdividing the transducer surface into smaller flat elements of which the spatial impulse response is known. This method is often applied to curved transducers because an analytical solution is unknown. In this work a semi-analytical algorithm for the exact solution to a first order in diffraction effect of the spatial impulse response of rectangular-shaped double curved transducers is presented. The solution and an approximation to it are investigated. The approximation reformulates the solution to an analytically integrable expression, which is computationally efficient to solve. Simulation results are compared to FIELD II simulations. Calculating the response from 200 different points yields a mean error for the different approximations ranging from 0.03% to 0.8% relative to a numerical solution for the spatial impulse response. It is also shown that the presented algorithm gives consistent results with FIELD II for a linear flat, a linear focused, and a convex nonfocused element. The solution involved a three-point Taylor expansion and gave an accuracy of 0.01%.

Performance Assessment of Row-Column Transverse Oscillation Tensor Velocity Imaging Using Computational Fluid Dynamics Simulation of Carotid Bifurcation Flow.

In this work, the accuracy of row-column tensor velocity imaging (TVI), i.e., 3-D vector flow imaging (VFI) in 3-D space over time, is quantified on a complex, clinically relevant flow. The quantification is achieved by transferring the flow simulated using computational fluid dynamics (CFD) to a Field II simulation environment, and this allows for a direct comparison between the actual and estimated velocities. The carotid bifurcation flow simulations were performed with a peak inlet velocity of 80 cm/s, nonrigid vessel walls, and a flow cycle duration of 1.2 s. The flow was simulated from two observation angles, and it was acquired using a 3-MHz 62+62 row-column addressed array (RCA) at a pulse repetition frequency ( fprf ) of 10 and 20 kHz. The tensor velocities were obtained at a frame rate of 208.3 Hz, at fprf = 10 kHz , and the results from two velocity estimators were compared. The two estimators were the directional transverse oscillation (TO) cross correlation estimator and the proposed autocorrelation estimator. Linear regression between the actual and estimated velocity components yielded, for the cross correlation estimator, an R 2 value in the range of 0.89-0.91, 0.46-0.77, and 0.91-0.97 for the x -, y -, and z -components, and 0.87-0.89, 0.40-0.83, and 0.91-0.96 when using the autocorrelation estimator. The results demonstrate that an RCA can, with just 62 receive channels, measure complex 3-D flow fields at a high volume rate.