Jacob Kortbek

Sequential beamforming for synthetic aperture imaging

Synthetic aperture sequential beamforming (SASB) is a novel technique which allows to implement synthetic aperture beamforming on a system with a restricted complexity, and without storing RF-data. The objective is to improve lateral resolution and obtain a more depth independent resolution compared to conventional ultrasound imaging. SASB is a two-stage procedure using two separate beamformers. The initial step is to construct and store a set of B-mode image lines using a single focal point in both transmit and receive. The focal points are considered virtual sources and virtual receivers making up a virtual array. The second stage applies the focused image lines from the first stage as input data, and take advantage of the virtual array in the delay and sum beamforming. The size of the virtual array is dynamically expanded and the image is dynamically focused in both transmit and receive and a range independent lateral resolution is obtained. The SASB method has been investigated using simulations in Field II and by off-line processing of data acquired with a commercial scanner. The lateral resolution increases with a decreasing F#. Grating lobes appear if F#≤2 for a linear array with λ-pitch. The performance of SASB with the virtual source at 20mm and F#=1.5 is compared with conventional dynamic receive focusing (DRF). The axial resolution is the same for the two methods. For the lateral resolution there is improvement in FWHM of at least a factor of 2 and the improvement at -40dB is at least a factor of 3. With SASB the resolution is almost constant throughout the range. For DRF the FWHM increases almost linearly with range and the resolution at -40dB is fluctuating with range. The theoretical potential improvement in SNR of SASB over DRF has been estimated. An improvement is attained at the entire range, and at a depth of 80mm the improvement is 8dB.

Synthetic Aperture Sequential Beamforming

A synthetic aperture focusing (SAF) technique denoted synthetic aperture sequential beamforming (SASB) suitable for 2D and 3D imaging is presented. The technique differ from prior art of SAF in the sense that SAF is performed on pre-beamformed data contrary to channel data. The objective is to improve and obtain a more range independent lateral resolution compared to conventional dynamic receive focusing (DRF) without compromising frame rate. SASB is a two-stage procedure using two separate beamformers. First a set of B-mode image lines using a single focal point in both transmit and receive is stored. The second stage applies the focused image lines from the first stage as input data. The SASB method has been investigated using simulations in Field II and by off-line processing of data acquired with a commercial scanner. The performance of SASB with a static image object is compared with DRF. For the lateral resolution the improvement in FWHM equals a factor of 2 and the improvement at -40 dB equals a factor of 3. With SASB the resolution is almost constant throughout the range. The resolution in the near field is slightly better for DRF. A decrease in performance at the transducer edges occur for both DRF and SASB, but is more profound for SASB.

Practical applications of synthetic aperture imaging

Synthetic aperture imaging has been a focus of research for almost 3 decades. The research carried out at the Center for Fast Ultrasound Imaging has demonstrated that synthetic aperture focusing not only can be used in-vivo, but that it also yields superior B-mode and blood flow images. In the last years synthetic aperture focusing has moved from the lab to commercial products. The implementations vary in their scope and purpose. Some scanners use synthetic aperture imaging to improve the detail and contrast resolution of the system. Others to increase the image uniformity. Yet others use synthetic aperture acquisition to achieve high frame rates and superior flow estimations. On the other end of the scale are the systems that utilize synthetic aperture techniques to reduce the data rate and take advantage of modern computer hardware. Retrospecitve transmit beamformation, zone sonography, and multiple angle flash imaging are just a few of the names used to describe the commercial implementations of synthetic aperture focusing. Although they sound like different algorithms, they are the same in their core, as revealed in this paper.

Estimation of velocity vector angles using the directional cross-correlation method

A method for determining both velocity magnitude and angle in any direction is suggested. The method uses focusing along the velocity direction and cross-correlation for finding the correct velocity magnitude. The angle is found from beamforming directional signals in a number of directions and then selecting the angle with the highest normalized correlation between directional signals. The approach is investigated using Field II simulations and data from the experimental ultrasound scanner RASMUS and a circulating flow rig with a parabolic flow having a peak velocity of 0.3 m/s. A 7-MHz linear array transducer is used with a normal transmission of a focused ultrasound field. In the simulations the relative standard deviation of the velocity magnitude is between 0.7% and 7.7% for flow angles between 45deg and 90deg. The study showed that angle estimation by directional beamforming can be estimated with a high precision. The angle estimation performance is highly dependent on the choice of the time kappatprfmiddotTprf (correlation time) between signals to correlate. One performance example is given with a fixed value of kappatprf for all flow angles. The angle estimation on measured data for flow at 60deg to 90deg yields a probability of valid estimates between 68% and 98%. The optimal value of kappatprf each flow angle is found from a parameter study; with these values, the performance on simulated data yields angle estimates with no outlier estimates and with standard deviations below 2deg

Recent advances in blood flow vector velocity imaging

A number of methods for ultrasound vector velocity imaging are presented in the paper. The transverse oscillation (TO) method can estimate the velocity transverse to the ultrasound beam by introducing a lateral oscillation in the received ultrasound field. The approach has been thoroughly investigated using both simulations, flow rig measurements, and in-vivo validation against MR scans. The TO method obtains a relative accuracy of 10% for a fully transverse flow in both simulations and flow rig experiments. In-vivo studies performed on 11 healthy volunteers comparing the TO method with magnetic resonance phase contrast angiography (MRA) revealed a correlation between the stroke volume estimated by TO and MRA of 0.91 (p<;0.01) with an equation for the line of regression given as: MRA = 1.1 · TO-0.4 ml. Several clinical examples of complex flow in e.g. bifurcations and around valves have been acquired using a commercial implementation of the method (BK Medical ProFocus Ultraview scanner). A range of other methods are also presented. This includes synthetic aperture imaging using either spherical or plane waves with velocity estimation performed with directional beamforming or speckle tracking. The key advantages of these techniques are very fast imaging that can attain an order of magnitude higher precision than conventional methods. SA flow imaging was implemented on the experimental scanner RASMUS using an 8-emission spherical emission sequence and reception of 64 channels on a BK Medical 8804 transducer. This resulted in a relative standard deviation of 1.2% for a fully transverse flow. Plane wave imaging was also implemented on the RASMUS scanner and a 100 Hz frame rate was attained. Several vector velocity image sequences of complex flow were acquired, which demonstrates the benefits of fast vector flow imaging. A method for extending the 2D TO method to 3D vector velocity estimation is presented and the implications for future vector velocity imaging is indicated.

Comparing interpolation schemes in dynamic receive ultrasound beamforming

In medical ultrasound interpolation schemes are of- ten applied in receive focusing for reconstruction of image points. This paper investigates the performance of various interpolation scheme by means of ultrasound simulations of point scatterers in Field II. The investigation includes conventional B-mode imaging and synthetic aperture (SA) imaging using a 192-element, 7 MHz linear array transducer with λ pitch as simulation model. The evaluation consists primarily of calculations of the side lobe to main lobe ratio, SLMLR, and the noise power of the interpolation error. When using conventional B-mode imaging and linear interpolation, the difference in mean SLMLR is 6.2 dB. With polynomial interpolation the ratio is in the range 6.2 dB to 0.3 dB using 2nd to 5th order polynomials, and with FIR interpolation the ratio is in the range 5.8 dB to 0.1 dB depending on the filter design. The SNR is between 21 dB and 45 dB with the polynomial interpolation and between 37 dB and 43 dB with FIR filtering. In the synthetic aperture imaging modality the difference in mean SLMLR ranges from 14 dB to 33 dB and 6d B to 31 dB for the polynomial and FIR filtering schemes respectively. By using a proper interpolation scheme it is possible to reduce the sampling frequency and avoid a decrease in performance. When replacing linear interpolation with a more advanced interpolation scheme it is possible to obtain a reduction of 18 dB and 33 dB in the SLMLR for the B-mode and SA imaging, respectively, and an improvement in SNR of 24 dB. I. INTRODUCTION In medical ultrasound receive focusing is a core signal processing element used for reconstruction of image points from the received transducer signals in both conventional and synthetic aperture imaging. In the delay-and-sum beamformer a sample is selected from each of the receive channels corresponding to the echo of the image point target. The sample index is based on the total transmit-receive time-of- flight. Due to the continuous nature of the time-of-flight, it will not necessarily lie at the discrete time indices of the sampled channel data. Thus, some form of interpolation is needed and this heavily influences the image quality and the hardware complexity for implementation. By using a proper interpolation scheme it is possible to reduce the sampling frequency or to improve performance. The investigation in this paper is based on the work of Henrik Andresen (1) and quantifies the change in performance as a function of interpolation type applied by means of ultrasound simulations of point scatterers in Field II (2). This paper introduces the beamformation toolbox, BFT2 which is used in the investigation. BFT2 (3),(4), developed at CFU is written in C and has a Matlab program interface. It performs dynamic receive focusing and offers choices between static or dynamic apodization and various interpolation schemes. The interpolation schemes investigated include linear, polynomial, and upsampling and FIR filtering. Various order polynomials and FIR filters are investigated. II. DESCRIPTION The investigation in this paper on the influence of the choice of interpolation scheme includes conventional B-mode imaging and synthetic aperture imaging (SAI). The ultrasound RF signals for the investigation is created using Field II and the beamforming is performed with BFT2. From a reference data set an evaluation data set is created, which is used for the evaluation. For the evaluation the point-spread function, PSF is useful when observing the characteristics of different imaging modalities. It is highly affected by the type of transmit-receive focusing used, and is, thus, also affected by the interpolation in receive beamforming. The lateral part of the PSF is especially interesting in terms of spatial distribution and amplitude of the side-lobe energy, which again directly affects the image contrast. The evaluation and comparison of interpolation schemes is done by partly observing the lateral PSF and quantizing the main-lobe and side-lobe energy distribution in terms of the full-width-half-maximum, FWHM and the side-lobe-main-lobe-ratio, SLMLR and partly by the noise power of the interpolation error. The FWHM and the SLMLR are calculated in the horizontal plane at the depth of each of the point scatterers and compared to the case where the reference data is used. A. Simulation setup The ultrasound RF signals for the investigation is created us- ing Field II with a 192-element, 7 MHz linear array transducer with λ pitch as simulation model and a 3-cycle sinusoid as excitation. The simulation is based on point scatterers placed at a depth of 10 mm to 80 mm with 5 mm between each, placed along the center of the transducer. A reference RF data set has been created using a sampling frequency of 1 GHz and linear interpolation and the evaluation RF data set is created by decimating the reference data (picking out samples) to a sampling frequency of 40 MHz. Two data sets are created. One by using conventional B-mode imaging, and one by using

P2B-1 Synthetic Aperture Focusing Applied to Imaging Using a Rotating Single Element Transducer

This paper applies the concept of virtual sources and mono-static synthetic aperture focusing (SAF) to 2-dimensional imaging with a single rotating mechanically focused concave element with the objective of improving lateral resolution and signal-to-noise ratio (SNR). The geometrical focal point of the concave element can be considered as a point source emitting a spherical wave in a limited angular region. The SAF can be formulated as creating a high resolution line as a sum over low resolution lines (LRL). A LRL is the contribution from a single emission. Simulation in Field II is based on moving the concave element of radius 2.5 mm along a circle of radius 10 mm. Elements with different concave curvatures are used to obtain geometrical focusing depths at 10 mm, 15 mm, and 20 mm. Point targets in the range from 5 mm to 65 mm are used as image objects. The high resolution images (HRI) are shown and the radial and angular resolution are extracted at -6 dB and -40 dB. The performance of the setup with a VS at 20 mm is superior to the other setups. Due to the rotation, the synthesized aperture only experiences a moderate expansion, which is not sufficient to reduce the extent of the wide point spread function of a single emission. The effect of SAF with focal depth at 20 mm is negligible, caused by the small number of LRL applied. The great profit of the SAF is the increase in SNR. For the setup with focal depth at 20 mm the SAF SNR gain is 11 dB. The SNR gain of a setup with a VS at radius 10 mm or 15 mm over conventional imaging with a VS at 20 mm, is also 11 dB.

Determination of velocity vector angles using the directional cross-correlation method

A method for determining both velocity magnitude and angle in any direction is suggested. The method uses focusing along the velocity direction and cross-correlation for finding the correct velocity magnitude. The angle is found from beamforming directional signals in a number of directions and then select the angle with the highest normalized correlation between directional signals. The approach is investigated using Field II simulations and data from the experimental ultrasound scanner RASMUS and with a parabolic flow having a peak velocity of 0.3 m/s. A 7 MHz linear array transducer is used with a normal transmission of a focused ultrasound field. The velocity profile estimates from simulations have relative mean standard deviations between 0.7% and 7.7% for flow between 45 ◦ and 90 ◦ . The angle estimation performance is highly dependent on the choice of the time ktprf · Tprf (correlation-time) between signals to correlate, and a proper choice varies with flow angle and flow velocity. One performance example is given with a fixed value of ktprf for all flow angles. The angle estimation on measured data for flow at 60 ◦ to 90 ◦ , yields a probability of valid estimates between 68% and 98% and with standard deviations between 1 ◦ and 4 ◦ . The optimal value of ktprf for each flow angle is found from a parameter study to reveal the potential of the method and with these values the performance on simulated data yields angle estimates with no outlier estimates and with standard deviations below 2 ◦ .

Effective and versatile software beamformation toolbox

Delay-and-sum array beamforming is an essential part of signal processing in ultrasound imaging. Although the principles are simple, there are many implementation details to consider for obtaining a reliable and computational efficient beamforming. Different methods for calculation of time-delays are used for different waveforms. Various inter-sample interpolation schemes such as FIR-filtering, polynomial, and spline interpolation can be chosen. Apodization can be any preferred window function of fixed size applied on the channel signals or it can be dynamic with an expanding and contracting aperture to obtain a preferred constant F-number. An effective and versatile software toolbox for off-line beamformation designed to address all of these issues has been developed. It is capable of exploiting parallelization of computations on a Linux cluster and is written in C++ with a MATLAB(MathWorks Inc.) interface. It is an aid to support simulations and experimental investigation of 3D imaging, synthetic aperture imaging, and directional flow estimation. A number of parameters are necessary to fully define the spatial beamforming and some parameters are optional. All spatial specifications are given in 3D space such as the physical positions of the transducer elements during transmit and receive and the positions of the points to beamform. The points of focus are defined as a collection of lines each having an origin, a direction, a distance between points and a length. The transducer, the points to beamform, and the apodization are defined as individual objects and a combination of these define the actual beamforming. Once the beamforming is defined, the time-delays and apodization values for every combination of transmit elements, receive elements and focus points can be calculated and stored in lookup-tables (LUT). Parametric beamforming can also be applied where calculations are done by demand, thus, reducing the storage demand dramatically. On a standard PC with a Pentium 4, 2.66 GHz processor running Linux the toolbox can beamform 100,000 points in lines of various directions in 20 seconds using a transducer of 128 elements, dynamic apodization and 3rd order polynomial interpolation. This is a decrease in computation time of at least a factor of 15 compared to an implementation directly in MATLAB of a similar beamformer.

Transverse correlation: An efficient transverse flow estimator - initial results

Color flow mapping has become an important clinical tool, for diagnosing a wide range of vascular diseases. Only the velocity component along the ultrasonic beam is estimated, so to find the actual blood velocity, the beam to flow angle has to be known. Because of the unpredictable nature of vascular hemodynamics, the flow angle cannot easily be found as the angle is temporally and spatially variant. Additionally the precision of traditional methods is severely lowered for high flow angles, and they breakdown for a purely transverse flow. To overcome these problems we propose a new method for estimating the transverse velocity component. The method measures the transverse velocity component by estimating the transit time of the blood between two parallel lines beamformed in receive. The method has been investigated using simulations performed with Field II. Using 15 emissions per estimate, a standard deviation of 1.64% and a bias of 1.13% are obtained for a beam to flow angle of 90 degrees. Using the same setup a standard deviation of 2.21% and a bias of 1.07% are obtained for a beam to flow angle of 75 degrees. Using 20 emissions a standard deviation of 3.4% and a bias of 2.06% are obtained at 45 degrees. The method performs stable down to a signal-to-noise ratio of 0 dB, where a standard deviation of 5.5% and a bias of 1.2% is achieved.