Anatomic and Functional Imaging Using Row–Column Arrays

Row–column (RC) arrays have the potential to yield full 3-D ultrasound imaging with a greatly reduced number of elements compared to fully populated arrays. They, however, have several challenges due to their special geometry. This review article summarizes the current literature for RC imaging and demonstrates that full anatomic and functional imaging can attain a high quality using synthetic aperture (SA) sequences and modified delay-and-sum beamforming. Resolution can approach the diffraction limit with an isotropic resolution of half a wavelength with low sidelobe levels, and the field of view can be expanded by using convex or lensed RC probes. GPU beamforming allows for three orthogonal planes to be beamformed at 30 Hz, providing near real-time imaging ideal for positioning the probe and improving the operator’s workflow. Functional imaging is also attainable using transverse oscillation and dedicated SA sequence for tensor velocity imaging for revealing the full 3-D velocity vector as a function of spatial position and time for both blood velocity and tissue motion estimation. Using RC arrays with commercial contrast agents can reveal super-resolution imaging (SRI) with isotropic resolution below $20~ \mu \text{m}$ . RC arrays can, thus, yield full 3-D imaging at high resolution, contrast, and volumetric rates for both anatomic and functional imaging with the same number of receive channels as current commercial 1-D arrays.

I. INTRODUCTION 28 C URRENTLY, 2-D ultrasound imaging is mostly con-29 ducted using 1-D array transducers with 192-256 ele-30 ments, which are employed to dynamically focus on the 31 image. Digital beamformers are used, where the signal from 32 each transducer element is sampled at 4-8 times the center 33 frequency for sampling rates between 12 and 60 MHz. A fully 34 populated 15-MHz array with 256 channels will, thus, give 35 data rates up to 30.7 GB/s, which are beamformed in real 36 time. Currently, most arrays have a fixed geometric focus in 37 the elevation plane (orthogonal to the imaging plane), and 38 the focusing is often poor in this direction, underlining the 39 necessity for 3-D focusing and imaging.

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Attaining 3-D ultrasound images requires electronic steering 41 in both the azimuth and elevation directions to allow dynamic 42 focusing along all three directions (axial, azimuth, and ele-43 vation). Matrix arrays were early conceived as they allow 44 full control in both directions in both transmit and receive. 45 However, it creates another practical problem as the number 46 of channels increased quadratically with the side length of 47 the array assuming a square array aperture. A straightforward 48 translation to 3-D would give arrays with 192 × 192 = 36 864 49 elements or 256 × 256 = 65 536 elements yielding data rates 50 of 2560 GB/s, which is clearly not possible to process in real 51 time. This has been solved by making sparse matrix probes, 52 where only part of the elements are connected resulting in 53 higher sidelobe levels [1]- [6]. A second approach is to make 54 micro-beamforming in the handle to reduce the amount of 55 data. Philips has introduced the fully sampled matrix phased 56 array x-matrix probe shown in Fig. 1 with 9212 elements, 57 which potentially could have 96 × 96 elements. Such a probe 58 can be steered in both directions, and this necessitates an 59 element size of half a wavelength λ given by 104 It is, thus, possible to have very large RC arrays without the 105 amount of connections to the array getting prohibitively large. 106 The consequence of this is a theoretical focusing capability, 107 which is much better than for a fully populated array, as the width of the array is larger, and the FWHM is correspondingly 109 smaller.

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The area of the array scales quadratically with the side 111 length or element count, which is beneficial for the transmitted 112 pressure and the received energy. RC probes can therefore have 113 an increased penetration depth compared to other probes as 114 demonstrated in [26].

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The initial idea of RC arrays was presented by Morton 116 and Lockwood [7] at Queen's University, Kingston, ON, 117 Canada, with simulations of a convex array for revealing the 118 imaging area and PSF. Further simulations were given in [17]. 119 Fabrication of such an array and data from its use was given 120 in [27].

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The group by Daher and Yen [9] at the University of 122 Southern California, Los Angeles, CA, USA, has also fabri-123 cated a number of arrays and extensively investigated their 124 performance. Initial simulations of a 256 × 256 RC array 125 were presented in [8] with more extensive simulations in [9]. 126 Results from a 64 × 64 PZT array operating at 5.6 MHz were 127 shown in [10] and later for an impressive 256×256 PZT array 128 operating at 6.4 MHz with a size of 40 mm × 40 mm [12]. 129 More results from a cyst phantom were presented in [13] and 130 a full overview of the results are given in [16]. A spatial 131 compounding method for RC arrays used on the 256 × 256 132 PZT array is described in [14]. Examples of a 32×32 elements and for 30 MHz in [36], demonstrating the good image quality 167 of these arrays and imaging schemes. 168 Flesch et al. [37] at the Institut Langevin, Paris, France, 169 have also worked extensively with RC arrays, especially for 170 flow estimation and super-resolution imaging (SRI). A plane 171 wave compounding scheme was described and used for power 172 Doppler imaging (detecting the presence of flow). Using that 173 scheme for flow imaging has unfortunately revealed fairly 174 high grating lobes [38]. The approach has also been used for 175 imaging a rat brain in [ lenses and probes with integrated lenses [42], [43]. The various 183 results and possibilities will be presented in the following. The 184 challenges of using the RC array are detailed in Section II, 185 the possibilities for making anatomic images are shown in 186 Section III, and the blood velocity estimation is presented in 187 Section V. A method for SRI is presented in Section VI, and 188 a discussion of the benefits, challenges, and future potential is 189 presented in Section VII.

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II. CHALLENGES FOR RC IMAGING 191 RC arrays have a number of challenges, which have to 192 be addressed before high-quality imaging, can be performed. 193 As for all ultrasound imaging schemes, data can be acquired 194 in principally two different ways: focused emissions or broad 195 insonation of the region of interest. The first option will, for 196 3-D imaging, give an unacceptably low volume rate, unless 197 multiple lines are beamformed in receive as in the early 198 approaches to volumetric imaging [44], [45]. The second 199 approach broadly insonates the volume of interest using cylin-200 drical or plane waves, which decouples the frame rate and the 201 number of image lines. Examples of such imaging will be 202 given in Section III.

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A second challenge is the large elements. In ordinary imag-204 ing, the elements can be considered point sources and delay-205 and-sum beamforming is employed based on the geometric 206 distance from emissions through the imaging point to the 207 receiving element. For an RC array, the elements are large, 208 and this changes the emitted field and the calculation of delays. 209 The long elements will give rise to an emitted field, which can 210 be considered a plane wave along the length of the element and 211 a circular wave across the element or essentially a cylindrical-212 shaped wave. This should be taken into consideration when 213 predicting the wavefront's position in focusing on the image, 214 as is done in the beamformers described in [24]. The focusing 215 calculation in the two orthogonal planes is shown in Fig. 3 for 216 the time-of-flight (ToF) calculation. A precise mathematical 217 description of this can be found in [24].

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The large-size elements only make it possible to image in 219 the rectangular region below the probe, and the beam cannot 220 be steered outside this region for pulse-echo imaging. How to 221 solve this problem is described in Section IV-B on lensed and 222 convex RC arrays.

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A third challenge from the long elements is the edge waves 224 generated at the ends of the element. The long elements 225 will delay these edge waves significantly compared to the 226 main wave, and this leads to ghost echos after the main 227 PSF, as shown in Fig. 4. The top image shows the PSF 228 for a 62 × 62 elements array, where edge echoes are seen 229 after the main response. This can be avoided by introducing 230 a roll-off apodization at the edge of the elements to taper 231 off their end response and reduce edge artifacts. This has 232 been employed on the bottom figure, where the ghost echoes 233 disappear.

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The major benefit of the RC arrays is of course their size, 235 which benefits their focusing ability and penetration depth. 236 This is shown in Fig. 5, where they are compared to both 237 fully populated arrays and sparse Mills cross arrays [46]. The 238 area, corresponding to penetration depth, is always larger for 239 RC arrays and the side length is the same as for the most 240 sparse 2-D array, yielding a comparable FWHM resolution. 241 The RC arrays, thus, attain both a good penetration depth and 242 a narrow focus. RC arrays, however, have several issues to address to attain 244 high-quality imaging, including that the contrast of the images 245 is often slightly lower than for current 2-D scanners. These  also called ultrafast imaging, has been studied in [37], [38], 261 and [47], which, however, seems to give fairly high sidelobe 262 and grating lobes.

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The second wave type is circular waves, which are plane both transmit and receive [48]. The imaging is performed by 272 circular transmission with a single or a collection of elements.

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The origo of the wave is therefore known precisely and can 274 be used in the beamformation. The scattered signal is then 275 received by all elements of the orthogonal transducer elements. 276 The path from transmission to reception can, thus, be precisely 277 calculated. A full volumetric image of the object is focused for 278 each emission as the whole image volume is insonified. This 279 is a low-resolution volume, as it is only focused in transmit. 280 Repeating the process for a number of virtual sources and 281 summing all the low-resolution volumes will yield a high-282 resolution volume, which is dynamically focused on both 283 transmit and receive.

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The spread of the virtual sources and the corresponding 285 largest distance span will determine the FWHM attainable in 286 the transmit direction and correspondingly, the spread of the 287 receive elements will determine the FWHM in the orthogonal 288 direction. The contrast for the resulting PSF is determined by 289 the number of transmit sources and the number of receiving 290 elements. Currently, the best image quality is attained by 291 emitting with a virtual source in one direction and then 292 receiving with the orthogonal elements. SA focusing will 293 then yield the optimal PSF if the beamformer described in 294 Section IV-A is employed. Often a group of elements is used 295 as emitters to increase the emitted energy [49], [50], and the 296 effective width of the aperture is then reduced by the number 297 of elements in the virtual source.

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The focusing ability is also dependent on how many receiv-299 ing element that can contribute to the receive focusing, which 300 is determined by the acceptance angle given by [51] 301 α = 2 arctan 1 2F# .

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A wide element will restrict the acceptance angle and increase 303 the possible F-number. The minimum attainable F-number 304 of 0.5 is obtained when the element has a size of half a 305 wavelength. This also applies for the transmitting elements, 306 and the ideal pitch of the RC array is, thus, λ/2.  Fig. 6, and Field II [53], [54] was used for 322 the corresponding simulation shown in the second row.

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An isotropic resolution of (1.05λ, 1.10λ, 0.62λ) = (x, y, z) 324 is attained for the measured data, and a similar performance 325 is seen for the simulated data. The data are also compared to   Finally, the bottom row in Fig. 6 shows the in vivo images 340 of a Sprague-Dawley rat kidney. The dynamic range is 60 dB 341 and an isotropic speckle pattern is seen in all three imaging 342 planes due to SA imaging, a constant F-number throughout 343 the image, and the large size of the RC array. The top row shows the measured images in the xz, yz, and yx planes (left to right). The corresponding simulated data from the phantoms are shown in the next row. Simulated data for a linear array probe translated across the phantom are shown in the next row for a GE 6-MHz linear array using an SA sequence. The bottom row shows the images of a rat kidney in all three planes.
The array used here is far from optimal for SA imaging.

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No edge apodization is included in the array and the probe 355 pitch is λ, which limits the acceptance angle in both transmit 356 and receive. An optimal array with both these properties 357 does currently not exist and can therefore only be simulated.

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The optimal resolution possible using SA imaging for a 359 192 × 192 elements RC array has been simulated for two 360 types of arrays in [55]. Both have λ/2 pitch for optimal 361 imaging with geometries shown in Fig. 8, where the first is a 362 traditional rectangular grid array and the other is an interwoven 363 array for increasing the active area of the array. The second 364 array is only possible to manufacture with silicon CMUT 365 fabrication processes, whereas the first array can be made 366 using the traditional PZT technology. The long elements are 367 edge apodized to avoid the ghost artifacts after the PSFs. 368 Imaging is conducted by emitting with one element at a 369 time and receiving with the orthogonal elements, so a full 370 volume uses 192 emissions, which is the same as for normal 371 Fig. 7. Two left columns: orthogonal wire phantom images for the Vermon RC probe for a matrix wire phantom with two rows of wires stretch out along the y-direction. Two right columns: orthogonal cyst phantom images for the Vermon RC probe for a tissue-mimicking phantom with an acoustical attenuation of 0.5 dB/[MHz·cm].  The large active area of the RC probe is advantageous for 385 attaining a large penetration depth, defined as the imaging 386 depth, where the signal-to-noise ratio attains a value of 0 dB. 387 This is shown in Fig. 9, where the 128 × 128 elements 388 Vermon RC array was used for imaging a cyst phantom with 389 an attenuation of 0.5 dB/[MHz·cm]. The 6-MHz PZT array 390 attains a penetration down to 11 cm or 428λ when using only 391 32 elements in transmit using an F-number of −1. Similar 392 results have been attained in [26] for two 62 × 62 elements 393 RC arrays, one fabricated using CMUT technology, and one 394 traditional PZT array. The 3-MHz PZT array attained a pen-395 etration down to 14 cm when using only a single element in 396 transmit, whereas using an F-number of 1 or −1 gave predicted 397 penetration depths of 25-30 cm, considerably more than the 398 conventional array's penetration of 300λ-400λ (15-20 cm). 399 Here, it should also be kept in mind that these are first version 400  spherical delay calculation is shown in Fig. 11, where the 435 received signal quickly attains the wrong geometric position, 436 if the new calculation method is not employed. This can 437 both lead to the geometric distortion shown but also leads 438 to a diminished resolution and contrast, if not implemented 439 properly.

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Efficient implementations of this type of beamforming have 441 been developed for a GPU in [58] and [59]. The software 442 is written under the CUDA environment and takes in radio 443 frequency (RF) data from the RC channels and then yields a 444 focused line, image, or volume. The beamformer is parametric 445 and can be used for very large volumes only limited by the 446 RAM of the GPU card. An example of performance for a 447 state-of-the-art Titan V Nvidia card is shown in Fig. 12    Lensed RC probes are in the early stage of development, 475 and very few results have so far been published [60], [61]. The diverging lens beamformer has been simulated for both 483 point and cyst phantoms with good results demonstrating the 484 larger field of view. The same general trend is seen for the cyst 485 phantom simulations, where a larger field of view is attained 486 along with a good contrast in the image [60]. Lenses for the 487 62 × 62 elements RC array have been fabricated and tested 488 on the arrays. Results for wire and cyst phantoms have been 489 measured and processed and are shown in Figs. 15 and 16. 490 They both show similar results as for the simulations that an 491 increased field of view is attained along with good focusing 492 abilities and an acceptable contrast. More results and details 493 can be found in [61]. 494 The current equations in the lensed beamformer give rea-495 sonable results, but it has been shown that ray-tracing theory 496 can further enhance the quality of the results and increase the 497 field of view [62]. This should be further investigated and 498 incorporated in the beamformers. An obvious method to avoid making a lens would be to 501 shape the RC probe in a double curved, convex shape as 502 suggested in [17]. The SA sequence developed for flat RC 503 arrays would be nearly directly applicable to a convex array, 504 where the beamforming then would take the geometry into 505 account. Such arrays would have many benefits for abdominal 506 ultrasound imaging. Their footprint could be made quite large, 507 which ensures a low F-number even for large depths. The 508 large size would also ensure a large penetration depth, as the 509 emitted energy is distributed over a large area keeping MI low 510 but still acquiring the returned energy from a large surface. 511 Démoré et al. [17] demonstrated that a 128 × 128 RC convex 512 array could cover at 60 • × 60 • sector with a good image 513 quality using their imaging scheme.  . Here, the full 3-D blood velocity is estimated 545 in the volume for each time instance for full tensor velocity 546 imaging (TVI). The probe can be placed to just cover the 547 vessel, and the full velocity vector is estimated for any position 548 in the volume with hundreds of estimates per second.

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An example of TVI is shown in Fig. 17 for measured pulsat-550 ing flow in a carotid artery phantom, where the arrows indicate 551 the direction and the colors indicate the velocity magnitude. 552 The velocities over time for different positions in the vessel are 553 shown in Fig. 17, showing that the velocity components in all 554 directions can be estimated as a function of time everywhere 555 in the volume. The full 3-D vector velocity field can therefore 556 be acquired for a couple of heartbeats, and the velocity for 557 any place and time can be determined retrospectively after 558 the acquisition has been made, thus increasing the clinical 559 relevance.

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Further validation of the TVI method was performed using 561 finite element method (FEM) simulations of pulsating flow 562 in an in silico carotid artery phantom [75], where the ground 563 truth is known. Motion correction was employed to improve 564 the estimates [72], and the result is shown in Fig. 18 for both 565 an autocorrelation estimator (left column) and cross correlation 566  . The 580 data are acquired over minutes and motion correction of 581 the acquired data must be performed to maintain resolu-582 tion [83]- [89], but as most of the current methods are in two 583 dimensions, they cannot compensate for large motions and 584 out-of-plane motion. 585 Fig. 19. Super-resolution images of the vasculature in a Sprague-Dawley rat kidney acquired in vivo using the 6 MHz 128 × 128 RC array. SonoVue was injected intravenously and the data acquired over 135 seconds. The images show the large segmental arteries and veins, the smaller arcuate vessels, and the small cortical radial vessels extending toward the surface of the kidney. The B-mode images are shown in Fig. 6.
It has been demonstrated that RC probes can also be 586 used for SRI [90].  Fig. 19 for three different views.

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The volume rate was fairly low, to keep the data rate low to  It has been shown that RC arrays essentially can be used for 629 any kind of ultrasound imaging for visualizing the anatomy, 630 blood flow, and tissue motion and performing SRI allowing 631 visualization of the microvasculature and measurement of flow 632 velocities in the microcirculation. The active number of array 633 elements is of the same order as for conventional 1-D arrays, 634 and the number of transmitters and receivers is therefore as 635 for conventional 2-D imaging. Demands on the transmit stage 636 receive data rates, and storage sizes are also the same as for 637 2-D imaging. The number of beamforming operations depends 638 on what should be visualized in terms on planes and volumes, 639 but high-end GPU cards are capable of attaining real-time 640 visualization of orthogonal planes, and 3-D solid volumes can 641 be calculated in seconds [58], [59].

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A good B-mode image quality can be attained by using SA 643 sequences with 2 × 96 emissions on a 128 × 128 elements 644 RC array, yielding an isotropic PSF in the region where a 645 constant F-number can be maintained. FWHM can be close to 646 the diffraction limit if the array is optimized for high-quality 647 imaging with edge apodization and a pitch of λ/2. Even the 648 first version substandard arrays with λ pitch and no edge 649 apodization can yield high-quality in vivo images as shown on 650 a rat kidney scan. Comparing these results to traditional 2-D 651 imaging, it should be kept in mind that the yz and x y planes 652 are never shown. These planes for traditional linear arrays 653 with a fixed geometric focusing have very poor resolution, 654 which at the optimal geometric focusing often is 3-5λ and 655 away from this focus can be 10λ-20λ instead of 0.6λ attained 656 here. With the RC arrays, it is, thus, possible to attain an 657 isotropic resolution, and much better imaging with a uniform 658 speckle pattern is possible, where any slice and orientation 659 can be attained retrospectively after the data have been 660 stored.

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The large size of the arrays, and the use of the full aperture 662 during reception and synthetic transmission, makes the signal-663 to-noise ratio high. The penetration depth is above 550λ 664 even for low-intensity and low MI transmission and can be 665 increased to be above 800λ for higher pressure transmission 666 surpassing that of conventional 1-D arrays. This is also sur-667 passing 2-D matrix arrays, as their elements are small and 668 often sparse arrays have to be used to keep the element count showed that edge apodization of the elements is vital for 717 avoiding ghost echoes, and the imaging also benefits from 718 having λ/2 pitch elements, which very few RC arrays have.

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Having better arrays with the correct geometry will obviously 720 improve both image quality and frame rate to mature RC  Overall, it can, however, be stated that RC arrays can fulfill 727 all the demands for fast, high-quality volumetric ultrasound 728 imaging. Anatomic, flow, functional, and SRI have all been 729 demonstrated for simulations and phantom measurements and 730 a few in vivo examples. It is our hope that the great potential 731 of general RC imaging will be demonstrated in future clinical 732 trials using optimized arrays. The combination of having a 733 large array capable of having a good focusing, contrast, and 734 penetration depth can, especially for abdominal imaging, lead 735 to high-quality 3-D anatomic and functional images.