PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Local Phase Velocity Imaging (LPVI) as a New Technique for Shear
Wave Elastography
Matthew W. Urban 1; Piotr Kijanka1,21
2

Department of Radiology, Mayo Clinic, Rochester, MN, USA

Department of Robotics and Mechatronics, AGH University of Science and Technology, Krakow, PolandABSTRACT
Shear wave elastography is used in many clinical settings to measure the mechanical properties of soft tissues
such as the liver, kidney, breast, and thyroid. In most implementations, the shear wave group velocity ismeasured using time-of-flight methods in the time-domain. However, different factors related to theestimation of the group velocity can cause variation in the results. Factors such as acquisition parameters,processing, tissue inhomogeneities and viscoelasticity can cause these variations. We propose to use methods
that rely on phase velocities, shear wave velocities at specific frequencies, to standardize measurements
across different clinical applications. We have developed methods for creating maps of phase velocity usingLocal Phase Velocity Imaging (LPVI). The LPVI method involves directional and wavenumber filtering
before applying various steps of Fourier-based operations to obtain localized maps of phase velocity overlarge bandwidths. We will demonstrate how LPVI works in numerical data, tissue mimicking phantoms, andin vivo liver tissue. The LPVI method has enormous potential because the frequency, for which the phasevelocity maps are reconstructed, can be controlled, optimized, and standardized for a wide array of clinicalapplications.
Keywords: Ultrasound, shear wave elastography, phase velocity, inclusion, viscoelasticity.

1. INTRODUCTION

Shear wave elastography (SWE) is increasingly being used for multiple clinical applications (1-3).
Typically, a focused ultrasound “push” beam to create acoustic radiation force (ARF) is used togenerate propagating shear waves. Ultrafast ultrasound imaging techniques are used for tracking thepropagation of the shear waves. Time-of-flight (TOF) algorithms are used to measure the groupvelocity, or propagation velocity of the time-domain wave packet. The group velocity or Young’s
modulus is typically reported in clinical implementations of SWE (2).
Generally, an assumption is made that the tissue is linear, elastic, homogeneous, isotropic, andincompressible. However, soft tissues are inherently viscoelastic and the frequency content of thewave can affect the group velocity estimate. As an alternative, the phase velocity, or wave velocity ata particular frequency, can be estimated. If a certain frequency or set of frequencies were used for anapplication, this could provide a level of standardization that may not be present in the case of usinggroup velocity estimates.
Multiple methods have been employed for generating two-dimensional (2D) images of the groupvelocity (4-7) using different TOF algorithms. Recently, several groups have pursued creating 2D
images of phase velocity. Budelli, et al., reported a method that used a sliding window to compute thephase gradient (8). Additionally, we developed a method called local phase velocity imaging (LPVI),
which is described in detail in this paper (9). The LPVI method uses a sliding window and Fourier
techniques, as well as, directional and wavenumber filtering to recover local estimates of phasevelocities at specified frequencies or bands of frequencies. Examples of the uses of LPVI in phantoms
and in vivo tissue will be shown.

128218urban.matthew@mayo.edu
kijanka.piotr@mayo.edu; piotr.kijanka@agh.edu.pl2. METHODS
2.1 Description of LPVI
A block diagram for the LPVI reconstruction is shown in Fig. 1. The three-dimensional (3D) shear
wave data v(z,x,t) is acquired after an acoustic radiation force push and ultrasound acquisition of datafor estimating the wave motion. The data is transformed into a Fourier domain with dimensions(kz,kx,f) for the purposes of applying directional and bandpass wavenumber filters. The directional
filter will typically isolate waves that are traveling left-to-right (LR) or right-to-left (RL). The
wavenumber filter can be applied to limit waves traveling over a certain range of wave velocities suchas from 0.5-10.0 m/s. After applying the filters, the inverse Fourier transform is applied to return to thespatiotemporal domain. The next step is to apply a one-dimensional (1D) Fourier transform and selecta frequency of interest, f0 . Once the frequency of interest is identified, a sliding window, W x,z , isapplied. A 2D spatial Fourier transform is applied for each set of windowed data and the dominant
wavenumber is identified. This wavenumber is used for the calculation of the phase velocity for thatspatial window. As the spatial window is applied over the whole imaging plane, the aforementioned
steps of calculating the 2D spatial Fourier transform and phase velocity calculation are performed until
the whole image is reconstructed. For more details, the reader is referred to (9). This process iscompleted for data acquired with an ARF push to the left of the region-of-interest (ROI) and another tothe right of the ROI, and the two reconstructions are averaged.

Figure 1 – Block diagram for LPVI image reconstruction.
2.2 Phantom Experiments
The LPVI method was tested on data sets acquired from imaging phantoms. The data was acquired
using a Verasonics system (V1, Verasonics, Kirkland, WA) equipped with a L7-4 linear arraytransducer (Philips Healthcare, Andover, MA). An ARF push beam was used to generate shear waves,and angular plane wave compounding was used for the motion tracking acquisition (10). Motion wasestimated using an autocorrelation algorithm (11).
Figure 2 shows the results in two elastic homogeneous phantoms (Model 039, CIRS, Inc., Norfolk,VA) at various frequencies. The results are relatively uniform and constant across frequency. Figure 3
shows results from Type IV inclusions with diameter of 6.49 mm with Young’s modulus of E = 80 kPa
in a background of E = 25 kPa (Model 049A, CIRS, Inc., Norfolk, VA) over a series of sliding windows,W x,z , for f 0 = 947 Hz. As the window size increases, the edge of the reconstructed inclusion becomessmoother.
Figure 4 shows the results in the inclusion phantom with a window of 4.0 x 4.0 mm for various
frequencies. The shape of the inclusion becomes more circular as the frequency increases, and theaverage value increases as well. Figure 5 shows the LPVI reconstructions for inclusions of different
size at f 0 = 1000 Hz. The inclusions have good contrast down to a diameter of 4.05 mm while theinclusion with a diameter of 2.53 mm is not well visualized.
Figure 6 shows LPVI reconstructions from custom made homogeneous viscoelastic phantoms(CIRS, Inc., Norfolk, VA). In the viscoelastic media, the phase velocity is fairly uniform and varies asa function of frequency.
Figure 7 shows the results from a simulation model with a background modulus E = 7.84 kPa, andinclusions with E = 25 and 3.24 kPa, for the top and bottom inclusions, respectively. Each8219

reconstruction used a different combination of motion (particle displacement or velocity), use of
directional and wavenumber filters, and the use of individual ARF push beams or simultaneous use ofARF push beams. The reconstructions using the particle velocity and directional and wavenumber
filters were the best reconstructions. The particle displacement at higher frequencies did not provide
valid reconstructions.
2.3 In Vivo Liver Experiments
Measurements were made in the liver of a healthy human subject. The experiment protocol wasapproved by the Mayo Clinic Institutional Review Board and written informed consent was obtained
prior to scanning. Under the guidance of B-mode imaging, a trained sonographer located a region ofinterest within the liver. A Verasonics Vantage system (Verasonics, Inc., Kirkland, WA) was used witha C5-2v transducer (Verasonics, Inc., Kirkland, WA). To produce shear waves, a single focused pushbeam with push duration of 600 μs was transmitted. The motion tracking was performed using wide
beams with an f /9.9 focal configuration transmitted with a frequency of 2 MHz. Received signals fromtwo steering angles were compounded (10), giving an effective pulse repetition frequency of 2.77 kHz.

3. RESULTS
3.1

Phantom Experiments

Figure 2 – LPVI results in elastic homogeneous phantoms with a sliding window of W x,z = 4.0 x 4.0mm. Top row: Phantom with E = 10 kPa with reconstructions at f0 = 350, 450, and 550 Hz. Bottom row:
Phantom with E = 25 kPa with reconstructions at f0 = 500, 700, and 900 Hz.

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Figure 3 – LPVI results in elastic phantom with a cylindrical inclusion at f0 = 947 Hz with different
sliding windows.

Figure 4 – LPVI results in elastic phantom with a cylindrical inclusion with Wx,z = 4.0 x 4.0 mm andvarying frequencies.

Figure 5 – LPVI results in elastic phantom with cylindrical inclusions of varying size at a frequency of1000 Hz.

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Figure 6 – LPVI results in viscoelastic homogeneous phantoms with varying frequencies.

Figure 7 – LPVI results in simulated elastic phantom with inclusions processed with different shear
wave motion and filtering. I. particle displacement signal as an input signal, with inactive directional
and wavenumber filters, for a single ultrasound focused push beam; II. particle velocity signal as aninput signal, with inactive directional and wavenumber filters, for a single ultrasound focused pushbeam; III. particle displacement signal as an input signal, with active directional and wavenumber
filters, for a single ultrasound focused push beam; IV. particle velocity signal as an input signal, withactive directional and wavenumber filters, for a single ultrasound focused push beam; V. particle
displacement signal as an input signal, with active directional and wavenumber filters, for multiple
ultrasound focused push beams; VI. particle velocity signal as an input signal, with active directional
and wavenumber filters, for multiple ultrasound focused push beams. Vertical, dashed lines separate
regions where the focused ultrasound push beams were located.
3.2 In Vivo Liver Experiments
Figure 8 shows the results from in vivo liver at 90, 130, and 170 Hz. The phase velocity increases

8222with frequency and the maps are generally uniform with ROIs of size 10 x 7 mm. The ROI is smaller inthe liver compared to the purely elastic materials due to the shear wave attenuation associated withviscoelastic materials.

Figure 8 – LPVI results in in vivo liver tissue with varying frequencies.

4. DISCUSSION

We presented a new method called local phase velocity imaging. This method has been extensivelytested in phantoms and we have explored how different parameters are related to how thereconstruction affects the resulting images. Among these parameters are the window size, thefrequency of interest, and motion type, and the use of directional and wavenumber filters.
The LPVI method produces very uniform reconstructions in homogeneous media as demonstratedin Figs. 2, 6, and 8. The ROI size can be larger in materials that more elastic compared to viscoelasticmaterials. In the viscoelastic material, the shear wave attenuates with distance and reduces theeffective ROI size.
There is a trade-off when choosing the window size. With smaller windows, the transition zone isshorter from the inclusion to the background, but there is more variation in the inclusion andbackground. With a larger window, the variation is reduced substantially, but the transition is increased.
As the frequency increases, the transition from the inclusion to the background is sharper. Additionally,as the frequency increases, the mean value of the inclusion increases.
We have generally used the particle velocity to perform the reconstructions with LPVI as thefrequency content of the shear waves covers a larger bandwidth as compared to the particle
displacement. However, as demonstrated in Fig. 7, the displacement can be used reliably if appropriate
directional and wavenumber filters are employed.
Also, in Fig. 7, we demonstrated that using two separate ARF pushes or one simultaneous push withtwo ARF push beams, we can reconstruct similar images. This is advantageous for saving time in theacquisition as is done with the comb push ultrasound shear elastography (CUSE) method (6, 12).
In the future, we need to evaluate using the LPVI method for in vivo use in homogeneous orheterogeneous tissues. There is a large potential for standardizing reconstructions to a particularfrequency for different applications for optimal separation of normal versus abnormal tissue.
The frequencies that have been used in some of the elastic reconstructions are high for most SWE
applications, >500 Hz. To produce shear waves with broad frequency content, we will also explore
ways to optimize the ARF pushes including the shape and duration.

5. CONCLUSIONSThe local phase velocity imaging method is a robust approach for reconstructing images of phasevelocity. We have demonstrated reconstructions in homogeneous elastic and viscoelastic materials. Inaddition, we have reconstructed images in elastic phantoms with simulated inclusions. We have tested
multiple parameters related to the LPVI reconstructions including the sliding window size, thefrequency of interest, the type of shear wave motion used, the used of directional and wavenumber
filters, and the type of ARF excitation that is employed. Optimal imaging is performed with the use ofparticle velocity with directional and wavenumber filters. Future work will be devoted towards
optimizations for specific in vivo applications.

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ACKNOWLEDGEMENTS

This work was supported in part by grant R01DK092255 from the National Institutes of Health andin part from Mayo Clinic Research Committee. The content is solely the responsibility of authors anddoes not necessarily represent the official views of the National Institute of Diabetes and Digestive andKidney Diseases or the National Institutes of Health.

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