# Shear Wave Elastography Implementation on a Portable Research Ultrasound System: Initial Results
## 2 Materials and Methods
### Stiffness Map Reconstruction Algorithm  
The data obtained during the acquisition were used as the inputs for a reconstruction algorithm that consisted of multiple steps. Firstly, to improve the signal to noise ratio (SNR) of the RF data, a finite impulse response (FIR) filter was used to filter out the components outside of the 4 MHz-7 MHz band of the probe. Then, standard PWI beamforming was performed, which produced a beamformed in-phase/quadrature (IQ) frame for each angle  
Figure 5: An example data acquisition scheme for the FCUSE-SSI method. To capture the RF data for a full receiving aperture, two transmissions were required, each followed by a 64 RX aperture size. Abbreviations: PRI, pulse repetition interval; FRI, frame repetition interval. transmission with a pixel size of 0.1 mm \(\times\) 0.1 mm. As angle compounding was utilized, an initial phase delay compensation was performed using the method that was proposed by [PERSON] et al. [24]. Once this was accomplished, the angle compounding was performed using a sliding average technique to maintain the high frame rate. The angle-compounded beamformed data were then used for the shear wave motion detection. Shear wave motion produces small tissue displacements that result in differences in the arrival times of the corresponding image line echoes from one frame to another. In the case of IQ data, shear wave motion manifests as a phase difference \(\delta\varphi\) in the corresponding pixels of consecutive frames. The detection of this phase shift allows us to obtain the local axial velocity \(v_{z}\):  
\[v_{z}=\frac{c\cdot\delta\varphi}{4\pi f_{c}\cdot FRI} \tag{4}\]  
where \(c\) is the speed of sound (average of 1540 m/s in soft tissue), \(f_{c}\) is the tracking pulse center frequency and FRI is the frame repetition interval. In this work, the Kasai 1D-autocorrelator algorithm [25] was used to calculate the \(\delta\varphi\) for each pixel in each frame. This method measures the average phase shift over axial sample ranges \(M\) and \(N\) in a slow-time domain. In this study, the values of \(N=2\) and \(M=8\) were used to obtain the 3D shear wave motion data \(v_{z}(x,z,T)\), which were the transient axial velocity as a function of the axial position \(z\), lateral position \(x\) and slow-time \(T\). To reduce the noise content in the signals and the random errors in the shear wave motion data due to finite window lengths or decorrelation, low-pass filtering was applied in the slow-time domain with a cut-off frequency of 700 Hz. The next step of the algorithm involved using a directional filter, which was similar to that proposed by [PERSON] et al. in [26]. As proposed in [27], a 2D filter was applied in the Fourier \((k_{x},\omega)\) space. The motion data were sliced along the depth dimension (\(z\)) to form 2D slices \(v_{z}(x,T)\). A 2D FFT was used to transfer the data from each slice to the Fourier domain and the filtering was performed by multiplying the slices by masks that were designed to extract the shear waves that were propagating from left to right (LR) \(v_{zLR}\) and right to left (RL) \(v_{zRL}\). In addition, the masks were designed to filter out all data components that were related to shear waves propagation speeds that were outside of the 0.5-5.5 m/s range. The mask edges were apodized to minimize the ripples in the spatio-temporal domain. Except separating shear waves that were traveling in opposite directions, these filters attenuated the wave reflections from the interferences of different stiffnesses, such as lesions or stiffer inclusions, which could possibly result in artifacts in the SWS estimates. A time-of-flight (ToF) algorithm, which was similar to that proposed in [4,8], was used in this work to obtain the local SWS in each pixel. The algorithm was run twice to obtain the SWS estimates from both the LR and RL datasets.