# Shear Wave Elastography Implementation on a Portable Research Ultrasound System: Initial Results
## 1 Introduction
### Shear Wave Elastography Principles  
Out of all of the elastography approaches that have been developed so far, shear wave elastography (SWE) has emerged as a promising technique of growing interest. In strain elastography (a longstanding and well-established method), tissue stiffness maps are obtained through an analysis of the strains within the tissue under stress, which is applied by the operator. It is typically conducted by pushing the ultrasound probe against the body. In contrast, the SWE technique relies on remotely inducing tissue displacement using the acoustic radiation force (ARF), as first proposed by [PERSON] et al. [2]. The ARF is generated by an ultrasound beam (also called a push beam or push pulse) and is defined in Equation (1) as follows:  
\[\vec{F}=\frac{2\alpha\vec{I}}{c} \tag{1}\]  
where \(\vec{F}\) is the generated force, \(\alpha\) is the absorption coefficient, \(I\) is the acoustic intensity and \(c\) is the speed of the longitudinal wave propagation. As a result of the tissue displacements from applying the ARF, transient shear waves that propagate in the perpendicular direction to the ARF are induced in the elastic medium, as shown in Figure 1. Assuming that soft tissues are incompressible, isotropic, linear and elastic, a local shear modulus \(\mu\) can beobtained by finding the local shear wave propagation speed \(c_{s}\), namely \(\mu=\rho\cdot c_{s}^{2}\), where \(\rho\) is the density (\(\approx\)1000 kg m\({}^{-3}\) for soft tissue). As for soft tissue, the bulk modulus \(B\) is much higher than the shear modulus (\(B>>\mu\)) and the Young's modulus \(E\) of the medium can be estimated using:  
\[E=3\mu=3\rho\cdot c_{s}^{2} \tag{2}\]  
A general SWE measurement procedure is shown in Figure 1. Just as in the vast majority of ultrasonic techniques, the process consists of two stages: data acquisition, followed by data processing with image reconstruction. First, the ARF is generated in the medium using a push pulse. The shear wave motions that result from the impulsive excitation of the ARF can be tracked ultrasonically by detecting small axial displacements along the shear wave propagation path using pulse-echo ultrasound. The shear wave speed (SWS) depends on the characteristics of the elastic medium. Typically, high-frame rate plane wave imaging (PWI) must be used for effective shear wave tracking. Immediately after the end of the push pulse generation, the scanner switches into a high-frame rate imaging mode and captures the RF data. Then, the RF data are used in the beamforming process to reconstruct a series of images. Successive beamformed images are the inputs for the correlation-based algorithm that performs shear wave detection by obtaining the particle axial displacement of each pixel. The known approaches are described in detail in [3]. Finally, shear wave motion data are used to obtain a tissue stiffness map. Several algorithms have been proposed for this, most of which are based on time-of-flight (ToF) methods. These approaches can be divided into two types: linear regression methods [4; 5; 6; 7; 8; 9] and shear wave trajectory detection methods [10; 11].  
The key advantage of SWE is that external, operator-dependent stress is not required due to use of the ARF. Moreover, whereas strain elastography only provides quantitative soft tissue stiffness maps, SWE can estimate soft tissue stiffness both qualitatively and quantitatively. It also possesses the common features of ultrasound imaging, i.e., it is non-invasive, fast and relatively low-cost and it has wide applications, such as [12] fibrosis assessment for chronic liver disease, breast cancer screening, thyroid nodules assessment, gastrointestinal wall diagnostics, prostate abnormality screening and cardiovascular system diagnostics [13].