## 4 Discussion
### Difference in \(c_{s}\) Estimates between Machines In Vivo  
This study found that _in vivo_, S2000 \(c_{s}\) estimates were on average less than \(c_{s}\) estimates obtained using the Aixplorer. The differences between machines were greater _in vivo_ than _in vitro_, with a maximum cross-machine \(c_{s}\)-ratio of 1.70 _in vivo_ compared to 1.07 _in vitro_. To the authors' knowledge, this is the first study comparing \(c_{s}\) estimates of different elastography machines in the normal breast _in vivo_. Furthermore, \(c_{s}\) estimates between machines were uncorrelated except for \(c_{s}\) estimates for parenchyma averaged across the whole breast. The observed bias and poor correlation between machines exclude the use of an absolute measure of breast stiffness such as \(c_{s}\) or Young's Modulus, i.e., a simple value of breast stiffness would not be reproducible between centres. Further studies comparing these machines are required to determine if these biases can be corrected to provide consistent measures of breast tissue between centres. It is important to note that there were large differences in the variation between machines observed _in vitro_ and _in vivo_. It appears from the data presented here that phantom studies would not be adequate to provide data for cross-calibrations of machines.  
Several studies have compared liver \(c_{s}\) measured using 2D-SWE and pSWE _in vivo_[17; 35; 36; 37] using a range of different commercially available pSWE and 2D-SWE machines and found that 2D-SWE and pSWE could not be used interchangeably to grade the severity of liver fibrosis in patients with liver disease. [PERSON] et al. [20] also compared two 2D-SWE machines (Aixplorer and Aplio 500 (Cancon/Toshiba, Japan)) in 21 patients with liver disease. The mean difference between the two 2D SWE machines was \(-0.6\) ms\({}^{-1}\) and \(95\%\) LOA \(-1.4\) ms\({}^{-1}\) and \(1.2\) ms\({}^{-1}\); which of the machines gave the greatest \(c_{s}\) estimate was not reported.  
Differences between \(c_{s}\) measured by different machines may, in part, be due to differences in the frequency content of the shear-waves. This would be consistent with our observation that such differences are greater for measurements in tissue than in phantoms since tissue is likely to possess increased shear wave dispersion due to viscoelastic damping or scattering of the shear wave relative to that in the phantom. Furthermore, it is possible that the way in which the ARFI pushing beams are executed, as described in the introduction, may result in different shear wave frequencies. Even with similar shear-wave bandwidth, if, to estimate \(c_{s}\), vendors rely on a model of shear-wave propagation that assumes the spatial and temporal characteristics of the acoustic radiation force impulse (ARFI) push and the elastic or viscoelastic properties of the tissue, differences in models may result in differences in estimated \(c_{s}\). It is also feasible that differences between machines arise due to differences in the ways in which their respective measurements of shear-wave speed are affected by the region within the lateral boundaries of the ARFI pushing beam, where a direct and immediate displacement from the ARFI push, whose magnitude decays with off-axis distance according to the ARFI intensity beam profile, is summed with the spatiotemporally varying displacement due to the propagating shear wave.  
Further work is required to improve our understanding of the cause of machine bias and why it appears to be greater in tissue than in current phantoms. Nevertheless, even if standardisation of the frequency content of shear wave pulses used in SWE is not feasible, it would be helpful if manufacturers were able to provide the shear-wave frequency spectrum generated in typical tissues at a number of imaging depths, as part of the machine specification, so that authors could incorporate the information into publications such as this, as called for by [PERSON] et al. [38].