## 4 Discussion
### Comparison of Tissue \(c_{s}\) Ratios and Anisotropy Ratios between Machines  
For both machines, tissue \(c_{s}\) ratios were greater than unity indicating that skin had higher \(c_{s}\) estimates than parenchyma, and parenchyma had higher \(c_{s}\) estimates than adipose tissue. No significant differences in any tissue \(c_{s}\) ratios between machines were detected, suggesting that whilst the machines differed in absolute values of \(c_{s}\) estimates, relative values between tissue types are similar. [PERSON] et al. [28] reported anisotropy ratios (radial to anti-radial) of 1.28 and 1.30 in adipose and parenchyma tissue in the normal breasts of 137 patients, respectively, measured using S2000 pSWE. These findings were consistent with the radial orientation of ducts and Cooper's ligaments and that material properties of the tissue are dependent on the orientation of tissue fibres. For example, [PERSON] et al. [39] and [PERSON] et al. [40] in observations of muscle, and [PERSON] et al. [41] and [PERSON] et al. [42] in observations of skin, found that shear modulus and stiffness vary according to the direction of shear wave propagation and strain respectively, with respect to the muscle or dermal collagen fibres, and that \(c_{s}\) and stiffness were greatest when measured parallel to the fibres. The current study detected a difference between \(c_{s}\) estimates measured in the radial and anti-radial orientations. The effect, however, was the reverse of that observed by [PERSON] et al. [28], with greater \(c_{s}\) measured with the transducer in the anti-radial orientation. The reason for this is unknown, although it may be significant that [PERSON] et al. [28] measured the \(c_{s}\) only at a single point with the probe in both orientations. The current study, which used a much smaller number of volunteers, compared average \(c_{s}\) across many measurement points in each image plane. The exact same volume of tissue was not being interrogated in each orientation, nor was the shear wave propagation direction truly anti-radial for any points other than at the central beamlines of the anti-radial scan, which may account for the different findings. For a direct comparison with the findings of [PERSON] et al., [28], a modification of our experimental method would be required, but this would be contrary to the objective of our study as discussed below. The differences in \(c_{s}\) estimates between transducer orientations indicate that one or both transducer orientations should be used to acquire \(c_{s}\) estimates. Care should be taken to acquire data in the correct orientation, and perhaps this can be performed with reference to anatomical landmarks such as the nipple. The focus of the current study is the comparison of the machines for their ability to pool data, and the observed anisotropy in \(c_{s}\) estimates, although not consistent with the findings of [PERSON] et al. [28], was consistent between machines. This may suggest bias in the measurement technique, for example, a change in gel stand-off between the different transducer orientations, however, no systematic differences in gel stand-off between the images acquired using radial and anti-radial orientations was observed. In the context of the future measurement of radiation toxicity to the breast and the use of the unirradiated breast as a reference measure of \(c_{s}\), large variation in relative \(c_{s}\) estimates between normal breasts between machines would reduce the sensitivity of 2D-SWE to detect a change in stiffness in the breast due to radiation-induced fibrosis, i.e., any radiation-induced change in \(c_{s}\), whether absolute or relative to the unirradiated breast, should be significantly greater than the equivalent natural variation in the population of women receiving radiotherapy for breast cancer. The magnitude of the effect of radiation on \(c_{s}\) in the tissues of the breast is as yet unknown.