Soft tissues are usually considered incompressible media.
10 In that case, the Young's modulus
E is proportional to the shear modulus μ:
In an incompressible, homogeneous, and isotropic medium, the shear modulus is linked to the speed
vT of a shear wave propagating in this medium
11:
where
ρ is the medium density. Thus, the elastic properties of soft tissues can be retrieved by creating a shear wave in the tissue and measuring its propagation speed, as proposed in shear wave elasticity imaging.
10
Supersonic shear wave imaging is an implementation of this principle using the ultrasound radiation force as a shear source and an ultrasound ultrafast imaging mode to follow the propagation of the resulting shear wave. All details about this technique can be found in earlier publications.
12–14 Our group recently implemented the SSI method with high-frequency linear ultrasonic probes (15 MHz, 128 elements; Vermon, Tours, France) for imaging of the cornea biomechanical properties, as detailed in previous works.
15,16 A conventional ultrasound probe is driven using a programmable ultrasound scanner (Aixplorer; Supersonic Imagine, Aix-en-Provence, France). The first step consists in applying a “pushing beam” by focusing an ultrasound beam in the tissue for a few tens of microseconds in order to induce a transient axial displacement of a few micrometers amplitude (
Fig. 2a). The tissue relaxation generates a shear wave that is polarized axially, that is, along the beam axis, and propagates transversally. In the second step, the probe is switched to an ultrafast imaging mode: Ultrasound plane waves are emitted, and the backscattered signals are beamformed to obtain images of the tissue during the shear wave propagation (
Fig. 2b) at very high frame rates (up to 30 kHz for a 1-cm imaging depth). As illustrated in
Figure 2c, several pushing beams are applied at different locations along the cornea to map the whole tissue. They are interleaved with ultrafast imaging acquisitions. A complete acquisition sequence typically lasts a few tens of microseconds. The phase differences between consecutive images are computed to retrieve the axial displacement field over time. The propagation speed of the shear wave is then determined using a time-of-flight algorithm applied independently for each depth of the imaging plane. It consists of cross-correlating the displacements from neighboring pixels to compute the travel time of the shear wave between these pixels. Cross-sectional elasticity maps of the anterior segment of the eye were reconstructed from the estimation of the shear wave speed at each point of the imaging plane with a typical lateral resolution of 400 μm.
15 The pixel size of the elasticity maps is 100 × 100 μm (axial × lateral).