## 4 FF-OCT and Biomechanics
### Transient Elastography Based on Shear Wave Imaging  
Transient elastography based on shear wave imaging is the second approach used to combine elastography with FF-OCT [38]. Transient elastography based on shear wave imaging was introduced in OCT by [PERSON] et al. [99]. As shown in Equation (6), a direct measurement of the local shear wave speed gives direct access to a quantitative value of [PERSON]'s modulus. Dynamic elastography methods involve two steps: first, a shear wave is locally sent onto the sample; then, the shear wave propagation is recorded. We were inspired by a technique named supersonic shear wave imaging, partly developed in our lab, which uses the ultrasound radiation force to create short shear impulses and ultrafast  
Figure 3: FF-OCT and biomechanical contrast in various tissues obtained with static elastography. **Panels A and B** show a standard four-phases FF-OCT of an ex vivo human breast tissue and the corresponding strain map (equivalent von Mises strain) after sample compression. As expected, a greater deformation can be observed around the adipose inclusions (black domains in panel A) when at the surrounding fibrous breast tissue. The color bar corresponds to a strain in percent from 0 for blue to 10 for red. **Panel C** corresponds to a FF-OCT cross-sectional image of an ex vivo rat heart. In **Panel D**, we show the corresponding angle of the principal strain direction. The color bar corresponds to the angle in degree from 0 for blue to 90 for red. **Panels E and G** respectively correspond to 3D volumetric FF-OCT images of a mechanically isotropic and anisotropic polyvinyl alcohol (PVA) polymers, and **panels F and H** correspond to their respective fractional anisotropy maps. The color bar corresponds to the fractional anisotropy from 0 for blue to 0.7 for red. **Panels I and J** finally show a standard FF-OCT image of a biopsy of bovine kidney, and its associated stress map obtained with the “tactile” approach. The color coded stress map varies from \(-0.5\) kPa in blue to 0.4 kPa in red. All the orange scale bars correspond to 100 μm. ultrasound imaging to image the shear wave propagation [100; 101]. We adapted this method to FF-OCT by generating shear waves using an ultrasound system and by recording the generated wave using a FF-OCT system operated with a high speed camera that can run at up to 30 kHz for a \(512\times 512\) pixel field of view [38]. Shear waves were induced using a programmable ultrasound scanner (Aixplorer(r), Supersonic Imaging, Aix-en-Provence, France), and a 15-MHz ultrasound linear array (128 elements, pitch 100 \(\upmu\)m, elevation focus at 12 mm, Vermon, France), as described in [PERSON]. [PERSON] et al. [38]. This system focuses ultrasonic beams for tens of microseconds in the sample, which create a local radiation force, localized at the ultrasound focal spot and oriented along the beam axis. In response to this force, the tissue relaxation generates a shear wave, polarized along the ultrasonic beam and propagating transversely [90; 102]. To increase the amplitude of the radiated shear wave, an original solution consisting of successively focusing the ultrasonic beams at different depths along the ultrasonic path is performed [38; 102]. If the shear source is moved at a higher speed than the speed of the radiated shear wave, the source induces constructive interference along a Mach cone between all the generated shear waves, and the resulting wave can propagate with minimized diffraction over a large area. For short ultrasonic bursts (shorter than one millisecond), the spatial distribution of large tissue displacements initially corresponds to the acoustic intensity distribution, i.e., a cylinder with a lateral extension of 200 \(\upmu\)m and an axial extension of about 1 mm in this configuration. The shear wave location can further be swept transversely by electronically focusing the ultrasound beam at different lateral locations, without any mechanical translation involved.