## 4 FF-OCT and Biomechanics
### Transient Elastography Based on Shear Wave Imaging
The pressure levels involved are within the limits set by the Food and Drug Administration (FDA) for the application of diagnostic ultrasound in several organs. By taking advantage of the interferometric sensitivity of FF-OCT to small axial displacement, we can further detect the propagation of the shear wave with high sensitivity. Unfortunately, high speed cameras do not offer large full well capacities (and it would be hard to generate hundreds of thousands of photoelectrons per pixel at 30 KHz), so our axial sensitivity is about 10 times lower than in our standard systems. Nevertheless, we could successfully follow shear waves in a sample and calculate their local speeds, by computing the temporal cross-correlation between neighboring pixels. One such propagation in an ex vivo brain tissue is shown in Figure 4. To better capture the propagation in time, we did not modulate the reference piezo, but only recorded direct images. However, we get rid of the incoherent intensity captured by the camera by subtracting the direct images to a few initial frames captured before the generation of the shear wave. The signal of each pixel is therefore directly proportional to the cosine of the phase:  
\[I_{diff}=I_{0}.a_{\delta}[cos(\frac{2\pi\delta}{\lambda_{0}}+\varphi(t))-cos( \frac{2\pi\delta}{\lambda_{0}}+\varphi_{ini})] \tag{10}\]  
where \(a_{\delta}\) is linked to the backscattered wave amplitude interfering with the reference signal; \(\delta\) is the path length difference at the considered pixel; \(\lambda_{0}\) the central wavelength; \(\varphi(t)\) the relative phase that depends on time; and \(\varphi_{ini}\) the initial phase. In Figure 4, we can see the wavefront of the shear wave crossing the field of view. With this method, we measured a shear wave speed of 0, 64 m\(\cdot\)s\({}^{-1}\), corresponding to a [PERSON]'s modulus of 1.25 kPa, which agrees well with the literature [103; 104]. We should add that although this dynamic measurement seems quite promising, it is performed here in an ideal case, since the brain is one of the softest tissues of an organism, and is quite reflective. In other cases, dynamic elastography FF-OCT can be challenging mainly due to current technological limitations. Indeed, we could not find any high sensitivity and high speed camera with parameters which would be sufficient to accurately follow shear waves in most tissues. However, since the shear wave source is controlled here, it should be possible to average several measurements to increase the sensitivity, or to perform a stroboscopic measurement by shifting the time delay between the shear wave generation and therefore measure the wave propagation with lower speed cameras. Ultimately, a shear speed can be calculated from only three measurements, so mechanical maps can be computed almost at video rate with dynamic elastography FF-OCT, and has been demonstrated at several thousand frames per second here. Here again, the penetration depth is only limited by FF-OCT characteristics. However, due to the low sensitivity provided by fast cameras, the penetration depth is, in practice, limited to 50 \(\upmu\)m.  
To conclude this section, we have shown that FF-OCT can be coupled with elastography to measure the local mechanical parameters of a tissue. In terms of coupling with biomechanical contrast, FF-OCT and standard OCT measurements are not very different, since they rely on similar techniques to generate the mechanical contrast. Although FF-OCT-based mechanical measurements should theoretically have an isotropic 1 \(\upmu\)m resolution, we could never measure any relevant differences at this scale. Additionally, the mechanical models used to link local deformations with mechanical stiffness are mesoscopic models, whose validity can become questionable when decreasing the resolution below 10 \(\upmu\)m.  
We should add that as the deformation is applied along the optical axis, it seems more natural to look at its propagation in the transverse plane, especially when looking at shear waves.