## 2 Equipment and Methods  
### 3D Strain Measurement by OCT Imaging and DVC  
A swept source OCT (SSOCT) system and a compressive loading device were developed in our laboratory. A schematic diagram of the system is shown in Figure 1a. Laser emitted from a swept laser source (HSL-20-100-B, Santec, Aichi, Japan) goes to a Mach-Zahnder interferometer. The interference signal was detected by a balanced photodetector (EBR370006-02, Exalos, Schlieren, Switzerland) then acquired by a data acquisition card in a computer. The central wavelength of the laser is 1315 nm; the bandwidth is 88 nm, which results in an axial resolution of 9.93 \(\upmu\)m. The refractive index of biological tissue is around 1.4, so the axial resolution in tissue is 7.09 \(\upmu\)m. Sample beams are scanned by two Galvo mirrors. The line scan rate is 100 kHz, so it takes 0.46 s to scan a bulk of 214 \(\times\) 214 \(\times\) 1024 voxels. A compressive loading device consisting of a base and an optical window was designed. A force sensor (FSH03221, FUTEK, Irvine, CA, USA) is set on the base to measure the applied load. An example of a 2D cross-sectional OCT image and a 3D volumetric image of a phantom are shown in Figure 1b,c.  
A DVC algorithm was developed by integrating a coarse search mechanism, an IC-GN based fine search algorithm and a local ternary quadratic polynomial fitting method for strain calculation. Firstly, because the ZNCC correlation function is not sensitive to noise, a ZNCC correlation function based coarse search was developed to find initial integer values of voxel shifts. Secondly, the IC-GN [21] based fine search algorithm was employed. The IC-GN algorithm changes the shape and location of target and reference sub-volumes simultaneously to find the maximum of the correlation function. Because the Hessian matrix does not need to update in each iteration, the computational speed can be \(\sim\)1.7 times faster than the conventional DVC method [21]. The computing speed is \(\sim\)4 s per point calculating OCT images by DVC. The convergence criterion was set as either the increment of each displacement component was less than 0.001 voxels, or the maximum iteration of 20 was reached. A cubic spline interpolation scheme with not-a-knot end condition was utilized for the calculation of sub-voxel intensities. More details about the IC-GN algorithm can be found in paper [21]. Through the coarse-fine search DVC calculation, the 3D displacements can be obtained with sub-voxel resolution. Thirdly, the local ternary quadratic polynomial fitting equations were used to fit 3 \(\times\) 3 \(\times\) 3 voxels of the displacement data with the least square method. Then, the strains were calculated using [PERSON]'s formulae [24]. The displacement and strain resolution of this system are around 0.06 voxels (\(\sim\)1 \(\upmu\)m)  
Figure 1: The SSOCT and compressive loading system. (**a**) A schematic diagram of the system; (**b**) a 2D OCT cross-sectional image (B-scan); (**c**) a 3D volumetric OCT image. Stationary experiment: (**d**) 3D displacements in the \(x\), \(y\) and \(z\) directions of the ROI; (**e**) 3D strain tensors of the ROI. The ROI is marked out with a blue rectangle in (**b**) and with a blue cube in (**c**).  
and 0.2%, respectively, tested by the stationary experiment as shown in Figure 1d,e, where the region of interest (ROI) is marked out with a blue rectangle in (b) and a blue cube in (c), which may become worse in deformation measurements due to the speckle blinking [25; 26].