## 3 Experiments
### Strain and Young's Modulus Measurement of Pork  
A piece of pork was bought from a grocery store. To test the DVC and VFM based method for the elasticity measurement of biological tissue, a fresh pork specimen was tested at room temperature. A small cube shown in Figure 8a was resected for measurement, which has a layer of pig's skin on the top. Dimensions of the pork sample were \(l_{x}\) = 10.36 mm, \(l_{y}\) = 10.30 mm and \(l_{z}\) = 7.50 mm. A reference volumetric OCT image was taken when 0.620 N preload was applied. Then another volumetric OCT image was taken when the specimen was compressed by 41.0 \(\upmu\)m and the applied load was 0.082 N. 6 mm in both the width and length directions were imaged by the OCT. A cross-sectional OCT image of the specimen with the ROI marked by a blue rectangle is shown in Figure 8b. A reference 3D volumetric OCT image is shown in Figure 8c with the ROI marked by a blue cube, which is 461.8 \(\upmu\)m below the top surface of the specimen as shown in Figure 8b. The average of the correlation coefficient of the ROI was tested to be 0.391. The coordinate was built with the origin \(O\) at the bottom left corner of the ROI, and the three axes were along the three edges of the ROI as shown in Figure 8c. The number of computed points was \(M\) = 31 \(\times\) 31 \(\times\) 8 = 7688. The step lengths were 7 voxels in the \(x\), \(y\) and \(z\) directions. The computed dimensions were \(Lx\) = \(Ly\) = 4057.9 \(\upmu\)m and \(Lz\) = 556.1 \(\upmu\)m. The 3D displacements and strains of the ROI with the defined coordinate system are shown in Figure 9. The displacements in the \(x\) and \(y\) directions are less than 6 \(\upmu\)m. The values of displacement and the normal strain in the \(z\)-direction shown in Figure 9c and f decrease with the increase of the depth. From Figure 9f the layered structure can be identified as the double-layered phantom. The other strain components are relatively small, mostly less than 1.0% but show heterogeneity of the tissue.  
Figure 8: Pork sample. (**a**) A photo of the pork sample; (**b**) a central cross-sectional OCT image before deformation, where the ROI is marked with a blue rectangle; (**c**) a 3D OCT image before deformation, where the ROI is marked with a blue cube.  
Figure 9: 3D deformation measurement of a pork specimen. (**a**–**c**) 3D displacements in the \(x\), \(y\) and \(z\) directions respectively; (**d**–**f**) 3D normal strains in the \(x\), \(y\) and \(z\) directions respectively; (**g**–**i**) 3D shear strains.  
After the full-field strain \(\varepsilon\) of the pork specimen was obtained, the constitutive parameters were derived by the same procedure as the double-layer phantom using the VFM. Some of the geometric parameters in this experiment were \(z_{t}\) = 1017.9 \(\upmu\)m as shown in Figure 8b; \(z_{b}\) = \(z_{t}\) - \(l_{z}\) = \(-\)6482.1 \(\upmu\)m. \(T_{0}\) = \(-\)0.082 \(\mathrm{N}\)/(10.36 \(\times\) 10\({}^{-3}\) m \(\times\) 10.30 \(\times\) 10\({}^{-3}\) m)= \(-\)768 Pa. By solving Equation (16), the Young's moduli and Poisson's ratios of the two layers were obtained. They were \(E_{1}\) = 123.9 kPa, \(\
u_{1}\) = 0.083 for the lower layer, and \(E_{2}\) = 31.62 kPa, \(\
u_{2}\) = 0.123 for the top layer. These values are in a similar range to the porcine skin's Young's modulus of 113 kPa measured by [PERSON] et al. [27].