2.6. Elastic Group Wave Velocity Calculations

Figure 2(a) shows a 3-D OCT structural image of a healthy skin sample with the OCE measurement region and excitation position. Figure 2(b) shows a two-dimensional (2-D) structural OCT image (B-scan) corresponding to the OCE measurement region. The stripe artifacts seen in the structural image are due to the respiration of the mouse. Figure 2(c) illustrates selected typical elastic wave vertical temporal displacement profiles at OCE measurement positions corresponding to the marked positions in Fig. 2(b).

The vertical temporal displacement profiles of the elastic wave at the surface, dsurface(t), were calculated from the raw unwrapped surface phase profiles, φsurface(t), using the following equation:³²

and the displacement profiles within the skin, dinside(t), were corrected due to the surface motion and refractive index mismatch between air and the tissue from the raw unwrapped phase profiles inside the skin, φinside(t), using the following equation:³³

where λ0 is the central wavelength of the laser source, and nskin=1.4 was the refractive index of the skin.³⁴ The time delay, Δt, of the elastic wave to propagate from a reference position near the excitation position to each of the OCE measurement position distance was determined by cross-correlation analysis of the normalized temporal displacement profiles. The elastic wave group velocity, cg, for a given imaged in-depth layer was computed by a least squares linear fit of the propagation time delays to the corresponding OCE measurement positions.³⁵ The depth-wise median velocity was used as the elastic wave group velocity for that given sample to calculate the elasticity. The elastic wave was considered as a Rayleigh wave due to the geometry of the sample and boundary conditions.³⁶ Young’s modulus was quantified from the group velocity, cg, using³⁷

where ρ=1100kg/m3 is the density of the tissue and ν=0.47 is the Poisson’s ratio.³⁸

The computational window was ∼1mm (90 pixels) along the skin surface and 0.2 mm (50 pixels) in depth. To avoid specular reflections from the skin surface and subsequent saturation artifacts, the computational window was shifted beneath the surface by 50μm (10 pixels). Because the elastic wave propagation was imaged in two directions, the Young’s modulus was averaged from both directions and used as the single value for a given sample.