2.5 Processing of LC-OCT images to estimateµs and g from skin layers in vivo
2.5.1 Theoretical background of the model
More detailed explanation of the model proposed by Jacques et al . and later adapted for LC-OCT imaging system by Waszczuk et al . can be found in[13,16]. To estimate the optical properties of scattering media considering multiple forward scattering, the following modified exponential decay model of the depth-resolved reflectance \(R\left(z\right)\), as proposed by Jacques et al .[13], was implemented:
\(R\left(z\right)=\ \rho\ \exp^{-2µ_{\text{eff}}z}\), (2)
with
\(\left\{\par\begin{matrix}µ_{\text{eff}}=\ G\left(g,\text{NA}\right)\left(µ_{a}+a\left(g\right)µ_{s}\right)\\ \rho=\ µ_{s}\Delta\text{Zb}\left(g,\text{NA}\right)\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\\ \end{matrix}\right.\ \), (3)
where ρ is the fraction of the light backscattered from the focus into the collection angle of the LC-OCT objective,µ a(λ ), µs(λ ) andg (λ ) are the absorption, scattering and anisotropy coefficients, NA is the numerical aperture, \(\Delta Z\) is the axial resolution of the imaging system, G (g, NA),a (g ) and b (g, NA) are the model parameters described in[13]. G (g , NA) takes into account the average photon path length considering the NA of the imaging system and the anisotropy factor g of the sample. For the LC-OCT setup used in this study, G was set to 1 (for NA = 0.5).[13] a (g ) reflects the possibility of photon to reach the focus in highly forward scattering media despite multiple scattering. For cases of isotropic scattering,a (g ) is close to 1, while for highly forward scattering medium a (g ) tends forward 0. This parameter describes the slowed down attenuation of light with depth by the so-called “serpentile phantoms”.[16] 0 ≤b (g , NA) ≤ 1 is the fraction of light that is scattered within the focus in such a way that it can be collected by the LC-OCT objective lens. It is ruled by the phase function of the sample and the numerical aperture of the imaging system.[13] The factor 2 in Equation 2 accounts for the round-trip light attenuation by the sample. Since scattering in most biological tissue dominates over absorption (µs >> µa ), the role of absorption was neglected in this study.[9]
2.5.2 Image processing algorithm to estimate µs and g values
The model described above assumed µeff andρ parameters as the experimental observables. Thus, to deduce optical properties (at the central wavelength λ = 800 nm of LC-OCT imaging system)µs 800) andg(λ 800) , the observables must be extracted from 3D LC-OCT images and then mapped to the model described by Equations 2 and 3. To do that, a mean intensity profileI (z ) (of a 0.8 mm × 0.3 mm (x × y ) central part of each individual horizontal section) over depth z of a 3D LC-OCT image (Figure 2 ) was calculated and then converted into reflectance R (z ) using relation fI (z ) =R (z ). Calibration constant f can be obtained using double integrating spheres measurements on a calibration phantom.[13] In this work, the calibration phantom with known optical properties (estimated by the integrating spheres measurement as 4.6 mm-1 and 0.68 forµ s and g , respectively) was kindly provided by Lena Waszczuk et al..[16]