Optical Fiber Sensors for Biomedical Applications

690 L.C.L. Chin et al.with∫F (λ) = p ( θ, λ, ¯d, d ) sin θ dθ (17.32)θ F∫B (λ) = p ( θ, λ, ¯d, d ) sin θ dθ (17.33)θ ηp ( θ, λ, ¯d, d ) = 〈 p ( θ, λ, ¯d, d )〉 ∫ ∞N(d) = p ( θ, λ, ¯d, d ) N (d) dd0(17.34)where d is the diameter of the nucleus, p ( θ, λ, ¯d, d ) is the scattering phase functionaveraged over a distribution of nuclear diameters, N(d), d is the standarddeviation of the average nuclear diameter, θ is the angle between the detection andillumination angles, θ D is the backward scattering angle range, θ F is the range ofscattering angles in the forward direction, a(ρ) and b(ρ) are nuclei density dependentparameters, and S(λ) is the depolarization ratio profile of underlying tissuethat can be determined experimentally. The term p ( θ, λ, ¯d, d ) is based on Mietheory – with the assumption that the nuclei are homogeneous spheres – and containsinformation regarding the nuclear diameter distribution, as well as, the spectraldependence of the scattering coefficient.Groner et al. [36] employed a similar approach to reduce confounding specularreflection signals and enhance the contribution of light detected from deep tissuelayers.17.4.2.3 Time-Resolved Reflectance SpectroscopyDiffusion theory can also be used to obtain the average penetration depth, 〈z〉 r ,asafunction of detection time for time-resolved fiber optic reflectance sensors [12].In the time-domain case, we are interested in the fluence rate as a function of timeat source-detector separation, r, and time, t, following an impulse source. Here, thedecrease in photons that escape the tissue due to an absorption inhomogeneity indt ′ at r ′ is:R ( r, t, t ′) = μ a φ ( r ′ , t ′) dV E ( r ′ , r, t − t ′) dt ′ (17.35)Here, φ ( r ′ , t ′) and E(r ′ , r, t − t ′ ) are the time-resolved equivalents to the continuouswave fluence rate and escape function, respectively. They are given by:φ ( κ, z, t ′) = c (4πDc) −3 /2 t ′ −3/2 exp ( −μ a ct ′){ [] [((z − z o ) 2 + κ 2) 2]}z − zp + κ2× exp4Dct ′ − exp4Dct ′(17.36)