Abstract
Oblique incidence reflectometry (OIR) is an established technique for the estimation of tissue optical properties. However, a sensing footprint of a few transport mean-free paths is often needed when diffusion-regime-based algorithms are used. Smaller-footprint probes require improved light-propagation models and inversion schemes for diffuse reflectance close to the point of entry but might enable micro-endoscopic form factors for clinical assessments of cancers and precancers. The phase-function corrected diffusion theory presented by Vitkin et al. [Nat. Commun. 2, 587 (2011)] to the case of pencil beams obliquely incident on a semi-infinite turbid medium is extended. The model requires minimal computational resources and offers improved accuracy over more traditional diffusion-theory approximations models when validated against Monte Carlo simulations. The computationally efficient nature of the models lends itself to rapid fitting procedures for inverse problems. The analytical model is used in a nonlinear fitting algorithm to demonstrate the recovery of optical properties using a measurement footprint that is significantly smaller than needed in previous diffusion-regime OIR methods.
Highlights
Various forms of light-scattering measurements and spectroscopy are showing promise as a biopsy-free means to measure the size distribution of nuclei and associated scattering as an indicator of preinvasive neoplasia and malignancy.[1,2,3,4,5,6,7,8,9,10,11,12] Many of these techniques require or would benefit from accurate models of light transport near the point of entry
We first validated that our phase-function corrected (PFC)-diffusion model agreed with Fig. 2 of Vitkin et al.[28] for the case of a pencil beam normally incident on a semi-infinite turbid medium with μa 1⁄4 0.1 cm−1, μs 1⁄4 150 cm−1 and g 1⁄4 0.95
The PFC-diffusion theory introduced by Vitkin et al.[28] has been adapted, with new derivations, to the case of pencil beams obliquely incident on a semi-infinite turbid medium
Summary
Various forms of light-scattering measurements and spectroscopy are showing promise as a biopsy-free means to measure the size distribution of nuclei and associated scattering as an indicator of preinvasive neoplasia and malignancy.[1,2,3,4,5,6,7,8,9,10,11,12] Many of these techniques require or would benefit from accurate models of light transport near the point of entry. Vitkin et al.[28] described an elegant phase-function corrected (PFC) diffusion approximation to the radiative transport equation which permitted an analytical description of a pencil beam normally incident on a semi-infinite turbid medium. Where L is radiance, S is the source radiance distribution, r is a field point, s is a unit vector, μt 1⁄4 μa þ μs is the total interaction coefficient, the sum of the absorption and scattering coefficients, respectively, with normally incident collimated pencil-beam Lcðr; sÞ 1⁄4 Poð2πÞ−2r−1δðrÞδð1 − s · zÞe−μt0z entering a semiinfinite turbid medium could be written as two equations, This one follows the diffusion approximation s · ∇Ldðr; sÞ 1⁄4 −μtLdðr; þ μs 4π Z Lðr; s 0Þds[0] þ.
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