Lookup table-based inverse model for determining optical properties of turbid media

Abstract

We present a lookup table (LUT)-based inverse model for determining the optical properties of turbid media from steady-state diffuse reflectance spectra that is valid for fiber-based probe geometries with close source-detector separations and tissue with low albedo. The lookup table is based solely on experimental measurements of calibration standards. We used tissue-simulating phantoms to validate the accuracy of the LUT inverse model. Our results show excellent agreement between the expected and extracted values of the optical parameters. In addition, the LUT represents a significant improvement in accuracy at short source-detector separations (300 microm) and low albedo (approximately 0.35). We also present in vivo data from clinically normal and malignant nonmelanoma skin cancers fit to the LUT-based model.

Fig. 1

(a) Spectrally resolved diffuse reflectance [R(λ)] for a subset of tissue phantoms, [ ${\mu }_{\text{s}}^{\prime }({\lambda }_0)=2{\text{mm}}^{-1}$ and four different ink concentrations corresponding to μ_a(λ) = 0–5.33 mm⁻¹], from the calibration set. (b) Diffuse reflectance as a sparse matrix mapped to optical property space, {R[ ${\mu }_{\text{s}}^{\prime }(\lambda )$, μ_a(λ)]}and (c) the resulting lookup table, [R( ${\mu }_{\text{s}}^{\prime }$, μ;_a)].

Fig. 2

(a) Diffuse reflectance spectrum [ ${\mu }_{\text{s}}^{\prime }({\lambda }_0)=2.49{\text{mm}}^{-1}$ and [Hb] = 2 mg/ml] and the LUT-fit from a tissue phantom (validation set). Scatter plot of the known versus measured values of (b) and ${\mu }_{\text{s}}^{\prime }(\lambda )$ and (c) μ_a(λ) for all tissue phantoms. The solid line indicates perfect agreement.

Fig. 3

(a) and (b) Physical parameters extracted from the LUT inverse model ( ${\mu }_{\text{s}}^{\prime }({\lambda }_0)=0.91{\text{mm}}^{-1}$ (□), 1.83 mm⁻¹ (○) and 2.75 mm⁻¹ (◇)). The solid line indicates perfect agreement. Error bars for these measurements were too small to show (<2%). (c) In vivo reflectance spectra from two representative groups: clinically normal and BCC. The thin solid line indicates the model fit.