Verification of a two-layer inverse Monte Carlo absorption model using multiple source-detector separation diffuse reflectance spectroscopy

Abstract

A two-layer Monte Carlo lookup table-based inverse model is validated with two-layered phantoms across physiologically relevant optical property ranges. Reflectance data for source-detector separations of 370 μm and 740 μm were collected from these two-layered phantoms and top layer thickness, reduced scattering coefficient and the top and bottom layer absorption coefficients were extracted using the inverse model and compared to the known values. The results of the phantom verification show that this method is able to accurately extract top layer thickness and scattering when the top layer thickness ranges from 0 to 550 μm. In this range, top layer thicknesses were measured with an average error of 10% and the reduced scattering coefficient was measured with an average error of 15%. The accuracy of top and bottom layer absorption coefficient measurements was found to be highly dependent on top layer thickness, which agrees with physical expectation; however, within appropriate thickness ranges, the error for absorption properties varies from 12-25%.

Keywords: (100.3190) Inverse problems; (170.6510) Spectroscopy, tissue diagnostics.

Fig. 1

Two-layer model geometry used in the Monte Carlo simulations. Absorption for the top and bottom layers, scattering for both layers, and the top-layer thickness are used as inputs to generate reflectance values for all SDSs. The coverslip was modeled as a middle layer with constant thickness of .625 mm, no scattering or absorption, and an index of refraction of 1.5.

Fig. 2

Flowchart for the forward model of diffuse reflectance for a two-layer tissue model. Tissue parameters are inputs into the model and the output is a diffuse reflectance spectrum. The Monte Carlo lookup table is used to determine reflectance based on the set of optical properties and top layer thickness.

Fig. 3

Inverse model of diffuse reflectance. First, an initial guess for the tissue parameters is used to generate a spectrum with the forward model. Next, the error between the measured and modeled spectra is calculated and the parameters are updated using an optimization routine that minimizes the error between the modeled and measured spectra.

Fig. 4

Schematic of the two-layered experiment and the DRS system used to collect the data, including the “photon flow” from: excitation provided by the xenon lamp, whose signal is passed through a long-pass filter and an optical lens system for collimation and focusing into a fiber-optic switch to be delivered to the two-layer phantom, consisting of a top layer (TL) and bottom layer (BL). The bottom layer is housed in a small vial cap with a coverslip placed on top, and the top layer poured on top of it. Collection is at 370 and 740 μm SDSs and passed into a spectrograph and imaged by a cooled CCD camera. Custom software provides the trigger for the light source and detector and also processes and stores the measured spectra for later analysis.

Fig. 5

Measured spectra (colored and dashed) and associated MCLUT fits (solid black) from phantom 3 with a top layer thickness of 300 μm.

Fig. 6

Measured reflectance spectra at selected heights for phantom 8. Top and bottom plots correspond to 370 and 740 μm source-detector separations, respectively. Scaled absorbance profiles of red (dashed red line) and blue (dashed blue line) dyes are also included for reference.

Fig. 7

Average calculated NRMSD values for each top layer thickness..

Fig. 8

Comparison between measured and predicted top layer thicknesses. The error bars in the figure represent the standard deviation of the thickness prediction at each particular height. The solid line is the line of perfect agreement.

Fig. 9

NRMSD for Z ₀ vs. known Z ₀ for when only one of the SDSs is used and for when both are used. This plot shows how using multiple SDSs can expand the range where Z ₀ can accurately be predicted.