Measurement of tissue scattering properties using multi-diameter single fiber reflectance spectroscopy: in silico sensitivity analysis

Abstract

Multiple diameter single fiber reflectance (MDSFR) measurements of turbid media can be used to determine the reduced scattering coefficient (μ'(s)) and a parameter that characterizes the phase function (γ). The MDSFR method utilizes a semi-empirical model that expresses the collected single fiber reflectance intensity as a function of fiber diameter (d(fiber)), μ'(s), and γ. This study investigated the sensitivity of the MDSFR estimates of μ'(s) and γ to the choice of fiber diameters and spectral information incorporated into the fitting procedure. The fit algorithm was tested using Monte Carlo simulations of single fiber reflectance intensities that investigated biologically relevant ranges of scattering properties (μ'(s) ∈ [0.4 - 4]mm(-1)) and phase functions (γ ∈ [1.4 - 1.9]) and for multiple fiber diameters (d(fiber) ∈ [0.2 - 1.5] mm). MDSFR analysis yielded accurate estimates of μ'(s) and γ over the wide range of scattering combinations; parameter accuracy was shown to be sensitive to the range of fiber diameters included in the analysis, but not to the number of intermediate fibers. Moreover, accurate parameter estimates were obtained without a priori knowledge about the spectral shape of γ. Observations were used to develop heuristic guidelines for the design of clinically applicable MDSFR probes.

Keywords: (170.1470) Blood or tissue constituent monitoring; (170.3660) Light propagation in tissues; (170.6510) Spectroscopy, tissue diagnostics; (290.7050) Turbid media; (300.6540) Spectroscopy, ultraviolet; (300.6550) Spectroscopy, visible.

Fig. 1

Single fiber reflectance spectroscopy setup.

Fig. 2

Wavelength dependent reduced scattering coefficient for the 3 scattering sets considered in simulations.

Fig. 3

a) Simulated MDSFR reflectance measurements for 7 fiber diameters as a function of wavelength, and b) simulated and fitted reflectance at a single wavelength (800 nm) as a function of fiber diameter.

Fig. 4

a) MDSFR estimated vs. simulated μ′_s, and b) MDSFR estimated vs. simulated γ for the entire data set for all 11 wavelengths (λ = 400 – 900 nm). Calculations utilized 7 fiber diameters in the fitting procedure in the range d_fiber ∈ [0.2 – 1.5] mm.

Fig. 5

Effect of different fiber diameter combinations on the mean residual error of μ′_s and γ estimated by single wavelength MDSFR analysis. a) and b) shows subsequent removal of large fibers; all remaining smaller fibers were included. c) and d) shows subsequent removal of small fibers; all remaining larger fibers were included. e) and f) shows removal of intermediate fibers; reflectance data from 0.2 mm and 1.5 mm fibers were always included. Note the difference in y-axis scale between panels a and b–f. Scattering set 1: μ′_s = 0.4 – 1.0 mm⁻¹; scattering set 2: μ′_s = 0.9 – 2.0 mm⁻¹; scattering set 3: μ′_s = 1.8 – 4.0 mm⁻¹.

Fig. 6

Example for spectrally resolved MDSFR fitting procedure using data from scattering set 3 (μ′_s(800 nm) = 2 mm⁻¹): a) simulated MDSFR intensities for 7 fiber diameters, b) MDSFR intensity vs. fiber diameter for all wavelengths, c) estimated and simulated γ as a function of wavelength and d) estimated and simulated μ′_s as a function of wavelength for I) wavelength independent γ and g₁, II) wavelength dependent γ and g₁ and III) random γ and g₁.

Fig. 7

Spectrally resolved MDSFR fitting procedure: a) estimated vs. real μ′_s; b) estimated vs. real γ for I) wavelength independent γ and g, II) wavelength dependent γ and g₁ and III) random γ and g₁. The analysis was performed over the whole dataset including all 3 scattering ranges and all 11 wavelengths (λ = 400 – 900 nm).

Fig. 8

Sensitivity of spectrally resolved MDSFR estimates of a) μ′_s and b) γ to the choice of fiber diameters within a 2 fiber MDSFR probe. Data from all 11 wavelengths (λ = 400 – 900 nm) were included.