Retrieving the optical parameters of biological tissues using diffuse reflectance spectroscopy and Fourier series expansions I theory and application

Aarón A Muñoz Morales,Sergio Vázquez Y Montiel

doi:10.1364/boe.3.002395

Abstract

The determination of optical parameters of biological tissues is essential for the application of optical techniques in the diagnosis and treatment of diseases. Diffuse Reflection Spectroscopy is a widely used technique to analyze the optical characteristics of biological tissues. In this paper we show that by using diffuse reflectance spectra and a new mathematical model we can retrieve the optical parameters by applying an adjustment of the data with nonlinear least squares. In our model we represent the spectra using a Fourier series expansion finding mathematical relations between the polynomial coefficients and the optical parameters. In this first paper we use spectra generated by the Monte Carlo Multilayered Technique to simulate the propagation of photons in turbid media. Using these spectra we determine the behavior of Fourier series coefficients when varying the optical parameters of the medium under study. With this procedure we find mathematical relations between Fourier series coefficients and optical parameters. Finally, the results show that our method can retrieve the optical parameters of biological tissues with accuracy that is adequate for medical applications.

Highlights

The determination of the optical parameters, which are defined by the absorption coefficient, the scattering coefficient, the refraction index (n) and the anisotropy factor (g), is of vital importance for the characterization of biological tissues using optical methods
In recent years models to predict the distribution of reflectance in turbid medium [2, 3, 4, 5] with different border conditions and levels of mathematical difficulty have been developed but our model allows us to perform the fitting of the diffuse reflectance curve regardless of the physical model, making use of the border conditions to calculate the retrieve of optical parameters
Using the results of the simulations obtained by Monte Carlo method as experimental data, we studied the behavior of Fourier series coefficients with the variation of the optical parameters and proceeded to propose an analytical relation to facilitate the future retrieval of the optical parameters

Summary

Introduction

The determination of the optical parameters, which are defined by the absorption coefficient (μa), the scattering coefficient (μs), the refraction index (n) and the anisotropy factor (g), is of vital importance for the characterization of biological tissues using optical methods. Many authors have presented different methods for retrieving optical parameters with different levels of difficulty and precision. Using a methodology of adjustment of the curve the least squares, this mathematical model allows the determination of optical parameters. In recent years models to predict the distribution of reflectance in turbid medium [2, 3, 4, 5] with different border conditions and levels of mathematical difficulty have been developed but our model allows us to perform the fitting of the diffuse reflectance curve regardless of the physical model, making use of the border conditions to calculate the retrieve of optical parameters. Other models extract optical properties (scattering and absorption coefficients) of the medium using small source-detector separations, for which the diffusion approximation is not valid [6, 7]

Methods

Results

Conclusion