Submitted to: Inverse Problems Symposium
Publication Type: Abstract only
Publication Acceptance Date: 4/1/2010
Publication Date: 6/6/2010
Citation: Cen, H., Lu, R., Dolan, K. 2010. Inverse Algorithm Optimization for Determining Optical Properties of Biological Materials from Spatially-Resolved Diffuse Reflectance [CD-ROM]. 2010 Inverse Problems Symposium. East Lansing, Michigan: Michigan State University. Interpretive Summary:
Technical Abstract: Optical characterization of biological materials is useful in many scientific and industrial applications like biomedical diagnosis and nondestructive quality evaluation of food and agricultural products. However, accurate determination of the optical properties from intact biological materials based on diffusion approximation theory is challenging because of the complex mathematical model and sophisticated instrumentation and experimental procedure. This research was, therefore, aimed to optimize the procedure of estimating the absorption and reduced scattering coefficients of turbid homogeneous media from spatially-resolved diffuse reflectance profiles. The diffusion model and inverse algorithm were validated by Monte Carlo simulations for 36 combinations of absorption and reduced scattering coefficients with the ranges of 0.004-0.800 (1/mm) for the absorption coefficient, 0.40-4.00 (1/mm) for the reduced scattering coefficient, and 5-100 for the ratio of absorption to reduced scattering coefficient. Sensitivity analysis was performed to study the relationship between the estimated parameters and the dependent variables in the inverse algorithm for improving the parameters estimation procedure. The reduced scattering coefficient was estimated more accurately than the absorption coefficient, which was also validated by the Monte Carlo simulation results. Data transformations including logarithm and integral, and relative weighting method were applied in the nonlinear least squares regression. The logarithm and integral data transformations and the relative weighting method greatly improved estimation accuracy with the relative errors of 10.4%, 10.7% and 11.4% for the absorption coefficient, and of 6.6%, 7.0% and 7.1% for the reduced scattering coefficient, respectively, which were much smaller than those obtained from the original diffusion model. Further statistical analysis showed that the logarithm transformation and relative weighting method gave more reliable estimations of the optical parameters. This research has demonstrated the importance of studying the behavior and characteristics of a mathematical model when it is used in an inverse algorithm for estimating its parameters. The methods proposed in the research provide an effective means for quantifying experimental and estimation errors for the optical properties. They will help to better interpret light propagation in biological materials and more accurately determine the optical properties.