Constrained optimization of Drude's equations eliminates effects of confounding molecules for the polarimetric measurement of glucose

Abstract

Common confounding factors for polarimetric concentration measurements include additional optical rotations from unknown optically active molecules, linear birefringence of the medium, and path length variability. We show that by approximating Drude's equation and taking several measurements from the same sample at different wavelengths, the error due to confounding rotations in the measurements can theoretically be canceled. The analysis is developed with regard to glucose sensing in aqueous humor. First, we show that the optical rotatory dispersions of the known molecules in bovine aqueous humor could be represented by Drude's equations. Then, the total optical rotation is approximated by a function combining Drude's equations for the major contributors in the sample, i.e., glucose, glutamine, fructose, and phenylalanine. The concentration-related unknown coefficients in the approximating function are found by constrained nonlinear optimization of the function at different wavelengths. This technique is tested on a published data set and four alterations of those data: (1) concentrations randomly varied within narrow limits, (2) similar to alteration 1 but with significantly elevated glucose concentration, (3) similar to alteration 1 but with significantly decreased glucose concentration, and (4) concentrations randomly varied within wider limits than alteration 1. The method produces very accurate glucose-concentration estimates in all of these data sets. The relative error was smaller than 1% in all except the low-glucose sample (1.4%). This method may prove useful in noninvasive glucose measurement in humans.