Application of the Mixtures of Experts algorithm for signal processing in a noninvasive glucose monitoring system

Abstract

The theory of Mixtures of Experts (MOE) [M. Jordan, R. Jacobs, Hierarchical mixtures of experts and the EM algorithm, Neural Computation 6 (2) (1994) 181–214; S.R. Waterhouse, D.J.C. MacKay, et al., in: D.S. Touretzky (Ed.), Bayesian methods for Mixtures of Experts, Advances in Neural Information Processing Systems, Vol. 8, MIT Press, Cambridge, MA, 1996, pp. 351–357; S.R. Waterhouse, Classification and regression using Mixtures of Experts, PhD Thesis, Cambridge University, Cambridge, 1997] was applied to the signal from a noninvasive glucose monitor for the purpose of converting raw signal data into blood glucose values. The MOE algorithm can be described as a generalized predictive method of data analysis. This method uses a superposition of multiple linear regressions, along with a switching algorithm, to predict outcomes. Any number of input/output variables are possible. The unknown coefficients in this method are determined by an optimization technique called the Expectation Maximization (EM) algorithm. The noninvasive GlucoWatch® biographer operation has been described [R.T. Kurnik, B. Berner, et al., Design and simulation of a reverse iontophoretic glucose monitoring device, J. Electrochem. Soc. 145 (12) (1998) 4119–4125]. Briefly, a small electrical current results in the transport of glucose beneath the skin to a hydrogel placed on the skin surface. Within the hydrogel, the glucose reacts with the enzyme glucose-oxidase to produce hydrogen peroxide. This hydrogen peroxide then diffuses to a platinum-based electrode, where it reacts to produce a current. The integral of this current (charge) over the sensing time is the signal used to measure extracted glucose. This process is repeated, yielding up to three measurements per hour. The data used for this analysis were obtained from diabetic subjects wearing the biographer over a 15-h period. The MOE inputs consisted of elapsed time, integrated current, blood glucose value at the calibration point, and a calibrated signal. The output was the value of blood glucose at each measurement. These training data were used to determine the unknown parameters in the MOE by the EM algorithm. Using a 3-h time point for calibrating the biographer, the mean absolute error (MAE) between the actual blood glucose and the blood glucose predicted with the MOE, was 14.4%.