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Inference of blood glucose concentrations from subcutaneous glucose concentrations: applications to glucose
1Department of Chemical Engineering, The University of Texas at Austin, 78712-1062, USA.
Abstract:
An approach for inference of blood glucose concentrations in real time is considered. First, a model that predicts the subcutaneous glucose concentration from the blood glucose concentration is presented. The model includes diffusive transport from the blood to the subcutaneous tissue and reactive-like cellular uptake of glucose. Next, the Phillips-Tikhonov regularization method is considered to solve the real-time input estimation problem that determines the blood glucose concentration given the subcutaneous glucose concentration. The inverse problem is regularized by imposing a smoothing condition to obtain a stable solution. Three different penalization functionals were considered in evaluating the regularization method using a synthetic function that approximates the subcutaneous glucose response to an oral glucose tolerance test in a human subject. Various levels of either white noise or time-correlated noise were superimposed onto the synthetic response to evaluate the sensitivity of the inverse to measurement error. For inversion assuming only diffusive transport, the optimal time interval of integration of previous subcutaneous measurements was found to be about 1.5/alpha, where alpha(-1) is the dominant time constant for the exchange of glucose between the blood and subcutaneous tissue. The optimal sampling rate was found to be 54alpha. Linear regularizations based on minimization of first or second derivatives of the blood glucose concentration were found to be satisfactory, each yielding a minimum error that was about 50% greater than the measurement error. Including nonlinear, reactive-like uptake of glucose was found to decrease the error magnification factor slightly. Both the model and the inverse method relating blood and subcutaneous glucose concentrations are successfully applied to experimental measurements using glucose biosensors reported by Schmidtke et al. (Proc. Natl. Acad. Sci. USA 95:294-299, 1998).