(96b) Dynamic Optimization Methods For Prediction Of Glycemia In Type 1 Diabetes Mellitus

Diabetes mellitus is a metabolic disorder affecting the body's ability to regulate blood glucose concentration. Typical complications from the disease include blindness, kidney failure, and amputation. With over 18 million people afflicted [1], it was the sixth leading cause of death in the US in 2003 [2].

Type 1 diabetes mellitus (T1DM) accounts for about 10% of all cases of diabetes [3]. T1DM is characterized by the inability of the pancreas to produce and secrete insulin; exogenous insulin must be administered throughout the day. In order to improve glycemia sufficiently to result in a significant reduction in the risk of complications, blood glucose determinations must be done as many as 12 times per day, which is a burdensome task. These glucose determinations are then used by the subject to decide on insulin dosing, which is complicated by variations in insulin sensitivity (the amount of insulin required to produce a certain change in blood glucose concentration) [4] that make calculation of insulin requirements difficult. Ideally, continuous feedback would be available to optimize insulin administration; in such a scenario, closed-loop control would be the ultimate goal.

Recent advances in insulin pump and glucose sensing technology suggest that a closed-loop artificial pancreatic beta cell could soon be achieved with suitable control algorithms [5]. The overall goal of this study is therefore the algorithms required for communication between pump and sensor.

Development of control algorithms is often facilitated through simulation studies, requiring models of the system in question; these models are therefore the focus of this work. Physiological models of insulin absorption [6], glucose absorption [7], and glucose-insulin kinetics [8] are widely published and were used as a basis for simulations.

Clinical data from subjects with type 1 diabetes mellitus were obtained from an Institutional Review Board approved protocol under a National Institutes of Health funded study (grant number R21-DK069833). Informed, witnessed consent was obtained from subjects. Data were acquired using the Continuous Glucose Monitoring System (CGMS®, Medtronic Minimed, Northridge CA) and comprised CGMS readings, insulin pump records, and subject-reported estimates of time and carbohydrate content of meals. The data analyzed in this study were collected from three subjects for a total of 27 days from midnight to midnight.

The Bergman minimal model [8] and its linearized form were used as the basis for glucose-insulin kinetics. Parameters were estimated for each data set using a global optimization routine (for the nonlinear model) and a linear least-squares estimate (for the linear models).

Given that circadian variations account for some variability in glucose-insulin kinetics, a dynamic aspect to model parameters was incorporated into optimization routines. Each data set was divided into sections corresponding to reported times at which insulin sensitivity changes (midnight-4am, 4am-10am, 10am-6pm, and 6pm to midnight) [9]. Parameter estimation was then performed for each part of the day. Further investigation of parameter variation was performed using a Kalman filter [10], with parameters allowed to change at any time.

Evaluation of the fit between clinical data and simulated results was quantified using five independent performance metrics, namely the Median Relative Absolute Deviation (MRAD), the coefficient of determination (R²), Pearson's Product Moment Correlation Coefficient (PMCC), the Clarke Error Grid (CEG), and the Rate Clarke Error Grid (RCEG). Identified models were then validated against the data from which they were not identified, with prediction horizons of up to 180 minutes.

Intra- and inter-patient variability of parameters was observed, as was the quality of the model fit. Results showed circadian variation in insulin sensitivity. Representative validation MRAD values for a 90 minute prediction ranged from 9% to 38%. Linearized versions of the Bergman minimal model outperformed the nonlinear model on some days. In the instances in which model predictions were highly unsatisfactory; this may have been due to inaccurate subject-reported data. This observation highlights the inefficiency of open-loop control.

This investigation has shown that the computational advantages of linearization outweigh the benefits of nonlinear dynamics for the Bergman minimal model. It is also worthwhile incorporating variation in model parameters, since this leads to improved model efficacy. Ultimately, a reliable prediction horizon must be extended to three hours for use in a model-based controller. Future work will involve applications of the presented techniques to more complex physiological models, with a view to achieving robust closed-loop control.

This study is a joint investigation between University of California, Santa Barbara and Sansum Diabetes Research Institute, supported by the Juvenile Diabetes Research Foundation and the National Institutes of Health grants R21-DK068706, R01-DK068683, R21-DK069833

Correspondence to: Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106-5080 frank.doyle@icb.ucsb.edu

References:

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