(487g) Human-Friendly and Control-Relevant Modeling for a Closed-Loop Artificial Pancreas

A closed-loop artificial pancreas composed of a continuous glucose sensor, insulin infusion pump, and a control algorithm, has been the ?holy grail? of engineering solutions for automated regulation of blood glucose in individuals with type 1 diabetes mellitus ([1],[2],[5],[6],[7],[9]). Model predictive control algorithms have the potential for improved performance compared to PID-based schemes, particularly if the insulin-glucose model is tailored to each individual. In this paper we address limitations to the current methods of model identification for model-based controller design, in both ambulatory subjects and those undergoing in-hospital clinical studies.

There is no shortage of mathematical models relating insulin and glucose dynamics (see [3],[6],[8], for example), but because of a large number of parameters these can be difficult to tailor to a specific individual and are hence more useful for in silico simulations of closed-loop behavior. As in the chemical process industries, the development of a good empirical model inherently requires a trade-off between keeping sufficient input excitation and low output variable deviations [7]. More frequent and large magnitude changes in the input (insulin delivery rate) result in more deviations of the output (glucose) away from the desired value. A methodology of ?human-friendly? identification that accounts for desirable limits in changes in the insulin infusion rate and acceptable deviations from the glucose setpoint with shorter test duration is desirable.

In this paper we show that the meal consumption, insulin infusion and glucose sensor data from typical ambulatory care or clinical studies is generally not adequate for model identification. Type 1 diabetic subjects normally administer an insulin bolus at or near a meal intake in to avoid high postprandial glucose excursions, resulting in two input signals (meal carbohydrate content and magnitude of insulin bolus) that are highly correlated since they are injected at very close times. This often yields an insulin-glucose gain that is estimated to be positive even though it is clearly negative (insulin is administered for the purpose of reducing the glucose concentration). The strong correlation between input signals makes it impossible to estimate accurately the dynamics of insulin and meal to glucose under normal living conditions.

Introducing a time-delay possible between the meal and an insulin bolus can reduce the input correlation and yield improved models for controller design. A meal generates an impulse response in glucose concentration with a shape that depends on the meal content and size. A meal insulin bolus produces an impulse response, and a change in basal rate results in a step response. The main goal of this paper is to present how to design human-friendly and control-relevant modeling experiments, leading to suitable models for a closed-loop artificial pancreas. A series of single-input single-output experiments are designed to reduce the correlation by perturbing either meal or insulin, one at a time. We illustrate the model identification procedures by using simulation studies based on two common compartmental models for insulin-glucose dynamics [3],[6].

It is clear that using meal knowledge to provide rapid feedforward control action yields significantly better glucose control performance compared to feedback-only control [10], however it is known that over 65% of adolescents fail to provide meal-time insulin boluses two or more times each week, resulting in higher mean glucose concentrations and the increased probability of long-term complications. In addition, it is common for individuals to underestimate meal size by the order of 30%, resulting in insulin boluses that are too low and yielding higher than necessary postprandial glucose values. We have developed a meal detection [4], and meal size estimation strategy to provide the benefits of feedforward-type control without requiring individuals to specify that they are consuming a meal or providing the meal size. We compare the closed-loop performance of our estimation-based strategy with feedback-only and feedforward-feedback where the feedforward portion is missing on two meals per week. Our estimation-based strategy results in lower mean and maximum glucose values than the other two strategies.

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