Modeling β-Cell Insulin Secretion - Implications for Closed-Loop Glucose Homeostasis

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Abstract
Glucose sensing and insulin delivery technology can potentially be linked to form a closed-loop insulin delivery system. Ideally, such a system would establish normal physiologic glucose profiles. To this end, a model of β-cell secretion can potentially provide insight into the preferred structure of the insulin delivery algorithm. Two secretion models were evaluated for their ability to describe plasma insulin dynamics during hyperglycemic clamps (humans; n = 7), and for their ability to establish and maintain fasting euglycemia under conditions simulated by the minimal model. The first β-cell model (SD) characterized insulin secretion as a static component that had a delayed response to glucose, and a dynamic component that responded to the rate of increase of glucose. The second model (PID) described the response in terms of a proportional component without delay, an integral component that adjusted basal delivery in proportion to hyper/hypoglycemia, and a derivative component that responded to the rate of glucose change. Both models fit the β-cell response during the clamp, and established fasting euglycemia under simulated closed-loop conditions; however, the SD model did not maintain euglycemia following simulated changes in insulin sensitivity or glucose appearance, whereas the PID model did. The PID model was more stable under the simulated closed-loop conditions. Both the SD and PID models described β-cell secretion in response to a rapid increase in glucose. However, the PID model could maintain fasting euglycemia and was more stable under closed-loop conditions, and thus is more suited for such conditions.

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