## 2 History of Closed Loop Systems  
Over the last half century, automated systems for delivery of insulin have been a topic of much interest, envisioned as an intelligent treatment paradigm for the insulin-deficient patient. The concept of an artificial pancreas and the evolving algorithms during this time parallel the rise of the electronic, digitized computer age. The control of blood glucose levels has been likened to industrial processes in which a monitoring system (glucose sensor) evaluates an input (glucose levels) and uses a control system (e.g. algorithm programmed into a computer) to predictably control the output of that system (insulin infusion rate, see figure 1). This system of artificially maintaining glycemic control requires three main components:  
1. Glucose sensing device (continuous or very frequent)
2. Control device for analyzing blood glucose data and computing insulin dosing (computer or microprocessor)
3. Insulin delivery device (usually a subcutaneous mechanical pump, potentially an implantable pump)  
Only within the last decade have continuous glucose sensing devices (the afferent limb of a closed loop system) been approved by regulatory agencies after overcoming accuracy and stability issues. Three currently-available models which are inserted into subcutaneous tissue have been approved in the USA due to success in clinical trials (Medtronic Guardian or Paradigm, Dexcom Seven, and Abbott Navigator). A fourth, the Gluco-Day sensor, a microdialysis device (Menarini), is approved in parts of Europe. Even without closed loop control, a recent 6-month study found that usage of these devices led to a substantial improvement in hemoglobin A1C without an increase in hypoglycemic episodes in persons with Type 1 diabetes [7]. Intravenous (IV) glucose sensors have been investigated in smaller trials [8] but IV devices are not typically used. In contrast to subcutaneous sensors, intravenous sensors are accompanied by more severe risks such as thrombosis, embolization, and intravascular infection. There have also been advances in insulin pump technology over the past 2 decades. Commercially-available insulin pumps deliver insulin by the subcutaneous route, though intraperitoneal delivery (leading to faster absorption and action than subcutaneous) is being studied in limited research settings [8]. Nonetheless, subcutaneous insulin delivery does not compare favorably with the physiological secretion of beta-cells directly into the blood stream, and confers risks when used in the setting of closed-loop management. For example, delay of subcutaneous insulin absorption and action, even with  
Figure 1: Principles of control systems applied to glycemic control. fast-acting analog insulin, constitutes a fundamental problem of most closed loop systems in persons with diabetes: the efferent delay. Specifically, elevated glucose levels after meals due to this delay lead to late and often excessive insulin delivery, leading in turn to hypoglycemia (overcorrection hypoglycemia). Stated in engineering terminology, there is an instability characterized by large oscillations in the controlled variable (glucose) due to marked efferent delay. Recently, a \"semi-closed loop\" or \"hybrid\" system involving open-loop insulin delivery before meals has been shown to lead to tighter glycemic control than fully closed loop treatment [9]. The attractiveness of a hybrid system rests on the well-known delay between administration of subcutaneous fast-acting insulin and its action. Insulin given before the meal in this fashion can be thought of as \"anticipatory\" rather than reactive. There have been multiple mathematical concepts with initial linear equations using first-order dynamics utilized in algorithms for closed loop glycemic control [10]. These early concepts could not be fully tested in animal or human studies and were rudimentary in terms of their ability to control blood glucose. Over the years, there came a clear need for models of glucose-insulin interaction that described the dynamics of carbohydrate homeostasis.