Automated insulin delivery for type 1 diabetes Garry M. Steil a and Mohammed F. Saad b

Automated insulin delivery for type 1 diabetes Garry M. Steil a and Mohammed F. Saad b Purpose of review Automated insulin delivery using the subcutaneous site for both glucose sensing and insulin delivery, while not commercially available, is starting to be implemented in the research environment. Here, we review issues with glucose sensing and insulin delivery algorithms that need to be resolved in order to achieve a closed-loop system. Recent findings Glucose sensing technology is improving. New studies demonstrating minimal delay in the subcutaneous interstitial fluid glucose response are reviewed, together with early studies indicating longer delay. The pharmacokinetics/ pharmacodynamics of subcutaneous insulin, which pose a significant obstacle to closing the delivery loop, are also reviewed, together with approaches being used to develop algorithms to overcome the delay in insulin absorption from this site. Closed-loop data using the Medtronic MiniMed external Physiologic Insulin Delivery system are presented. Summary Initial closed-loop data in both animals and humans suggest that a completely automated insulin delivery system is attainable, although substantial research remains to be conducted prior to such a system being available for home patient use. Keywords continuous subcutaneous insulin infusion, continuous glucose monitoring system, external Physiologic Insulin Delivery (epid), insulin secretion, minimal model Curr Opin Endocrinol Diabetes 13:205 211. ß 2006 Lippincott Williams & Wilkins. a Medtronic MiniMed, Northridge, California and b Stony Brook School of Medicine, Stony Brook, New York, USA Correspondence to Dr Garry Steil, Division of Research and Development, Medtronic MiniMed, 18000 Devonshire Street, Northridge, CA 91325, USA Tel: +1 818 576 4330; fax: +1 818 576 6206; e-mail: garry.steil@medtronic.com Current Opinion in Endocrinology & Diabetes 2006, 13:205 211 Abbreviations epid ISF MPC external Physiologic Insulin Delivery interstitial fluid model predictive control ß 2006 Lippincott Williams & Wilkins 1068-3097 Introduction The desire and demand for an automated artificial pancreas have existed almost from the time insulin was first discovered in 1921. Insulin pumps capable of delivering insulin subcutaneously have been in use since the early 1980s, systems that can continuously sense subcutaneous glucose have been available since the late 1990s (Medtronic MiniMed continuous glucose monitoring system), and algorithms for calculating the insulin delivery rate have been studied for more than 40 years [1]. One may reasonably ask: what remains to be done? What remains is still substantial. It is virtually impossible to consider a completely automated closed-loop insulin delivery system being used by patients at home without adequate studies being performed to address a wide range of clinical concerns. Starting with the sensor, it is well known that subcutaneous interstitial fluid (ISF) poses unique challenges when used as a surrogate for blood glucose estimation. These include putative delays in the response due to glucose equilibration between blood and subcutaneous ISF, and the challenges related to calibrating the sensor following insertion. Insulin delivery is likely to be either subcutaneous using an external insulin pump, or intraperitoneal using an implantable pump. Both delivery sites introduce additional delays in insulin kinetics not seen with intravenous delivery. Fast-acting insulin analogues have reduced the subcutaneous absorption time, but the kinetics are still delayed. The ability of any closed-loop algorithm to cope with these delays has not been adequately demonstrated. Ambulatory closed-loop systems are unlikely to have glucagon available to correct hypoglycemia, as no pump-stable formulation exists for this hormone. Finally, variability in insulin requirement related to diurnal variations in insulin sensitivity or endogenous glucose production needs to be addressed, as does controller stability during periods of intense exercise, and the responses to various meal types. The subcutaneous glucose sensing site Use of the subcutaneous ISF for glucose sensing has been the subject of intense focus for many years, with the primary concern being the putative differences between blood and ISF glucose concentrations. The basic problem is that the capillary presents a barrier to glucose entry into the subcutaneous ISF space, leading to a complex dynamic relation involving both glucose diffusion and glucose uptake (Fig. 1) [2]. This barrier is thought to result in insulin-induced changes in the plasma-to-isf 205

206 Diabetes and the endocrine pancreas Figure 1 Two-compartment model of capillary blood glucose (G 1 ) and interstitial fluid (ISF) glucose (G 2 ) Figure 2 Plasma insulin concentrations following an intravenous (IV), intraperitoneal (IP) or subcutaneous (SC) bolus of insulin at 0 min Sensor Insulin (µu/ml) 300 IV IP SC Capillary K G 1 G K 2 K Fat/ muscle cell 200 100 0 0 60 120 180 240 300 360 Time (min) Interstitial fluid Glucose (closed circles) moves from the capillary space to the ISF space by diffusion (rate determined by K 12 and K 21 ), and is cleared from the ISF space by uptake into insulin-sensitive tissues (fat or muscle) via a process that may be enhanced by insulin (triangles) binding to its receptor (recessed triangle on cell membrane). Figure adapted with permission from Rebrin et al. [2]. glucose gradient [2,3], different response times for falling and rising glucose signals [4], protracted recovery times following hypoglycemia [5,6], and the possibility that ISF glucose can fall in advance of plasma glucose [7,8]. While each of the aforementioned possibilities is theoretically possible based on a glucose distribution model (Fig. 1), we have shown the delay in ISF glucose to be no more than 6 8 min during hyperglycemic [9] or hypoglycemic [10 ] clamps, and that there is no difference in delay during a fall compared with a rise in glucose. While our studies [9,10 ] were conducted in non-diabetic individuals, the delay estimates are consistent with those reported by Boyne et al. [11] in individuals with type 1 diabetes mellitus. A 6 10-min delay is unlikely to pose a substantial barrier in the development of a closed-loop insulin delivery system. This is not to say that other significant issues do not exist with glucose sensors. In particular, sensors that exist today require an initial calibration in vivo following insertion, and can require recalibration during use (typically two per day for the Medtronic MiniMed continuous glucose monitoring system [12]; and four over 3 days for the Therasense Freestyle [13]). This process cannot be completely error-free, as the calibration is performed against home glucose meters, which are themselves a source of error [14 17]. Site of insulin delivery The applicability of the subcutaneous site for insulin delivery has been greatly enhanced by the development of rapidly absorbed insulin analogues. Subcutaneous insulin kinetics (Fig. 2) [18,19,20 ] are still substantially The intravenous response is shown with an assumed half-life of 10 min, subcutaneous data (open circles) are adapted from Mudaliar et al. [18], and intraperitoneal data (solid circle) are adapted from Kelley et al. [19]. Dashed and chain dashed lines represent fits to a two-compartment insulin clearance model (see [20 ]). delayed, however, with peak plasma insulin levels not being achieved for 40 60 min and requiring a total of 3 6 h to fully dissipate [18]. Intraperitoneal insulin kinetics are faster (peak value of 40 min [19]), but this is still far slower than the kinetics of intravenous insulin, which has a half life of 5 10 min. System variability All systems have variability, and the glucose response to exogenous insulin is no exception. Even in healthy individuals insulin sensitivity varies both day-to-day [21] and throughout the day [22]. Diurnal variance can result from either a change in insulin sensitivity per se,ora change in endogenous glucose production [23], both of which may be mediated by changes in free fatty acids [24]. For an individual with type 1 diabetes, this results in varying basal insulin requirements throughout the day that are reflected in pump basal profiles. Insulin requirements for meals of identical carbohydrate content can also vary depending on the type of carbohydrate [25,26] and past exercise [27,28]. Ultimately, the list of potential factors influencing insulin requirement is long, and the question is: can a closed-loop insulin delivery algorithm automatically adjust to all these varying needs? Closed-loop insulin delivery algorithms Approaches to developing the closed-loop algorithm have traditionally relied on control theory developed by engineers for any number of different systems (e.g. aerospace or process control). A historical review of closed-loop insulin delivery is likely to provide a complete overview of the past 40 years of research into control theory per se. While such a review is beyond the scope of the present paper (recent reviews are available [29,30]), we make note of what would be considered today to be a state-ofthe-art control approach known as model predictive

Automated insulin delivery for type 1 diabetes Steil and Saad 207 control (MPC) [31]. In MPC, a mathematical model of the subject s glucose response is derived, and the difference between the measured glucose and the modelpredicted values is corrected by calculating a sequence of insulin delivery rates looking n samples into the future the number of samples into the future being termed the control horizon. The insulin delivery rates are then optimized based on the difference in the modelpredicted glucose response m-points into the future, in which m is termed the prediction horizon (m and n need not be the same). The algorithm is of particular interest in that it may be able to compensate for delays in glucose sensing (Fig. 1) and insulin appearance (Fig. 2). Successful implementation of an MPC strategy depends largely on the ability of the glucose model to accurately predict future glucose values. Much work has been done in the past decade to develop and validate such models. We have recently compared the description of insulin action in the more common models and found systematic differences among them [32 ]. Nonetheless, these differences could potentially be resolved based on the large amount of data now available from continuous glucose monitoring systems; various existing models have already shown promise in predicting future glucose values [33,34], and MPC has been shown to provide good results in a simulated environment [31,35 ]. MPC represents just one of numerous closed-loop control methods developed primarily from an engineering control theory approach. While the potential for automated insulin delivery algorithms to benefit from the large body of control systems research cannot be overestimated, a strong argument can also be made for understanding the mechanisms by which the b-cell maintains tight glucose control. The b-cell argument has dominated in the development of the Medtronic MiniMed external Physiologic Insulin Delivery (epid) system [1]. The main points are that the b-cell adapts its secretory response to the individual s underlying insulin sensitivity [36 38], and that it adjusts the ratio of first- to second-phase insulin to compensate for a delay in insulin action [39]. In an effort to emulate the b-cell as a basis for closed-loop insulin delivery, we have extended existing mathematical models of the b-cell secretory response that use two phases [40 48] to include a third phase. The existing models are deeply rooted in the monumental work of Gerald Grodsky [49 51], and typically describe the b-cell response to glucose as the sum of two components which variously react proportionally to changes in glucose, have a delayed reaction to glucose, or react to the rate-ofchange of glucose. In our model, all three terms are included (Fig. 3) [52]. We have compared the ability of the three-phase model to compensate for changes in basal insulin requirement with that of the two-phase model proposed by Cobelli and colleagues [40,41]. In our simulations [52], the three-phase model was able to adjust insulin delivery to compensate for changes in insulin sensitivity or endogenous glucose production, whereas the two-phase model was not. The b-cell algorithm has been implemented on a laptop computer modified to receive the glucose sensor signal at 1-min intervals and to transmit insulin delivery commands to the Medtronic-MiniMed insulin pump (Fig. 4). The epid device is labelled for investigation use only and is not commercially available. Nonetheless, research studies have been performed in both animals (diabetic canine) and humans. An example response (Fig. 5), obtained in the canine diabetic model, illustrates the three-phase response during a meal. For these data, the desired glucose set point was 120 mg/dl and the initial glucose concentration was 100 mg/dl. Basal insulin delivery is determined by the slow component (Fig. 3c). Once the meal begins, the rate-of-change component (Fig. 3d) results in a rapid rise in insulin delivery, which is accompanied by more proportionalphase insulin (Fig. 3b) as glucose rises above a set-point. One of the challenges of controlling this response is to recreate the normal diurnal variations in insulin secretion and glucose levels seen in healthy individuals [53]. Two points are particularly relevant in discussing the epid algorithm. The first is that the b-cell model is identical to a classical proportional integral derivative controller [54]. In that system, proportional refers to a control response in proportion to the difference between a measured variable and its desired value, for example, providing gas in proportion to the difference between the speed and a target set-point in an automobile cruise system. Note that, by definition, the proportional component has no output when the system being controlled is at target, that is, no gas in the automobile example when the car is at target speed, and no insulin delivery in the artificial b-cell when glucose is at target concentration. Integral refers to a component of the controller that increments from its most recent value (initial condition if the controller is just turned on) in response to the measured variable being above or below target (mathematically an integral for continuous control). In the cruise control example, the gas would increment up when the car climbs a hill. While starting up the hill the car will temporarily slow down, but will re-achieve the target speed as more gas is given by the integral component. This example is analogous to the situation in which a patient s insulin delivery needs to be increased following a decrease in insulin sensitivity. The integral component holds its last value when the system is at target and is the only non-zero component when a system is stable. Finally, derivative refers to the rate-of-change. The derivative component stabilizes the closed-loop system, in that it always counteracts change (gives gas when the car slows

208 Diabetes and the endocrine pancreas Figure 3 Plasma insulin response obtained by the b-cell during a hyperglycemic glucose clamp (a) Plasma insulin concentration (circles) and model fit (solid line through data) of the three-phase b-cell model to the plasma insulin response (data adapted from Steil et al. [52]). Schematic representation of the epid algorithm showing simulated proportional (b; blue), integral (c; green) and derivative (d; magenta) phases, together with their sum (e). Mathematical formulae are shown in (b d), with K P, K I and K D defining the relative magnitude of the proportional (P), integral (I) and derivative (D) phases respectively; G and G b indicating the measured glucose and desired basal glucose concentrations respectively; and P con, I con and D con indicating the proportional, integral and derivative control phases, respectively. Figure 4 Closed-loop insulin delivery developmental system The system is composed of a subcutaneous glucose sensor and a radio-frequency transmitter (a) transmitting subcutaneous glucose sensor values to a laptop computer (c) which calibrates and performs insulin delivery calculations at 1-min intervals, and transmits the rate to an external insulin delivery pump (b) in a sequence of small (0.1 U) boluses [sensor, pump and catheter all from Medtronic MiniMed; glucose transmitter and receiving unit (attached to laptop) are investigation devices only].

Automated insulin delivery for type 1 diabetes Steil and Saad 209 Figure 5 Plasma glucose and insulin delivery during a meal controlled by the epid system (a) Plasma glucose ( ) concentration obtained with the epid algorithm (Fig. 3) and system (Fig. 4). Glucose values were obtained every 1 min (solid line), with the meal administered at 06:00 hours. Target glucose was 120 mg/dl. (b) Three-phase insulin delivery based on the model of Fig. 3. down, or insulin when glucose goes up). That the b-cell response has many similarities to a classical control response should not be surprising, as the b-cell largely serves as the body s closed-loop insulin delivery system. The second point is that the b-cell delivers insulin directly into the portal vein, whereas an artificial system is likely to use a peripheral or peritoneal route. Thus, it can be expected that the algorithm will need to be adjusted for differences in insulin pharmacokinetics and dynamics. With regard to the latter, insulin secreted into the portal vein is thought to have a rapid direct effect to suppress hepatic glucose output [55 57] and alter other metabolites [58]. The effect on hepatic glucose output is also mediated by indirect effects, however the so-called single gateway hypothesis that has been extensively studied by Bergman and colleagues [59 65]. In either case, differences exist in the pharmacokinetics of insulin delivered portally compared with peripherally (Fig. 2), and these differences will need to be taken into consideration. To date, the only change in the profile used in the Medtronic MiniMed epid system is a change in the relative proportions of the three phases. For example, in the meal response of Fig. 5, first-phase insulin has been increased approximately 50% compared with that shown in Fig. 3, and the rate of rise in the second phase has been reduced by approximately half (specifically, the ratio K D /K P in Fig. 3 was increased 50%, and the ratio K P /K I was decreased 50%). A more optimal adjustment of the algorithm can likely only be made by modelling the effect of insulin on glucose metabolism. Thus, while MPC strategies can be used as a means of calculating insulin delivery per se, the same model can also be used to formulate optimal adjustments in the relative contributions of the proportional, integral and derivative terms to compensate for known differences in insulin kinetics (Fig. 2) or for known effects of portal insulin delivery (if any). Model-based optimization of the epid algorithm has been investigated using historical canine data [20 ], but has yet to be applied to studies with human subjects. Adding characteristics of the b-cell accounting for diurnal variation in insulin secretion, the effect of insulin concentration to suppress insulin secretion, and the effect of incretins (see [1] for a review) may further aid the optimization process. While this is the present strategy embraced by Medtronic, it must be stated that the use of a b-cell model as a basis for the closed-loop algorithm, or the contention that the b- cell can be described in control theory terms, has not been universally accepted [66 ]. Conclusion While work remains to be done to validate aspects of the epid system, we have used the model as a basis for closedloop insulin delivery in humans, based on subcutaneous glucose sensing with subcutaneous insulin delivery [67], and intravenous glucose sensing with intraperitoneal insulin delivery [68]. Preliminary results from our clinical

210 Diabetes and the endocrine pancreas trials using this model/algorithm are promising [67,68], suggesting that a completely closed-loop system will be attainable in the near future. Steps towards automating open-loop pump therapy are ongoing and can be expected to be of increasing benefit for continuous glucose measurement and metabolic modelling. Achieving near-normal glycemic profiles with an automated system will decrease the risk of diabetic complications and improve the patient s quality of life. Acknowledgements This work was partially funded by National Institutes of Health grant RO1-DK64567 to G.M.S. References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: of special interest of outstanding interest Additional references related to this topic can also be found in the Current World Literature section in this issue (pp. 225 226). 1 Steil GM, Panteleon AE, Rebrin K. Closed-loop insulin delivery: the path to physiological glucose control. Adv Drug Deliv Rev 2004; 56:125 144. 2 Rebrin K, Steil GM, Van Antwerp WP, Mastrototaro JJ. Subcutaneous glucose predicts plasma glucose independent of insulin: implications for continuous monitoring. Am J Physiol Endocrinol Metab 1999; 277:E561 E571. 3 Baron AD. Hemodynamic actions of insulin. Am J Physiol Endocrinol Metab 1994; 267:E187 E202. 4 Kulcu E, Tamada JA, Reach G, et al. Physiological differences between interstitial glucose and blood glucose measured in human subjects. Diabetes Care 2003; 26:2405 2409. 5 Moberg E, Hagström-Toft E, Arner P, et al. Protracted glucose fall in subcutaneous adipose tissue and skeletal muscle compared with blood during insulin-induced hypoglycaemia. Diabetologia 1997; 40:1320 1326. 6 Cheyne EH, Cavan DA, Kerr D. Performance of a continuous glucose monitoring system during controlled hypoglycaemia in healthy volunteers. Diabetes Technol Ther 2002; 4:607 613. 7 Thome-Duret V, Reach G, Gangnerau MN, et al. Use of a subcutaneous glucose sensor to detect decreases in glucose concentration prior to observation in blood. Anal Chem 1996; 68:3822 3826. 8 Sternberg F, Meyerhoff C, Mennel FJ, et al. Does fall in tissue glucose precede fall in blood glucose? Diabetologia 1996; 39:609 612. 9 Steil GM, Rebrin K, Mastrototaro J, et al. Determination of plasma glucose during rapid glucose excursions with a subcutaneous glucose sensor. Diabetes Technol Ther 2003; 5:27 31. 10 Steil GM, Rebrin K, Hariri F, et al. Interstitial fluid glucose dynamics during insulin-induced hypoglycaemia. Diabetologia 2005; 48:1833 1840. Study demonstrating that much of the delay that has been reported during recovery from hypoglycemia is not inherent in ISF, but rather is due to routines implemented in the devices to create smooth signals (continuous glucose monitoring system) or to delays in the device itself (microdialysis membranes). 11 Boyne MS, Silver DM, Kaplan J, et al. Timing of changes in interstitial and venous blood glucose measured with a continuous subcutaneous glucose sensor. Diabetes 2003; 52:2790 2794. 12 Gross TM, Bode BW, Einhorn D, et al. Performance evaluation of the MiniMed continuous glucose monitoring system during patient home use. Diabetes Technol Ther 2000; 2:49 56. 13 Feldman B, Brazg R, Schwartz S, et al. A continuous glucose sensor based on wired enzyme technology: results from a 3-day trial in patients with type 1 diabetes. Diabetes Technol Ther 2003; 5:769 779. 14 Brunner GA, Ellimerer ME, Sendlhofer G, et al. Validation of home blood glucose meters with respect to clinical and analytical approaches. Diabetes Care 1998; 21:585 590. 15 Guatier JF, Bigard AX, Douce P, et al. Influence of simulated altitude on the performance of five blood glucose meters. Diabetes Care 1996; 19:1430 1432. 16 Heinemann L, Overmann H, Muhlhauser I. How well do patients with type 1 diabetes measure their blood glucose in daily life? Diabetes Care 1998; 21:461 462. 17 Tate PF, Clements CA, Walters JE. Accuracy of home blood glucose monitors. Diabetes Care 1992; 15:536 538. 18 Mudaliar SR, Lindberg FA, Joyce M, et al. Insulin aspart (B28 asp-insulin): a fast-acting analog of human insulin: absorption kinetics and action profile compared with regular human insulin in healthy nondiabetic subjects. Diabetes Care 1999; 22:1501 1506. 19 Kelley DE, Henry RR, Edelman SV. Acute effects of intraperitoneal versus subcutaneous insulin delivery on glucose homeostasis in patients with NIDDM. Veterans Affairs Implantable Insulin Pump Study Group. Diabetes Care 1996; 19:1237 1242. 20 Steil GM, Rebrin K. Closed loop insulin delivery: what lies between where we are and where we are going? Exp Opin Drug Deliv 2005; 2:353 362. Includes a review of current trends in bolus estimation and linking blood glucose meters to insulin pumps (where we are), together with arguments as to how a metabolic model might be used to optimize pump therapy/closed-loop insulin delivery. 21 Steil GM, Murray J, Bergman RN, et al. Repeatability of insulin sensitivity and glucose effectiveness from the minimal model: implications for study design. Diabetes 1994; 43:1365 1371. 22 Morgan LM, Aspostolakou F, Wright J, et al. Diurnal variations in peripheral insulin resistance and plasma non-esterified fatty acid concentrations: a possible link? Ann Clin Biochem 1999; 36:447 450. 23 Boden G, Chen X, Urbain JL. Evidence for a circadian rhythm of insulin sensitivity in patients with NIDDM caused by cyclic changes in hepatic glucose production. Diabetes 1996; 45:1044 1050. 24 Arasaradnam MP, Morgan L, Wright J, et al. Diurnal variation in lipoprotein lipase activity. Ann Clin Biochem 2002; 39:136 139. 25 Mohammed NH, Wolever TM. Effect of carbohydrate source on post-prandial blood glucose in subjects with type 1 diabetes treated with insulin lispro. Diabetes Res Clin Pract 2004; 65:29 35. A well controlled study showing variability in responses to meals with identical carbohydrate content and insulin bolus; the study demonstrates variability in achieving good open-loop meal responses. 26 Capani F, Casalini G, Consoli A, et al. Insulin requirement of simple and complex carbohydrate foods in type 1 (insulin-dependent) CSII-treated diabetic subjects, obtained by biostator: correlation with glycaemic index. Acta Diabetol Lat 1991; 28:47 53. 27 Galassetti P, Coker RH, Lacy DB, et al. Prior exercise increases net hepatic glucose uptake during a glucose load. Am J Physiol Endocrinol Metab 1999; 276:E1022 E1029. 28 Steppel JH, Horton ES. Exercise in the management of type 1 diabetes mellitus. Rev Endocr Metab Disord 2003; 4:355 360. 29 Parker RS, Doyle FJ III, Peppas NA. The intravenous route to blood glucose control. IEEE Eng Med Biol Mag 2001; 20:65 73. 30 Bellazzi R, Nucci G, Cobelli C. The subcutaneous route to insulin-dependent diabetes therapy. IEEE Eng Med Biol Mag 2001; 20:54 64. 31 Parker RS, Doyle FJ, Peppas NA. A model-based algorithm for blood glucose control in type 1 diabetic patients. IEEE Trans Biomed Eng 1999; 46:148 157. 32 Steil GM, Clark B, Kanderian S, Rebrin K. Modeling insulin action for development of a closed-loop artificial pancreas. Diabetes Technol Ther 2005; 7:94 108. A comparison of several common metabolic models, highlighting differences in dose response characteristics (insulin and glucose) and kinetic structure. 33 Hovorka R, Canonico V, Chassin LJ, et al. Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol Meas 2004; 25:905 920. 34 Hovorka R, Chassin LJ, Wilinska ME, et al. Closing the loop: the adicol experience. Diabetes Technol Ther 2004; 6:307 318. 35 Chassin LJ, Wilinska ME, Hovorka R. Evaluation of glucose controllers in virtual environment: methodology and sample application. Artif Intell Med 2004; 32:171 181. This paper looks at using computer simulation to evaluate insulin delivery algorithms. Good companion reference to consider with [65 ], which also utilizes a model to aid closed-loop algorithm development, and [31 ], which looks at the limitations of the modelling approach. 36 Bergman RN, Phillips LS, Cobelli C. Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and betacell glucose sensitivity from the response to intravenous glucose. J Clin Invest 1981; 68:1456 1467. 37 Bergman RN, Ader M, Huecking K, et al. Accurate assessment of beta-cell function: the hyperbolic correction. Diabetes 2002; 51 (Suppl 1):S212 S220.

Automated insulin delivery for type 1 diabetes Steil and Saad 211 38 Kahn SE, Prigeon RL, McCulloch DK, et al. Quantification of the relationship between insulin sensitivity and beta-cell function in human subjects: evidence for a hyperbolic function. Diabetes 1993; 42:1663 1672. 39 Getty L, Hamilton-Wessler M, Ader M, et al. Biphasic insulin secretion during intravenous glucose tolerance test promotes optimal interstitial insulin profile. Diabetes 1998; 47:1941 1947. 40 Breda E, Cavaghan MK, Toffolo G, et al. Oral glucose tolerance test minimal model indexes of beta-cell function and insulin sensitivity. Diabetes 2001; 50:150 158. 41 Breda E, Toffolo G, Polonsky KS, et al. Insulin release in impaired glucose tolerance: oral minimal model predicts normal sensitivity to glucose but defective response times. Diabetes 2002; 51 (Suppl 1):S227 S233. 42 Mari A, Camastra S, Toschi E, et al. A model for glucose control of insulin secretion during 24 h of free living. Diabetes 2001; 50 (Suppl 1):S164 S168. 43 Mari A, Schmitz O, Gastaldelli A, et al. Meal and oral glucose tests for assessment of beta-cell function: modeling analysis in normal subjects. Am J Physiol Endocrinol Metab 2002; 283:E1159 E1166. 44 Mari A, Tura A, Gastaldelli A, et al. Assessing insulin secretion by modeling in multiple-meal tests: role of potentiation. Diabetes 2002; 51 (Suppl 1):S221 S226. 45 Cretti A, Lehtovirta M, Bonora E, et al. Assessment of B-cell function during oral glucose tolerance test by minimal model of insulin secretion. Exp Clin Endocrinol 2003; 31:405 416. 46 Hovorka R, Chassin L, Luzio SD, et al. Pancreatic beta-cell responsiveness during meal tolerance test: model assessment in normal subjects and subjects with newly diagnosed non-insulin-dependent diabetes mellitus. J Clin Endocrinol Metab 1998; 83:744 750. 47 Cerasi E, Fick G, Rudemo M. A mathematical model for the glucose induced insulin release in man. Eur J Clin Invest 1974; 4:267 278. 48 Nesher R, Cerasi E. Modeling phasic insulin release: immediate and time-dependent effects of glucose. Diabetes 2002; 51 (Suppl 1):S53 S59. 49 Grodsky G, Tarver H, Light A, et al. Paper chromatography of insulin. Nature 1956; 177:223 225. 50 Bonner-Weir S, Grodsky G. Analysis: assessment of human islet preparations to be used for islet expansion, survival, or transplant. Diabetes Technol Ther 2004; 6:493 494. 51 Grodsky GM, Curry D, Landahl H, et al. Further studies on the dynamic aspects of insulin release in vitro with evidence for a two-compartmental storage system. Acta Diabetol Lat 1969; 6 (Suppl 1):554 578. 52 Steil GM, Rebrin K, Janowski R, et al. Modeling beta-cell insulin secretion: implications for closed-loop glucose homeostasis. Diabetes Technol Ther 2003; 5:953 964. 53 Steil GM, Hwu CM, Janowski R, et al. Evaluation of insulin sensitivity and betacell function indexes obtained from minimal model analysis of a meal tolerance test. Diabetes 2004; 53:1201 1207. 54 Bequette BW. A critical assessment of algorithms and challenges in the development of a closed-loop artificial pancreas. Diabetes Technol Ther 2005; 7:28 47. 55 Sindelar DK, Chu CA, Venson P, et al. Basal hepatic glucose production is regulated by the portal vein insulin concentration. Diabetes 1998; 47:523 529. 56 Satake S, Moore MC, Igawa K, et al. Direct and indirect effects of insulin on glucose uptake and storage by the liver. Diabetes 2002; 51:1663 1671. 57 Cherrington AD, Sindelar D, Edgerton D, et al. Physiological consequences of phasic insulin release in the normal animal. Diabetes 2002; 51 (Suppl 1): S103 S108. 58 Freyse EJ, Rebrin K, Schneider T, et al. Increased urea synthesis in insulindependent diabetic dogs maintained normoglycemic: effect of portal insulin administration and food protein content. Diabetes 1996; 45:667 674. 59 Ader M, Bergman RN. Peripheral effects of insulin dominate suppression of fasting hepatic glucose production. Am J Physiol Endocrinol Metab 1990; 258:E1020 E1032. 60 Bergman RN. New concepts in extracellular signaling for insulin action: the single gateway hypothesis. Recent Prog Horm Res 1997; 52:359 385. 61 Mittelman SD, Fu Y-Y, Steil GM, et al. Indirect effect of insulin to suppress endogenous glucose production is dominant even with hyperglycemia. J Clin Invest 1997; 100:3129 3139. 62 Poulin RA, Steil GM, Moore DM, et al. Dynamics of glucose production and uptake are more closely related to insulin in hindlimb lymph than in thoracic duct lymph. Diabetes 1994; 43:180 190. 63 Rebrin K, Steil GM, Getty L, et al. Free fatty acid as a link in the regulation of hepatic glucose output by peripheral insulin. Diabetes 1995; 44:1038 1045. 64 Rebrin K, Steil GM, Mittelman SD, et al. Causal linkage between insulin suppression of lipolysis and suppression of liver glucose output in dogs. J Clin Invest 1996; 98:741 749. 65 Steil GM, Rebrin K, Mittelman SD, et al. Role of portal insulin delivery in the disappearance of intravenous glucose and assessment of insulin sensitivity. Diabetes 1998; 47:714 720. 66 Hovorka R. Continuous glucose monitoring and closed-loop systems. Diabet Med 2006; 23:1 12. This paper details historical achievements by numerous groups. Arguments are presented that minute-to-minute glucose measurement will not be needed, that achieving true physiologic glucose control will require glucagon, and that the b-cell first phase does not occur under physiologic conditions. The arguments presented provide a timely and balanced alternative to the arguments for using the b-cell model that are presented in the present review and in [1]. 67 Steil GM, Rebrin K, Hariri F, et al. Continuous automated closed-loop insulin delivery based on subcutaneous glucose sensing and external insulin pump. Diabetes 2004; Suppl. 53 (abstract A3). 68 Renard E, Panteleon AE, Leong P, et al. Efficacy of a closed-loop control of blood glucose based on an implantable intravenous sensor and intraperitoneal insulin pump. Diabetes 2004; 53:A114.