W. Kenneth Ward

Quantification of the Relationship Between Insulin Sensitivity and β-Cell Function in Human Subjects: Evidence for a Hyperbolic Function

To determine the relationship between insulin sensitivity and β-cell function, we quantified the insulin sensitivity index using the minimal model in 93 relatively young, apparently healthy human subjects of varying degrees of obesity (55 male, 38 female; 18–44 yr of age; body mass index 19.5–52.2 kg/m2) and with fasting glucose levels <6.4 mM. SI was compared with measures of body adiposity and β-cell function. Although lean individuals showed a wide range of SI, body mass index and SI were related in a curvilinear manner (P < 0.0001) so that on average, an increase in body mass index was associated generally with a lower value for SI. The relationship between the SI and the β-cell measures was more clearly curvilinear and reciprocal for fasting insulin (P < 0.0001), first-phase insulin response (AIRglucose; P < 0.0001), glucose potentiation slope (n = 56; P < 0.005), and β-cell secretory capacity (AIRmax; n = 43; P < 0.0001). The curvilinear relationship between SI and the β-cell measures could not be distinguished from a hyperbola, i.e., SI × β-cell function = constant. This hyperbolic relationship described the data significantly better than a linear function (P < 0.05). The nature of this relationship is consistent with a regulated feedback loop control system such that for any difference in SI, a proportionate reciprocal difference occurs in insulin levels and responses in subjects with similar carbohydrate tolerance. We conclude that in human subjects with normal glucose tolerance and varying degrees of obesity, β-cell function varies quantitatively with differences in insulin sensitivity. Because the function governing this relationship is a hyperbola, when insulin sensitivity is high, large changes in insulin sensitivity produce relatively small changes in insulin levels and responses, whereas when insulin sensitivity is low, small changes in insulin sensitivity produce relatively large changes in insulin levels and responses. Percentile plots based on knowledge of this interaction are presented for evaluating β-cell function in populations and over time.

The Insulin Sensitivity Index in Nondiabetic Man: Correlation Between Clamp-derived and IVGTT-derived Values

Although the minimal-model-based insulin sensitivity index (S1) can be estimated from the results of a simple 180-min intravenous glucose tolerance test (IVGTT), its relationship to widely accepted but technically more difficult clamp-based techniques has not been resolved in humans. Therefore we measured S1 by standard IVGTT, modified IVGTT, and clamp methods in 10 nondiabetic men with %IBW of 109 ± 12 (mean ± SD). In the euglycemic clamp studies, insulin was infused to bring insulin levels (IRI) from basal, 8 ± 4 μU/ml, to plateaus of 21 ± 5 and 35 ± 6 μU/ml. S1[clamp], measured as the increase in glucose (G) clearance per increase in IRI [δINF/(δIRI × G)], averaged 0.29 ± 0.09 ml/kg·min per μU/ml. In the IVGTT studies, 300 mg/kg G was given as an i.v. bolus, and G and IRI were measured for 180 min; in the modified (mod) IVGTT, tolbutamide (300–500 mg) was given i.v. 20 min after the G to observe the effect of an IRI peak on G removal after G level was free of initial “mixing” effects. The S1 estimated by computer did not differ significantly between standard [(6.9 ± 3.4) × 1O−4 min−1 per μU/ml] and modified [(6.7 ± 3.5) × 10−4 min−1 per μU/ml] tests, indicating no bias due to the differing insulin patterns and levels. There was a strong positive correlation between S1 (mod IVGTT) and S1(clamp): r = 0.84; N = 10; P < 0.002. The correlation between S1(standard IVGTT) and S1(clamp) was 0.54, suggesting the modified test is less “noisy” Nonetheless, in eight euglycemic women with a wider range of adiposity, S1(standard IVGTT) has been significantly correlated with %IBW (r = −0.72) and basal IRI (r = −0.84). The correlation between S1 measures by clamp and IVGTT methods provides one step toward validation of the minimal model for studies of insulin action in man.

Novel Use of Glucagon in a Closed-Loop System for Prevention of Hypoglycemia in Type 1 Diabetes

OBJECTIVE To minimize hypoglycemia in subjects with type 1 diabetes by automated glucagon delivery in a closed-loop insulin delivery system. RESEARCH DESIGN AND METHODS Adult subjects with type 1 diabetes underwent one closed-loop study with insulin plus placebo and one study with insulin plus glucagon, given at times of impending hypoglycemia. Seven subjects received glucagon using high-gain parameters, and six subjects received glucagon in a more prolonged manner using low-gain parameters. Blood glucose levels were measured every 10 min and insulin and glucagon infusions were adjusted every 5 min. All subjects received a portion of their usual premeal insulin after meal announcement. RESULTS Automated glucagon plus insulin delivery, compared with placebo plus insulin, significantly reduced time spent in the hypoglycemic range (15 ± 6 vs. 40 ± 10 min/day, P = 0.04). Compared with placebo, high-gain glucagon delivery reduced the frequency of hypoglycemic events (1.0 ± 0.6 vs. 2.1 ± 0.6 events/day, P = 0.01) and the need for carbohydrate treatment (1.4 ± 0.8 vs. 4.0 ± 1.4 treatments/day, P = 0.01). Glucagon given with low-gain parameters did not significantly reduce hypoglycemic event frequency (P = NS) but did reduce frequency of carbohydrate treatment (P = 0.05). CONCLUSIONS During closed-loop treatment in subjects with type 1 diabetes, high-gain pulses of glucagon decreased the frequency of hypoglycemia. Larger and longer-term studies will be required to assess the effect of ongoing glucagon treatment on overall glycemic control.

A Review of the Foreign-body Response to Subcutaneously-implanted Devices: The Role of Macrophages and Cytokines in Biofouling and Fibrosis

The biological response to implanted biomaterials in mammals is a complex series of events that involves many biochemical pathways. Shortly after implantation, fibrinogen and other proteins bind to the device surface, a process known as biofouling. Macrophages then bind to receptors on the proteins, join into multinucleated giant cells, and release transforming growth factor β and other inflammatory cytokines. In response to these signals, quiescent fibroblasts are transformed into myofibroblasts, which synthesize procollagen via activation of Smad mediators. The procollagen becomes crosslinked after secretion into the extracellular space. Mature crosslinked collagen and other extracellular matrix proteins gradually contribute to formation of a hypocellular dense fibrous capsule that becomes impermeable or hypopermeable to many compounds. Porous substrates and angiogenic growth factors can stimulate formation of microvessels, which to some extent can maintain analyte delivery to implanted sensors. However, stimulation by vascular endothelial growth factor alone may lead to formation of leaky, thin-walled, immature vessels. Other growth factors are most probably needed to act upon these immature structures to create more robust vessels. During implantation of foreign bodies, the foreign-body response is difficult to overcome, and thousands of biomaterials have been tested. Biomimicry (i.e., creating membranes whose chemical structure mimics natural cellular compounds) may diminish the response, but as of this writing, it has not been possible to create a stealth material that circumvents the ability of the mammalian surveillance systems to distinguish foreign from self.

The effect of microgeometry, implant thickness and polyurethane chemistry on the foreign body response to subcutaneous implants

We addressed the effect of implant thickness, implant porosity, and polyurethane (PU) chemistry on angiogenesis and on the foreign body response in rats. The following materials were implanted subcutaneously for 7 weeks then excised for histologic analysis: a solid PU; a solid polyurethane with silicone and polyethylene oxide (PU-S-PEO); porous expanded polytetrafluoroethylene (ePTFE); and porous polyvinyl alcohol sponge (PVA). Two thicknesses of PU-S-PEO were compared: 300 microns (thin) and 2000 microns (thick). Foreign body capsule (FBC) thickness was much less in PU-S-PEO implants than in PU implants. In addition, FBC were thinner in thin implants than in thick implants. FBC was much more dense in solid implants than in porous implants. As compared with solid implants, porous implants (PVA and ePTFE) led to a marked increase in the number of microvessels that developed adjacent to the implant, as observed both with hematoxylin/eosin staining and with an immunohistochemical anti-endothelial stain. We conclude that the polyethylene oxide and silicone moieties in PU reduce the thickness of the subsequent FBC. In addition, thin implants lead to a thin FBC. Porous implants (PVA and ePTFE) cause more angiogenesis than solid implants. These results may have implications for the measurement of blood-derived analytes by biosensors.

Predictive Monitoring for Improved Management of Glucose Levels

Background: Recent developments and expected near-future improvements in continuous glucose monitoring (CGM) devices provide opportunities to couple them with mathematical forecasting models to produce predictive monitoring systems for early, proactive glycemia management of diabetes mellitus patients before glucose levels drift to undesirable levels. This article assesses the feasibility of data-driven models to serve as the forecasting engine of predictive monitoring systems. Methods: We investigated the capabilities of data-driven autoregressive (AR) models to (1) capture the correlations in glucose time-series data, (2) make accurate predictions as a function of prediction horizon, and (3) be made portable from individual to individual without any need for model tuning. The investigation is performed by employing CGM data from nine type 1 diabetic subjects collected over a continuous 5-day period. Results: With CGM data serving as the gold standard, AR model-based predictions of glucose levels assessed over nine subjects with Clarke error grid analysis indicated that, for a 30-minute prediction horizon, individually tuned models yield 97.6 to 100.0% of data in the clinically acceptable zones A and B, whereas cross-subject, portable models yield 95.8 to 99.7% of data in zones A and B. Conclusions: This study shows that, for a 30-minute prediction horizon, data-driven AR models provide sufficiently-accurate and clinically-acceptable estimates of glucose levels for timely, proactive therapy and should be considered as the modeling engine for predictive monitoring of patients with type 1 diabetes mellitus. It also suggests that AR models can be made portable from individual to individual with minor performance penalties, while greatly reducing the burden associated with model tuning and data collection for model development.

Modeling the Glucose Sensor Error

Continuous glucose monitoring (CGM) sensors are portable devices, employed in the treatment of diabetes, able to measure glucose concentration in the interstitium almost continuously for several days. However, CGM sensors are not as accurate as standard blood glucose (BG) meters. Studies comparing CGM versus BG demonstrated that CGM is affected by distortion due to diffusion processes and by time-varying systematic under/overestimations due to calibrations and sensor drifts. In addition, measurement noise is also present in CGM data. A reliable model of the different components of CGM inaccuracy with respect to BG (briefly, “sensor error”) is important in several applications, e.g., design of optimal digital filters for denoising of CGM data, real-time glucose prediction, insulin dosing, and artificial pancreas control algorithms. The aim of this paper is to propose an approach to describe CGM sensor error by exploiting n multiple simultaneous CGM recordings. The model of sensor error description includes a model of blood-to-interstitial glucose diffusion process, a linear time-varying model to account for calibration and sensor drift-in-time, and an autoregressive model to describe the additive measurement noise. Model orders and parameters are identified from the n simultaneous CGM sensor recordings and BG references. While the model is applicable to any CGM sensor, here, it is used on a database of 36 datasets of type 1 diabetic adults in which n = 4 Dexcom SEVEN Plus CGM time series and frequent BG references were available simultaneously. Results demonstrates that multiple simultaneous sensor data and proper modeling allow dissecting the sensor error into its different components, distinguishing those related to physiology from those related to technology.

Rise in background current over time in a subcutaneous glucose sensor in the rabbit: relevance to calibration and accuracy

In order to calibrate a continuous glucose monitor, accurate determination of the background current (I0) is necessary, in part because I0 could change over time. We compared two methods of I0 measurement: (1), extrapolation of sensor output data (as a function of glucose level) to the intercept at zero glucose and (2) direct measurement of the output of a blank anode with no enzyme coat. We implanted telemetric sensors subcutaneously in rabbits and measured their outputs during tri-level glucose clamps once per week for 5 weeks. The two methods yielded similar results. I0 rose substantially over time and this increase reached significance during week 3 by the direct method but not until week 5 by the extrapolation method. Using the direct method, I0 rose from 3.41 (0.60-8.48 nanoamperes (nA), median and range) during week 1 to 13.42 (9.1-14.3) during week 5. Using the extrapolation method, I0 rose from 0.57 (0-16.7) during week 1 to 15.3 (12.2-21.6) during week 5. We conclude that I0 can rise over time. If this rise went undetected and was assumed to be stable, a one-point calibration procedure would overestimate glycemia in the hypoglycemic range, i.e. fail to appreciate the severity of hypoglycemia. It is recommended that during validation of a chronic glucose sensor, I0 be measured sequentially over time.

Understanding spontaneous output fluctuations of an amperometric glucose sensor: effect of inhalation anesthesia and use of a nonenzyme containing electrode.

Implantable glucose sensors are often unstable in vivo. Possible causes include local oscillations of glucose or oxygen levels, fluctuation of interferants, and external electromagnetic interference. To better understand glucose versus nonglucose mediated fluctuations, we compared sensors fabricated with glucose oxidase versus blank electrodes without enzyme in rabbits. We also investigated the effect of general anesthesia. We used power spectral analysis to investigate transmitted signals from amperometric peroxide sensing devices 2–3 weeks after subcutaneous implantation. Fasted animals were studied for 90 minutes in the conscious state and for 90 minutes during halothane anesthesia. Animals exhibited almost no body movement during the studies. In the conscious state, enzyme active sensors demonstrated more oscillations than blank electrodes at almost all frequencies from 2 to > 8 cycles per hour. This finding suggested that the spontaneous fluctuations were secondary to local changes in glucose or oxygen. Because fluctuations were not seen in the blank electrode, periodic changes in interferant concentrations, electromyographic activity, or in external electromagnetic interference are unlikely. General inhalation anesthesia was associated with markedly reduced sensor output fluctuation at almost all frequencies in enzyme active sensors. We conclude that fluctuation of electrochemical glucose sensor output, unrelated to fluctuations in blood glucose, is likely secondary to spontaneous changes in the local concentration or vascular delivery of glucose or oxygen. Anesthesia may have stabilized blood flow, preventing normal spontaneous autoregulatory variation.

A Review of Closed-Loop Algorithms for Glycemic Control in the Treatment of Type 1 Diabetes

With the discovery of insulin came a deeper understanding of therapeutic options for one of the most devastating chronic diseases of the modern era, diabetes mellitus. The use of insulin in the treatment of diabetes, especially in those with severe insulin deficiency (type 1 diabetes), with multiple injections or continuous subcutaneous infusion, has been largely successful, but the risk for short term and long term complications remains substantial. Insulin treatment decisions are based on the patient’s knowledge of meal size, exercise plans and the intermittent knowledge of blood glucose values. As such, these are open loop methods that require human input. The idea of closed loop control of diabetes treatment is quite different: automated control of a device that delivers insulin (and possibly glucagon or other medications) and is based on continuous or very frequent glucose measurements. Closed loop insulin control for type 1 diabetes is not new but is far from optimized. The goal of such a system is to avoid short-term complications (hypoglycemia) and long-term complications (diseases of the eyes, kidneys, nerves and cardiovascular system) by mimicking the normal insulin secretion pattern of the pancreatic beta cell. A control system for automated diabetes treatment consists of three major components, (1) a glucose sensing device that serves as the afferent limb of the system; (2) an automated control unit that uses algorithms which acquires sensor input and generates treatment outputs; and (3) a drug delivery device (primarily for delivery of insulin), which serves as the system’s efferent limb. There are several major issues that highlight the difficulty of interacting with the complex unknowns of the biological world. For example, development of accurate continuous glucose monitors is crucial; the state of the art in 2009 is that such devices sometimes experience drift and are intended only to supplement information received from standard intermittent blood glucose data. In addition, it is important to acknowledge that an “automated” closed loop pancreas cannot approach the complexity of the normal human endocrine pancreas, which takes continuous data from substrates, hormones, paracrine compounds and autonomic neural inputs, and in response, secretes four hormones. Another major issue is the substantial absorption/action delay of insulin given by the subcutaneous route. Because of this delay, some researchers have recently given a portion of the meal-related insulin in an open loop manner before the meal and found this hybrid approach to be superior to closed loop control. Proportional-Integral-Derivative (PID) systems adapted from the industrial sector utilize control algorithms that alter output based on proportional (difference between actual and target levels), derivative (rate of change) and integral (time-related summative) errors in glucose. These algorithms have proven to be very promising in limited clinical trials. Related algorithms include a “fading memory” system that combines the proportional-derivative components of a classic PID system with time-relating decay of input signals that allow greater emphasis on more recent glucose values, a characteristic noted in mammalian beta-cells. Model Predictive Control (MPC) systems are highly adaptive methods that utilize mathematical models based on observations of biological behavior patterns using system identification and are now undergoing testing in humans. The application of further mathematical models, such as fuzzy control and artificial neural networks, are also promising, but are largely clinically untested. In summary, the prospects for closed loop control of glycemia in persons with diabetes have improved considerably. Major limitations include the delayed absorption/action of subcutaneous insulin and the imperfect stability of currently-available continuous glucose sensors. The potential for improved glycemic control in persons with diabetes brings with it the potential for reduction in the frequency of acute and chronic complications of diabetes.