Logistic model of glucose-regulated C-peptide secretion: hysteresis pathway disruption in impaired fasting glycemia

A glucose-insulin-glucagon coupled model of the isoglycemic intravenous glucose infusion experiment

Type 2 diabetes (T2D) is a pathophysiology that is characterized by insulin resistance, beta- and alpha-cell dysfunction. Mathematical models of various glucose challenge experiments have been developed to quantify the contribution of insulin and beta-cell dysfunction to the pathophysiology of T2D. There is a need for effective extended models that also capture the impact of alpha-cell dysregulation on T2D. In this paper a delay differential equation-based model is developed to describe the coupled glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment. As the glucose profile in IIGI is tailored to match that of a corresponding oral glucose tolerance test (OGTT), it provides a perfect method for studying hormone responses that are in the normal physiological domain and without the confounding effect of incretins and other gut mediated factors. The model was fit to IIGI data from individuals with and without T2D. Parameters related to glucagon action, suppression, and secretion as well as measures of insulin sensitivity, and glucose stimulated response were determined simultaneously. Significant impairment in glucose dependent glucagon suppression was observed in patients with T2D (duration of T2D: 8 (6–36) months) relative to weight matched control subjects (CS) without diabetes (k1 (mM)−1: 0.16 ± 0.015 (T2D, n = 7); 0.26 ± 0.047 (CS, n = 7)). Insulin action was significantly lower in patients with T2D (a1 (10 pM min)−1: 0.000084 ± 0.0000075 (T2D); 0.00052 ± 0.00015 (CS)) and the Hill coefficient in the equation for glucose dependent insulin response was found to be significantly different in T2D patients relative to CS (h: 1.4 ± 0.15; 1.9 ± 0.14). Trends in parameters with respect to fasting plasma glucose, HbA1c and 2-h glucose values are also presented. Significantly, a negative linear relationship is observed between the glucagon suppression parameter, k1, and the three markers for diabetes and is thus indicative of the role of glucagon in exacerbating the pathophysiology of diabetes (Spearman Rank Correlation: (n = 12; (−0.79, 0.002), (−0.73,.007), (−0.86,.0003)) respectively).

Towards the Integration of an Islet-Based Biosensor in Closed-Loop Therapies for Patients With Type 1 Diabetes

In diabetes mellitus (DM) treatment, Continuous Glucose Monitoring (CGM) linked with insulin delivery becomes the main strategy to improve therapeutic outcomes and quality of patients' lives. However, Blood Glucose (BG) regulation with CGM is still hampered by limitations of algorithms and glucose sensors. Regarding sensor technology, current electrochemical glucose sensors do not capture the full spectrum of other physiological signals, i.e., lipids, amino acids or hormones, relaying the general body status. Regarding algorithms, variability between and within patients remains the main challenge for optimal BG regulation in closed-loop therapies. This work highlights the simulation benefits to test new sensing and control paradigms which address the previous shortcomings for Type 1 Diabetes (T1D) closed-loop therapies. The UVA/Padova T1DM Simulator is the core element here, which is a computer model of the human metabolic system based on glucose-insulin dynamics in T1D patients. That simulator is approved by the US Food and Drug Administration (FDA) as an alternative for pre-clinical testing of new devices and closed-loop algorithms. To overcome the limitation of standard glucose sensors, the concept of an islet-based biosensor, which could integrate multiple physiological signals through electrical activity measurement, is assessed here in a closed-loop insulin therapy. This investigation has been addressed by an interdisciplinary consortium, from endocrinology to biology, electrophysiology, bio-electronics and control theory. In parallel to the development of an islet-based closed-loop, it also investigates the benefits of robust control theory against the natural variability within a patient population. Using 4 meal scenarios, numerous simulation campaigns were conducted. The analysis of their results then introduces a discussion on the potential benefits of an Artificial Pancreas (AP) system associating the islet-based biosensor with robust algorithms.

Integrating an Islet-Based Biosensor in the Artificial Pancreas: In Silico Proof-of-Concept

OBJECTIVE

Current treatment of type 1 diabetes by closed-loop approaches depends on continuous glucose monitoring. However, glucose readings alone are insufficient for an artificial pancreas to truthfully restore glucose homeostasis where additional physiological regulators of insulin secretion play a considerable role. Previously, we have developed an electrophysiological biosensor of pancreatic islet activity, which integrates these additional regulators through electrical measurement. This work aims at investigating the performance of the biosensor in a blood glucose control loop, to establish an in silico proof-of-concept.

METHODS

Two islet algorithm models were identified on experimental data recorded with the biosensor. First, we validated electrical measurement as a means to exploit the inner regulation capabilities of islets for intravenous glucose measurement and insulin infusion. Then, an artificial pancreas integrating the islet-based biosensor was compared to standard treatment approaches using subcutaneous routes. The closed-loop simulations were performed in the UVA/Padova T1DM Simulator where a series of realistic meal scenarios were applied to virtual diabetic patients.

RESULTS

With intravenous routes, the endogenous islet algorithms successfully restored glucose homeostasis for all patient categories (mean time in range exceeds 90%) while mitigating the risk of adverse glycaemic events (mean BGI < 2). Using subcutaneous routes, the biosensor-based artificial pancreas was as performing as standard treatments, and outperformed them under challenging conditions.

CONCLUSION

This work validates the concept of using pancreatic islets algorithms in an artificial pancreas in silico.

SIGNIFICANCE

Pancreatic islet endogenous algorithms obtained via an electrophysiological biosensor successfully regulate blood glucose levels of virtual type 1 diabetic patients.

A novel measure of glucose homeostasis (or loss thereof) comprising the joint dynamics of glucose, insulin, glucagon, and cortisol

Quantification of disturbances in glucose-insulin homeostasis has been the cornerstone of appraising insulin resistance and detecting early-stage diabetes. Metabolic homeostasis arises from feedback and feed-forward interactions among (at least) all four of glucose, insulin, glucagon, and cortisol. Quantifying such tetrapartite interactions in the fasting (endogenously regulated) state overnight could elucidate very early regulatory disruption. In the present study, healthy subjects without diabetes (ND; n = 20) and patients with Type 2 diabetes (T2D; n = 21) were investigated by repeated overnight blood sampling of all four of glucose, insulin, glucagon, and cortisol concentrations. To obviate confounding by hormone-specific disappearance rates, analyses were performed at the level of production (glucose) or secretion (insulin, glucagon, and cortisol) rates estimated by regularized deconvolution analysis. Then, a novel method for quantifying the loss of homeostasis among glucose, insulin, and glucagon (and, when available, cortisol) secretion patterns was developed. Potential early stage prediabetic candidates were identified. The new methodology avoids many of the difficulties encountered in the conventional estimation of insulin-glucose sensitivity or resistance, while incorporating the dynamics of the key coregulators under fasting conditions.

Bioelectronic organ-based sensor for microfluidic real-time analysis of the demand in insulin

On-line and real-time analysis of micro-organ activity permits to use the endogenous analytical power of cellular signal transduction algorithms as biosensors. We have developed here such a sensor using only a few pancreatic endocrine islets and the avoidance of transgenes or chemical probes reduces bias and procures general usage. Nutrient and hormone-induced changes in islet ion fluxes through channels provide the first integrative read-out of micro-organ activity. Using extracellular electrodes we captured this read-out non-invasively as slow potentials which reflect glucose concentration-dependent (3-15 mM) micro-organ activation and coupling. Custom-made PDMS-based microfluidics with platinum black micro-electrode arrays required only some tens of islets and functioned at flow rates of 1-10 µl/min which are compatible with microdialysis. We developed hardware solutions for on-line real-time analysis on a reconfigurable Field-Programmable Gate Array (FPGA) that offered resource-efficient architecture and storage of intermediary processing stages. Moreover, real-time adaptive and reconfigurable algorithms accounted for signal disparities and noise distribution. Based on islet slow potentials, this integrated set-up allowed within less than 40 μs the discrimination and precise automatic ranking of small increases (2 mM steps) of glucose concentrations in real time and within the physiological glucose range. This approach shall permit further development in continuous monitoring of the demand for insulin in type 1 diabetes as well as monitoring of organs-on-chip or maturation of stem-cell derived islets.

Pulsatility of Hypothalamo-Pituitary Hormones: A Challenge in Quantification

Neuroendocrine systems control many of the most fundamental physiological processes, e.g., reproduction, growth, adaptations to stress, and metabolism. Each such system involves the hypothalamus, the pituitary, and a specific target gland or organ. In the quantification of the interactions among these components, biostatistical modeling has played an important role. In the present article, five key challenges to an understanding of the interactions of these systems are illustrated and discussed critically.

Slow potentials encode intercellular coupling and insulin demand in pancreatic beta cells

AIMS/HYPOTHESIS

Ion fluxes constitute a major integrative signal in beta cells that leads to insulin secretion and regulation of gene expression. Understanding these electrical signals is important for deciphering the endogenous algorithms used by islets to attain homeostasis and for the design of new sensors for monitoring beta cell function.

METHODS

Mouse and human islets were cultured on multielectrode arrays (MEAs) for 3-13 days. Extracellular electrical activities received on each electrode were continuously amplified and recorded for offline characterisation.

RESULTS

Differential band-pass filtering of MEA recordings of mouse islets showed two extracellular voltage waveforms: action potentials (lasting 40-60 ms) and very robust slow potentials (SPs, lasting 800-1,500 ms), the latter of which have not been described previously. The frequency of SPs directly correlated with glucose concentration, peaked at 10 mmol/l glucose and was further augmented by picomolar concentrations of glucagon-like peptide-1. SPs required the closure of ATP-dependent potassium channels as they were induced by glucose or glibenclamide but were not elicited by KCl-induced depolarisation. Pharmacological tools and the use of beta cell specific knockout mice showed that SPs reflected cell coupling via connexin 36. Moreover, increasing and decreasing glucose ramps showed hysteresis with reduced glucose sensitivity during the decreasing phase. SPs were also observed in human islets and could be continuously recorded over 24 h.

CONCLUSIONS/INTERPRETATION

This novel electrical signature reflects the syncytial function of the islets and is specific to beta cells. Moreover, the observed hysteresis provides evidence for an endogenous algorithm naturally present in islets to protect against hypoglycaemia.