modelling the variability in the insuline-glucose feedback system
DESCRIPTION
Diabetes Mellitus (DM) can be considered as the 21st century pandemic and it therefore represents an alarming threat to public health with rising trends and severity worldwide. DM comprises a set of metabolic disorders, which share the phenotype of hyperglycaemia (increment in blood glucose concentration). Blood glucose concentration fluctuates considerably in response of food intake, hormonal cycles, or behavioral factors. These fluctuations may range from 70 to 180 mg/dL for most normal subjects, although blood glucose concentration remains within the normo glycaemic zone (10-110 mg/dL) for most of the time. The internal physiological regulation of these wide fluctuations is a complex and multifactorial process. The most critical regulatory role is played by the pancreas, wich upon sensing an elevation of blood glucose concentration, secretes insulin through its beta cells, while an opposite change in the glucose causes the secretion of glucagon through its alpha cells. The secreted insuline assists the uptake of glucose by the cells and then storage the excess of glucose in the liver in the form of glycogen. Secreted glucagon assists the catabolism of glycogen into glucose that is released from the liver into the bloodstream, while insulin inhibits glycogen synthase. Furthermore, free fatty acids in blood potentiate the short-term responsiveness of pancratic beta cells to glucose oscillations, but may inhibit long-term responsiveness. Finally, blood glucose concentration and its relation to insulin concentration depend on the action of several other hormones (e.g. epinephrine, norepinephrine, and cortisol, making the complexity of this multifactorial regulatory system evident. The primary effect of blood glucose is exercised by insulin, and most efforts to date have focused on the study of this causal relation. Prolonged hyperglycaemia is normally caused by defects in insulin secretion by the pancreatic beta cells or in the efficiency of insulin-facilitated glucose uptake by the cells. The exact quantitative nature of the dependence between blood glucose concentration and the action of the other hormones mentioned above, or factors such as diet, endocrine cycles, exercise, stress and so on, remains largely unknown (primarily because of the lack of appropriate data), although the qualitative effect has been established, the aggregate effects of all these factors for modeling purposes set the basis for the study of glucose variability.TRANSCRIPT
Modelling the Variability in the Insuline-Glucose Feedback System
Vicent Ribas
Introduction
• Diabetes Mellitus (DM) can be considered as the 21st century pandemic and it therefore represents an alarming threat to public health with rising trends and severity worldwide.• DM comprises a set of metabolic disorders, which share the phenotype of hyperglycaemia (increment in blood glucose concentration).• There are different types of DM, which are the result of the complex interaction between genetic factors with other environmental and way of life factors (sedentarism, diet, and so on).• Depending on the etiology of DM, the factors that contribute to hyperglycaemia may include:
• the reduction of the secretion of insulin, • insufficiency in the expense of glucose at a metabolic level• an incremented glucose production by the organism.
Introduction
• The disorders associated with DM suppose a serious compromise in the organism whilst imposing a great burden on the National Health System. In developed countries DM is the primary cause for renal failure, amputations not associated to trauma of inferior limbs and blindness in adults. It has been documented that 1.7% of the population worldwide suffers DM and this incidence is suspected to grow in the mid and long term. DM is an important cause for morbidity and mortality.• There is an urgent need for improved diagnostic methods that provide more precise clinical assessments and sensitive detection of symptoms associated to DM (such as glucose variability). This critical task may be enabled by the utilization of mathematical models that reliably describe the dynamic interrelationships among key physiological variables in the underlying physiology (i.e. blood glucose concentration and various hormones such as insulin, glucagon, epinephrine, norepinephrine, cortisol and so on) under a variety of metabolic and behavioral conditions (e.g. pre/postpandrial, exercise/rest, stress/relaxation, treatment/no-treatment).
Physiology
• The Pancreas is composed by two different kinds of tissue:1. The acini, which secrete gastric juices into the duodenum.2. The Langerhans Islets, which secrete insuline, glucagon and
somatostatine.•The human pancreas consists of about 1-2 million Langerhans Islets (0.3 mm diameter). These islets are organized around small capillaries into which they convey their hormones (i.e. the Islets have no connection whatsoever with the gastric system). • The islets contain three different kinds of cells: alpha, beta and delta, which differentiate by their morphology and tinction properties. Here we are only interested in the pancreatic beta-cells, which account for about 60% of the cell population in the Langerhans Islets, and are in charge of the secretion of insuline and amiline. The function of the amiline hormone is not yet fully understood.
Physiology
Physiology
• Insuline mediates the uptake and metabolism of glucose.• During most of the day, the energy available for the muscle tissue comes from the fatty acids and not glucose. This is due to the fact that muscular membranes are not very permeable to glucose unless they are stimulated by insuline. However, there are two situations where muscle consumes glucose: moderate/intense exercise and during digestion.• In response to glucose, beta-cells of the Langerhans islet secrete insuline, which causes the increased use or uptake of glucose in target tissues (like muscle, liver and adipose tissue as it has been stated above). • When blood levels of glucose decline, insuline secretion stops, and the tissues begin to use their energy stores instead (fatty acids). • Of course, interruption of this control system results in Diabetes Mellitus (DM), which may result in heart disease, kidney failure, amputations and death if left untreated.
Physiology
• A sudden increase in plasma glucose results in the immediate opening of the insuline reservoirs in the pancreatic islets (beta-cells) during the first 5-10 minutes. In a second phase, a part from this release the beta-cells start an enzymatic reaction to produce and release more insuline into the bloodstream (note that the rate now is much higher than in the first phase). • This behavior is due to bursting in the pancreatic beta-cells (Islets) as it will be discussed below (i.e. opening of Ca2+ and K+ channels).
Bursting in Pancreatic Beta-Cells
• Bursting in Beta-Cells begin at a saddle-node bifurcation and ends at a homoclinic bifurcation. The fast subsystem is bistable, and requires only one slow variable. The spike period tends to increase monotonically through the active phase. • In other words, Bursting arises from hysteresis and bistability in the beta-cell model.
Main Hypothesis
•The frequency analysis of the ultradian glucose recording of 24 presented in figure shows that there are oscillations at 64.12 min, 32 min and 21.4 min.
Frequency Analysis
• The frequency analysis of the ultradian glucose recording of 24 presented here shows that there are oscillations at 64.12 min, 32 min and 21.4 min.
Frequency Analysis
• Oscillations occur during constant intravenous glucose infusion and are not dependent on periodic nutrient absorption from the gut. • Damped oscillations occur after a meal. Second, glucose and insuline concentrations are highly correlated, with the glucose peak occurring at about 10-20 minutes earlier than that of insuline. • The amplitude of the oscillations is an increasing function of glucose concentration, while the frequency is not. • The oscillations do not appear to depend on glucagon.
Pulsatile Insuline Secretion Model
Pulsatile Insuline Secretion Model (Dynamics)
Pulsatile Insuline Secretion Model (Dynamics)
• Plasma insuline is produced at a rate f1(G) that is dependent on plasma glucose.• Insuline exchange with the remote pool Ii is a linear function of the concentration difference between the pools (Ip/Vp-Ii-Vi) with constant rate E and Vp is the distribution volume for insuline in plasma. Vi is the effective volume of the intercellular space.
Pulsatile Insuline Secretion Model (Dynamics)
• Pancreatic insuline production is controlled by:
• Insuline dependent glucose utilization (uptake by the brain and nerve cells) is controlled by:
• Glucose utilization by the muscle and fat cells is modelled by:
• And the insuline dependent term is given by:
Numerical Study (Phase-Space and Nullclines)
Numerical Study (Frequency and Bifurcation Analysis)
• HB1: Ig=99.94 mg/dl.• HB2: Ig=253.9 mg/dl.• Oscillation Period: [60,120] min.
Numerical Study (Bi-parametric Analysis)
Conclusions
• It is quite likely that bursting oscillations are modulated by ultradian Glucose intake.• Insuline production is oscillatory by nature (both from the cell standpoint and ultradian).• Intermediate oscillations in Insuline-Glucose are yet not fully understood although they become apparent in IVGTT and Induced Hypoglycaemic tests.• The Insuline-Glucose Feedback system results in oscillations with physiologic relevance (i.e. almost equivalent to those observed in real data).• The presence of two hopf-bifurcations for most of the system settings has been shown by means of a bi-parametric plot. However, it may be interesting to update the model in order to account for intermediate oscillations (for example, by changing the glucose input Ig and changing parameters).• As future work, it may interesting to study the parameter tying and estimation in order to draw more physiologically relevant conclusions for the model and, also, be able to make predictions in glucose variability.