A Unifying Organ Model of Pancreatic Insulin Secretion

Abstract

The secretion of insulin by the pancreas has been the object of much attention over the past several decades. Insulin is known to be secreted by pancreatic β-cells in response to hyperglycemia: its blood concentrations however exhibit both high-frequency (period approx. 10 minutes) and low-frequency oscillations (period approx. 1.5 hours). Furthermore, characteristic insulin secretory response to challenge maneuvers have been described, such as frequency entrainment upon sinusoidal glycemic stimulation; substantial insulin peaks following minimal glucose administration; progressively strengthened insulin secretion response after repeated administration of the same amount of glucose; insulin and glucose characteristic curves after Intra-Venous administration of glucose boli in healthy and pre-diabetic subjects as well as in Type 2 Diabetes Mellitus. Previous modeling of β-cell physiology has been mainly directed to the intracellular chain of events giving rise to single-cell or cell-cluster hormone release oscillations, but the large size, long period and complex morphology of the diverse responses to whole-body glucose stimuli has not yet been coherently explained. Starting with the seminal work of Grodsky it was hypothesized that the population of pancreatic β-cells, possibly functionally aggregated in islets of Langerhans, could be viewed as a set of independent, similar, but not identical controllers (firing units) with distributed functional parameters. The present work shows how a single model based on a population of independent islet controllers can reproduce very closely a diverse array of actually observed experimental results, with the same set of working parameters. The model’s success in reproducing a diverse array of experiments implies that, in order to understand the macroscopic behaviour of the endocrine pancreas in regulating glycemia, there is no need to hypothesize intrapancreatic pacemakers, influences between different islets of Langerhans, glycolitic-induced oscillations or β-cell sensitivity to the rate of change of glycemia.

Long-term feeding of high-fat plus high-fructose diet induces isolated impaired glucose tolerance and skeletal muscle insulin resistance in miniature pigs

“…Moreover, individuals with isolated IGT also showed a severely diminished second-phase insulin secretory response [ 5 , 6 ]. However, a recent study proposed a mathematical model of pancreatic insulin secretion that is in disagreement with the above reports [ 7 ]. In insulin resistance associated with prediabetes, the insulin secretory response increases as a compensatory mechanism.…”

Mathematical investigation of diabetically impaired ultradian oscillations in the glucose–insulin regulation

“…Firstly, appropriately designed clinical trials aiming at evaluating variations in oscillatory patterns in subjects at various diabetic states under glucose infusions would be of great value. Secondly, new multiscale simulations taking into account dynamics at the β-cell secretion level as performed in [4] in the case of decreased insulin sensitivity could lead to a further assessment of the current model against clinical observations. Moreover, we have shown that taking into account an instantaneous glucose-dependent insulin production, through the introduction of an additional coefficient, enables us to characterise the existence of sinusoidal solutions by investigating roots of a cubic polynomial.…”

Consistency of compact and extended models of glucose-insulin homeostasis: The role of variable pancreatic reserve

“…The islet equations are coupled to a metabolism sub-model to complete the description of the feed-back control of the glucose/insulin system dynamics. This islet population model was shown to reproduce very closely a wide array of actually observed, diverse in vivo and in vitro experiments, including the pioneering work of Grodsky, with the same set of working parameters [17]. While the model does not include any dependency on the rate of change of glycemia, it is able to reproduce accurately the double phase of insulin release during a prolonged glucose stimulus: a first phase of impulsive insulin release, immediately upon glucose administration, and a second phase of more gradual release, also linked with the potentiation effect of persistent hyperglycemia on the secretory units.…”

“…Now, a few years after the publication of the SDM model, a comprehensive model for insulin secretion exists [15, 17], which is in fact able to explain mechanistically why a host of morphologically diverse insulin secretion responses to glycemic perturbations occur. We can therefore go back and attempt to understand why the nonlinearity γ was so essential in the representation of insulin secretion within the compact SDM model: this is the aim of the present work.…”

“…Starting from the extended and validated model [17], the following procedure is implemented: a) a sample of IVGTT data sets is generated from the extended model portraying a group of virtual patients with a range of insulin sensitivities; b) the generated IVGTTs are fitted with the SDM compact model; c) a comparison is made between the set of generating extended model parameter values and the set of estimated compact-model parameter values to clarify their relationships.…”