Glucose metabolism and oscillatory behavior of pancreatic islets

A variety of oscillations are observed in pancreatic islets.We establish a model, incorporating two oscillatory systems of different time scales: One is the well-known bursting model in pancreatic beta-cells and the other is the glucose-insulin feedback model which considers direct and indirect feedback of secreted insulin. These two are coupled to interact with each other in the combined model, and two basic assumptions are made on the basis of biological observations: The conductance g_{K(ATP)} for the ATP-dependent potassium current is a decreasing function of the glucose concentration whereas the insulin secretion rate is given by a function of the intracellular calcium concentration. Obtained via extensive numerical simulations are complex oscillations including clusters of bursts, slow and fast calcium oscillations, and so on. We also consider how the intracellular glucose concentration depends upon the extracellular glucose concentration, and examine the inhibitory effects of insulin.Comment: 11 pages, 16 figure

Population Physiology: Leveraging Electronic Health Record Data to Understand Human Endocrine Dynamics

Studying physiology and pathophysiology over a broad population for long periods of time is difficult primarily because collecting human physiologic data can be intrusive, dangerous, and expensive. One solution is to use data that have been collected for a different purpose. Electronic health record (EHR) data promise to support the development and testing of mechanistic physiologic models on diverse populations and allow correlation with clinical outcomes, but limitations in the data have thus far thwarted such use. For example, using uncontrolled population-scale EHR data to verify the outcome of time dependent behavior of mechanistic, constructive models can be difficult because: (i) aggregation of the population can obscure or generate a signal, (ii) there is often no control population with a well understood health state, and (iii) diversity in how the population is measured can make the data difficult to fit into conventional analysis techniques. This paper shows that it is possible to use EHR data to test a physiological model for a population and over long time scales. Specifically, a methodology is developed and demonstrated for testing a mechanistic, time-dependent, physiological model of serum glucose dynamics with uncontrolled, population-scale, physiological patient data extracted from an EHR repository. It is shown that there is no observable daily variation the normalized mean glucose for any EHR subpopulations. In contrast, a derived value, daily variation in nonlinear correlation quantified by the time-delayed mutual information (TDMI), did reveal the intuitively expected diurnal variation in glucose levels amongst a random population of humans. Moreover, in a population of continuously (tube) fed patients, there was no observable TDMI-based diurnal signal. These TDMI-based signals, via a glucose insulin model, were then connected with human feeding patterns. In particular, a constructive physiological model was shown to correctly predict the difference between the general uncontrolled population and a subpopulation whose feeding was controlled

Complex Dynamics and Multistability in a Damped Harmonic Oscillator with Delayed Negative Feedback

A center manifold reduction and numerical calculations are used to demonstrate the presence of limit cycles, two-tori, and multistability in the damped harmonic oscillator with delayed negative feedback. This model is the prototype of a mechanical system operating with delayed feedback. Complex dynamics are thus seen to arise in very plausible and commonly occurring mechanical and neuromechanical feedback systems

A mathematical model of brain glucose homeostasis

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