Modelling the effects of glucagon during glucose tolerance testing.

BACKGROUND: Glucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship. RESULTS: Both models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (sG) and insulin sensitivity (sI). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (sE) and glucagon sensitivity (δ). CONCLUSIONS: The models are used to investigate how different degrees of pax'tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted.

Shock formation and non-linear dispersion in a microvascular capillary network.

Temporal and spatial fluctuations are a common feature of blood flow in microvascular networks. Among many possible causes, previous authors have suggested that the non-linear rheological properties of capillary blood flow (notably the Fåhraeus effect, the Fåhraeus-Lindqvist effect and the phase-separation effect at bifurcations) may be sufficient to generate temporal fluctuations even in very simple networks. We have simulated blood flow driven by a fixed pressure drop through a simple arcade network using coupled hyperbolic partial differential equations (PDEs) that incorporate well-established empirical descriptions of these rheological effects, accounting in particular for spatially varying haematocrit distributions; we solved the PDE system using a characteristic-based method. Our computations indicate that, under physiologically realistic conditions, there is a unique steady flow in an arcade network which is linearly stable and that plasma skimming suppresses the oscillatory decay of perturbations. In addition, we find that non-linear perturbations to haematocrit distributions can develop shocks via the Fåhraeus effect, providing a novel mechanism for non-linear dispersion in microvascular networks.