A Dynamic Model for in vivo Glucose-Insulin Metabolism
Multi-scale and/or multi-disciplinary approach to process-product innovation
Nanotechnology: New Developments (T3-6)
Keywords: Artificial Pancreas, Glucose-Insulin Metabolism, Compartmental Model, Simulation
In this paper we present a mathematical model that describes glucose and insulin metabolism in man. The model is based on the models by Sorensens (1985) and Pucketts (1990). It is a compartmental model that includes the major organs of the body, i.e. the brain, heart & lungs, kidney, liver, gut and periphery are represented as compartments. The interconnection of these compartments is dictated by the topology of the flow of blood in man. Each compartment contains a mass balance for glucose and insulin. The model describes the effect of having meals as well as the effect of doing exercises. The model is used in the development of an artificial pancreas based on predictive control. In the artificial pancreas, the insulin dosage is computed by the predictive controller based on continuous-glucose measurements.
The compartments for the gut, brain and heart & lungs are modeled to have constant glucose uptake. The peripheral tissue and hepatic glucose uptake is regulated by local changes in the glucose and insulin level. Glucose enters the system through hepatic glucose production and through meals. Hepatic glucose production is influenced by changes in the hepatic glucose, glucagon and insulin levels. The meal glucose uptake enters the gut and the rate of adsorption is based on a 2nd order adsorption model. Insulin present in the kidney, liver and peripheral tissues is cleared at constant rates. Insulin is synthesized in the pancreas and stored in labile form that can be released in response to stimulatory factors, mainly glucose levels. Due to the anatomical position of the pancreas in the circulation, pancreatic released insulin enters the portal vein and thus traverses the liver prior to entering the system circulation. The effects of exercise are modeled by accounting for increase and redistribution of blood flow, the increase of glucose uptake and the increased glucose production by the liver.
The model is population based and therefore applicable to people of all weights. In addition it is constructed such that it can be used in the simulation of both healthy and diabetic individuals. Diabetic individuals have reduced or no pancreatic insulin production and release. For diabetic individuals, subcutaneous insulin diffusion is included in the model and pancreatic insulin production is removed. Inclusion of sub-models that account for subcutaneous insulin and glucose diffusion allows the model to be applied in the simulation of an artificial pancreas as glucose is measured subcutaneously, and insulin is injected subcutaneously.
The model assumptions and principles are described in the paper. And the dynamic behavior of the model is illustrated by simulations.
References:
J. T. Sorensen. A Physiologic Model of Glucose Metabolism in Man and Its Use to Design and Assess Improved Insulin Therapies for Diabetes. PhD thesis, Massachusetts Institute of Technology, Department of Chemical Engineering, 1985.
W. R. Puckett. Dynamic Modeling of Diabetes Mellitus. PhD thesis, University of Wisconsin-Madison, Department of Chemical Engineering, 1992
Presented Tuesday 18, 11:40 to 12:00, in session Nanotechnology: New Developments (T3-6).
