In vivo measurement of the rate constant of liver handling of glucose and glucose uptake by insulin-dependent tissues, using a mathematical model for glucose homeostasis in diabetic rats.

Diabetes mellitus is a disease that affects glucose homeostasis. The World Health Organization informs that there are over 347 million people in the world with diabetes. The diagnosis and characterization of glucose homeostasis in different metabolic conditions are subjects of great importance with high clinical impact. There are many mathematical models that describe the glucoregulatory system in detail. However, the use of these models is limited because they have a large number of mathematical equations and parameters and they require complex methodologies to estimate of them. This forced to work with average values that decrease the validity of results and the applicability of the models. In this study two mathematical models for rats with diabetes mellitus were developed. The difference between these models and others lies in the possibility of obtaining all parameters for each animal from simple measurements (glucose and insulin plasma levels). Moreover, the models allow to measure in vivo the different physiological processes involved in glucose homeostasis in animals: insulin secretion and its plasma clearance, absorption of insulin from a subcutaneous injection, the liver handling of glucose, intestine absorption of glucose, glucose uptake rate of insulin-independent tissues, glucose uptake rate of insulin-dependent tissues, and renal glucose excretion.

Mathematical model of glucose-insulin homeostasis in healthy rats.

According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat.