A comparison among three maximal mathematical models of the glucose-insulin system.

The most well-known and widely used mathematical representations of the physiology of a diabetic individual are the Sorensen and Hovorka models as well as the UVAPadova Simulator. While the Hovorka model and the UVAPadova Simulator only describe the glucose metabolism of a subject with type 1 diabetes, the Sorensen model was formulated to simulate the behaviour of both normal and diabetic individuals. The UVAPadova model is the most known model, accepted by the FDA, with a high level of complexity. The Hovorka model is the simplest of the three models, well documented and used primarily for the development of control algorithms. The Sorensen model is the most complete, even though some modifications were required both to the model equations (adding useful compartments for modelling subcutaneous insulin delivery) and to the parameter values. In the present work several simulated experiments, such as IVGTTs and OGTTs, were used as tools to compare the three formulations in order to establish to what extent increasing complexity translates into richer and more correct physiological behaviour. All the equations and parameters used for carrying out the simulations are provided.

A revised Sorensen model: Simulating glycemic and insulinemic response to oral and intra-venous glucose load.

In 1978, Thomas J. Sorensen defended a thesis in chemical engineering at the University of California, Berkeley, where he proposed an extensive model of glucose-insulin control, model which was thereafter widely employed for virtual patient simulation. The original model, and even more so its subsequent implementations by other Authors, presented however a few imprecisions in reporting the correct model equations and parameter values. The goal of the present work is to revise the original Sorensen's model, to clearly summarize its defining equations, to supplement it with a missing gastrio-intestinal glucose absorption and to make an implementation of the revised model available on-line to the scientific community.

A new gastro-intestinal mathematical model to study drug bioavailability.

This work focuses on a new mathematical model which describes the gastro-intestinal absorption of drugs and the effect of food interactions on drugs bioavailability. The model structure consists of five compartments (stomach, duodenum, jejunum feeding, intestine and blood) simulated though different in-series reactors. All the enzymatic reactions taking place in the gastro-intestinal system are described through the Michaelis-Menten kinetic equations. The model has been tested for drug administration (paracetamol and ketoprofen) with and without the meal digestion. The model has been validated through pharmacokinetics curves obtained from in vivo tests (reported in the literature) and used to simulate the drug absorption dynamics in different conditions. The maximum blood concentration were 0.153 mmol L-1 and 0.0243 mmol L-1, respectively for paracetamol and ketoprofen. The time to reach the maximum concentration for the paracetamol and ketoprofen was around 55 min. In case of contemporary meal digestion, the maximum concentration of paracetamol in the blood was 0.100 mmol L-1 and 0.0135 mmol L-1 for ketoprofen; the time to reach the maximum concentration was 3 h and 45 min for paracetamol and 3 h and 35 min for ketoprofen. The drugs showed different pharmacokinetics, in agreement with the literature, during the digestion of food. To show the predictive capacity of the model, the simulations were also compared against additional experimental data (obtained from in vivo tests available in the literature) relative to ketoprofen administration with food.