Prediction of a glucose appearance function from foods using deconvolution

Abstract

The glycaemic response of an insulin-treated diabetic patient goes through many transitory phases, leading to a steady state glycaemic profile following a change in either insulin regimen or diet. Most models attempting to model the glucose and insulin relationship try to model the effect of oral or injected glucose rather than that from the digestion of food. However, it is clear that a better understanding of the glycaemic response would arise from consideration of intestinal absorption from the gut. It is assumed that this type of absorption can be modelled by a so-called glucose appearance function (systemic appearance of glucose via glucose absorption from the gut) predicting the glucose load from the food. Much research has been carried out in the areas of hepatic balance, insulin absorption and insulin independent/dependent utilization. However, little is known about intestinal absorption patterns or their corresponding glucose appearance profiles. The strategy under investigation herein is to use deconvolution or backward engineering. By starting with specific results i.e. blood glucose and insulin therapy, it is possible to work backwards to predict the glucose forcing functions responsible for the outcome. Assuming compartmental consistency, this will allow a clearer insight into the true gut absorption process. If successful, the same strategy can be applied to more recent glucose and insulin models to further our understanding of the food to blood glucose problem. This paper investigates the Lehmann-Deutsch modified model of glucose and insulin interaction, created from the model proposed by Berger-Rodbard. The model attempts to simulate the steady state glycaemic and plasma insulin responses, independent of the initial values from which the simulation is started. Glucose enters the model via both intestinal absorption and hepatic glucose production. We considered a 70 kg male insulin-dependent diabetic patient with corresponding hepatic and insulin sensitivity parameters of 0.6 and 0.3 respectively. Net hepatic glucose balance was modelled piecewise by linear and symmetric functions. A first-order Euler method with step size of 15 minutes was employed. For the simulation, only Actrapid and NPH injections were considered. The injection of insulin and the glucose flux to the gut were started simultaneously to avoid any delay associated with gastric emptying. The systemic appearance of glucose was compared from two view points, not only to assess the strategic principle, but also to assess the suitability of the modifications made by Lehmann and Deutsch. The first is a forward prediction using the compartmental structure. This analysis involves the rate of gastric emptying without time delay. The second is a backward prediction from experimentally observed blood glucose profiles. Investigations involved porridge, white rice and banana containing the same carbohydrate content (25 g). Results obtained from the first analysis were dependent on the rate of gastric emptying, especially its ascending and descending branches. Results from the second analysis were dependent on the dose and type of insulin administered. Both predicted profiles showed consistency with physiological reasoning, although it became apparent that such solutions could be unstable. Furthermore, both types of prediction were similar in structure and appearance, especially in simulations for porridge and banana. This emphasized the consistency and suitability of both analyses when investigating the compartmental accuracy and limitations within a model. The new strategic approach was deemed a success within the model, and the modifications made by Lehmann and Deutsch appropriate. We suggest that a gastric emptying curve with a possible gastric delay is the way forward in regulating the appearance of glucose via gut absorption. The Lehmann-Deutsch gastric curve is described by either a trapezoidal or triangular function dependent on the carbohydrate cont