Prediction of a glucose appearance function from foods using deconvolution

The glycaemic response of an insulin-treated diabetic patientgoes through many transitory phases, leading to a steady stateglycaemic profile following a change in either insulin regimenor diet. Most models attempting to model the glucose and insulinrelationship try to model the effect of oral or injected glucoserather than that from the digestion of food. However, it isclear that a better understanding of the glycaemic responsewould arise from consideration of intestinal absorption fromthe gut. It is assumed that this type of absorption can be modelledby a so-called glucose appearance function (systemic appearanceof glucose via glucose absorption from the gut) predicting theglucose load from the food. Much research has been carried outin the areas of hepatic balance, insulin absorption and insulinindependent/dependent utilization. However, little is knownabout intestinal absorption patterns or their correspondingglucose appearance profiles. The strategy under investigation herein is to use deconvolutionor backward engineering. By starting with specific results i.e.blood glucose and insulin therapy, it is possible to work backwardsto predict the glucose forcing functions responsible for theoutcome. Assuming compartmental consistency, this will allowa clearer insight into the true gut absorption process, If successful,the same strategy can be applied to more recent glucose andinsulin models to further our understanding of the food to bloodglucose problem. This paper investigates the Lehmann-Deutsch modified model ofglucose and insulin interaction, created from the model proposedby Berger-Rodbard. The model attempts to simulate the steadystate glycaemic and plasma insulin responses, independent ofthe initial values from which the simulation is started. Glucoseenters the model via both intestinal absorption and hepaticglucose production. We considered a 70kg male insulindependentdiabetic patient with corresponding hepatic and insulin sensitivityparameters of 0.6 and 0.3 respectively. Net hepatic glucosebalance was modelled piecewise by linear and symmetric functions.A first-order Euler method with step size of 15 minutes wasemployed. For the simulation, only Actrapid and NPH injectionswere considered. The injection of insulin and the glucose fluxto the gut were started simultaneously to avoid any delay associatedwith gastric emptying. The systemic appearance of glucose was compared from two viewpoints, not only to assess the strategic principle, but alsoto assess the suitability of the modifications made by Lehmannand Deutsch. The first is a forward prediction using the compartmentalstructure. This analysis involves the rate of gastric emptyingwithout time delay. The second is a backward prediction fromexperimentally observed blood glucose profiles. Investigationsinvolved porridge, white rice and banana containing the samecarbohydrate content (25 g). Results obtained from the firstanalysis were dependent on the rate of gastric emptying, especiallyits ascending and descending branches. Results from the secondanalysis were dependent on the dose and type of insulin administered.Both predicted profiles showed consistency with physiologicalreasoning, although it became apparent that such solutions couldbe unstable. Furthermore, both types of prediction were similarin structure and appearance, especially in simulations for porridgeand banana. This emphasized the consistency and suitabilityof both analyses when investigating the compartmental accuracyand 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 gastricdelay is the way forward in regulating the appearance of glucosevia gut absorption. The Lehmann-Deutsch gastric curve is describedby either a trapezoidal or triangular function dependent onthe carbohydrate content of the meal. However, it was clearfrom the results obtained that carbohydrate content is onlyone factor in carbohydrate absorption, and further progressmust inevitably involve other food characteristics and propertiesif we are to improve the glucose flux.     

ChemInform Abstract: The Infrared Spectrum of F-·H2O.

The geometry and vibrational frequencies of the F-·H₂O system are determined by ab initio calculations (SCF and CISD levels of theory).     

The Generalized Matrix Sector Function and the Separation of Matrix Eigenvalues

The matrix sector function of A is introduced and generalizedto the matrix sector function of g(A), where the complex matrixA may have a real or complex characteristic polynomial and g(A)is a matrix function of a conformal mapping. The generalizedmatrix sector function of A is employed to separate the matrixeigenvalues relative to a sector, a circle, and a sector ofa circle in the complex plane without actually seeking the characteristicpolynomial and the matrix eigenvalues relative to a sector,a circle, and a sector of a circle in the complex plane withoutactually seeking the characteristic polynomial and the matrixeigenvalues themselves. Also, the generalized matrix sectorfunction of A is utilized to carry out the block-diagonalizationand block-triangularization of a system matrix, which are usefulin developing applications to mathematical science and control-systemproblems.