Abstract
We presents two models of glucose metabolism in astrocytes based on ordinary differential equations calibrated on18 F-deoxyglucose PET images. The signals detected during physiological activation of the brain with18 F-deoxyglucose PET reflect predominantly uptake of this tracer into astrocytes. This notion provides a cellular and molecular basis for the FDG PET technique. In recent years the functional brain imaging has experienced enormous advances. These advancements provided new observational data about the inter- and intra-cellular mechanisms of the brain glucose metabolism. Our models specify of the molecular interactions governing the energy metabolism. The first model describes the glutamate-stimulated glucose uptake and use into astrocytes. It consists of a set of ordinary differential equations, each of which specifying the time-behavior of the main molecular species involved in the astrocytic glucose use (i.e. glutamate, glucose, Na+, β-threohydroxyaspartate) and the dynamical rates of glutamate, glucose and Na+ uptake. The second model includes also the effects of inter-cellular waves of Na+ and Ca2+ generated by astrocytes on the glucose metabolism. The kinetic rates constants of the models have been identified by fitting the sets of ordinary differential equations to dynamic Positron Emision Tomography scans of 31 patients.