Modelling of calcium dynamics in brain energy metabolism and Alzheimer's disease.

Functional imaging techniques play a major role in the study of brain activation by monitoring the changes in blood flow and energy metabolism. In order to interpret functional neuroimaging data better, the existing mathematical models describing the links that may exist between electrical activity, energy metabolism and hemodynamics in literature are thoroughly analyzed for their advantages and disadvantages in terms of their prediction of available experimental data. Then, these models are combined within a single model that includes membrane ionic currents, glycolysis, mitochondrial activity, exchanges through the blood-brain barrier, as well as brain hemodynamics. Particular attention is paid to the transport and storage of calcium ions in neurons since calcium is not only an important molecule for signalling in neurons, but it is also essential for memory storage. Multiple efforts have underlined the importance of calcium dependent cellular processes in the biochemical characterization of Alzheimer's disease (AD), suggesting that abnormalities in calcium homeostasis might be involved in the pathophysiology of the disease. The ultimate goal of this study is to investigate the hypotheses about the physiological or biochemical changes in health and disease and to correlate them to measurable physiological parameters obtained from functional neuroimaging data as in the time course of blood oxygenation level dependent (BOLD) signal. When calcium dynamics are included in the model, both BOLD signal and metabolite concentration profiles are shown to exhibit temporal behaviour consistent with the experimental data found in literature. In the case of Alzheimer's disease, the effect of halved cerebral blood flow increase results in a negative BOLD signal implying suppressed neural activity.