ATP consumption and neural electrical activity: A physiological model for brain imaging

The relation between neural electrical activity and oxygen consumption is the key issue in almost all brain image modalities based on perfusion. Despite the large amount of physiological information available in the literature about the processes involved in neural activation, a practical, tractable and simultaneously accurate mathematical model to describe this relation is needed. The sodium-potassium pump (Na,K-ATPase) and its adenosine triphosphate (ATP) consumption seems to play a central role in this process. The Na,K-ATPase activity is deeply related with the spike density and this pump is the main consumer of the energy used in the brain, particularly, within the neuron. In this paper we present a mathematical model relating the temporal spike density across the neuron, which reflects the electrical activity, with the corresponding ATP consumption rate. The expenditure of ATP stimulate the metabolic pathways responsible for the ATP synthesis, for instance, the aerobic pathway via the Krebs cycle. The main motivation to derive this model is its inclusion in a larger model of the Haemodynamic Response Function (HRF) for functional Magnetic Resonance Imaging (fMRI) analysis. The model, depending on several parameters, is linear and was tunned with physiological information obtained from the literature.