Modeling the link between functional imaging and neuronal activity: synaptic metabolic demand and spike rates.

Functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) measurements reflect changes in the hemodynamics which are thought to be related to local synaptic input to neuron populations. The local neuronal spiking activity, which is believed to form the basis of neuronal coding and communication, is not directly reflected in fMRI/PET measurements. We used a mean-field neuronal model of recurrently coupled excitatory and inhibitory neuronal populations to characterize the relationship between the synaptic activity (reflected in the PET and fMRI measurements) and the neuronal spike rates, averaged over brain areas. We analyzed this relation for a number of cases. For a single brain area and in the absence of external input to its inhibitory neurons, the relation between average spike rates and synaptic activity is linear. However, departures from linearity are found when: (i) the local synaptic strengths vary, (ii) the external inputs vary, in the presence of external input to the inhibitory population, or (iii) the synchronization between oscillations of the average spike rates of two areas changes. We further show that an increase in the imaging signal can reflect a decrease in average spiking activity, in the presence of external input to the inhibitory population. Synaptic activity can also be associated with silent neuronal populations, when input to the excitatory population does not reach the activation threshold or for certain synchronizations between oscillations of two areas. In conclusion, caution should be used when interpreting neuroimaging results in terms of mean spike rates.