Modeling the effect of cerebral capillary blood flow on neuronal firing

Adequate cerebral blood flow has long been recognized as essential for the maintenance of the neuronal function while interruption of cerebral blood flow for durations as short as minutes can result in permanent brain damage. A primary goal of this work is to determine how a neuron's ability to respond to synaptic input depends on parameters that control cerebral blood flow. A complex mathematical model is constructed that integrates detailed biophysical models of neuronal action potentials, mitochondrial ATP production and cerebral capillary blood flow. The model also provides insights of the role of astrocytes in maintaining neuronal responses, as well as the impact of elevated cytosolic calcium, due to increased synaptic activity, on mitochondrial ATP production. Both dynamical systems analysis and numerical simulations are used to determine how the maximum frequency at which the neurons can respond to synaptic input depends on capillary blow flow, as well as the ability of astrocytes to buffer extracellular potassium and cytosolic calcium handling. Results are presented for both the cases of homogenous and heterogeneous capillary networks. These results demonstrate, through this interconnected model, that heterogeneity of the capillary flow results in a decrease in the ability of neurons to respond to synaptic stimulation and that intact glial function provides a further protective role for the neurons.