Ion Gradient-driven Bifurcations of a Multi-Scale Neuronal Model
Metabolic limitations within the brain frequently arise in the context of aging and disease. As the largest consumers of energy within the brain, ion pumps that maintain the neuronal membrane potential are the most affected when energy supply becomes limited. To characterize the effects of such limitations, we analyze the ion gradients present in the Larter-Breakspear neural mass model. We show the existence and locations of Neimark-Sacker and period-doubling bifurcations in the sodium, calcium, and potassium reversal potentials, and demonstrate that these bifurcations form physiologically relevant bounds of ion gradient variability. Within these bounds, we show how depolarization of the gradients will cause decreased neural activity. We also show that the depolarization of ion gradients decreases inter-regional coherence, causing a shift in the critical point at which the coupling occurs and thereby inducing loss of synchrony between regions. In this way, we show that the Larter-Breakspear model captures ion gradient variability present at the microscale level and propagates these changes to the macroscale effects congruent with those observed in human neuroimaging studies.