State-space analysis of Hodgkin-Huxley axonal neural mass model during subthreshold high frequency alternating current stimulation

The Hodgkin-Huxley model describes the dynamics of action potentials and the resultant currents that pass through voltage-dependent ion channels in the neuronal membrane. Another type of ion channels, transmitter-activated ion channels primarily expressed on dendrites, are involved in synaptic transmission from presynaptic neurons. Along these cable-like dendrites, the effect of spatial potential gradients can be mimicked by appropriate transmembrane current density injections, producing summated postsynaptic membrane potential alterations at the axon hillock of the soma. Alterations of membrane potentials at the axon hillock will open or close the voltage-dependent ion channels, where the kinetics as well as the activation/deactivation properties of the ion channels will determine the neuronal response. To explore this phenomenon, the sensitivity of lumped membrane potentials to current pulse perturbation (i.e., excitability) was explored at a population level where the Hodgkin-Huxley (HH) type axonal neural mass model (specifically, axon hillock) was driven by subthreshold sinusoidal transmembrane current injections from a somatodendritic synaptic mass model. Although knowledge about both, ion channel distributions and their response properties is necessary to delineate and parameterize a realistic lumped mass compartment model, we investigated a simplified HH model to primarily evaluate our dynamical systems analysis approach. Specifically, the lumped membrane potential of the axonal neural mass model was found to settle to one of two possible stable states based on the stimulation frequency during the subthreshold alternating current (AC) stimulation via the synaptic mass model. These altered stable states of the axonal neural mass model were explored for excitability using current perturbations via the synaptic mass model. One of the states (activated potassium depolarization blockade) was found to be less excitable than the other (inactivated sodium refractor- blockade). It is interesting to note that even with such a simplified HH model, two mechanisms - activated potassium depolarization blockade and inactivated sodium refractory blockade - were detected, and we concluded that at a population level, the propensity to neuronal response may be reduced under AC stimulation via different mechanisms where high (~kHz) frequencies may provide another neuromodulation tool.