Fig. 6: Endogenous alpha oscillations in a thalamo-cortical model and synchronization by tACS.

a The structure of the thalamo-cortical network with excitatory, inhibitory, and gap-junction connections between neuronal populations. The cortical network includes fast-spiking inhibitory (FS) and regular-spiking pyramidal (PY) neurons. The thalamic network includes relay thalamo-cortical (RTC), reticular (RE), high-threshold bursting (HTC), and thalamic local inhibitory (IN) neurons. The tACS is applied only to pyramidal neurons (blue arrows). b Endogenous oscillations shown by (top) 1-s cortical and thalamic local field potential (LFP) traces, and (bottom left) the raster plot with each dot representing the firing instant of a neuron. (Bottom right) The cortical LFP has a dominant spectral peak at the alpha range (13.5 Hz), and a smaller peak at theta range (3.6 Hz). The thalamic LFP has a dominant theta peak (3.6 Hz), its harmonic (7.3 Hz), and a weak alpha peak (13.5 Hz). c Network response to a 13.5 Hz, 8 pA tACS. The cortical and thalamic LFP traces, and the raster plot showing the firing of all neurons (left), and the membrane voltage traces of sample neuron from each cell type (right). d Network response to a group of stimuli with frequencies between 3 and 30 Hz, and amplitudes between 0 and 10 pA. Top left heat-maps: The color-coded phase-locking value (PLV) as a function of stimulation frequency (horizontal axis), and stimulation amplitude (vertical axis) for each neuron type. Darker colors indicate higher synchronization between individual neurons and tACS with corresponding frequency and amplitude. The FS and PY neurons show triangular-shape high PLV regions centered on the alpha peak frequency (13.5 Hz). Bottom left heat-maps: The firing rate (FR) maps for each neuron type. The color at each point indicates the average firing rate (in Hz) across neurons in response to tACS with corresponding frequency (horizontal axis) and amplitude (vertical axis). Two points on PLV and FR maps are selected for further analysis: (i) A point with high PLV on Arnold tongue region with tACS parameters of 13.5 Hz and 8 pA. The tACS waveform and membrane potential of a sample PY neuron (top right) show that the PY neuron fires regularly after the peak of the tACS wave (red circles). The phase distribution of tACS wave at firing instances of PY neuron shows a phase preference between 90 and 180 degrees. (ii) A point with low PLV outside of the Arnold tongue region with tACS parameters of 18.5 Hz and 8 pA. The tACS waveform and membrane potential of a sample PY neuron (bottom right) show that the PY neuron fires at random phases of tACS wave (red circles). The phase distribution of the tACS waveform when PY neurons fired shows a uniform phase distribution.