Modulation of Cortical Oscillations by Low-Frequency Direct Cortical Stimulation Is State-Dependent

Abstract

Cortical oscillations play a fundamental role in organizing large-scale functional brain networks. Noninvasive brain stimulation with temporally patterned waveforms such as repetitive transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS) have been proposed to modulate these oscillations. Thus, these stimulation modalities represent promising new approaches for the treatment of psychiatric illnesses in which these oscillations are impaired. However, the mechanism by which periodic brain stimulation alters endogenous oscillation dynamics is debated and appears to depend on brain state. Here, we demonstrate with a static model and a neural oscillator model that recurrent excitation in the thalamo-cortical circuit, together with recruitment of cortico-cortical connections, can explain the enhancement of oscillations by brain stimulation as a function of brain state. We then performed concurrent invasive recording and stimulation of the human cortical surface to elucidate the response of cortical oscillations to periodic stimulation and support the findings from the computational models. We found that (1) stimulation enhanced the targeted oscillation power, (2) this enhancement outlasted stimulation, and (3) the effect of stimulation depended on behavioral state. Together, our results show successful target engagement of oscillations by periodic brain stimulation and highlight the role of nonlinear interaction between endogenous network oscillations and stimulation. These mechanistic insights will contribute to the design of adaptive, more targeted stimulation paradigms.

Fig 1. Simple Static Model Explains State-Dependence.

(A) The endogenous oscillation is denoted as a pure sine wave, and the amplitude of the sine wave represents the strength of oscillation in the three states studied here. Dotted line denotes the threshold above which stimulation produces a change (denoted by arrow). When the change produced by stimulation is below the threshold, no change in the oscillation is observed. However, when the threshold is crossed, stimulation produces a response that decays with time. The bands denote the phases of the oscillation at which stimulation produces a change in the oscillation. For stronger oscillations (eyes-closed), the phases at which stimulation produces change are minimal. For very weak oscillations (task-engaged), stimulation produces change at all phases. (B) The function used to model the stimulation response. The stimulation response is modeled as the linear convolution between the stimulation pulse and this response function. (C) Convolution between stimulation pulses and stimulation response function. (D) Example traces illustrating the model behavior. The red lines at the bottom denote the timing of the stimulation pulses. The gray line denotes the stimulation response that is added to the oscillation waveform (black dashed line) to produce the stimulation effect (orange solid line). (E) Example traces produced using the model described in (A). In the eyes-closed state, stimulation-induced changes are minimal. In the eyes-open state, the stimulation-induced change is still constrained by the endogenous frequency. In the task-engaged state, stimulation produces change at all phases resulting in entrainment. Black dashed line represents the endogenous oscillation. Red solid line represents the waveform resulting from the addition of the stimulation waveform to the endogenous oscillation. (F) Top: Effect of varying endogenous oscillation strength. The change in power at the endogenous frequency increases until a certain limit and then decreases when the strength of oscillation relative to stimulation strength is high (violet line). The power at stimulation frequency (green line) decreases with increasing oscillation strength as stimulation effect is observed in a restricted range of phases. Bottom: Effect of varying stimulation strength for a given oscillation strength. As stimulation strength increases, the power at oscillation frequency increases until the strength relative to oscillation strength is high enough to cause increase in power at stimulation frequency. Beyond this, the increase in power at oscillation frequency is minimal, and power at stimulation frequency increases monotonically. The data shown in this figure are available online: http://dx.doi.org/10.5281/zenodo.45811

Fig 2. Computational Model Explains Outlasting Effects of Periodic Stimulation.

(A) Schematic of computational model that includes the different components and interactions among them. The region of the cortex being stimulated is denoted by a gray circle encompassing excitatory and inhibitory neurons. The model neurons exhibit reciprocal as well as recurrent connections. The cortico-thalamic and cortico-cortical interactions are also modeled to be reciprocal. (B) Membrane potential observed from excitatory neurons in the model shows task-dependent differences in stimulation effect. During the eyes-closed state (blue trace), a strong oscillation is observed in the alpha frequency range. Stimulation onset does not alter the dynamics significantly. In the eyes-open state (magenta trace), an oscillation is still observed in the alpha frequency range. However, the strength is decreased compared to the eyes-closed state. Stimulation onset causes the amplification of this oscillation, which persists after stimulation offset and then slowly decays. In the task-engaged state (yellow trace), no strong oscillation is observed due to the external inputs that model task-related input. In this state, stimulation causes the network to oscillate at the stimulation frequency, which persists and decays in the epoch after stimulation. (C) Spectral analysis of membrane potential reveals state-dependent effect of stimulation. Refer to S1 Fig for dynamics in the absence of cortico-thalamic and cortico-cortical interactions. The data shown in this figure are available online: http://dx.doi.org/10.5281/zenodo.45811

Fig 3. Electrode Locations and Artifact Suppression.

(A) Surface model of an atlas brain showing locations of electrodes over the parietal regions in each of the three patients. Signals measured from only these electrodes were used in the analysis. Refer to S2 Fig for the stimulation electrodes and electrodes over other regions. (B) Schematic of stimulation waveform used. Stimulation consisted of one biphasic pulse 400 μs in duration every 100 ms for 5 s. (C) Stimulation artifacts in representative sample traces from four electrodes (top). Enlarged portion denoted by the black line (bottom). Artifacts appear as periodic sharp deflections with stereotyped waveforms. (D) Traces from the same four electrodes as in (B) after the artifact suppression procedure. The artifacts are suppressed compared to the signal amplitude. (E) Spectrum of the fourth waveform in (B) showing peaks at 10 Hz and harmonics of 10 Hz corresponding to artifact waveform. Top: Full frequency range. Bottom: Zoom-in on low frequencies. (F) Spectra of the same waveform after artifact suppression confirming the effectiveness of the algorithm. The only remaining exogenous peak is at 60 Hz, caused by electric line noise.

Fig 4. State-Dependent Modulation by Periodic Stimulation.

(A) Power spectra in the epochs before stimulation (black trace), during stimulation (orange trace), and after stimulation (blue trace) for the three participants during the different states. Participant P001’s spectra showed no appreciable change in the eyes-closed state in the endogenous frequency band (violet shaded region) and minimal change in the stimulation frequency band (green shaded region) in eyes-closed state during stimulation. However, there was a change in dominant oscillation frequency from endogenous frequency to stimulation frequency in the task-engaged state. P005 showed no change in power at endogenous frequency in the eyes-closed state, while there was an increase in the eyes-open state. Power at stimulation frequency was decreased in both states. P008 showed an increase in both states in the endogenous and stimulation frequencies. (B) Mean modulation indices at the endogenous frequency (left) and the stimulation frequency (right) in the epochs during stimulation (top) and after stimulation (bottom) for each of the three participants. Bars denote standard error of mean. * denotes statistical significance (p < 0.05) from a paired t test. The data shown in this figure are available online: http://dx.doi.org/10.5281/zenodo.45811