Quantitative analysis and biophysically realistic neural modeling of the MEG mu rhythm: rhythmogenesis and modulation of sensory-evoked responses

Abstract

Variations in cortical oscillations in the alpha (7-14 Hz) and beta (15-29 Hz) range have been correlated with attention, working memory, and stimulus detection. The mu rhythm recorded with magnetoencephalography (MEG) is a prominent oscillation generated by Rolandic cortex containing alpha and beta bands. Despite its prominence, the neural mechanisms regulating mu are unknown. We characterized the ongoing MEG mu rhythm from a localized source in the finger representation of primary somatosensory (SI) cortex. Subjects showed variation in the relative expression of mu-alpha or mu-beta, which were nonoverlapping for roughly 50% of their respective durations on single trials. To delineate the origins of this rhythm, a biophysically principled computational neural model of SI was developed, with distinct laminae, inhibitory and excitatory neurons, and feedforward (FF, representative of lemniscal thalamic drive) and feedback (FB, representative of higher-order cortical drive or input from nonlemniscal thalamic nuclei) inputs defined by the laminar location of their postsynaptic effects. The mu-alpha component was accurately modeled by rhythmic FF input at approximately 10-Hz. The mu-beta component was accurately modeled by the addition of approximately 10-Hz FB input that was nearly synchronous with the FF input. The relative dominance of these two frequencies depended on the delay between FF and FB drives, their relative input strengths, and stochastic changes in these variables. The model also reproduced key features of the impact of high prestimulus mu power on peaks in SI-evoked activity. For stimuli presented during high mu power, the model predicted enhancement in an initial evoked peak and decreased subsequent deflections. In agreement, the MEG-evoked responses showed an enhanced initial peak and a trend to smaller subsequent peaks. These data provide new information on the dynamics of the mu rhythm in humans and the model provides a novel mechanistic interpretation of this rhythm and its functional significance.

Figures

Fig. 1.

Schematic of primary somatosensory cortex (SI) computational model network architecture. A: local network synaptic connections between multiple-compartment pyramidal neurons (PNs, green) and single-compartment inhibitory neurons (INs, red). Bold outlined dendrites were contacted. Within-layer PN-to-PN synapses (not shown) were also present on dark green outlined dendrites. B: excitatory feedforward (FF) input connections. The black arrow is only schematic because lemniscal thalamic input was not explicitly modeled. C: excitatory feedback (FB) input connections from presumed higher-order cortical and/or nonspecific thalamic neurons. The FF and FB inputs were modeled as spike train generators with a predetermined temporal profile and synaptic strength. D: schematic of expanded SI cortical column model containing a 2-dimensional grid of 100 PNs and 35 INs evenly spaced between every 2 PNs, in the supra- (PNs shown in orange) and infragranular layers (PNs shown in green); INs not shown. Each set of synaptic weights had a Gaussian spatial profile (Table 1).

Fig. 2.

Schematic illustration of alternating 10-Hz FF and FB drive to the SI network. Approximately every 100 ms (Gaussian, mean interstimulus interval [ISI] 100 ms, SD = 20 ms), 10 “bursts” of input (doublet spike trains, ISI 10 ms) excite the SI network in an FF connection pattern followed by an analogous delayed FB input. Red and blue arrows depict intracellular current flow. FF inputs induce current flow up the dendrites and FB inputs current flow down the dendrites.

Fig. 3.

Magnetoencephalographic (MEG) SI mu rhythms. A, blue curve: grand mean power spectral density (PSD) vs. frequency averaged across 10 subjects, 200 trials each (SE bars) showing 2 peaks of activity in the mu-band between 7 and 29 Hz. Gray curve: analogous curve with removal of data from 3 subjects with nonstandard SI dipole localization methods. B: PSD vs. frequency in each subject; subjects with nonstandard dipole localization are shown in black. C: example frequency vs. time spectrograms averaged over 100 trials (1-s prestimulus time period) from 2 subjects, emphasizing that the SI mu rhythm is a 2-component rhythm containing separate bands of mu-alpha and mu-beta activity. The unit of power is (Am)2.

Fig. 4.

Single-trial mu rhythms. Two examples of single-trial SI frequency spectrograms and waveforms from 4 subjects. The unit of power is (Am)2. On a single-trial basis, peaks in mu-alpha and mu-beta power often occur at different points in time, indicating that the rhythms are not harmonics of each other and may have different neural sources. The corresponding waveforms oscillation around zero polarity.

Fig. 5.

Mu-alpha and mu-beta components of the MEG SI mu rhythm are nonoverlapping MEG data showing a histogram of the ratio of alpha to beta power over 100-ms time bins (n = 2,000 trials, 10 Ss). The mean (2.4) and median (1.3) of this histogram are >1, underscoring the relative prevalence of alpha power in the mu signal. Inset: MEG data showing probability that high mu-alpha and mu-beta power (top 33% of all power) occur simultaneously roughly 50% of the time (mean = 50.31%; SD = 0.056%).

Fig. 6.

Modeling SI mu rhythms with alternating nearly synchronous approximately 10-Hz FF and FB input. A: MEG data showing an example prestimulus SI mu rhythm from a single trial. B: simulating 10-Hz stochastic FF inputs only to SI (depicted schematically in Fig. 2) reproduces a strong 10-Hz MEG signal and very weak 20 Hz. The unit of power is (Am)2. C: alternating 10-Hz FF followed by 10-Hz FB inputs (5-ms delay) reproduces equal power, nonoverlapping, 10- and 20-Hz components, with a waveform that oscillates around zero, analogous to the experimental MEG data. Red boxes show that mu-beta cycles emerge when the FB input is strong enough to cut the mu-alpha oscillation in half. D, top: mean and SD of the symmetry index (SInd) of the MEG SI mu rhythm waveform around zero, for each subject. Bottom: histogram of SInd across all subjects and trials. Inset: mean and SD of histogram. The SInd is not significantly different from zero (P < 0.001). E: analogous histogram of SInd across trials in the model (n = 40, 1-s trials, parameters as in C), which is also not significantly different from zero (P < 0.001). Inset: mean and SD of histogram.

Fig. 7.

Mu-alpha and mu-beta components of model SI mu rhythms are nonoverlapping. A: PSD vs. frequency averaged across 50 trials (SE bars) showing 2 peaks of activity in the mu-band between 7 and 29 Hz, in agreement with the MEG data (compare with Fig. 3A). B: model data showing a histogram of the ratio of variance to power over 100-ms time windows (n = 1,000 trials). The mean (1.4) and median (1.1) of this histogram are >1, analogous to the MEG data (compare with MEG data in Fig. 5). Inset: model data showing probability that high mu-alpha and mu-beta power (top 33% of all power) occur simultaneously roughly 50% of the time (mean = 48.6%, calculated from 100 0.1-s time windows of simulated data; compare with MEG data in Fig. 5, inset).

Fig. 8.

Statistics of FF and FB input that influence relative mu-alpha and mu-beta power. A: small delays (mean <10 ms) between approximately 10-Hz FF and FB drives create nearly equal mu-alpha and mu-beta power (mu-beta/mu-alpha ≃ 1). If the FF inputs are increased via increased synchrony (decreased variance, B), amplitude (C), or postsynaptic conductance (D), the relative mu-alpha dominance increases (mu-beta/mu-alpha decreases, red curves). Analogous increases in the FB input increase the relative mu-beta power (mu-beta/mu-alpha increases, blue lines). E: simulated high and low mu rhythms (Low Mu FF = FB postsynaptic conductance = 0.4e-4 millisiemens [mS], High Mu FF = FB postsynaptic conductance = 0.6e-4; each FF = FB variance = 400 ms and amplitude = 10 input bursts). The unit of power is (Am)2. Black bars represent time windows in which evoked responses are simulated in Fig. 9A.

Fig. 9.

Modeling the impact of mu on SI-evoked responses. A: simulated evoked responses under high and low mu conditions. High mu creates an early positive peak at about 50 ms (M50) and subsequent suppressed response at about 70 ms and later (difference between high and low mu; purple stars, P < = 0.01; red stars, P < = 0.05, paired t-test, mean n = 30 trials each, with starting phases equally spaced in mu-alpha and mu-beta cycles shown with black bars in Fig. 8E). B: MEG SI-evoked responses sorted over high and low prestimulus mu power (50% detection rate) reveals early M50 peak and trend to decreased M70 peak under high mu, as predicted by the model (red stars, P < = 0.05). C: evoked spike rates of neuron populations under high and low prestimulus mu. Under high mu conditions, the initial roughly 25-ms evoked input to the SI network induces greater firing in the INs and PNs and thus an early positive peak near 50 ms (M50) in the SI-evoked response. Activity in the INs suppresses subsequent firing and a slight decrease in the magnitude of the evoked response, beginning at about 70 ms. In contrast, under low mu conditions, the initial evoked input induces little inhibitory firing from the initial FF at ≃25 ms input and thus a slightly greater evoked response beginning at about 70 ms.