Local Field Potential Power Spectra Research Articles

Phase transitions in cortical dynamics explain improved information processing under attention

A major aspect of cortical information processing is its rapid adaptation to the actual behavioral demands. Highly representative for such processes is selective visual attention, which has been shown to improve performance in visual perception (see e.g. [1]). The neural mechanisms supporting these effects have been investigated in electrophysiological studies: Besides firing rate modulations and tuning curve changes in visual cortical neurons, they revealed a strong increase of oscillations in the gamma frequency band (35-90 Hz) [2]. These findings indicate that gamma oscillations might play an important role in optimizing information processing under attention, but their functional role is currently not yet understood. The dynamics of cortical networks exhibit certain properties that have been suggested to be linked to optimization of information processing: criticality and balance. Experimental studies indicate that cortical networks operate near a 'critical' state in which scale-free avalanches of spike events occur [3], generating neural patterns which are 'rich' in structure [4]. These critical states are indicators of a phase transition from an asynchronous regime of activity in the network towards a synchronous regime. Furthermore, it has been observed that excitatory and inhibitory synaptic currents to cortical neurons are balanced [5], which allows cells to detect rapid changes in the stimulus and provides an explanation for the high variability of neural activity. Here we explore the relationship between the phase transition towards synchrony, balance, and enhanced stimulus representation in a simple network of integrate-and-fire neurons driven by an external stimulus. By increasing the efficacy of recurrent couplings, attention improves spontaneous synchronization and renders activation patterns for different stimuli more distinct. We compare this result to experimental evidence demonstrating that object representation in cortical local field potentials (LFPs) is improved in macaque monkeys under attention [6], and find a near-perfect match between model and LFP data. By analyzing the LFPs and avalanche statistics of the simulated network activity, we show that the enhancement of discriminability of LFP power spectra is strongly correlated with phase transitions towards synchrony. More importantly, our results indicate that networks operating near phase transitions reside in a regime where a dramatic enhancement of stimulus representation may require only fine modulations of synaptic strengths. Taken together, our study implies that attention drives the cortex towards a critical state, inducing oscillatory activity and hereby improving the discriminability of different stimuli represented in the corresponding network activity. Furthermore, our framework suggests a novel role for synchronization in cortical information processing.

Input dependence of local field potential spectra: experiment vs theory

How sensory stimuli are encoded in neuronal activity is a major challenge for understanding perception. A prominent effect of sensory stimulation is to elicit oscillations in EEG and Local Field Potential (LFP) recordings over a broad range of frequencies. Belitski et al. [1] recorded LFPs and spiking activity in the primary visual cortex of anaesthetized macaques presented with naturalistic movies and found that the power of the gamma and low-frequency bands of LFP carried largely independent information about visual stimuli, while the information carried by the spiking activity was largely redundant with that carried by the gamma-band LFPs. To understand better how different frequency bands of the LFP are controlled by sensory input, we computed analytically the power spectrum of the LFP of a theoretical model of V1 (a network composed of two populations of neurons - excitatory and inhibitory), subjected to time-dependent external inputs modelling inputs from the LGN, as a function of the parameters characterizing single neurons, synaptic connectivity, as well as parameters characterizing the statistics of external inputs. Our model consists in a two populations network of excitatory and inhibitory leaky integrate-and-fire neurons. Standard analytical methods using the Fokker-Planck formalism can be used to compute average firing rates of both populations in the asynchronous state of the network, as well as the region of parameters for which this state is stable ([2,3]). The power spectrum of the global activity and the LFP (sum of average excitatory and inhibitory currents onto pyramidal cells of the network) can also be computed in a network of finite size ([2]). Using linear response theory we then calculated the response of the network to a dynamic input ([4]). The final result was an equation giving the LFP power spectrum as a function of the intrinsic parameters of the network and of the parameters characterizing the dynamic input. We then used the analytical expression of the LFP power to fit the experimental data of [1]. The data consists in LFP recordings from primary visual cortex of monkeys, during the presentation of a movie that last several minutes. In order to capture the LFP power changes during the movie presentation, the LFP traces were divided into 2 seconds non-overlapping scenes. We then fitted the LFP power of all the scenes with the same network parameters, but with input parameters free to vary scene-by-scene. We used a simplex method repeatedly applied for different initial conditions. The parameter set that was selected was the one that minimized the reduced chisquare, among sets for which the asynchronous state was stable. The model provided excellent fits of the data. The fitting procedure permitted to extract the values of the firing rates of the excitatory and inhibitory populations and the parameters characterizing the external input for most of the scenes of the movie. These outcomes could be then correlated with experimental firing rates and the features of the movie itself, such as temporal and spatial contrast as well as orientation. We found a significant correlation both between firing rates extracted from fit and the multi-unit activity recorded during the movie and between the parameters characterizing the external input and the features of the movie. These results show how an analytical approach can be used to estimate the key parameters underlying changes in the LFP spectral dynamics.

A neuronal network model for simulating the effects of repetitive transcranial magnetic stimulation on local field potential power spectra.

Repetitive transcranial magnetic stimulation (rTMS) holds promise as a non-invasive therapy for the treatment of neurological disorders such as depression, schizophrenia, tinnitus, and epilepsy. Complex interdependencies between stimulus duration, frequency and intensity obscure the exact effects of rTMS stimulation on neural activity in the cortex, making evaluation of and comparison between rTMS studies difficult. To explain the influence of rTMS on neural activity (e.g. in the motor cortex), we use a neuronal network model. The results demonstrate that the model adequately explains experimentally observed short term effects of rTMS on the band power in common frequency bands used in electroencephalography (EEG). We show that the equivalent local field potential (eLFP) band power depends on stimulation intensity rather than on stimulation frequency. Additionally, our model resolves contradictions in experiments.

The Laminar Cortex Model: A New Continuum Cortex Model Incorporating Laminar Architecture

Local field potentials (LFPs) are widely used to study the function of local networks in the brain. They are also closely correlated with the blood-oxygen-level-dependent signal, the predominant contrast mechanism in functional magnetic resonance imaging. We developed a new laminar cortex model (LCM) to simulate the amplitude and frequency of LFPs. Our model combines the laminar architecture of the cerebral cortex and multiple continuum models to simulate the collective activity of cortical neurons. The five cortical layers (layer I, II/III, IV, V, and VI) are simulated as separate continuum models between which there are synaptic connections. The LCM was used to simulate the dynamics of the visual cortex under different conditions of visual stimulation. LFPs are reported for two kinds of visual stimulation: general visual stimulation and intermittent light stimulation. The power spectra of LFPs were calculated and compared with existing empirical data. The LCM was able to produce spontaneous LFPs exhibiting frequency-inverse (1/ƒ) power spectrum behaviour. Laminar profiles of current source density showed similarities to experimental data. General stimulation enhanced the oscillation of LFPs corresponding to gamma frequencies. During simulated intermittent light stimulation, the LCM captured the fundamental as well as high order harmonics as previously reported. The power spectrum expected with a reduction in layer IV neurons, often observed with focal cortical dysplasias associated with epilepsy was also simulated.

REM Sleep Reorganizes Hippocampal Excitability

Sleep is composed of an alternating sequence of REM and non-REM episodes, but their respective roles are not known. We found that the overall firing rates of hippocampal CA1 neurons decreased across sleep concurrent with an increase in the recruitment of neuronal spiking to brief "ripple" episodes, resulting in a net increase in neural synchrony. Unexpectedly, within non-REM episodes, overall firing rates gradually increased together with a decrease in the recruitment of spiking to ripples. The rate increase within non-REM episodes was counteracted bya larger and more rapid decrease of discharge frequency within the interleaved REM episodes. Both the decrease in firing rates and the increase in synchrony during the course of sleep were correlated with the power of theta activity during REM episodes. These findings assign a prominent role of REM sleep in sleep-related neuronal plasticity.

Subthalamic deep brain stimulation at individualized frequencies for Parkinson disease

The oscillation model of Parkinson disease (PD) states that, in the subthalamic nucleus (STN), increased θ (4-10 Hz) and β (11-30 Hz) frequencies were associated with worsening whereas γ frequencies (31-100 Hz) were associated with improvement of motor symptoms. However, the peak STN frequency in each band varied widely from subject to subject. We hypothesized that STN deep brain stimulation (DBS) at individualized γ frequencies would improve whereas θ or β frequencies would worsen PD motor signs. We prospectively studied 13 patients with PD. STN local field potential (LFP) was recorded after electrode implantations, in the OFF and then in ON dopaminergic medication states while patients performed wrist movements. Six individual peak frequencies of the STN LFP power spectra were obtained: the greatest decrease in θ and β and greatest increase in γ frequencies in the ON state (MED) and during movements (MOVE). Eight DBS frequencies were applied including 6 MED and MOVE frequencies, high frequency (HF) used for chronic stimulation, and no stimulation. The patients were assessed using the motor Unified Parkinson's Disease Rating Scale (mUPDRS). STN DBS at γ frequencies (MED and MOVE) and HF significantly improved mUPDRS scores compared to no stimulation and both γ frequencies were not different from HF. DBS at θ and β frequencies did not worsen mUPDRS scores compared to no stimulation. Short-term administration of STN DBS at peak dopamine-dependent or movement-related γ frequencies were as effective as HF for reducing parkinsonian motor signs but DBS at θ and β frequencies did not worsen PD motor signs. This study provides Class III evidence that STN DBS at patient-specific γ frequencies and at usual high frequencies both improved mUPDRS scores compared to no stimulation and did not differ in effect.

Spectral Analysis of Local Field Potentials from Rat Primary Visual Cortex (V1)

In primary visual cortex (V1) of rats, orientation selective neurons do not show topographic organization on a larger scale (Ohki et al., 2005), in contrast to the columnar organization of orientation selective cells in V1 of cat and monkey. Accordingly, while orientation tuning in mass signals like the local field potential (LFP) has been described in recordings from cat V1, it can be assumed to be weak or absent in rodent V1. However, in monkey motor cortex, which also shows no clear columnar organization, information about the direction of the monkey’s hand movement could be extracted from LFP power spectra with high predictive power (Rickert et al., 2005). To reveal in how far global network tuning properties could be extracted from mass signals of primary sensory areas which do not show clear topographic organization, we performed in vivo multi-electrode recordings in V1 of anesthetized rats while presenting visual stimuli with clear direction information (moving edges and gratings). Spectral analysis of LFP signals from multiple channels was performed using adaptive multivariate auto-regression (AMVAR; Ding et al., 2000) after removing the first two statistical moments (mean and standard deviation across trials) from the signal. This method allows high spectral estimation accuracy with high temporal resolution superior to other methods of time-dependent spectral analysis like multi-tapering (Nalatore & Rangarajan, 2009). Direction tuning was assessed using circular statistical measures. For moving edges, significant directional tuning in the LFP power spectrum can be found during the onset transient up to 500 ms after stimulus onset. Tuning strength was not distributed evenly across the whole observed spectrum (<200 Hz), however, but limited to mainly two distinct frequency bands centered around ~30 Hz and ~70 Hz. Preliminary analysis of moving grating stimuli did not reveal significant tuning either in the onset transient or the steady state during stimulus presentation. These results suggest that, even in the absence of coarse scale organization of cortical networks with respect to tuning properties, information about the stimulus properties can be inferred with appropriate methods.

Origins of 1/f2 scaling in the power spectrum of intracortical local field potential

It has been noted that the power spectrum of intracortical local field potential (LFP) often scales as 1/f(-2). It is thought that LFP mostly represents the spiking-related neuronal activity such as synaptic currents and spikes in the vicinity of the recording electrode, but no 1/f(2) scaling is detected in the spike power. Although tissue filtering or modulation of spiking activity by UP and DOWN states could account for the observed LFP scaling, there is no consensus as to how it arises. We addressed this question by recording simultaneously LFP and single neurons ("single units") from multiple sites in somatosensory cortex of anesthetized rats. Single-unit data revealed the presence of periods of high activity, presumably corresponding to the "UP" states when the neuronal membrane potential is depolarized, and periods of no activity, the putative "DOWN" states when the membrane potential is close to resting. As expected, the LFP power scaled as 1/f(2) but no such scaling was found in the power spectrum of spiking activity. Our analysis showed that 1/f(2) scaling in the LFP power spectrum was largely generated by the steplike transitions between UP and DOWN states. The shape of the LFP signal during these transitions, but not the transition timing, was crucial to obtain the observed scaling. These transitions were probably induced by synchronous changes in the membrane potential across neurons. We conclude that a 1/f(2) scaling in the LFP power indicates the presence of steplike transitions in the LFP trace and says little about the statistical properties of the associated neuronal firing.

Synchronous Chaos and Broad Band Gamma Rhythm in a Minimal Multi-Layer Model of Primary Visual Cortex

Visually induced neuronal activity in V1 displays a marked gamma-band component which is modulated by stimulus properties. It has been argued that synchronized oscillations contribute to these gamma-band activity. However, analysis of Local Field Potentials (LFPs) across different experiments reveals considerable diversity in the degree of oscillatory behavior of this induced activity. Contrast-dependent power enhancements can indeed occur over a broad band in the gamma frequency range and spectral peaks may not arise at all. Furthermore, even when oscillations are observed, they undergo temporal decorrelation over very few cycles. This is not easily accounted for in previous network modeling of gamma oscillations. We argue here that interactions between cortical layers can be responsible for this fast decorrelation. We study a model of a V1 hypercolumn, embedding a simplified description of the multi-layered structure of the cortex. When the stimulus contrast is low, the induced activity is only weakly synchronous and the network resonates transiently without developing collective oscillations. When the contrast is high, on the other hand, the induced activity undergoes synchronous oscillations with an irregular spatiotemporal structure expressing a synchronous chaotic state. As a consequence the population activity undergoes fast temporal decorrelation, with concomitant rapid damping of the oscillations in LFPs autocorrelograms and peak broadening in LFPs power spectra. We show that the strength of the inter-layer coupling crucially affects this spatiotemporal structure. We predict that layer VI inactivation should induce global changes in the spectral properties of induced LFPs, reflecting their slower temporal decorrelation in the absence of inter-layer feedback. Finally, we argue that the mechanism underlying the emergence of synchronous chaos in our model is in fact very general. It stems from the fact that gamma oscillations induced by local delayed inhibition tend to develop chaos when coupled by sufficiently strong excitation.

Alpha frequency modulation in the human basal ganglia is dependent on motor task

Depth recordings from the basal ganglia of patients suffering from Parkinson's disease (PD) or dystonia have revealed local field potential (LFP) activity in specific frequency bands. Depth recordings also allow us to study LFP power spectra during different types of limb movements, thus helping to elucidate the role of the basal ganglia in specific motor tasks. Accordingly, we recorded bilateral LFP activity from the subthalamic nucleus (STN) of patients with PD (n=9) and from the globus pallidus internum (GPi) of patients with dystonia (n=8). Recordings were taken during the performance of repetitive passive, active and ballistic fast extensions and flexions of the elbow joint and during rest. The first result was that the frequency spectra varied task-specifically in a similar fashion in GPi and STN. The amplitude of the alpha frequency on the contralateral side was significantly higher in ballistic fast movements compared with rest, passive and active performance in both STN and GPi. In conclusion, ballistic fast movements cause synchronized basal ganglia activity in the alpha range. Because this was seen in both patient groups (PD and dystonia) we consider this activity as task-specific rather than disease-related.

Closed-Loop Control of Deep Brain Stimulation: A Simulation Study

Deep brain stimulation (DBS) is an effective therapy to treat movement disorders including essential tremor, dystonia, and Parkinson's disease. Despite over a decade of clinical experience the mechanisms of DBS are still unclear, and this lack of understanding makes the selection of stimulation parameters quite challenging. The objective of this work was to develop a closed-loop control system that automatically adjusted the stimulation amplitude to reduce oscillatory neuronal activity, based on feedback of electrical signals recorded from the brain using the same electrode as implanted for stimulation. We simulated a population of 100 intrinsically active model neurons in the Vim thalamus, and the local field potentials (LFPs) generated by the population were used as the feedback (control) variable for closed loop control of DBS amplitude. Based on the correlation between the spectral content of the thalamic activity and tremor (Hua , 1998), (Lenz , 1988), we implemented an adaptive minimum variance controller to regulate the power spectrum of the simulated LFPs and restore the LFP power spectrum present under tremor conditions to a reference profile derived under tremor free conditions. The controller was based on a recursively identified autoregressive model (ARX) of the relationship between stimulation input and LFP output, and showed excellent performances in tracking the reference spectral features through selective changes in the theta (2-7 Hz), alpha (7-13 Hz), and beta (13-35 Hz) frequency ranges. Such changes reflected modifications in the firing patterns of the model neuronal population, and, differently from open-loop DBS, replaced the tremor-related pathological patterns with patterns similar to those simulated in tremor-free conditions. The closed-loop controller generated a LFP spectrum that approximated more closely the spectrum present in the tremor-free condition than did open loop fixed intensity stimulation and adapted to match the spectrum after a change in the neuronal oscillation frequency. This computational study suggests the feasibility of closed-loop control of DBS amplitude to regulate the spectrum of the local field potentials and thereby normalize the aberrant pattern of neuronal activity present in tremor.

Intrinsic dendritic filtering gives low-pass power spectra of local field potentials

The local field potential (LFP) is among the most important experimental measures when probing neural population activity, but a proper understanding of the link between the underlying neural activity and the LFP signal is still missing. Here we investigate this link by mathematical modeling of contributions to the LFP from a single layer-5 pyramidal neuron and a single layer-4 stellate neuron receiving synaptic input. An intrinsic dendritic low-pass filtering effect of the LFP signal, previously demonstrated for extracellular signatures of action potentials, is seen to strongly affect the LFP power spectra, even for frequencies as low as 10 Hz for the example pyramidal neuron. Further, the LFP signal is found to depend sensitively on both the recording position and the position of the synaptic input: the LFP power spectra recorded close to the active synapse are typically found to be less low-pass filtered than spectra recorded further away. Some recording positions display striking band-pass characteristics of the LFP. The frequency dependence of the properties of the current dipole moment set up by the synaptic input current is found to qualitatively account for several salient features of the observed LFP. Two approximate schemes for calculating the LFP, the dipole approximation and the two-monopole approximation, are tested and found to be potentially useful for translating results from large-scale neural network models into predictions for results from electroencephalographic (EEG) or electrocorticographic (ECoG) recordings.

LFP spectral peaks in V1 cortex: network resonance and cortico-cortical feedback.

This paper is about how cortical recurrent interactions in primary visual cortex (V1) together with feedback from extrastriate cortex can account for spectral peaks in the V1 local field potential (LFP). Recent studies showed that visual stimulation enhances the γ-band (25-90 Hz) of the LFP power spectrum in macaque V1. The height and location of the γ-band peak in the LFP spectrum were correlated with visual stimulus size. Extensive spatial summation, possibly mediated by feedback connections from extrastriate cortex and long-range horizontal connections in V1, must play a crucial role in the size dependence of the LFP. To analyze stimulus-effects on the LFP of V1 cortex, we propose a network model for the visual cortex that includes two populations of V1 neurons, excitatory and inhibitory, and also includes feedback to V1 from extrastriate cortex. The neural network model for V1 was a resonant system. The model's resonance frequency (ResF) was in the γ-band and varied up or down in frequency depending on cortical feedback. The model's ResF shifted downward with stimulus size, as in the real cortex, because increased size recruited more activity in extrastriate cortex and V1 thereby causing stronger feedback. The model needed to have strong local recurrent inhibition within V1 to obtain ResFs that agree with cortical data. Network resonance as a consequence of recurrent excitation and inhibition appears to be a likely explanation for γ-band peaks in the LFP power spectrum of the primary visual cortex.

Broadband Shifts in Local Field Potential Power Spectra Are Correlated with Single-Neuron Spiking in Humans

A fundamental question in neuroscience concerns the relation between the spiking of individual neurons and the aggregate electrical activity of neuronal ensembles as seen in local field potentials (LFPs). Because LFPs reflect both spiking activity and subthreshold events, this question is not simply one of data aggregation. Recording from 20 neurosurgical patients, we directly examined the relation between LFPs and neuronal spiking. Examining 2030 neurons in widespread brain regions, we found that firing rates were positively correlated with broadband (2-150 Hz) shifts in the LFP power spectrum. In contrast, narrowband oscillations correlated both positively and negatively with firing rates at different recording sites. Broadband power shifts were a more reliable predictor of neuronal spiking than narrowband power shifts. These findings suggest that broadband LFP power provides valuable information concerning neuronal activity beyond that contained in narrowband oscillations.

Electrical hippocampal activity during danger and safety signals in classical conditioning in the rat.

The effect of stimuli predicting danger (DS) and safety (SS) in Pavlovian aversive conditioning on hippocampal local field potentials (LFP) was studied in 25 partially restrained adult male rats (Long-Evans). DS lasting 5 s preceded tail-shock, while SS overlapping DS during DS last 3 s predicted omission of shock. The power spectra of LFPs during trials were analyzed in theta and delta frequency bands. In DS, theta frequency during the last 3 s was lower that in first 2 s. In danger and safety situation theta peak frequency was different for dorsal CA1 activity (5.99 Hz vs. 6.86 Hz, respectively) while delta peak frequency was different for ventral CA1 (1.56 Hz vs. 1.07 Hz) for the last 3 s of trial. Differences in theta frequency in danger and safety situation may reflect differences in sensory processing during induced emotional states and/or related differences in motor behavior.

LFP Power Spectra in V1 Cortex: The Graded Effect of Stimulus Contrast

We recorded local field potentials (LFPs) and single-unit activity simultaneously in the macaque primary visual cortex (V1) and studied their responses to drifting sinusoidal gratings that were chosen to be "optimal" for the single units. Over all stimulus conditions, the LFP spectra have much greater power in the low-frequency band (< or = 10 Hz) than higher frequencies and can be described as "1/f." Analysis of the total power limited to the low, gamma (25-90 Hz), or broad (8-240 Hz) frequency bands of the LFP as a function of stimulus contrast indicates that the LFP power gradually increases with stimulus strength across a wide band in a manner roughly comparable to the increase in the simultaneously recorded spike activity. However, the low-frequency band power remains approximately constant across all stimulus contrasts. More specifically the gamma-band LFP power increases differentially more with respect to baseline than either higher or lower bands as stimulus contrast increases. At the highest stimulus contrasts, we report as others have previously, that the power spectrum of the LFP typically contains an obvious peak in the gamma-frequency band. The gamma-band peak emerges from the overall broadband enhancement in LFP power at stimulus contrasts where most single units' responses have begun to saturate. The temporal/spectral structures of the LFP located in the gamma band-which become most evident at the highest contrasts-provide additional constraints on potential mechanisms underlying the stimulus response properties of spiking neurons in V1.

On oscillating neuronal responses in the visual cortex of the monkey.

1. Recent studies of visual processing in the cat have shown stimulus-related oscillations in the 30- to 70-Hz range. We sought to replicate these findings in the monkey. 2. We recorded multiunit activity (MUA) and local field potentials (LFP) in areas V1 and middle-temporal area (MT), and MUA from the inferotemporal cortex (IT) of monkeys (Macaca fuscata). Recordings in all areas were made under conditions of anesthesia as close as possible to those in previous studies of oscillating responses in the cat. In addition, we recorded MUA in the IT of behaving monkeys while the monkeys performed a face discrimination task. 3. In areas V1 and MT, LFP power spectra showed broadband increases (1-100 Hz) in amplitude on stimulation by swept optimally oriented light bars, and not a shift in power from low to midfrequency, as has been reported in the cat. 4. MUA autocorrelograms (ACGs) classified by fitting Gabor functions, showed oscillations at approximately 10% of recording sites in V1 and MT, but these oscillations were in the alpha range (12-13 Hz). 5. MUA ACGs from IT in the anesthetized monkey showed no oscillations. 6. For MUA ACGs from IT in the behaving monkey, only two recording sites (out of 50) showed an oscillating response, with frequencies of 44 and 48 Hz. One oscillating response was associated with stimulation, and the other was associated with the absence of stimulation. 7. The very low incidence in the monkey of oscillating responses in the 30- to 70-Hz range (2 in 424 recordings made at 142 recording sites) and the absence of stimulus dependence suggest that such oscillations are unlikely to serve a function in the monkey, and that there may be a species difference between monkey and cat in the dynamics of neural activity in the visual cortex. 8. We found that methods of classifying responses as oscillating used in some of the studies of the cat may have led to overestimation of both the number of sites showing oscillation and the number of pairs of sites showing phase coherence. These problems arise from the failure to take account of badness of fit between Gabor functions and their corresponding ACGs, and from Gabor functions "ringing" in response to short phasic phenomena that could be consistent with nonoscillatory activity.