Encoding of Naturalistic Stimuli by Local Field Potential Spectra in Networks of Excitatory and Inhibitory Neurons

Recordings of local field potentials (LFPs) reveal that the sensory cortex displays rhythmic activity and fluctuations over a wide range of frequencies and amplitudes. Yet, the role of this kind of activity in encoding sensory information remains largely unknown. To understand the rules of translation between the structure of sensory stimuli and the fluctuations of cortical responses, we simulated a sparsely connected network of excitatory and inhibitory neurons modeling a local cortical population, and we determined how the LFPs generated by the network encode information about input stimuli. We first considered simple static and periodic stimuli and then naturalistic input stimuli based on electrophysiological recordings from the thalamus of anesthetized monkeys watching natural movie scenes. We found that the simulated network produced stimulus-related LFP changes that were in striking agreement with the LFPs obtained from the primary visual cortex. Moreover, our results demonstrate that the network encoded static input spike rates into gamma-range oscillations generated by inhibitory–excitatory neural interactions and encoded slow dynamic features of the input into slow LFP fluctuations mediated by stimulus–neural interactions. The model cortical network processed dynamic stimuli with naturalistic temporal structure by using low and high response frequencies as independent communication channels, again in agreement with recent reports from visual cortex responses to naturalistic movies. One potential function of this frequency decomposition into independent information channels operated by the cortical network may be that of enhancing the capacity of the cortical column to encode our complex sensory environment.     

Electrical signals propagate unbiased in cortex

The greater spatial coherence of local field potentials (LFPs) compared with that of spiking activity has been attributed to frequency-dependent propagation of signals through the cortical medium. However, in this issue of Neuron, Logothetis and colleagues show that signal propagation within cortex is largely unbiased across different frequencies, thus suggesting a more functional and interpretable basis of LFP coherence.     

In vivo measurement of cortical impedance spectrum in monkeys: implications for signal propagation

To combine insights obtained from electric field potentials (LFPs) and neuronal spiking activity (MUA) we need a better understanding of the relative spatial summation of these indices of neuronal activity. Compared to MUA, the LFP has greater spatial coherence, resulting in lower spatial specificity and lower stimulus selectivity. A differential propagation of low- and high-frequency electric signals supposedly underlies this phenomenon, which could result from cortical tissue specifically attenuating higher frequencies, i.e., from a frequency-dependent impedance spectrum. Here we directly measure the cortical impedance spectrum in vivo in monkey primary visual cortex. Our results show that impedance is independent of frequency, is homogeneous and tangentially isotropic within gray matter, and can be theoretically predicted assuming a pure-resistive conductor. We propose that the spatial summation of LFP and MUA is determined by the size of these signals' generators and the nature of neural events underlying them, rather than by biophysical properties of gray matter.     

How local is the local field potential?

Local field potentials (LFPs) are of growing importance in neurophysiological investigations. LFPs supplement action potential recordings by indexing activity relevant to EEG, magnetoencephalographic, and hemodynamic (fMRI) signals. Recent reports suggest that LFPs reflect activity within very small domains of several hundred micrometers. We examined this conclusion by comparing LFP, current source density (CSD), and multiunit activity (MUA) signals in macaque auditory cortex. Estimated by frequency tuning bandwidths, these signals' "listening areas" differ systematically with an order of MUA?< CSD?< LFP. Computational analyses confirm that observed LFPs receive local contributions. Direct measurements indicate passive spread of LFPs to sites more than a centimeter from their origins. These findings appear to be independent of the frequency content of the LFP. Our results challenge the idea that LFP recordings typically integrate over extremely circumscribed local domains. Rather, LFPs appear as a mixture of local potentials with "volume conducted" potentials from distant sites.     

Application of matched filtering to identify behavioral modulation of brain oscillations

Brain oscillations modulated by motor behaviors are coupled to steady-state and other potentially unrelated to movement oscillations, with energy in the same frequency bands as the signals of interest. We applied matched filtering, a quasi-optimum signal detection technique, to decouple and extract movement-related signals from local field potentials (LFPs) recorded in monkey motor cortical areas during the execution of a visually instructed reach-out task. Using a matched-filterbank, we examined coupling and interference of pre-movement and initial steady-state oscillations with movement-induced signals. Once these signal contributions were eliminated, we were able to identify significant correlations of the residual signals with behavioral parameters, which appeared attenuated by pre-movement signal interference in the raw LFPs. Specifically, the maximum and minimum amplitudes of filtered LFPs were directly modulated by peak movement velocity and micro-movements, respectively, identified in recorded hand velocity profiles. In addition, we identified phase correlations between signals during the delay (when the instructional cue was presented) and movement intervals, as well as modulation of LFP phase by movement direction. For pairs of orthogonal movement directions, corresponding LFP signals were consistently out of phase. Finally, β-band energy which is typically reduced during movement execution, possibly partly due to destructive interference between the modulated by behavior signal and unrelated oscillations, appeared to be recovered in the filtered signals.     

The local and non-local components of the local field potential in awake primate visual cortex

The Local Field Potential (LFP) is the analog signal recorded from a microelectrode inserted into cortex, typically in the frequency band of approximately 1 to 200 Hz. Here visual stimuli were flashed on in the receptive fields of primary visual cortical neurons in awake behaving macaques, and both isolated single units (neurons) and the LFP signal were recorded from the same unipolar microelectrode. The fall-off of single unit activity as a visual stimulus was moved from near the center to near the edge of the receptive field paralleled the fall-off of the stimulus-locked (evoked) LFP response. This suggests that the evoked LFP strongly reflects local neuronal activity. However, the evoked LFP could be significant even when the visual stimulus was completely outside the receptive field and the single unit response had fallen to zero, although this phenomenon was variable. Some of the non-local components of the LFP may be related to the slow distributed, or non-retinotopic, LFP signal previously observed in anesthetized animals. The induced (not time-locked to stimulus onset) component of the LFP showed significant increases only for stimuli within the receptive field of the single units. While the LFP primarily reflects local neuronal activity, it can also reflect neuronal activity at more distant sites, although these non-local components are typically more variable, slower, and weaker than the local components.     

Predicting stimulus-locked single unit spiking from cortical local field potentials

The rapidly increasing use of the local field potential (LFP) has motivated research to better understand its relation to the gold standard of neural activity, single unit (SU) spiking. We addressed this in an in vivo, awake, restrained mouse auditory cortical electrophysiology preparation by asking whether the LFP could actually be used to predict stimulus-evoked SU spiking. Implementing a Bayesian algorithm to predict the likelihood of spiking on a trial by trial basis from different representations of the despiked LFP signal, we were able to predict, with high quality and fine temporal resolution (2 ms), the time course of a SU’s excitatory or inhibitory firing rate response to natural species-specific vocalizations. Our best predictions were achieved by representing the LFP by its wide-band Hilbert phase signal, and approximating the statistical structure of this signal at different time points as independent. Our results show that each SU’s action potential has a unique relationship with the LFP that can be reliably used to predict the occurrence of spikes. This “signature” interaction can reflect both pre- and post-spike neural activity that is intrinsic to the local circuit rather than just dictated by the stimulus. Finally, the time course of this “signature” may be most faithful when the full bandwidth of the LFP, rather than specific narrow-band components, is used for representation.     

Predicting spike occurrence and neuronal responsiveness from LFPs in primary somatosensory cortex

Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neuronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role.     

Local field potentials indicate network state and account for neuronal response variability

Multineuronal recordings have revealed that neurons in primary visual cortex (V1) exhibit coordinated fluctuations of spiking activity in the absence and in the presence of visual stimulation. From the perspective of understanding a single cell’s spiking activity relative to a behavior or stimulus, these network fluctuations are typically considered to be noise. We show that these events are highly correlated with another commonly recorded signal, the local field potential (LFP), and are also likely related to global network state phenomena which have been observed in a number of neural systems. Moreover, we show that attributing a component of cell firing to these network fluctuations via explicit modeling of the LFP improves the recovery of cell properties. This suggests that the impact of network fluctuations may be estimated using the LFP, and that a portion of this network activity is unrelated to the stimulus and instead reflects ongoing cortical activity. Thus, the LFP acts as an easily accessible bridge between the network state and the spiking activity.     

Cortical Neurovascular Coupling Driven by Stimulation of Channelrhodopsin-2

While functional imaging is widely used in studies of the brain, how well the hemodynamic signal represents the underlying neural activity is still unclear. And there is a debate on whether hemodynamic signal is more tightly related to synaptic activity or action potentials. This study intends to address these questions by examining neurovascular coupling driven by pyramidal cells in the motor cortex of rats. Pyramidal cells in the motor cortex of rats were selectively transduced with the light sensitive cation channel channelrhodopsin-2 (ChR2). Electrophysiological recordings and optical intrinsic signal imaging were performed simultaneously and synchronously to capture the neural activity and hemodynamics induced by optical stimulation of ChR2-expressing pyramidal cells. Our results indicate that both synaptic activity (local field potential, LFP) and action potentials (multi-unit activity, MUA) are tightly related to hemodynamic signals. While LFPs in γ band are better in predicting hemodynamic signals elicited by short stimuli, MUA has better predictions to hemodynamic signals elicited by long stimuli. Our results also indicate that strong nonlinearity exists in neurovascular coupling.     

Neuronal Functional Connection Graphs among Multiple Areas of the Rat Somatosensory System during Spontaneous and Evoked Activities

Small-World Networks (SWNs) represent a fundamental model for the comprehension of many complex man-made and biological networks. In the central nervous system, SWN models have been shown to fit well both anatomical and functional maps at the macroscopic level. However, the functional microscopic level, where the nodes of a network are represented by single neurons, is still poorly understood. At this level, although recent evidences suggest that functional connection graphs exhibit small-world organization, it is not known whether and how these maps, potentially distributed in multiple brain regions, change across different conditions, such as spontaneous and stimulus-evoked activities. We addressed these questions by analyzing the data from simultaneous multi-array extracellular recordings in three brain regions of rats, diversely involved in somatosensory information processing: the ventropostero-lateral thalamic nuclei, the primary somatosensory cortex and the centro-median thalamic nuclei. From both spike and Local Field Potential (LFP) recordings, we estimated the functional connection graphs by using the Normalized Compression Similarity for spikes and the Phase Synchrony for LFPs. Then, by using graph-theoretical statistics, we characterized the functional topology both during spontaneous activity and sensory stimulation. Our main results show that: (i) spikes and LFPs show SWN organization during spontaneous activity; (ii) after stimulation onset, while substantial functional graph reconfigurations occur both in spike and LFPs, small-worldness is nonetheless preserved; (iii) the stimulus triggers a significant increase of inter-area LFP connections without modifying the topology of intra-area functional connections. Finally, investigating computationally the functional substrate that supports the observed phenomena, we found that (iv) the fundamental concept of cell assemblies, transient groups of activating neurons, can be described by small-world networks. Our results suggest that activity of neurons from multiple areas of the rat somatosensory system contributes to the integration of local computations arisen in distributed functional cell assemblies according to the principles of SWNs.     

Measurements of simultaneously recorded spiking activity and local field potentials suggest that spatial selection emerges in the frontal eye field

The frontal eye field (FEF) participates in selecting the location of behaviorally relevant stimuli for guiding attention and eye movements. We simultaneously recorded local field potentials (LFPs) and spiking activity in the FEF of monkeys performing memory-guided saccade and covert visual search tasks. We compared visual latencies and the time course of spatially selective responses in LFPs and spiking activity. Consistent with the view that LFPs represent synaptic input, visual responses appeared first in the LFPs followed by visual responses in the spiking activity. However, spatially selective activity identifying the location of the target in the visual search array appeared in the spikes about 30 ms before it appeared in the LFPs. Because LFPs reflect dendritic input and spikes measure neuronal output in a local brain region, this temporal relationship suggests that spatial selection necessary for attention and eye movements is computed locally in FEF from spatially nonselective inputs.     

A Simple Stimulatory Device for Evoking Point-like Tactile Stimuli: A Searchlight for LFP to Spike Transitions

Current neurophysiological research has the aim to develop methodologies to investigate the signal route from neuron to neuron, namely in the transitions from spikes to Local Field Potentials (LFPs) and from LFPs to spikes.LFPs have a complex dependence on spike activity and their relation is still poorly understood¹. The elucidation of these signal relations would be helpful both for clinical diagnostics (e.g. stimulation paradigms for Deep Brain Stimulation) and for a deeper comprehension of neural coding strategies in normal and pathological conditions (e.g. epilepsy, Parkinson disease, chronic pain). To this aim, one has to solve technical issues related to stimulation devices, stimulation paradigms and computational analyses. Therefore, a custom-made stimulation device was developed in order to deliver stimuli well regulated in space and time that does not incur in mechanical resonance. Subsequently, as an exemplification, a set of reliable LFP-spike relationships was extracted.The performance of the device was investigated by extracellular recordings, jointly spikes and LFP responses to the applied stimuli, from the rat Primary Somatosensory cortex. Then, by means of a multi-objective optimization strategy, a predictive model for spike occurrence based on LFPs was estimated.The application of this paradigm shows that the device is adequately suited to deliver high frequency tactile stimulation, outperforming common piezoelectric actuators. As a proof of the efficacy of the device, the following results were presented: 1) the timing and reliability of LFP responses well match the spike responses, 2) LFPs are sensitive to the stimulation history and capture not only the average response but also the trial-to-trial fluctuations in the spike activity and, finally, 3) by using the LFP signal it is possible to estimate a range of predictive models that capture different aspects of the spike activity.     

Frequency Dependence of Signal Power and Spatial Reach of the Local Field Potential

Despite its century-old use, the interpretation of local field potentials (LFPs), the low-frequency part of electrical signals recorded in the brain, is still debated. In cortex the LFP appears to mainly stem from transmembrane neuronal currents following synaptic input, and obvious questions regarding the ‘locality’ of the LFP are: What is the size of the signal-generating region, i.e., the spatial reach, around a recording contact? How far does the LFP signal extend outside a synaptically activated neuronal population? And how do the answers depend on the temporal frequency of the LFP signal? Experimental inquiries have given conflicting results, and we here pursue a modeling approach based on a well-established biophysical forward-modeling scheme incorporating detailed reconstructed neuronal morphologies in precise calculations of population LFPs including thousands of neurons. The two key factors determining the frequency dependence of LFP are the spatial decay of the single-neuron LFP contribution and the conversion of synaptic input correlations into correlations between single-neuron LFP contributions. Both factors are seen to give low-pass filtering of the LFP signal power. For uncorrelated input only the first factor is relevant, and here a modest reduction (<50%) in the spatial reach is observed for higher frequencies (>100 Hz) compared to the near-DC () value of about . Much larger frequency-dependent effects are seen when populations of pyramidal neurons receive correlated and spatially asymmetric inputs: the low-frequency () LFP power can here be an order of magnitude or more larger than at 60 Hz. Moreover, the low-frequency LFP components have larger spatial reach and extend further outside the active population than high-frequency components. Further, the spatial LFP profiles for such populations typically span the full vertical extent of the dendrites of neurons in the population. Our numerical findings are backed up by an intuitive simplified model for the generation of population LFP.     

Subthalamic local field beta oscillations during ongoing deep brain stimulation in Parkinson's disease in hyperacute and chronic phases

In the past years, local field potential (LFP) signals recorded from the subthalamic nucleus (STN) in patients undergoing deep brain stimulation (DBS) for Parkinson's disease (PD) disclosed that DBS has a controversial effect on STN beta oscillations recorded 2-7 days after surgery for macroelectrode implantation. Nothing is known about these DBS-induced oscillatory changes 30 days after surgery. We recorded STN LFPs during ongoing DBS in 7 patients with PD, immediately (hyperacute phase) and 30 days (chronic phase) after surgery. STN LFP recordings showed stationary intranuclear STN beta LFP activity in hyperacute and chronic phases, confirming that beta peaks were also present in chronic recordings. Power spectra of nuclei with significant beta activity (54% of the sample) showed that it decreased significantly during DBS (p=0.021) under both recording conditions. The time course of beta activity showed more evident DBS-induced changes in the chronic than in the hyperacute phase (p=0.014). DBS-induced changes in STN beta LFPs in patients undergoing DBS in chronic phase provide useful information for developing a new neurosignal-controlled adaptive DBS system.     

Neurophysiology of the BOLD fMRI signal in awake monkeys

BACKGROUND: Simultaneous intracortical recordings of neural activity and blood-oxygen-level-dependent (BOLD) functional magnetic resonance imaging (fMRI) in primary visual cortex of anesthetized monkeys demonstrated varying degrees of correlation between fMRI signals and the different types of neural activity, such as local field potentials (LFPs), multiple-unit activity (MUA), and single-unit activity (SUA). One important question raised by the aforementioned investigation is whether the reported correlations also apply to alert subjects. RESULTS: Monkeys were trained to perform a fixation task while stimuli within the receptive field of each recording site were used to elicit neural responses followed by a BOLD response. We show -- also in alert behaving monkeys -- that although both LFP and MUA make significant contributions to the BOLD response, LFPs are better and more reliable predictors of the BOLD signal. Moreover, when MUA responses adapt but LFP remains unaffected, the BOLD signal remains unaltered. CONCLUSIONS: The persistent coupling of the BOLD signal to the field potential when LFP and MUA have different time evolutions suggests that BOLD is primarily determined by the local processing of inputs in a given cortical area. In the alert animal the largest portion of the BOLD signal's variance is explained by an LFP range (20-60 Hz) that is most likely related to neuromodulation. Finally, the similarity of the results in alert and anesthetized subjects indicates that at least in V1 anesthesia is not a confounding factor. This enables the comparison of human fMRI results with a plethora of electrophysiological results obtained in alert or anesthetized animals.     

Coherence Potentials: Loss-Less,All-or-None Network Events in the Cortex

Transient associations among neurons are thought to underlie memory and behavior. However, little is known about how such associations occur or how they can be identified. Here we recorded ongoing local field potential (LFP) activity at multiple sites within the cortex of awake monkeys and organotypic cultures of cortex. We show that when the composite activity of a local neuronal group exceeds a threshold, its activity pattern, as reflected in the LFP, occurs without distortion at other cortex sites via fast synaptic transmission. These large-amplitude LFPs, which we call coherence potentials, extend up to hundreds of milliseconds and mark periods of loss-less spread of temporal and amplitude information much like action potentials at the single-cell level. However, coherence potentials have an additional degree of freedom in the diversity of their waveforms, which provides a high-dimensional parameter for encoding information and allows identification of particular associations. Such nonlinear behavior is analogous to the spread of ideas and behaviors in social networks.     

Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models

Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best “LFP proxy”, we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with “ground-truth” LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.     

Spatial Representations in Local Field Potential Activity of Primate Anterior Intraparietal Cortex (AIP)

The execution of reach-to-grasp movements in order to interact with our environment is an important subset of the human movement repertoire. To coordinate such goal-directed movements, information about the relative spatial position of target and effector (in this case the hand) has to be continuously integrated and processed. Recently, we reported the existence of spatial representations in spiking-activity of the cortical fronto-parietal grasp network (Lehmann & Scherberger 2013), and in particular in the anterior intraparietal cortex (AIP). To further investigate the nature of these spatial representations, we explored in two rhesus monkeys (Macaca mulatta) how different frequency bands of the local field potential (LFP) in AIP are modulated by grip type, target position, and gaze position, during the planning and execution of reach-to-grasp movements. We systematically varied grasp type, spatial target, and gaze position and found that both spatial and grasp information were encoded in a variety of frequency bands (1–13Hz, 13–30Hz, 30–60Hz, and 60–100Hz, respectively). Whereas the representation of grasp type strongly increased towards and during movement execution, spatial information was represented throughout the task. Both spatial and grasp type representations could be readily decoded from all frequency bands. The fact that grasp type and spatial (reach) information was found not only in spiking activity, but also in various LFP frequency bands of AIP, might significantly contribute to the development of LFP-based neural interfaces for the control of upper limb prostheses.