Macroscopic models of local field potentials and the apparent 1/f noise in brain activity

Advanced qEEG analyses discriminate between dementia subtypes

BACKGROUND

Dementia is caused by neurodegenerative conditions and characterized by cognitive decline. Diagnostic accuracy for dementia subtypes, such as Alzheimer's Disease (AD), Dementia with Lewy Bodies (DLB) and Parkinson's Disease with dementia (PDD), remains challenging.

METHODS

Here, different methods of quantitative electroencephalography (qEEG) analyses were employed to assess their effectiveness in distinguishing dementia subtypes from healthy controls under eyes closed (EC) and eyes open (EO) conditions.

RESULTS

Classic Fast-Fourier Transform (FFT) and autoregressive (AR) power analyses differentiated between all conditions for the 4-8 Hz theta range. Only individuals with dementia with Lewy Bodies (DLB) differed from healthy subjects for the wider 4-15 Hz frequency range, encompassing the actual dominant frequency of all individuals. FFT results for this range yielded wider significant discriminators vs AR, also detecting differences between AD and DLB. Analyses of the inclusive dominant / peak frequency range (4-15 Hz) indicated slowing and reduced variability, also discriminating between synucleinopathies vs controls and AD. Dissociation of periodic oscillations and aperiodic components of AR spectra using Fitting-Oscillations-&-One-Over-F (FOOOF) modelling delivered a reliable and subtype-specific slowing of brain oscillatory peaks during EC and EO for all groups. Distinct and robust differences were particularly strong for aperiodic parameters, suggesting their potential diagnostic power in detecting specific changes resulting from age and cognitive status.

CONCLUSION

Our findings indicate that qEEG methods can reliably detect dementia subtypes. Spectral analyses comprising an integrated, multi-parameter EEG approach discriminating between periodic and aperiodic components under EC and EO conditions may enhance diagnostic accuracy in the future.

Simulation-based Inference of Developmental EEG Maturation with the Spectral Graph Model

The spectral content of macroscopic neural activity evolves throughout development, yet how this maturation relates to underlying brain network formation and dynamics remains unknown. Here, we assess the developmental maturation of electroencephalogram spectra via Bayesian model inversion of the spectral graph model, a parsimonious whole-brain model of spatiospectral neural activity derived from linearized neural field models coupled by the structural connectome. Simulation-based inference was used to estimate age-varying spectral graph model parameter posterior distributions from electroencephalogram spectra spanning the developmental period. This model-fitting approach accurately captures observed developmental electroencephalogram spectral maturation via a neurobiologically consistent progression of key neural parameters: long-range coupling, axonal conduction speed, and excitatory:inhibitory balance. These results suggest that the spectral maturation of macroscopic neural activity observed during typical development is supported by age-dependent functional adaptations in localized neural dynamics and their long-range coupling across the macroscopic structural network.

Tracing conflict-induced cognitive-control adjustments over time using aperiodic EEG activity

Cognitive-control theories assume that the experience of response conflict can trigger control adjustments. However, while some approaches focus on adjustments that impact the selection of the present response (in trial N), other approaches focus on adjustments in the next upcoming trial  (N + 1). We aimed to trace control adjustments over time by quantifying cortical noise by means of the fitting oscillations and one over f algorithm, a measure of aperiodic activity. As predicted, conflict trials increased the aperiodic exponent in a large sample of 171 healthy adults, thus indicating noise reduction. While this adjustment was visible in trial N already, it did not affect response selection before the next trial. This suggests that control adjustments do not affect ongoing response-selection processes but prepare the system for tighter control in the next trial. We interpret the findings in terms of a conflict-induced switch from metacontrol flexibility to metacontrol persistence, accompanied or even implemented by a reduction of cortical noise.

Aperiodic components of local field potentials reflect inherent differences between cortical and subcortical activity

Information flow in brain networks is reflected in local field potentials that have both periodic and aperiodic components. The 1/fχ aperiodic component of the power spectra tracks arousal and correlates with other physiological and pathophysiological states. Here we explored the aperiodic activity in the human thalamus and basal ganglia in relation to simultaneously recorded cortical activity. We elaborated on the parameterization of the aperiodic component implemented by specparam (formerly known as FOOOF) to avoid parameter unidentifiability and to obtain independent and more easily interpretable parameters. This allowed us to seamlessly fit spectra with and without an aperiodic knee, a parameter that captures a change in the slope of the aperiodic component. We found that the cortical aperiodic exponent χ, which reflects the decay of the aperiodic component with frequency, is correlated with Parkinson's disease symptom severity. Interestingly, no aperiodic knee was detected from the thalamus, the pallidum, or the subthalamic nucleus, which exhibited an aperiodic exponent significantly lower than in cortex. These differences were replicated in epilepsy patients undergoing intracranial monitoring that included thalamic recordings. The consistently lower aperiodic exponent and lack of an aperiodic knee from all subcortical recordings may reflect cytoarchitectonic and/or functional differences.

SIGNIFICANCE STATEMENT

The aperiodic component of local field potentials can be modeled to produce useful and reproducible indices of neural activity. Here we refined a widely used phenomenological model for extracting aperiodic parameters (namely the exponent, offset and knee), with which we fit cortical, basal ganglia, and thalamic intracranial local field potentials, recorded from unique cohorts of movement disorders and epilepsy patients. We found that the aperiodic exponent in motor cortex is higher in Parkinson's disease patients with more severe motor symptoms, suggesting that aperiodic features may have potential as electrophysiological biomarkers for movement disorders symptoms. Remarkably, we found conspicuous differences in the aperiodic parameters of basal ganglia and thalamic signals compared to those from neocortex.

A Full-wave Solution of Deep Sources in the Lossy Human Head to Accurate Electroencephalography and Magnetoencephalography

Introduction

Currents in the brain flow inside neurons and across their boundaries into the extracellular medium, create electric and magnetic fields. These fields, which contain suitable information on brain activity, can be measured by electroencephalography (EEG), magnetoencephalography (MEG), and direct neural imaging.

Methods

In this paper, we employed an electromagnetic model of the neuron activity and human head to derive electric and magnetic fields (brain waves) using a full-wave approach (ie. without any approximation). Currently, the brain waves are only derived using the quasi-static approximation (QSA) of Maxwell's equations in electromagnetic theory.

Results

As a result, source localization in brain imaging will produce some errors. So far, the error rate of the QSA on the output results of electric and magnetic fields has not been investigated. This issue has become more noticeable due to the increased sensitivity of modern electroencephalography (EEG) and magnetoencephalography (MEG) devices. This work introduces issues that QSA encounters in this problem and reveals the necessity of a full-wave solution. Then, a full-wave solution of the problem in closed-form format is presented for the first time. This solution is done in two scenarios: the source (active neurons) is in the center of a sphere, and when the source is out of the center but deeply inside the sphere. The first scenario is simpler, but the second one is much more complicated and is solved using a partial-wave series expression.

Conclusion

One of the significant achievements of this model is improving the interpretation of EEG and MEG measurements, resulting in more accurate source localization.

Cortical origin of theta error signals

A multi-scale approach elucidated the origin of the error-related-negativity (ERN), with its associated theta-rhythm, and the post-error-positivity (Pe) in macaque supplementary eye field (SEF). Using biophysical modeling, synaptic inputs to a subpopulation of layer-3 (L3) and layer-5 (L5) pyramidal cells (PCs) were optimized to reproduce error-related spiking modulation and inter-spike intervals. The intrinsic dynamics of dendrites in L5 but not L3 error PCs generate theta rhythmicity with random phases. Saccades synchronized the phases of the theta-rhythm, which was magnified on errors. Contributions from error PCs to the laminar current source density (CSD) observed in SEF were negligible and could not explain the observed association between error-related spiking modulation in L3 PCs and scalp-EEG. CSD from recorded laminar field potentials in SEF was comprised of multipolar components, with monopoles indicating strong electro-diffusion, dendritic/axonal electrotonic current leakage outside SEF, or violations of the model assumptions. Our results also demonstrate the involvement of secondary cortical regions, in addition to SEF, particularly for the later Pe component. The dipolar component from the observed CSD paralleled the ERN dynamics, while the quadrupolar component paralleled the Pe. These results provide the most advanced explanation to date of the cellular mechanisms generating the ERN.

Resting EEG power spectra across middle to late life: associations with age, cognition, APOE-ɛ4 carriage, and cardiometabolic burden

We investigated how resting electroencephalography (EEG) measures are associated with risk factors for late-life cognitive impairment and dementia, including age, apolipoprotein E ɛ4 (APOE-ɛ4) carriage, and cardiometabolic burden. Resting EEG was recorded from 86 adults (50-80 years of age). Participants additionally completed the Addenbrooke's Cognitive Examination (ACE) III and had blood drawn to assess APOE-ɛ4 carriage status and cardiometabolic burden. EEG power spectra were decomposed into sources of periodic and aperiodic activity to derive measures of aperiodic component slope and alpha (7-14 Hz) and beta (15-30 Hz) peak power and peak frequency. Alpha and beta peak power measures were corrected for aperiodic activity. The aperiodic component slope was correlated with ACE-III scores but not age. Alpha peak frequency decreased with age. Individuals with higher cardiometabolic burden had lower alpha peak frequencies and lower beta peak power. APOE-ɛ4 carriers had lower beta peak frequencies. Our findings suggest that the slope of the aperiodic component of resting EEG power spectra is more closely associated with measures of cognitive performance rather than chronological age in older adults.

Isolation of the murine Glut1 deficient thalamocortical circuit: wavelet characterization and reverse glucose dependence of low and gamma frequency oscillations

Glucose represents the principal brain energy source. Thus, not unexpectedly, genetic glucose transporter 1 (Glut1) deficiency (G1D) manifests with encephalopathy. G1D seizures, which constitute a prominent disease manifestation, often prove refractory to medications but may respond to therapeutic diets. These seizures are associated with aberrant thalamocortical oscillations as inferred from human electroencephalography and functional imaging. Mouse electrophysiological recordings indicate that inhibitory neuron failure in thalamus and cortex underlies these abnormalities. This provides the motivation to develop a neural circuit testbed to characterize the mechanisms of thalamocortical synchronization and the effects of known or novel interventions. To this end, we used mouse thalamocortical slices on multielectrode arrays and characterized spontaneous low frequency oscillations and less frequent 30-50 Hz or gamma oscillations under near-physiological bath glucose concentration. Using the cortical recordings from layer IV among other regions recorded, we quantified oscillation epochs via an automated wavelet-based algorithm. This method proved analytically superior to power spectral density, short-time Fourier transform or amplitude-threshold detection. As expected from human observations, increased bath glucose reduced the lower frequency oscillations while augmenting the gamma oscillations, likely reflecting strengthened inhibitory neuron activity, and thus decreasing the low:high frequency ratio (LHR). This approach provides an ex vivo method for the evaluation of mechanisms, fuels, and pharmacological agents in a crucial G1D epileptogenic circuit.

Isolation of the murine Glut1 deficient thalamocortical circuit: wavelet characterization and reverse glucose dependence of low and gamma frequency oscillations

Glucose represents the principal brain energy source. Thus, not unexpectedly, genetic glucose transporter 1 (Glut1) deficiency (G1D) manifests with encephalopathy. G1D seizures, which constitute a prominent disease manifestation, often prove refractory to medications but may respond to therapeutic diets. These seizures are associated with aberrant thalamocortical oscillations as inferred from human electroencephalography and functional imaging. Mouse electrophysiological recordings indicate that inhibitory neuron failure in thalamus and cortex underlies these abnormalities. This provides the motivation to develop a neural circuit testbed to characterize the mechanisms of thalamocortical synchronization and the effects of known or novel interventions. To this end, we used mouse thalamocortical slices on multielectrode arrays and characterized spontaneous low frequency oscillations and less frequent 30-50 Hz or gamma oscillations under near-physiological bath glucose concentration. Using the cortical recordings from layer IV, we quantified oscillation epochs via an automated wavelet-based algorithm. This method proved analytically superior to power spectral density, short-time Fourier transform or amplitude-threshold detection. As expected from human observations, increased bath glucose reduced the lower frequency oscillations while augmenting the gamma oscillations, likely reflecting strengthened inhibitory neuron activity. This approach provides an ex vivo method for the evaluation of mechanisms, fuels, and pharmacological agents in a crucial G1D epileptogenic circuit.

Slope of the power spectral density flattens at low frequencies (<150 Hz) with healthy aging but also steepens at higher frequency (>200 Hz) in human electroencephalogram

The power spectral density (PSD) of the brain signals is characterized by two distinct features: oscillations, which are represented as distinct "bumps," and broadband aperiodic activity, that reduces in power with increasing frequency and is characterized by the slope of the power falloff. Recent studies have shown a change in the slope of the aperiodic activity with healthy aging and mental disorders. However, these studies analyzed slopes over a limited frequency range (<100 Hz). To test whether the PSD slope is affected over a wider frequency range with aging and mental disorder, we analyzed the slope till 800 Hz in electroencephalogram data recorded from elderly subjects (>49 years) who were healthy (n = 217) or had mild cognitive impairment (MCI; n = 11) or Alzheimer's Disease (AD; n = 5). Although the slope reduced up to ~ 150 Hz with healthy aging (as shown previously), surprisingly, at higher frequencies (>200 Hz), it increased with age. These results were observed in all electrodes, for both eyes open and eyes closed conditions, and for different reference schemes. However, slopes were not significantly different in MCI/AD subjects compared with healthy controls. Overall, our results constrain the biophysical mechanisms that are reflected in the PSD slopes in healthy and pathological aging.

Validating MEG source imaging of resting state oscillatory patterns with an intracranial EEG atlas

BACKGROUND

Magnetoencephalography (MEG) is a widely used non-invasive tool to estimate brain activity with high temporal resolution. However, due to the ill-posed nature of the MEG source imaging (MSI) problem, the ability of MSI to identify accurately underlying brain sources along the cortical surface is still uncertain and requires validation.

METHOD

We validated the ability of MSI to estimate the background resting state activity of 45 healthy participants by comparing it to the intracranial EEG (iEEG) atlas (https://mni-open-ieegatlas.

RESEARCH

mcgill.ca/). First, we applied wavelet-based Maximum Entropy on the Mean (wMEM) as an MSI technique. Next, we converted MEG source maps into intracranial space by applying a forward model to the MEG-reconstructed source maps, and estimated virtual iEEG (ViEEG) potentials on each iEEG channel location; we finally quantitatively compared those with actual iEEG signals from the atlas for 38 regions of interest in the canonical frequency bands.

RESULTS

The MEG spectra were more accurately estimated in the lateral regions compared to the medial regions. The regions with higher amplitude in the ViEEG than in the iEEG were more accurately recovered. In the deep regions, MEG-estimated amplitudes were largely underestimated and the spectra were poorly recovered. Overall, our wMEM results were similar to those obtained with minimum norm or beamformer source localization. Moreover, the MEG largely overestimated oscillatory peaks in the alpha band, especially in the anterior and deep regions. This is possibly due to higher phase synchronization of alpha oscillations over extended regions, exceeding the spatial sensitivity of iEEG but detected by MEG. Importantly, we found that MEG-estimated spectra were more comparable to spectra from the iEEG atlas after the aperiodic components were removed.

CONCLUSION

This study identifies brain regions and frequencies for which MEG source analysis is likely to be reliable, a promising step towards resolving the uncertainty in recovering intracerebral activity from non-invasive MEG studies.

Decreased aperiodic neural activity in Parkinson's disease and dementia with Lewy bodies

Neural oscillations and signal complexity have been widely studied in neurodegenerative diseases, whereas aperiodic activity has not been explored yet in those disorders. Here, we assessed whether the study of aperiodic activity brings new insights relating to disease as compared to the conventional spectral and complexity analyses. Eyes-closed resting-state electroencephalography (EEG) was recorded in 21 patients with dementia with Lewy bodies (DLB), 28 patients with Parkinson's disease (PD), 27 patients with mild cognitive impairment (MCI) and 22 age-matched healthy controls. Spectral power was differentiated into its oscillatory and aperiodic components using the Irregularly Resampled Auto-Spectral Analysis. Signal complexity was explored using the Lempel-Ziv algorithm (LZC). We found that DLB patients showed steeper slopes of the aperiodic power component with large effect sizes compared to the controls and MCI and with a moderate effect size compared to PD. PD patients showed steeper slopes with a moderate effect size compared to controls and MCI. Oscillatory power and LZC differentiated only between DLB and other study groups and were not sensitive enough to detect differences between PD, MCI, and controls. In conclusion, both DLB and PD are characterized by alterations in aperiodic dynamics, which are more sensitive in detecting disease-related neural changes than the traditional spectral and complexity analyses. Our findings suggest that steeper aperiodic slopes may serve as a marker of network dysfunction in DLB and PD features.

Glutamatergic and GABAergic Receptor Modulation Present Unique Electrophysiological Fingerprints in a Concentration-Dependent and Region-Specific Manner

Brain function depends on complex circuit interactions between excitatory and inhibitory neurons embedded in local and long-range networks. Systemic GABAA-receptor (GABAAR) or NMDA-receptor (NMDAR) modulation alters the excitatory-inhibitory balance (EIB), measurable with electroencephalography (EEG). However, EEG signatures are complex in localization and spectral composition. We developed and applied analytical tools to investigate the effects of two EIB modulators, MK801 (NMDAR antagonist) and diazepam (GABAAR modulator), on periodic and aperiodic EEG features in freely-moving male Sprague Dawley rats. We investigated how, across three brain regions, EEG features are correlated with EIB modulation. We found that the periodic component was composed of seven frequency bands that presented region-dependent and compound-dependent changes. The aperiodic component was also different between compounds and brain regions. Importantly, the parametrization into periodic and aperiodic components unveiled correlations between quantitative EEG and plasma concentrations of pharmacological compounds. MK-801 exposures were positively correlated with the slope of the aperiodic component. Concerning the periodic component, MK-801 exposures correlated negatively with the peak frequency of low-γ oscillations but positively with those of high-γ and high-frequency oscillations (HFOs). As for the power, θ and low-γ oscillations correlated negatively with MK-801, whereas mid-γ correlated positively. Diazepam correlated negatively with the knee of the aperiodic component, positively to β and negatively to low-γ oscillatory power, and positively to the modal frequency of θ, low-γ, mid-γ, and high-γ. In conclusion, correlations between exposures and pharmacodynamic effects can be better-understood thanks to the parametrization of EEG into periodic and aperiodic components. Such parametrization could be key in functional biomarker discovery.

Broadband aperiodic components of local field potentials reflect inherent differences between cortical and subcortical activity

Information flow in brain networks is reflected in intracerebral local field potential (LFP) measurements that have both periodic and aperiodic components. The 1/fχ broadband aperiodic component of the power spectra has been shown to track arousal level and to correlate with other physiological and pathophysiological states, with consistent patterns across cortical regions. Previous studies have focused almost exclusively on cortical neurophysiology. Here we explored the aperiodic activity of subcortical nuclei from the human thalamus and basal ganglia, in relation to simultaneously recorded cortical activity. We elaborated on the FOOOF (fitting of one over f) method by creating a new parameterization of the aperiodic component with independent and more easily interpretable parameters, which allows seamlessly fitting spectra with and without an aperiodic knee, a component of the signal that reflects the dominant timescale of aperiodic fluctuations. First, we found that the aperiodic exponent from sensorimotor cortex in Parkinson's disease (PD) patients correlated with disease severity. Second, although the aperiodic knee frequency changed across cortical regions as previously reported, no aperiodic knee was detected from subcortical regions across movement disorders patients, including the ventral thalamus (VIM), globus pallidus internus (GPi) and subthalamic nucleus (STN). All subcortical region studied exhibited a relatively low aperiodic exponent (χSTN=1.3±0.2, χVIM=1.4±0.1, χGPi =1.4±0.1) that differed markedly from cortical values (χCortex=3.2±0.4, fkCortex=17±5 Hz). These differences were replicated in a second dataset from epilepsy patients undergoing intracranial monitoring that included thalamic recordings. The consistently lower aperiodic exponent and lack of an aperiodic knee from all subcortical recordings may reflect cytoarchitectonic and/or functional differences between subcortical nuclei and the cortex.

Long-Term Recording of Subthalamic Aperiodic Activities and Beta Bursts in Parkinson's Disease

BACKGROUND

Local field potentials (LFPs) represent the summation of periodic (oscillations) and aperiodic (fractal) signals. Although previous studies showed changes in beta band oscillations and burst characteristics of the subthalamic nucleus (STN) in Parkinson's disease (PD), how aperiodic activity in the STN is related to PD pathophysiology is unknown.

OBJECTIVES

The study aimed to characterize the long-term effects of STN-deep brain stimulation (DBS) and dopaminergic medications on aperiodic activities and beta bursts.

METHODS

A total of 10 patients with PD participated in this longitudinal study. Simultaneous bilateral STN-LFP recordings were conducted in six separate visits during a period of 18 months using the Activa PC + S device in the off and on dopaminergic medication states. We used irregular-resampling auto-spectral analysis to separate oscillations and aperiodic components (exponent and offset) in the power spectrum of STN-LFP signals in beta band.

RESULTS

Our results revealed a systematic increase in both the exponent and the offset of the aperiodic spectrum over 18 months following the DBS implantation, independent of the dopaminergic medication state of patients with PD. In contrast, beta burst durations and amplitudes were stable over time and were suppressed by dopaminergic medications.

CONCLUSIONS

These findings indicate that oscillations and aperiodic activities reflect at least partially distinct yet complementary neural mechanisms, which should be considered in the design of robust biomarkers to optimize adaptive DBS. Given the link between increased gamma-aminobutyric acidergic (GABAergic) transmission and higher aperiodic activity, our findings suggest that long-term STN-DBS may relate to increased inhibition in the basal ganglia. © 2022 International Parkinson and Movement Disorder Society.

Unveiling age-independent spectral markers of propofol-induced loss of consciousness by decomposing the electroencephalographic spectrum into its periodic and aperiodic components

Background

Induction of general anesthesia with propofol induces radical changes in cortical network organization, leading to unconsciousness. While perioperative frontal electroencephalography (EEG) has been widely implemented in the past decades, validated and age-independent EEG markers for the timepoint of loss of consciousness (LOC) are lacking. Especially the appearance of spatially coherent frontal alpha oscillations (8-12 Hz) marks the transition to unconsciousness.Here we explored whether decomposing the EEG spectrum into its periodic and aperiodic components unveiled markers of LOC and investigated their age-dependency. We further characterized the LOC-associated alpha oscillations by parametrizing the adjusted power over the aperiodic component, the center frequency, and the bandwidth of the peak in the alpha range.

Methods

In this prospective observational trial, EEG were recorded in a young (18-30 years) and an elderly age-cohort (≥ 70 years) over the transition to propofol-induced unconsciousness. An event marker was set in the EEG recordings at the timepoint of LOC, defined with the suppression of the lid closure reflex. Spectral analysis was conducted with the multitaper method. Aperiodic and periodic components were parametrized with the FOOOF toolbox. Aperiodic parametrization comprised the exponent and the offset. The periodic parametrization consisted in the characterization of the peak in the alpha range with its adjusted power, center frequency and bandwidth. Three time-segments were defined: preLOC (105 - 75 s before LOC), LOC (15 s before to 15 s after LOC), postLOC (190 - 220 s after LOC). Statistical significance was determined with a repeated-measures ANOVA.

Results

Loss of consciousness was associated with an increase in the aperiodic exponent (young: p = 0.004, elderly: p = 0.007) and offset (young: p = 0.020, elderly: p = 0.004) as well as an increase in the adjusted power (young: p < 0.001, elderly p = 0.011) and center frequency (young: p = 0.008, elderly: p < 0.001) of the periodic alpha peak. We saw age-related differences in the aperiodic exponent and offset after LOC as well as in the power and bandwidth of the periodic alpha peak during LOC.

Conclusion

Decomposing the EEG spectrum over induction of anesthesia into its periodic and aperiodic components unveiled novel age-independent EEG markers of propofol-induced LOC: the aperiodic exponent and offset as well as the center frequency and adjusted power of the power peak in the alpha range.

Inter-individual variability in dorsal stream dynamics during word production

The current standard model of language production involves a sensorimotor dorsal stream connecting areas in the temporo-parietal junction with those in the inferior frontal gyrus and lateral premotor cortex. These regions have been linked to various aspects of word production such as phonological processing or articulatory programming, primarily through neuropsychological and functional imaging group studies. Most if not all the theoretical descriptions of this model imply that the same network should be identifiable across individual speakers. We tested this hypothesis by quantifying the variability of activation observed across individuals within each dorsal stream anatomical region. This estimate was based on electrical activity recorded directly from the cerebral cortex with millisecond accuracy in awake epileptic patients clinically implanted with intracerebral depth electrodes for pre-surgical diagnosis. Each region's activity was quantified using two different metrics-intra-cerebral evoked related potentials and high gamma activity-at the level of the group, the individual and the recording contact. The two metrics show simultaneous activation of parietal and frontal regions during a picture naming task, in line with models that posit interactive processing during word retrieval. They also reveal different levels of between-patient variability across brain regions, except in core auditory and motor regions. The independence and non-uniformity of cortical activity estimated through the two metrics push the current model towards sub-second and sub-region explorations focused on individualized language speech production. Several hypotheses are considered for this within-region heterogeneity.

State space methods for phase amplitude coupling analysis

Phase amplitude coupling (PAC) is thought to play a fundamental role in the dynamic coordination of brain circuits and systems. There are however growing concerns that existing methods for PAC analysis are prone to error and misinterpretation. Improper frequency band selection can render true PAC undetectable, while non-linearities or abrupt changes in the signal can produce spurious PAC. Current methods require large amounts of data and lack formal statistical inference tools. We describe here a novel approach for PAC analysis that substantially addresses these problems. We use a state space model to estimate the component oscillations, avoiding problems with frequency band selection, nonlinearities, and sharp signal transitions. We represent cross-frequency coupling in parametric and time-varying forms to further improve statistical efficiency and estimate the posterior distribution of the coupling parameters to derive their credible intervals. We demonstrate the method using simulated data, rat local field potentials (LFP) data, and human EEG data.

Site-dependent shaping of field potential waveforms

The activity of neuron populations gives rise to field potentials (FPs) that extend beyond the sources. Their mixing in the volume dilutes the original temporal motifs in a site-dependent manner, a fact that has received little attention. And yet, it potentially rids of physiological significance the time-frequency parameters of individual waves (amplitude, phase, duration). This is most likely to happen when a single source or a local origin is erroneously assumed. Recent studies using spatial treatment of these signals and anatomically realistic modeling of neuron aggregates provide convincing evidence for the multisource origin and site-dependent blend of FPs. Thus, FPs generated in primary structures like the neocortex and hippocampus reach far and cross-contaminate each other but also, they add and even impose their temporal traits on distant regions. Furthermore, both structures house neurons that act as spatially distinct (but overlapped) FP sources whose activation is state, region, and time dependent, making the composition of so-called local FPs highly volatile and strongly site dependent. Since the spatial reach cannot be predicted without source geometry, it is important to assess whether waveforms and temporal motifs arise from a single source; otherwise, those from each of the co-active sources should be sought.

Spectral and spatial distribution of subthalamic beta peak activity in Parkinson's disease patients

Current efforts to optimize subthalamic deep brain stimulation in Parkinson's disease patients aim to harness local oscillatory activity in the beta frequency range (13-35 Hz) as a feedback-signal for demand-based adaptive stimulation paradigms. A high prevalence of beta peak activity is prerequisite for this approach to become routine clinical practice. In a large dataset of postoperative rest recordings from 106 patients we quantified occurrence and identified determinants of spectral peaks in the alpha, low and high beta bands. At least one peak in beta band occurred in 92% of patients and 84% of hemispheres off medication, irrespective of demographic parameters, clinical subtype or motor symptom severity. Distance to previously described clinical sweet spot was significantly related both to beta peak occurrence and to spectral power (rho -0.21, p 0.006), particularly in the high beta band. Electrophysiological landscapes of our cohort's dataset in normalised space showed divergent heatmaps for alpha and beta but found similar regions for low and high beta frequency bands. We discuss potential ramifications for clinicians' programming decisions. In summary, this report provides robust evidence that spectral peaks in beta frequency range can be detected in the vast majority of Parkinsonian subthalamic nuclei, increasing confidence in the broad applicability of beta-guided deep brain stimulation.

Simulating epileptic seizures using the bidomain model

Epileptic seizures are due to excessive and synchronous neural activity. Extensive modelling of seizures has been done on the neuronal level, but it remains a challenge to scale these models up to whole brain models. Measurements of the brain's activity over several spatiotemporal scales follow a power-law distribution in terms of frequency. During normal brain activity, the power-law exponent is often found to be around 2 for frequencies between a few Hz and up to 150 Hz, but is higher during seizures and for higher frequencies. The Bidomain model has been used with success in modelling the electrical activity of the heart, but has been explored far less in the context of the brain. This study extends previous models of epileptic seizures on the neuronal level to the whole brain using the Bidomain model. Our approach is evaluated in terms of power-law distributions. The electric potentials were simulated in 7 idealized two-dimensional models and 3 three-dimensional patient-specific models derived from magnetic resonance images (MRI). Computed electric potentials were found to follow power-law distributions with slopes ranging from 2 to 5 for frequencies greater than 10-30 Hz.

Extracellular and intracellular components of the impedance of neural tissue

Electric phenomena in brain tissue can be measured using extracellular potentials, such as the local field potential, or the electro-encephalogram. The interpretation of these signals depends on the electric structure and properties of extracellular media, but the measurements of these electric properties are still debated. Some measurements point to a model in which the extracellular medium is purely resistive, and thus parameters such as electric conductivity and permittivity should be independent of frequency. Other measurements point to a pronounced frequency dependence of these parameters, with scaling laws that are consistent with capacitive or diffusive effects. However, these experiments correspond to different preparations, and it is unclear how to correctly compare them. Here, we provide for the first time, impedance measurements (in the 1-10 kHz frequency range) using the same setup in various preparations, from primary cell cultures to acute brain slices, and a comparison with similar measurements performed in artificial cerebrospinal fluid with no biological material. The measurements show that when the current flows across a cell membrane, the frequency dependence of the macroscopic impedance between intracellular and extracellular electrodes is significant, and cannot be captured by a model with resistive media. Fitting a mean-field model to the data shows that this frequency dependence could be explained by the ionic diffusion mainly associated with Debye layers surrounding the membranes. We conclude that neuronal membranes and their ionic environment induce strong deviations to resistivity that should be taken into account to correctly interpret extracellular potentials generated by neurons.

Monofractal analysis of functional magnetic resonance imaging: An introductory review

The following review will aid readers in providing an overview of scale-free dynamics and monofractal analysis, as well as its applications and potential in functional magnetic resonance imaging (fMRI) neuroscience and clinical research. Like natural phenomena such as the growth of a tree or crashing ocean waves, the brain expresses scale-invariant, or fractal, patterns in neural signals that can be measured. While neural phenomena may represent both monofractal and multifractal processes and can be quantified with many different interrelated parameters, this review will focus on monofractal analysis using the Hurst exponent (H). Monofractal analysis of fMRI data is an advanced analysis technique that measures the complexity of brain signaling by quantifying its degree of scale-invariance. As such, the H value of the blood oxygenation level-dependent (BOLD) signal specifies how the degree of correlation in the signal may mediate brain functions. This review presents a brief overview of the theory of fMRI monofractal analysis followed by notable findings in the field. Through highlighting the advantages and challenges of the technique, the article provides insight into how to best conduct fMRI fractal analysis and properly interpret the findings with physiological relevance. Furthermore, we identify the future directions necessary for its progression towards impactful functional neuroscience discoveries and widespread clinical use. Ultimately, this presenting review aims to build a foundation of knowledge among readers to facilitate greater understanding, discussion, and use of this unique yet powerful imaging analysis technique.

Fractal-Based Analysis of fMRI BOLD Signal During Naturalistic Viewing Conditions

Background: Temporal fractals are characterized by prominent scale-invariance and self-similarity across time scales. Monofractal analysis quantifies this scaling behavior in a single parameter, the Hurst exponent (H). Higher H reflects greater correlation in the signal structure, which is taken as being more fractal. Previous fMRI studies have observed lower H during conventional tasks relative to resting state conditions, and shown that H is negatively correlated with task difficulty and novelty. To date, no study has investigated the fractal dynamics of BOLD signal during naturalistic conditions. Methods: We performed fractal analysis on Human Connectome Project 7T fMRI data (n = 72, 41 females, mean age 29.46 ± 3.76 years) to compare H across movie-watching and rest. Results: In contrast to previous work using conventional tasks, we found higher H values for movie relative to rest (mean difference = 0.014; p = 5.279 × 10^-7; 95% CI [0.009, 0.019]). H was significantly higher in movie than rest in the visual, somatomotor and dorsal attention networks, but was significantly lower during movie in the frontoparietal and default networks. We found no cross-condition differences in test-retest reliability of H. Finally, we found that H of movie-derived stimulus properties (e.g., luminance changes) were fractal whereas H of head motion estimates were non-fractal. Conclusions: Overall, our findings suggest that movie-watching induces fractal signal dynamics. In line with recent work characterizing connectivity-based brain state dynamics during movie-watching, we speculate that these fractal dynamics reflect the configuring and reconfiguring of brain states that occurs during naturalistic processing, and are markedly different than dynamics observed during conventional tasks.

Directed Spectral Measures Improve Latent Network Models Of Neural Populations

Systems neuroscience aims to understand how networks of neurons distributed throughout the brain mediate computational tasks. One popular approach to identify those networks is to first calculate measures of neural activity (e.g. power spectra) from multiple brain regions, and then apply a linear factor model to those measures. Critically, despite the established role of directed communication between brain regions in neural computation, measures of directed communication have been rarely utilized in network estimation because they are incompatible with the implicit assumptions of the linear factor model approach. Here, we develop a novel spectral measure of directed communication called the Directed Spectrum (DS). We prove that it is compatible with the implicit assumptions of linear factor models, and we provide a method to estimate the DS. We demonstrate that latent linear factor models of DS measures better capture underlying brain networks in both simulated and real neural recording data compared to available alternatives. Thus, linear factor models of the Directed Spectrum offer neuroscientists a simple and effective way to explicitly model directed communication in networks of neural populations.

Fly seizure EEG: field potential activity in the Drosophila brain

Hypersynchronous neural activity is a characteristic feature of seizures. Although many Drosophila mutants of epilepsy-related genes display clear behavioral spasms and motor unit hyperexcitability, field potential measurements of aberrant hypersynchronous activity across brain regions during seizures have yet to be described. Here, we report a straightforward method to observe local field potentials (LFPs) from the Drosophila brain to monitor ensemble neural activity during seizures in behaving tethered flies. High frequency stimulation across the brain reliably triggers a stereotypic sequence of electroconvulsive seizure (ECS) spike discharges readily detectable in the dorsal longitudinal muscle (DLM) and coupled with behavioral spasms. During seizure episodes, the LFP signal displayed characteristic large-amplitude oscillations with a stereotypic temporal correlation to DLM flight muscle spiking. ECS-related LFP events were clearly distinct from rest- and flight-associated LFP patterns. We further characterized the LFP activity during different types of seizures originating from genetic and pharmacological manipulations. In the 'bang-sensitive' sodium channel mutant bangsenseless (bss), the LFP pattern was prolonged, and the temporal correlation between LFP oscillations and DLM discharges was altered. Following administration of the pro-convulsant GABA_A blocker picrotoxin, we uncovered a qualitatively different LFP activity pattern, which consisted of a slow (1-Hz), repetitive, waveform, closely coupled with DLM bursting and behavioral spasms. Our approach to record brain LFPs presents an initial framework for electrophysiological analysis of the complex brain-wide activity patterns in the large collection of Drosophila excitability mutants.

Conductance of porous media depends on external electric fields

In obstacle-filled media, such as extracellular or intracellular lumen of brain tissue, effective ion-diffusion permeability is a key determinant of electrogenic reactions. Although this diffusion permeability is thought to depend entirely on structural features of the medium, such as porosity and tortuosity, brain tissue shows prominent nonohmic properties, the origins of which remain poorly understood. Here, we explore Monte Carlo simulations of ion diffusion in a space filled with overlapping spheres to predict that diffusion permeability of such media decreases with stronger external electric fields. This dependence increases with lower medium porosity while decreasing with radial (two-dimensional or three-dimensional) compared with homogenous (one-dimensional) fields. We test our predictions empirically in an electrolyte chamber filled with microscopic glass spheres and find good correspondence with our predictions. A theoretical insight relates this phenomenon to a disproportionately increased dwell time of diffusing ions at potential barriers (or traps) representing geometric obstacles when the field strength increases. The dependence of medium ion-diffusion permeability on electric field could be important for understanding conductivity properties of porous materials, in particular for the accurate interpretation of electric activity recordings in brain tissue.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Ambiguity in the interpretation of the low-frequency dielectric properties of biological tissues

The frequency-dependent behaviour of the dielectric properties of biological tissues in the frequency range below 1 kHz has been under debate since the past century. Here, we reanalyse the raw data of the main resource of the dielectric properties of biological tissues in impedance representation. Employing a Kramers-Kronig validity test and parameter estimation techniques, we can describe the data by two physical parametric models that correspond to opposing biophysical interpretations: on the one hand the data can be explained only by intrinsic tissue properties, but on the other hand evidence for electrode-specific effects can be found for all tissues under investigation. The first interpretation would justify the continued use of a parametric model comprising four Cole-Cole dispersions, which describe the dielectric properties from extremely low to very high frequencies. As an alternative that is in accordance with the second interpretation, we suggest to omit the slowest of the four dispersions in the model and increase the static conductivity to account for a frequency-independent conductivity below 1 kHz.

A proof of concept 'phase zero' study of neurodevelopment using brain organoid models with Vis/near-infrared spectroscopy and electrophysiology

Homeostatic control of neuronal excitability by modulation of synaptic inhibition (I) and excitation (E) of the principal neurons is important during brain maturation. The fundamental features of in-utero brain development, including local synaptic E-I ratio and bioenergetics, can be modeled by cerebral organoids (CO) that have exhibited highly regular nested oscillatory network events. Therefore, we evaluated a 'Phase Zero' clinical study platform combining broadband Vis/near-infrared(NIR) spectroscopy and electrophysiology with studying E-I ratio based on the spectral exponent of local field potentials and bioenergetics based on the activity of mitochondrial Cytochrome-C Oxidase (CCO). We found a significant effect of the age of the healthy controls iPSC CO from 23 days to 3 months on the CCO activity (chi-square (2, N = 10) = 20, p = 4.5400e-05), and spectral exponent between 30-50 Hz (chi-square (2, N = 16) = 13.88, p = 0.001). Also, a significant effect of drugs, choline (CHO), idebenone (IDB), R-alpha-lipoic acid plus acetyl-L-carnitine (LCLA), was found on the CCO activity (chi-square (3, N = 10) = 25.44, p = 1.2492e-05), spectral exponent between 1 and 20 Hz (chi-square (3, N = 16) = 43.5, p = 1.9273e-09) and 30-50 Hz (chi-square (3, N = 16) = 23.47, p = 3.2148e-05) in 34 days old CO from schizophrenia (SCZ) patients iPSC. We present the feasibility of a multimodal approach, combining electrophysiology and broadband Vis-NIR spectroscopy, to monitor neurodevelopment in brain organoid models that can complement traditional drug design approaches to test clinically meaningful hypotheses.

Multifractal and Entropy-Based Analysis of Delta Band Neural Activity Reveals Altered Functional Connectivity Dynamics in Schizophrenia

Dynamic functional connectivity (DFC) was established in the past decade as a potent approach to reveal non-trivial, time-varying properties of neural interactions – such as their multifractality or information content –, that otherwise remain hidden from conventional static methods. Several neuropsychiatric disorders were shown to be associated with altered DFC, with schizophrenia (SZ) being one of the most intensely studied among such conditions. Here we analyzed resting-state electroencephalography recordings of 14 SZ patients and 14 age- and gender-matched healthy controls (HC). We reconstructed dynamic functional networks from delta band (0.5–4 Hz) neural activity and captured their spatiotemporal dynamics in various global network topological measures. The acquired network measure time series were made subject to dynamic analyses including multifractal analysis and entropy estimation. Besides group-level comparisons, we built a classifier to explore the potential of DFC features in classifying individual cases. We found stronger delta-band connectivity, as well as increased variance of DFC in SZ patients. Surrogate data testing verified the true multifractal nature of DFC in SZ, with patients expressing stronger long-range autocorrelation and degree of multifractality when compared to controls. Entropy analysis indicated reduced temporal complexity of DFC in SZ. When using these indices as features, an overall cross-validation accuracy surpassing 89% could be achieved in classifying individual cases. Our results imply that dynamic features of DFC such as its multifractal properties and entropy are potent markers of altered neural dynamics in SZ and carry significant potential not only in better understanding its pathophysiology but also in improving its diagnosis. The proposed framework is readily applicable for neuropsychiatric disorders other than schizophrenia.

Pallidal 1/f asymmetry in patients with cervical dystonia

Lateralized differences in pallidal outflow are putatively linked to asymmetric tonic contractions of the neck muscles in cervical dystonia (CD). At the population level, the interhemispheric asymmetry has been traditionally studied for the estimation of the spectral power in specified frequency bands. Broadband spectral features, however, were not taken into consideration. The contemporary analysis revealed that the aperiodic (1/f) broadband activity could be a neurophysiological marker of the excitation/inhibition ratio. During deep brain stimulation (DBS) surgery, we measured bilateral pallidal local field potentials (LFP) in nine CD patients, examining the effects of lateralized asymmetry on 1/f broadband activity. All patients showed a trend towards an asymmetric difference in the 1/f broadband activity. The ipsilateral 1/f slope was significantly higher in internal (GPi) segment of the globus pallidus that is on the contralateral side of the direction of the dystonia. We also found lateralized differences in the beta oscillations for GPi and in the alpha oscillations for GPe. Our findings emphasize the importance of mainstreaming broadband activity in the estimation of LFP spectral features together with periodic features and provide further evidence for the pallidal asymmetry in CD patients.

Random Recurrent Networks Near Criticality Capture the Broadband Power Distribution of Human ECoG Dynamics

Brain electric field potentials are dominated by an arrhythmic broadband signal, but the underlying mechanism is poorly understood. Here we propose that broadband power spectra characterize recurrent neural networks of nodes (neurons or clusters of neurons), endowed with an effective balance between excitation and inhibition tuned to keep the network on the edge of dynamical instability. These networks show a fast mode reflecting local dynamics and a slow mode emerging from distributed recurrent connections. Together, the 2 modes produce power spectra similar to those observed in human intracranial EEG (i.e., electrocorticography, ECoG) recordings. Moreover, such networks convert spatial input correlations across nodes into temporal autocorrelation of network activity. Consequently, increased independence between nodes reduces low-frequency power, which may explain changes observed during behavioral tasks. Lastly, varying network coupling causes activity changes that resemble those observed in human ECoG across different arousal states. The model links macroscopic features of empirical ECoG power to a parsimonious underlying network structure, and suggests mechanisms for changes observed across behavioral and arousal states. This work provides a computational framework to generate and test hypotheses about cellular and network mechanisms underlying whole brain electrical dynamics, their variations across states, and potential alterations in brain diseases.

Criticality as a Determinant of Integrated Information Φ in Human Brain Networks

Integrated information theory (IIT) describes consciousness as information integrated across highly differentiated but irreducible constituent parts in a system. However, in a complex dynamic system such as the brain, the optimal conditions for large integrated information systems have not been elucidated. In this study, we hypothesized that network criticality, a balanced state between a large variation in functional network configuration and a large constraint on structural network configuration, may be the basis of the emergence of a large Φ¯, a surrogate of integrated information. We also hypothesized that as consciousness diminishes, the brain loses network criticality and Φ¯ decreases. We tested these hypotheses with a large-scale brain network model and high-density electroencephalography (EEG) acquired during various levels of human consciousness under general anesthesia. In the modeling study, maximal criticality coincided with maximal Φ¯. The EEG study demonstrated an explicit relationship between Φ¯, criticality, and level of consciousness. The conscious resting state showed the largest Φ¯ and criticality, whereas the balance between variation and constraint in the brain network broke down as the response rate dwindled. The results suggest network criticality as a necessary condition of a large Φ¯ in the human brain.

Electro-plasmonic nanoantenna: A nonfluorescent optical probe for ultrasensitive label-free detection of electrophysiological signals

Harnessing the unprecedented spatiotemporal resolution capability of light to detect electrophysiological signals has been the goal of scientists for nearly 50 years. Yet, progress toward that goal remains elusive due to lack of electro-optic translators that can efficiently convert electrical activity to high photon count optical signals. Here, we introduce an ultrasensitive and extremely bright nanoscale electric-field probe overcoming the low photon count limitations of existing optical field reporters. Our electro-plasmonic nanoantennas with drastically enhanced cross sections (~10⁴ nm² compared to typical values of ~10^-2 nm² for voltage-sensitive fluorescence dyes and ~1 nm² for quantum dots) offer reliable detection of local electric-field dynamics with remarkably high sensitivities and signal-to-shot noise ratios (~60 to 220) from diffraction-limited spots. In our electro-optics experiments, we demonstrate high-temporal resolution electric-field measurements at kilohertz frequencies and achieved label-free optical recording of network-level electrogenic activity of cardiomyocyte cells with low-intensity light (11 mW/mm²).

Field potential 1/f activity in the subcallosal cingulate region as a candidate signal for monitoring deep brain stimulation for treatment-resistant depression

Subcallosal cingulate cortex deep brain stimulation (SCC-DBS) is an experimental therapy for treatment-resistant depression (TRD). Refinement and optimization of SCC-DBS will benefit from increased study of SCC electrophysiology in context of ongoing high-frequency SCC-DBS therapy. The study objective was a 7-mo observation of frequency-domain 1/f slope in off-stimulation local field potentials (SCC-LFPs) alongside standardized measurements of depression severity in 4 patients undergoing SCC-DBS. SCC was implanted bilaterally with a combined neurostimulation-LFP recording system. Following a 1-mo off-stimulation postoperative phase with multiple daily recordings, patients received bilateral SCC-DBS therapy (130 Hz, 90 μs) and weekly resting-state SCC-LFP recordings over a 6-mo treatment phase. 1/f slopes for each time point were estimated via linear regression of log-transformed Welch periodograms. General linear mixed-effects models were constructed to estimate pretreatment sources of 1/f slope variance, and 95% bootstrap confidence intervals were constructed to estimate treatment phase 1/f slope association with treatment response (50% decrease in preimplantation symptom severity). Results show the time of recording was a prominent source of pretreatment 1/f slope variance bilaterally, with increased 1/f slope magnitude observed during night hours (2300-0659). Increase in right 1/f slope was observed in the setting of treatment response, with bootstrap analysis supporting this observation in 3 of 4 subjects. We conclude that 1/f slope can be measured longitudinally in a combined SCC-DBS/LFP recording system and likely conforms to known 1/f circadian variability. The preliminary evidence of 1/f slope increase during treatment response suggests a potential utility as a candidate biomarker for ongoing development of adaptive TRD-neuromodulation strategies.NEW & NOTEWORTHY In four patients with treatment-resistant depression undergoing therapeutic deep brain stimulation (DBS), we present the first longitudinal observations of local field potentials (LFP) from the subcallosal cingulate region outside the postoperative period. Specifically, our results demonstrate that frequency-domain 1/f activity is measurable in a combined DBS-LFP recording system and that right hemisphere recordings appear sensitive to mood state, thus suggesting a potential readout suitable for consideration in ongoing efforts to develop adaptive DBS delivery systems.

PyPNS: Multiscale Simulation of a Peripheral Nerve in Python

Bioelectronic Medicines that modulate the activity patterns on peripheral nerves have promise as a new way of treating diverse medical conditions from epilepsy to rheumatism. Progress in the field builds upon time consuming and expensive experiments in living organisms. To reduce experimentation load and allow for a faster, more detailed analysis of peripheral nerve stimulation and recording, computational models incorporating experimental insights will be of great help. We present a peripheral nerve simulator that combines biophysical axon models and numerically solved and idealised extracellular space models in one environment. We modelled the extracellular space as a three-dimensional resistive continuum governed by the electro-quasistatic approximation of the Maxwell equations. Potential distributions were precomputed in finite element models for different media (homogeneous, nerve in saline, nerve in cuff) and imported into our simulator. Axons, on the other hand, were modelled more abstractly as one-dimensional chains of compartments. Unmyelinated fibres were based on the Hodgkin-Huxley model; for myelinated fibres, we adapted the model proposed by McIntyre et al. in 2002 to smaller diameters. To obtain realistic axon shapes, an iterative algorithm positioned fibres along the nerve with a variable tortuosity fit to imaged trajectories. We validated our model with data from the stimulated rat vagus nerve. Simulation results predicted that tortuosity alters recorded signal shapes and increases stimulation thresholds. The model we developed can easily be adapted to different nerves, and may be of use for Bioelectronic Medicine research in the future.

The Impact of Frequency Scale on the Response Sensitivity and Reliability of Cortical Neurons to 1/fβ Input Signals

What type of principle features intrinsic inside of the fluctuated input signals could drive neurons with the maximal excitations is one of the crucial neural coding issues. In this article, we examined both experimentally and theoretically the cortical neuronal responsivity (including firing rate and spike timing reliability) to input signals with different intrinsic correlational statistics (e.g., white-type noise, showed 1/f0 power spectrum, pink noise 1/f, and brown noises 1/f2) and different frequency ranges. Our results revealed that the response sensitivity and reliability of cortical neurons is much higher in response to 1/f noise stimuli with long-term correlations than 1/f0 with short-term correlations for a broad frequency range, and also higher than 1/f2 for all frequency ranges. In addition, we found that neuronal sensitivity diverges to opposite directions for 1/f noise comparing with 1/f0 white noise as a function of cutoff frequency of input signal. As the cutoff frequency is progressively increased from 50 to 1,000 Hz, the neuronal responsiveness increased gradually for 1/f noise, while decreased exponentially for white noise. Computational simulations of a general cortical model revealed that, neuronal sensitivity and reliability to input signal statistics was majorly dominated by fast sodium inactivation, potassium activation, and membrane time constants.

Cortical Electrocorticogram (ECoG) Is a Local Signal

Electrocorticogram (ECoG), obtained by low-pass filtering the brain signal recorded from a macroelectrode placed on the cortex, is extensively used to find the seizure focus in drug-resistant epilepsy and is of growing importance in cognitive and brain-machine-interfacing studies. To accurately estimate the epileptogenic cortex or to make inferences about cognitive processes, it is important to determine the "spatial spread" of ECoG (i.e., the extent of cortical tissue that contributes to its activity). However, the ECoG spread is currently unknown; even the spread of local field potential (LFP) obtained from microelectrodes is debated, with estimates ranging from a few hundred micrometers to several millimeters. Spatial spread can be estimated by measuring the receptive field (RF) and multiplying by the cortical magnification factor, but this method overestimates the spread because RF size gets inflated due to several factors. This issue can be partially addressed using a model that compares the RFs of two measures, such as LFP and multi-unit activity (MUA). To use this approach for ECoG, we designed a customized array containing both microelectrodes and ECoG electrodes to simultaneously map MUA, LFP, and ECoG RFs from the primary visual cortex of awake monkeys (three female Macaca radiata). The spatial spread of ECoG was surprisingly local (diameter ∼3 mm), only 3 times that of the LFP. Similar results were obtained using a model to simulate ECoG as a sum of LFPs of varying electrode sizes. Our results further validate the use of ECoG in clinical and basic cognitive research.SIGNIFICANCE STATEMENT Brains signals capture different attributes of the neural network depending on the size and location of the recording electrode. Electrocorticogram (ECoG), obtained by placing macroelectrodes (typically 2-3 mm diameter) on the exposed surface of the cortex, is widely used by neurosurgeons to identify the source of seizures in drug-resistant epileptic patients. The brain area responsible for seizures is subsequently surgically removed. Accurate estimation of the epileptogenic cortex and its removal requires the estimation of spatial spread of ECoG. Here, we estimated the spatial spread of ECoG in five behaving monkeys using two different approaches. Our results suggest that ECoG is a local signal (diameter of ∼3 mm), which can provide a useful tool for clinical, cognitive neuroscience, and brain-machine-interfacing applications.

Is the Extracellular Impedance High and Non-resistive in Cerebral Cortex?

A recent commentary to Biophysical Journal criticized a previous study published in the same journal by Gomes et al. in 2016, and an alternative interpretation of the measurements was proposed. We reply here to these criticisms and provide some additional clarification, in particular, about a possible misinterpretation of the electrical circuit corresponding to these experiments. We suggest that, indeed, the extracellular impedance in cerebral cortex could be high and non-resistive, and we propose further experiments to settle this issue.

Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noise : Spontaneous activity in networks with synaptic noise

Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter diagram spanned by the relative inhibitory synaptic strength and the magnitude of synaptic noise. In absence of noise, networks display transient activity patterns, either oscillatory or at constant level. The effect of noise is to turn transient patterns into persistent ones: for weak noise, all activity patterns are asynchronous non-oscillatory independently of synaptic strengths; for stronger noise, patterns have oscillatory and synchrony characteristics that depend on the relative inhibitory synaptic strength. In the region of parameter space where inhibitory synaptic strength exceeds the excitatory synaptic strength and for moderate noise magnitudes networks feature intermittent switches between oscillatory and quiescent states with characteristics similar to those of synchronous and asynchronous cortical states, respectively. We explain these oscillatory and quiescent patterns by combining a phenomenological global description of the network state with local descriptions of individual neurons in their partial phase spaces. Our results point to a bridge from events at the molecular scale of synapses to the cellular scale of individual neurons to the collective scale of neuronal populations.

Biophysical basis of subthalamic local field potentials recorded from deep brain stimulation electrodes

Clinical deep brain stimulation (DBS) technology is evolving to enable chronic recording of local field potentials (LFPs) that represent electrophysiological biomarkers of the underlying disease state. However, little is known about the biophysical basis of LFPs, or how the patient's unique brain anatomy and electrode placement impact the recordings. Therefore, we developed a patient-specific computational framework to analyze LFP recordings within a clinical DBS context. We selected a subject with Parkinson's disease implanted with a Medtronic Activa PC+S DBS system and reconstructed their subthalamic nucleus (STN) and DBS electrode location using medical imaging data. The patient-specific STN volume was populated with 235,280 multicompartment STN neuron models, providing a neuron density consistent with histological measurements. Each neuron received time-varying synaptic inputs and generated transmembrane currents that gave rise to the LFP signal recorded at DBS electrode contacts residing in a finite element volume conductor model. We then used the model to study the role of synchronous beta-band inputs to the STN neurons on the recorded power spectrum. Three bipolar pairs of simultaneous clinical LFP recordings were used in combination with an optimization algorithm to customize the neural activity parameters in the model to the patient. The optimized model predicted a 2.4-mm radius of beta-synchronous neurons located in the dorsolateral STN. These theoretical results enable biophysical dissection of the LFP signal at the cellular level with direct comparison to the clinical recordings, and the model system provides a scientific platform to help guide the design of DBS technology focused on the use of subthalamic beta activity in closed-loop algorithms. NEW & NOTEWORTHY The analysis of deep brain stimulation of local field potential (LFP) data is rapidly expanding from scientific curiosity to the basis for clinical biomarkers capable of improving the therapeutic efficacy of stimulation. With this growing clinical importance comes a growing need to understand the underlying electrophysiological fundamentals of the signals and the factors contributing to their modulation. Our model reconstructs the clinical LFP from first principles and highlights the importance of patient-specific factors in dictating the signals recorded.

1/f electrophysiological spectra in resting and drug-induced states can be explained by the dynamics of multiple oscillatory relaxation processes

Neurophysiological recordings are dominated by arhythmical activity whose spectra can be characterised by power-law functions, and on this basis are often referred to as reflecting scale-free brain dynamics (1/f^β). Relatively little is known regarding the neural generators and temporal dynamics of this arhythmical behaviour compared to rhythmical behaviour. Here we used Irregularly Resampled AutoSpectral Analysis (IRASA) to quantify β, in both the high (5-100 Hz, β_hf) and low frequency bands (0.1-2.5 Hz, β_lf) in MEG/EEG/ECoG recordings and to separate arhythmical from rhythmical modes of activity, such as, alpha rhythms. In MEG/EEG/ECoG data, we demonstrate that oscillatory alpha power dynamically correlates over time with β_hf and similarly, participants with higher rhythmical alpha power have higher β_hf. In a series of pharmaco-MEG investigations using the GABA reuptake inhibitor tiagabine, the glutamatergic AMPA receptor antagonist perampanel, the NMDA receptor antagonist ketamine and the mixed partial serotonergic agonist LSD, a variety of effects on both β_hf and β_lf were observed. Additionally, strong modulations of β_hf were seen in monkey ECoG data during general anaesthesia using propofol and ketamine. We develop and test a unifying model which can explain, the 1/f nature of electrophysiological spectra, their dynamic interaction with oscillatory rhythms as well as the sensitivity of 1/f activity to drug interventions by considering electrophysiological spectra as being generated by a collection of stochastically perturbed damped oscillators having a distribution of relaxation rates.

Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation

New technologies to record electrical activity from the brain on a massive scale offer tremendous opportunities for discovery. Electrical measurements of large-scale brain dynamics, termed field potentials, are especially important to understanding and treating the human brain. Here, our goal is to provide best practices on how field potential recordings (electroencephalograms, magnetoencephalograms, electrocorticograms and local field potentials) can be analyzed to identify large-scale brain dynamics, and to highlight critical issues and limitations of interpretation in current work. We focus our discussion of analyses around the broad themes of activation, correlation, communication and coding. We provide recommendations for interpreting the data using forward and inverse models. The forward model describes how field potentials are generated by the activity of populations of neurons. The inverse model describes how to infer the activity of populations of neurons from field potential recordings. A recurring theme is the challenge of understanding how field potentials reflect neuronal population activity given the complexity of the underlying brain systems.

h-Type Membrane Current Shapes the Local Field Potential from Populations of Pyramidal Neurons

In cortex, the local field potential (LFP) is thought to mainly stem from correlated synaptic input to populations of geometrically aligned neurons. Computer models of single cortical pyramidal neurons showed that subthreshold voltage-dependent membrane conductances can also shape the LFP signal, in particular the hyperpolarization-activated cation current (I_h; h-type). This ion channel is prominent in various types of pyramidal neurons, typically showing an increasing density gradient along the apical dendrites. Here, we investigate how I_h affects the LFP generated by a model of a population of cortical pyramidal neurons. We find that the LFP from populations of neurons that receive uncorrelated synaptic input can be well predicted by the LFP from single neurons. In this case, when input impinges on the distal dendrites, where most h-type channels are located, a strong resonance in the LFP was measured near the soma, whereas the opposite configuration does not reveal an I_h contribution to the LFP. Introducing correlations in the synaptic inputs to the pyramidal cells strongly amplifies the LFP, while maintaining the differential effects of I_h for distal dendritic versus perisomatic input. Previous theoretical work showed that input correlations do not amplify LFP power when neurons receive synaptic input uniformly across the cell. We find that this crucially depends on the membrane conductance distribution: the asymmetric distribution of I_h results in a strong amplification of the LFP when synaptic inputs to the cell population are correlated. In conclusion, we find that the h-type current is particularly suited to shape the LFP signal in cortical populations.SIGNIFICANCE STATEMENT The local field potential (LFP), the low-frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. While the cortical LFP is thought to mainly reflect synaptic inputs onto pyramidal neurons, little is known about the role of subthreshold active conductances in shaping the LFP. By means of biophysical modeling we obtain a comprehensive, qualitative understanding of how LFPs generated by populations of cortical pyramidal neurons depend on active subthreshold currents, and identify the key importance of the h-type channel. Our results show that LFPs can give information about the active properties of neurons and that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Extrapolating meaning from local field potential recordings

Local field potentials (LFP) reflect the spatially weighted low-frequency activity nearest to a recording electrode. LFP recording is a window to a wide range of cellular activities and has gained increasing attention over recent years. We here review major conceptual issues related to LFP with the goal of creating a resource for non-experts considering implementing LFP into their research. We discuss the cellular activity that constitutes the local field potential; recording techniques, including recommendations and limitations; approaches to analysis of LFP data (with focus on power-banded analyses); and finally we discuss reports of the successful use of LFP in clinical applications.