Mathematical modeling and parameter estimation of axonal cargo transport

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

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.     

Methods for predicting cortical UP and DOWN states from the phase of deep layer local field potentials

During anesthesia, slow-wave sleep and quiet wakefulness, neuronal membrane potentials collectively switch between de- and hyperpolarized levels, the cortical UP and DOWN states. Previous studies have shown that these cortical UP/DOWN states affect the excitability of individual neurons in response to sensory stimuli, indicating that a significant amount of the trial-to-trial variability in neuronal responses can be attributed to ongoing fluctuations in network activity. However, as intracellular recordings are frequently not available, it is important to be able to estimate their occurrence purely from extracellular data. Here, we combine in vivo whole cell recordings from single neurons with multi-site extracellular microelectrode recordings, to quantify the performance of various approaches to predicting UP/DOWN states from the deep-layer local field potential (LFP). We find that UP/DOWN states in deep cortical layers of rat primary auditory cortex (A1) are predictable from the phase of LFP at low frequencies (< 4 Hz), and that the likelihood of a given state varies sinusoidally with the phase of LFP at these frequencies. We introduce a novel method of detecting cortical state by combining information concerning the phase of the LFP and ongoing multi-unit activity.     

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.     

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.     

Neurite growth-inhibitory activity in the adult rat cerebral cortical gray matter

Axon growth-promoting and -inhibitory molecules are likely to work in concert to promote and guide axons in vivo. In adult mammals, inhibitory molecules associated with myelin in the white matter of the central nervous system (CNS) play an important role in the failure of long-distance axon regeneration. The presence of neurite growth-inhibitory molecules in the adult rat gray matter has not been extensively studied. In this article we describe work on the characterization of neurite growth-inhibitory activity in the adult rat cerebral cortical gray matter using various biochemical and cell culture approaches. We show using a neuronal cell line (NG108–-15 cells) that neurite growth-inhibitory activity is present in membrane preparations of the cortical gray matter. Purified gray matter membranes also induce growth cone collapse of cultured embryonic rat dorsal root ganglion neurons. The inhibitory activity in the membrane preparations is extractable with 3-[(3-cholamidoprophyl)-dimethylammonio]-1-propane-sulfonate, but does not appear to be depleted by various lectins. Western blots and enzyme treatments showed that the inhibitory effect of the gray-matter preparations is not likely to be mediated by myelin-associated inhibitors or chondroitin sulfate proteoglycans. However, tenascin was detected in these samples and may contribute to some of the inhibitory activity. Selective separation of the inhibitory molecules can be achieved by ion-exchange chromatography, which also suggests the presence of multiple inhibitors in cortical gray matter membranes. © 1997 John Wiley & Sons, Inc. J Neurobiol 32 : 671–683, 1997     

Cortical local field potential encodes movement intentions in the posterior parietal cortex

The cortical local field potential (LFP) is a summation signal of excitatory and inhibitory dendritic potentials that has recently become of increasing interest. We report that LFP signals in the parietal reach region (PRR) of the posterior parietal cortex of macaque monkeys have temporal structure that varies with the type of planned or executed motor behavior. LFP signals from PRR provide better decode performance for reaches compared to saccades and have stronger coherency with simultaneously recorded spiking activity during the planning of reach movements than during saccade planning. LFP signals predict the animal's behavioral state (e.g., planning a reach or saccade) and the direction of the currently planned movement from single-trial information. This new evidence provides further support for a role of the parietal cortex in movement planning and the potential application of LFP signals for a brain-machine interface.     

Estimating the contribution of assembly activity to cortical dynamics from spike and population measures

The hypothesis that cortical networks employ the coordinated activity of groups of neurons, termed assemblies, to process information is debated. Results from multiple single-unit recordings are not conclusive because of the dramatic undersampling of the system. However, the local field potential (LFP) is a mesoscopic signal reflecting synchronized network activity. This raises the question whether the LFP can be employed to overcome the problem of undersampling. In a recent study in the motor cortex of the awake behaving monkey based on the locking of coincidences to the LFP we determined a lower bound for the fraction of spike coincidences originating from assembly activation. This quantity together with the locking of single spikes leads to a lower bound for the fraction of spikes originating from any assembly activity. Here we derive a statistical method to estimate the fraction of spike synchrony caused by assemblies—not its lower bound—from the spike data alone. A joint spike and LFP surrogate data model demonstrates consistency of results and the sensitivity of the method. Combining spike and LFP signals, we obtain an estimate of the fraction of spikes resulting from assemblies in the experimental data.     

Layer-specific fMRI reflects different neuronal computations at different depths in human V1

Recent work has established that cerebral blood flow is regulated at a spatial scale that can be resolved by high field fMRI to show cortical columns in humans. While cortical columns represent a cluster of neurons with similar response properties (spanning from the pial surface to the white matter), important information regarding neuronal interactions and computational processes is also contained within a single column, distributed across the six cortical lamina. A basic understanding of underlying neuronal circuitry or computations may be revealed through investigations of the distribution of neural responses at different cortical depths. In this study, we used T(2)-weighted imaging with 0.7 mm (isotropic) resolution to measure fMRI responses at different depths in the gray matter while human subjects observed images with either recognizable or scrambled (physically impossible) objects. Intact and scrambled images were partially occluded, resulting in clusters of activity distributed across primary visual cortex. A subset of the identified clusters of voxels showed a preference for scrambled objects over intact; in these clusters, the fMRI response in middle layers was stronger during the presentation of scrambled objects than during the presentation of intact objects. A second experiment, using stimuli targeted at either the magnocellular or the parvocellular visual pathway, shows that laminar profiles in response to parvocellular-targeted stimuli peak in more superficial layers. These findings provide new evidence for the differential sensitivity of high-field fMRI to modulations of the neural responses at different cortical depths.     

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.     

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.     

The Limited Utility of Multiunit Data in Differentiating Neuronal Population Activity

To date, single neuron recordings remain the gold standard for monitoring the activity of neuronal populations. Since obtaining single neuron recordings is not always possible, high frequency or ‘multiunit activity’ (MUA) is often used as a surrogate. Although MUA recordings allow one to monitor the activity of a large number of neurons, they do not allow identification of specific neuronal subtypes, the knowledge of which is often critical for understanding electrophysiological processes. Here, we explored whether prior knowledge of the single unit waveform of specific neuron types is sufficient to permit the use of MUA to monitor and distinguish differential activity of individual neuron types. We used an experimental and modeling approach to determine if components of the MUA can monitor medium spiny neurons (MSNs) and fast-spiking interneurons (FSIs) in the mouse dorsal striatum. We demonstrate that when well-isolated spikes are recorded, the MUA at frequencies greater than 100Hz is correlated with single unit spiking, highly dependent on the waveform of each neuron type, and accurately reflects the timing and spectral signature of each neuron. However, in the absence of well-isolated spikes (the norm in most MUA recordings), the MUA did not typically contain sufficient information to permit accurate prediction of the respective population activity of MSNs and FSIs. Thus, even under ideal conditions for the MUA to reliably predict the moment-to-moment activity of specific local neuronal ensembles, knowledge of the spike waveform of the underlying neuronal populations is necessary, but not sufficient.     

Theoretical Analysis of the Local Field Potential in Deep Brain Stimulation Applications

Deep brain stimulation (DBS) is a common therapy for treating movement disorders, such as Parkinson’s disease (PD), and provides a unique opportunity to study the neural activity of various subcortical structures in human patients. Local field potential (LFP) recordings are often performed with either intraoperative microelectrodes or DBS leads and reflect oscillatory activity within nuclei of the basal ganglia. These LFP recordings have numerous clinical implications and might someday be used to optimize DBS outcomes in closed-loop systems. However, the origin of the recorded LFP is poorly understood. Therefore, the goal of this study was to theoretically analyze LFP recordings within the context of clinical DBS applications. This goal was achieved with a detailed recording model of beta oscillations (∼20 Hz) in the subthalamic nucleus. The recording model consisted of finite element models of intraoperative microelectrodes and DBS macroelectrodes implanted in the brain along with multi-compartment cable models of STN projection neurons. Model analysis permitted systematic investigation into a number of variables that can affect the composition of the recorded LFP (e.g. electrode size, electrode impedance, recording configuration, and filtering effects of the brain, electrode-electrolyte interface, and recording electronics). The results of the study suggest that the spatial reach of the LFP can extend several millimeters. Model analysis also showed that variables such as electrode geometry and recording configuration can have a significant effect on LFP amplitude and spatial reach, while the effects of other variables, such as electrode impedance, are often negligible. The results of this study provide insight into the origin of the LFP and identify variables that need to be considered when analyzing LFP recordings in clinical DBS applications.     

Changes in the phasic activity of neuron microsystems of the somatosensory cortex of the cat during extinction of activation reactions to unreinforced stimuli

In chronic experiments on cats, three-phasic responses of neuronal microsystems in the cortical somatic area I were studied during habituation of the EEG activation reactions. Repeated stimuli of different modalities were used: electrical pulses to the forepaw, sounds, direct stimulation of the mesencephalic RF. Simultaneously with the extinction of EEG activation reactions, the three-phasic responses of the multiunit activity (MUA) also became progressively extinct: the 1st phase of primary excitation--only a little, the 2nd phase (inhibitory)--greatly, as well as the 3rd phase--the phase of secondary excitation (if it existed at the beginning). The MUA responses to all stimuli show that these neuronal microsystems are polysensory. Relatively to the nonspecific activating RF macrosystem, the investigated neuronal microsystems are autonomous because their two functionally opposed response phases--the 1st excitatory and the 2nd inhibitory--occur against the monotonous excitatory background of the EEG activation. But in some way the neuronal microsystems are connected with the RF-system because of the parallel development of the extinction process.     

Arousal increases the representational capacity of cortical tissue

Arousal patently transforms the faculties of complex organisms. Although typical changes in cortical activity such as seen in EEG and LFP measurements are associated with change in state of arousal, it remains unclear what in the constitution of such state dependent activity enables this profound enhancement of ability. We put forward the hypothesis that arousal modulates cortical activity by rendering it more fit to represent information. We argue that representational capacity is of a dual nature—it requires not only that cortical tissue generate complex activity (i.e. spatiotemporal neuronal events), but also a complex cortical activity space (which is comprised of such spatiotemporal events). We explain that the topological notion of complexity—homology—is the pertinent measure of the complexity of neuronal activity spaces, as homological structure indicates not only the degree to which underlying activity is inherently clustered but also registers the effective dimensionality of the configurations formed by such clusters. Changes of this sort in the structure of cortical activity spaces can serve as the basis of the enhanced capacity to make perceptual/behavioral distinctions brought about by arousal. To show the feasibility of these ideas, we analyzed voltage sensitive dye imaging (VSDI) data acquired from primate visual cortex in disparate states of arousal. Our results lend some support to the theory: first as arousal increased so did the complexity of activity (that is the complexity of VSDI movies). Moreover, the complexity of structure of activity space (that is VSDI movie space) as measured by persistent homology—a multi scale topological measure of complexity—increased with arousal as well.     

Modeling the spatial reach of the LFP

The local field potential (LFP) reflects activity of many?neurons in the vicinity of the recording electrode and is therefore useful for studying local network dynamics. Much of the nature of the LFP is, however, still unknown. There are, for instance, contradicting reports on the spatial extent of the region generating the LFP. Here, we use a detailed biophysical modeling approach to investigate the size of the contributing region by simulating the LFP from a large number of neurons around the electrode. We find that the size of the generating region depends on the neuron morphology, the synapse distribution, and the correlation in synaptic activity. For uncorrelated activity, the LFP represents cells in a small region (within a radius of a few hundred micrometers). If the LFP contributions from different cells are correlated, the size of the generating region is determined by the spatial extent of the correlated activity.     

Sensory information in local field potentials and spikes from visual and auditory cortices: time scales and frequency bands

Studies analyzing sensory cortical processing or trying to decode brain activity often rely on a combination of different electrophysiological signals, such as local field potentials (LFPs) and spiking activity. Understanding the relation between these signals and sensory stimuli and between different components of these signals is hence of great interest. We here provide an analysis of LFPs and spiking activity recorded from visual and auditory cortex during stimulation with natural stimuli. In particular, we focus on the time scales on which different components of these signals are informative about the stimulus, and on the dependencies between different components of these signals. Addressing the first question, we find that stimulus information in low frequency bands (<12 Hz) is high, regardless of whether their energy is computed at the scale of milliseconds or seconds. Stimulus information in higher bands (>50 Hz), in contrast, is scale dependent, and is larger when the energy is averaged over several hundreds of milliseconds. Indeed, combined analysis of signal reliability and information revealed that the energy of slow LFP fluctuations is well related to the stimulus even when considering individual or few cycles, while the energy of fast LFP oscillations carries information only when averaged over many cycles. Addressing the second question, we find that stimulus information in different LFP bands, and in different LFP bands and spiking activity, is largely independent regardless of time scale or sensory system. Taken together, these findings suggest that different LFP bands represent dynamic natural stimuli on distinct time scales and together provide a potentially rich source of information for sensory processing or decoding brain activity.     

Coronary Heart Disease and Cortical Thickness,Gray Matter and White Matter Lesion Volumes on MRI

Coronary heart disease (CHD) has been linked with cognitive decline and dementia in several studies. CHD is strongly associated with blood pressure, but it is not clear how blood pressure levels or changes in blood pressure over time affect the relation between CHD and dementia-related pathology. The aim of this study was to investigate relations between CHD and cortical thickness, gray matter volume and white matter lesion (WML) volume on MRI, considering CHD duration and blood pressure levels from midlife to three decades later. The study population included 69 elderly at risk of dementia who participated in the Cardiovascular Risk Factors, Aging and Dementia (CAIDE) study. CAIDE participants were examined in midlife, re-examined 21 years later, and then after additionally 7 years (in total up to 30 years follow-up). MRIs from the second re-examination were used to calculate cortical thickness, gray matter and WML volume. CHD diagnoses were obtained from the Finnish Hospital Discharge Register. Linear regression analyses were adjusted for age, sex, follow-up time and scanner type, and additionally total intracranial volume in GM volume analyses. Adding diabetes, cholesterol or smoking to the models did not influence the results. CHD was associated with lower thickness in multiple regions, and lower total gray matter volume, particularly in people with longer disease duration (>10 years). Associations between CHD, cortical thickness and gray matter volume were strongest in people with CHD and hypertension in midlife, and those with CHD and declining blood pressure after midlife. No association was found between CHD and WML volumes. Based on these results, long-term CHD seems to have detrimental effects on brain gray matter tissue, and these effects are influenced by blood pressure levels and their changes over time.     

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.     

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.