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.     

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.     

Persistance of phase-coupling between the circadian rhythms of hypophyseal hormones in free-running rats

The circadian rhythms in plasma ACTH, TSH, LH and PRL were explored in sighted or blind, spayed and estrogen-implanted rats. A marked endogenous circadian rhythmicity was shown to persist in the blind animals for the 4 endocrine rhythms. The endogenous rhythms also kept very close reciprocal phase relationship as in the synchronized state, and they were peaking almost simultaneously, after 60 d. of free-running. Finally the endogenous hormonal rhythm maintained their usual phase relationships with the endogenous activity rhythm, so that the circadian phase of increased hormonal secretion coincided with the circadian resting phase of the sleep/wake rhythm. These results are discussed in the light of the alternate theory of one vs multiple but phase-locked circadian pacemakers driving endocrine and behavioral circadian rhythms.     

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.     

Time and Frequency-Dependent Modulation of Local Field Potential Synchronization by Deep Brain Stimulation

High-frequency electrical stimulation of specific brain structures, known as deep brain stimulation (DBS), is an effective treatment for movement disorders, but mechanisms of action remain unclear. We examined the time-dependent effects of DBS applied to the entopeduncular nucleus (EP), the rat homolog of the internal globus pallidus, a target used for treatment of both dystonia and Parkinson’s disease (PD). We performed simultaneous multi-site local field potential (LFP) recordings in urethane-anesthetized rats to assess the effects of high-frequency (HF, 130 Hz; clinically effective), low-frequency (LF, 15 Hz; ineffective) and sham DBS delivered to EP. LFP activity was recorded from dorsal striatum (STR), ventroanterior thalamus (VA), primary motor cortex (M1), and the stimulation site in EP. Spontaneous and acute stimulation-induced LFP oscillation power and functional connectivity were assessed at baseline, and after 30, 60, and 90 minutes of stimulation. HF EP DBS produced widespread alterations in spontaneous and stimulus-induced LFP oscillations, with some effects similar across regions and others occurring in a region- and frequency band-specific manner. Many of these changes evolved over time. HF EP DBS produced an initial transient reduction in power in the low beta band in M1 and STR; however, phase synchronization between these regions in the low beta band was markedly suppressed at all time points. DBS also enhanced low gamma synchronization throughout the circuit. With sustained stimulation, there were significant reductions in low beta synchronization between M1-VA and STR-VA, and increases in power within regions in the faster frequency bands. HF DBS also suppressed the ability of acute EP stimulation to induce beta oscillations in all regions along the circuit. This dynamic pattern of synchronizing and desynchronizing effects of EP DBS suggests a complex modulation of activity along cortico-BG-thalamic circuits underlying the therapeutic effects of GPi DBS for conditions such as PD and dystonia.     

Neuronal Shot Noise and Brownian 1/f2 Behavior in the Local Field Potential

We demonstrate that human electrophysiological recordings of the local field potential (LFP) from intracranial electrodes, acquired from a variety of cerebral regions, show a ubiquitous 1/f² scaling within the power spectrum. We develop a quantitative model that treats the generation of these fields in an analogous way to that of electronic shot noise, and use this model to specifically address the cause of this 1/f² Brownian noise. The model gives way to two analytically tractable solutions, both displaying Brownian noise: 1) uncorrelated cells that display sharp initial activity, whose extracellular fields slowly decay in time and 2) rapidly firing, temporally correlated cells that generate UP-DOWN states.     

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

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

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

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

Local and global measures of shape dynamics

The shape and motion of cells can yield significant insights into the internal operation of a cell. We present a simple, yet versatile, framework that provides multiple metrics of cell shape and cell shape dynamics. Analysis of migrating Dictyostelium discoideum cells shows that global and local metrics highlight distinct cellular processes. For example, a global measure of shape shows rhythmic oscillations suggestive of contractions, whereas a local measure of shape shows wave-like dynamics indicative of protrusions. From a local measure of dynamic shape, or boundary motion, we extract the times and locations of protrusions and retractions. We find that protrusions zigzag, while retractions remain roughly stationary along the boundary. We do not observe any temporal relationship between protrusions and retractions. Our analysis framework also provides metrics of the boundary as whole. For example, as the cell speed increases, we find that the cell shape becomes more elongated. We also observe that while extensions and retractions have similar areas, their shapes differ.     

Dynamic relationship between the slow potential and spikes in cockroach ocellar neurons

The relationship between the slow potential and spikes of second-order ocellar neurons of the cockroach, Periplaneta americana, was studied. The stimulus was a sinusoidally modulated light with various mean illuminances. A solitary spike was generated at the depolarizing phase of the modulation response. Analysis of the relationship between the amplitude/frequency of voltage modulation and the rate of spike generation showed that (a) the spike initiation process was bandpass at approximately 0.5-5 Hz, (b) the process contained a dynamic linearity and a static nonlinearity, and (c) the spike threshold at optimal frequencies (0.5-5 Hz) remained unchanged over a mean illuminance range of 3.6 log units, whereas (d) the spike threshold at frequencies of less than 0.5 Hz was lower at a dimmer mean illuminance. The voltage noise in the response was larger and the mean membrane potential level was more positive at a dimmer mean illuminance. Steady or noise current injection during sinusoidal light stimulation showed that (a) the decrease in the spike threshold at a dimmer mean illuminance was due to the increase in the noise variance: the noise had facilitatory effects on the spike initiation; and (b) the change in the mean potential level had little effect on the spike threshold. We conclude that fundamental signal modifications occur during the spike initiation in the cockroach ocellar neuron, a finding that differs from the spike initiation process in other visual systems, including Limulus eye and vertebrate retina, in which it is presumed that little signal modification occurs at the analog-to-digital conversion process.     

A Neuronal Network Model for Simulating the Effects of Repetitive Transcranial Magnetic Stimulation on Local Field Potential Power Spectra

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

Real-time analysis of hippocampal neural activity in the intervals between interictal spikes

Previously the electroencephalogram (EEG) was modeled as consisting of faster, smaller waves superimposed on larger, slower waves. The intent of this study is to modify the program to sample neural activity over specific intervals of time following detection of a distinct wave pattern. The use of conditional sampling is illustrated by considering wave detection following epileptic interictal spikes in the rabbit hippocampus. To create an epileptic focus, small pellets of sodium penicillin suspended in agar were placed on the rabbit hippocampus. This produced regularly recurring, spontaneous, large amplitude discharges, or interictal spikes, at the site of application. Following detection of an interictal spike, the program delayed the onset of a sample period for either 1.0 s or 6.0 s. The neural activity was then sampled for 5.1 s, and fast and slow waves were detected over the sample period. The frequency distribution of waves in four of these 5.1 s intervals was calculated. Comparison of the frequency distributions following the 1.0 s and 6.0 s delays showed no discernible differences. The data illustrate that not all types of neural activity are markedly modified by interictal spikes and suggest that hippocampal cellular populations generate similar waves 1.0 s and 6.0 s after such a spike. Moreover, this experiment illustrates adaptation of the program to sample activity over a limited period of time following detection of a specific cortical waveform.     

Negative occurrence between hippocampal rhythmic slow activity and epileptiform spikes: influence of the striatum

The effects of caudate and septal stimulation on hippocampal activity were studied. Sodium penicillin was intravenously injected in order to induce a steady rate of interictal epileptic activity. Penicillin injection caused significant reduction of the rate of occurrence and duration of hippocampal rhythmic slow activity (RSA). Spontaneous RSA as well as RSA-eliciting caudate and septal stimulation induced a marked inhibition on frequency of epileptiform complexes. Lesions of the medial septal nucleus made it impossible to record RSA or to observe any sort of influence on hippocampal epileptiform activity by caudate stimulation. This result suggests that the septum is important for RSA genesis in the striato-hippocampal pathway or in the reciprocal septo-hippocampal connections.     

基于联合锋电位-局部场电位的整合野调制特性研究

整合野调制在生物视觉系统的图形背景分离和轮廓检测中具有重要作用。为了研究整合野空间频率调制特性,首先测定单个神经元的感受野范围和整合类型,挑选出要研究的抑制性神经元;然后,用匹配追踪算法和希尔伯特变换提取Spike触发的伽马频带LFP瞬时能量;最后,将Spike触发的伽马频带LFP(local field potential,LFP)瞬时能量用于分析神经元的整合调制特性.对在大鼠初级视觉皮层(primary visual cortex,V1区)采集的96个神经元进行统计分析,实验结果表明:1)Spike触发的伽马频带LFP瞬时能量可以作为分析V1区整合野调制特性的有效指标;2)基于Spike触发的伽马频带LFP瞬时能量所获得的抑制指数要显著高于通过Spike发放率以及伽马频带LFP功率的结果(P0.001),并且整合野的调制规律性更加明显,个体适用性更好。     

Some Relations between Action Potential and Resting Potential of the Lobster Giant Axon

Experiments were performed to determine the quantitative relation existing between action potential and resting potential of the lobster giant axon. Resting potential changes were induced by either increasing the external potassium concentration or by reducing the external calcium concentration. For either treatment the action potential amplitude is proportional to the logarithm of the resting potential minus a constant. This constant is equivalent to the minimum resting potential at which a propagated spike is possible, and is larger for depolarization in low calcium than in high potassium. Thus the change in action potential per unit change in resting potential is greater in low external calcium than in high external potassium. Analog computer solutions to the Hodgkin-Huxley equations for squid axon membrane potentials show that, if the initial conditions are properly specified, the action potential is proportional to the logarithm of the potassium potential minus a constant. The experimental results and the analog computations suggest that reducing external calcium produces changes in the invertebrate axon that cannot be accounted for solely on the basis of alterations in the potassium potential.     

A Field Method for Estimation of the Potential Evapotranspiration Rate

The integrals of the difference between wet and dry thermocouplereadings correlated closely with the daily amounts of evaporationfrom a Petri dish. A close relationship was also found betweenthe integral and the daily amount of transpiration of pot-grownbirch seedlings which were daily re-watered to near field capacity.