Modulation of hippocampal rhythms by subthreshold electric fields and network topology

Terahertz radiation affects the dynamics of neurons by decreasing membrane area ratio

Terahertz radiation at specific frequencies and energies can mediate cellular morphology or function changes by exciting nonlinear resonance effects in proteins or DNA. However, the effects of terahertz radiation on neuronal morphology and function are currently unknown, and the correlation between neuronal morphology and kinetic properties after terahertz radiation remains to be elucidated. In this paper, we first characterized the changes in neuronal morphology by the relative ratio of neuronal cytosol to protruding membrane area. Analyzed the pattern of the influence of terahertz radiation on neuronal morphology and the cumulative effect. On this basis, this paper constructs a kinetic model of neurons regulated by terahertz radiation, investigates the influence law of terahertz radiation on the kinetic properties of neurons, and analyzes the correlation between neuronal morphology and kinetic properties. The results showed that terahertz radiation caused a decrease in the membrane area ratio of neuronal cytosol to protrusion, and this effect started on the first day of terahertz radiation and lasted until the end of terahertz radiation; terahertz radiation changed the neuronal discharge pattern by decreasing the membrane area ratio of neuronal cytosol to protrusion and lowered the frequency of neuronal inter-cluster discharges and amplitude of action potentials, and increased the neuronal intra-cluster discharge. In addition, terahertz radiation can increase the peak value of neuronal postsynaptic currents by decreasing the membrane area ratio. In summary, terahertz radiation can modulate neurons' morphology and change their firing patterns and kinetic properties by affecting their morphology. These predict that terahertz radiation at specific frequencies and energies can be developed as a novel, molecular-level neuromodulation technique for intervening or treating neuronal degenerative diseases.

Influence of sinusoidal forcing on the master FitzHugh-Nagumo neuron model and global dynamics of a unidirectionally coupled two-neuron system

In this paper, we investigate a seven-parameter, five-dimensional dynamical system, specifically a unidirectional coupling of two FitzHugh-Nagumo neuron models, with one neuron being sinusoidally driven. This master-slave configuration features neuron N1 as the master, subjected to an external sinusoidal electrical current, and neuron N2 as the slave, interacting with N1 through an electrical force. We report numerical results for three distinct scenarios where N1 operates in (i) periodic, (ii) quasiperiodic, and (iii) chaotic regimes. The primary objective is to explore how the dynamics of the master neuron N1 influence the coupled system's behavior. To achieve this, we generated cross sections of the seven-dimensional parameter space, known as parameter planes. Our findings reveal that in the periodic regime of N1, the coupled system exhibits period-adding sequences of Arnold tongue-like structures in the parameter planes. Furthermore, regions of multistability can also be identified in these parameter planes of the coupled system. In the quasiperiodic regime, regions of periodic motion are absent, with only regions of quasiperiodic and chaotic dynamics present. In the chaotic regime of N1, the parameter planes display regions of chaos, hyperchaos, and transient hyperchaos.

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Electric field effects on neuronal input-output relationship by regulating NMDA spikes

Evidence shows that the dendritic polarization induced by weak electrical field (EF) can affect the neuronal input-output function via modulating dendritic integration of AMPA synapses, indicating that the supralinear dendritic integration of NMDA synapses can also be influenced by dendritic polarization. However, it remains unknown how dendritic polarization affects NMDA-type dendritic integration, and then contributes to neuronal input-output relationship. Here, we used a computational model of pyramidal neuron with inhomogeneous extracellular potentials to characterize the relationship among EF, dendritic integration, and somatic output. Basing on singular perturbation we analyzed the subthreshold dynamics of membrane potentials in response to NMDA synapses, and found that the equilibrium mapping of a fast subsystem can characterize the asymptotic subthreshold input-output (sI/O) relationship for EF-regulated supralinear dendritic integration, allowing us to predict the tendency of EF-regulated dendritic integration by showing the variation of equilibrium mapping under EF stimulation. EF-induced depolarization at distal dendrites receiving synapses plays a crucial role in shifting the steep change of sI/O left by facilitating dendritic NMDA spike generation and in decreasing the plateau of sI/O via reducing driving force. And more effective EF modulation appears at sparsely activated NMDA receptors compared with clustered synaptic inputs. During the action potential (AP) generation, the respective contribution of EF-regulated dendritic integration and EF-induced somatic polarization was identified to show their synergetic or antagonistic effect on AP generation, depending on neuronal excitability. These results provided insight in understanding the modulation effect of EF on neuronal computation, which is important for optimizing noninvasive brain stimulation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09922-y.

State-dependent modulation of low-threshold-current-regulated dendritic Ca2+ response in thalamic reticular neurons with extracellular electric fields

Deep brain stimulation (DBS) in thalamic reticular nucleus (TRN) neuron provides a novel treatment for drug-resistant epilepsy via the induced electrical field (EFs). However, the mechanisms underlying EF effects remain unclear. This paper investigated how EFs regulate low-threshold dendritic Ca2+ (dCa) response and thus contribute to the input-output relationship of TRN cell. Our results showed that EFs modulate firing modes differently in a neuronal state-dependent manner. At the depolarized state, EFs only regulate the spike timing of a somatic stimulus-evoked single action potential (AP) with less contribution in the regulation of dCa response but could induce the transition between a dendritic stimulus-evoked single AP and a tonic burst of APs via the moderate regulation of dCa response. At the hyperpolarized state, EFs have significant effects on the dCa response, which modulate the large dCa response-dependent burst discharge and even cause a transition from this type of burst discharge to a single AP with less dCa response. Moreover, EF effects on stimulation threshold of somatic spiking prominently depend on EF-regulated dCa responses and the onset time differences between the stimulus and EF give rise to the distinct effect in the EF regulation of dCa responses. Finally, the larger neuronal axial resistance tends to result in the dendritic stimulus-evoked dCa response independent of somatic state. Interestingly, in this case, the EF application could reproduce the similar somatic state-dependent dCa response to dendritic stimulus which occurs in the case of lower axial resistance. These results suggest that the influence of EF on neuronal activities depends on neuronal intrinsic properties, which provides insight into understanding how DBS in TRN neuron modulates epilepsy from the point of view of biophysics.

Multielectrode Cortical Stimulation Selectively Induces Unidirectional Wave Propagation of Excitatory Neuronal Activity in Biophysical Neural Model

Cortical stimulation is emerging as an experimental tool in basic research and a promising therapy for a range of neuropsychiatric conditions. As multielectrode arrays enter clinical practice, the possibility of using spatiotemporal patterns of electrical stimulation to induce desired physiological patterns has become theoretically possible, but in practice can only be implemented by trial-and-error because of a lack of predictive models. Experimental evidence increasingly establishes traveling waves as fundamental to cortical information-processing, but we lack an understanding of how to control wave properties despite rapidly improving technologies. This study uses a hybrid biophysical-anatomical and neural-computational model to predict and understand how a simple pattern of cortical surface stimulation could induce directional traveling waves via asymmetric activation of inhibitory interneurons. We found that pyramidal cells and basket cells are highly activated by the anodal electrode and minimally activated by the cathodal electrodes, while Martinotti cells are moderately activated by both electrodes but exhibit a slight preference for cathodal stimulation. Network model simulations found that this asymmetrical activation results in a traveling wave in superficial excitatory cells that propagates unidirectionally away from the electrode array. Our study reveals how asymmetric electrical stimulation can easily facilitate traveling waves by relying on two distinct types of inhibitory interneuron activity to shape and sustain the spatiotemporal dynamics of endogenous local circuit mechanisms.SIGNIFICANCE STATEMENT Electrical brain stimulation is becoming increasingly useful to probe the workings of brain and to treat a variety of neuropsychiatric disorders. However, stimulation is currently performed in a trial-and-error fashion as there are no methods to predict how different electrode arrangements and stimulation paradigms will affect brain functioning. In this study, we demonstrate a hybrid modeling approach, which makes experimentally testable predictions that bridge the gap between the microscale effects of multielectrode stimulation and the resultant circuit dynamics at the mesoscale. Our results show how custom stimulation paradigms can induce predictable, persistent changes in brain activity, which has the potential to restore normal brain function and become a powerful therapy for neurological and psychiatric conditions.

A mean-field model of glutamate and GABA synaptic dynamics for functional MRS

Advances in functional magnetic resonance spectroscopy (fMRS) have enabled the quantification of activity-dependent changes in neurotransmitter concentrations in vivo. However, the physiological basis of the large changes in GABA and glutamate observed by fMRS (>10%) over short time scales of less than a minute remain unclear as such changes cannot be accounted for by known synthesis or degradation metabolic pathways. Instead, it has been hypothesized that fMRS detects shifts in neurotransmitter concentrations as they cycle from presynaptic vesicles, where they are largely invisible, to extracellular and cytosolic pools, where they are detectable. The present paper uses a computational modelling approach to demonstrate the viability of this hypothesis. A new mean-field model of the neural mechanisms generating the fMRS signal in a cortical voxel is derived. The proposed macroscopic mean-field model is based on a microscopic description of the neurotransmitter dynamics at the level of the synapse. Specifically, GABA and glutamate are assumed to cycle between three metabolic pools: packaged in the vesicles; active in the synaptic cleft; and undergoing recycling and repackaging in the astrocytic or neuronal cytosol. Computational simulations from the model are used to generate predicted changes in GABA and glutamate concentrations in response to different types of stimuli including pain, vision, and electric current stimulation. The predicted changes in the extracellular and cytosolic pools corresponded to those reported in empirical fMRS data. Furthermore, the model predicts a selective control mechanism of the GABA/glutamate relationship, whereby inhibitory stimulation reduces both neurotransmitters, whereas excitatory stimulation increases glutamate and decreases GABA. The proposed model bridges between neural dynamics and fMRS and provides a mechanistic account for the activity-dependent changes in the glutamate and GABA fMRS signals. Lastly, these results indicate that echo-time may be an important timing parameter that can be leveraged to maximise fMRS experimental outcomes.

Effects of transcranial alternating current stimulation on spiking activity in computational models of single neocortical neurons

Neural oscillations are a key mechanism for information transfer in brain circuits. Rhythmic fluctuations of local field potentials control spike timing through cyclic membrane de- and hyperpolarization. Transcranial alternating current stimulation (tACS) is a non-invasive neuromodulation method which can directly interact with brain oscillatory activity by imposing an oscillating electric field on neurons. Despite its increasing use, the basic mechanisms of tACS are still not fully understood. Here, we investigate in a computational study the effects of tACS on morphologically realistic neurons with ongoing spiking activity. We characterize the membrane polarization as a function of electric field strength and subsequent effects on spiking activity in a set of 25 neurons from different neocortical layers. We find that tACS does not affect the firing rate of investigated neurons for electric field strengths applicable to human studies. However, we find that the applied electric fields entrain the spiking activity of large pyramidal neurons and large basket neurons at < 1 mV/mm field strengths. Our model results are in line with recent experimental studies and can provide a mechanistic framework to understand the effects of oscillating electric fields on single neuron activity. They highlight the importance of neuron morphology and biophysics in responsiveness to electrical stimulation.

Efficient metadata mining of web-accessible neural morphologies

Advancements in neuroscience research have led to steadily accelerating data production and sharing. The online community repository of neural reconstructions NeuroMorpho.Org grew from fewer than 1000 digitally traced neurons in 2006 to more than 140,000 cells today, including glia that now constitute 10.1% of the content. Every reconstruction consists of a detailed 3D representation of branch geometry and connectivity in a standardized format, from which a collection of morphometric features is extracted and stored. Moreover, each entry in the database is accompanied by rich metadata annotation describing the animal subject, anatomy, and experimental details. The rapid expansion of this resource in the past decade was accompanied by a parallel rise in the complexity of the available information, creating both opportunities and challenges for knowledge mining. Here, we introduce a new summary reporting functionality, allowing NeuroMorpho.Org users to efficiently download digests of metadata and morphometrics from multiple groups of similar cells for further analysis. We demonstrate the capabilities of the tool for both glia and neurons and present an illustrative statistical analysis of the resulting data.

Effects of direct current stimulation on synaptic plasticity in a single neuron

BACKGROUND

Transcranial direct current stimulation (DCS) has lasting effects that may be explained by a boost in synaptic long-term potentiation (LTP). We hypothesized that this boost is the result of a modulation of somatic spiking in the postsynaptic neuron, as opposed to indirect network effects. To test this directly we record somatic spiking in a postsynaptic neuron during LTP induction with concurrent DCS.

METHODS

We performed rodent in-vitro patch-clamp recordings at the soma of individual CA1 pyramidal neurons. LTP was induced with theta-burst stimulation (TBS) applied concurrently with DCS. To test the causal role of somatic polarization, we manipulated polarization via current injections. We also used a computational multi-compartment neuron model that captures the effect of electric fields on membrane polarization and activity-dependent synaptic plasticity.

RESULTS

TBS-induced LTP was enhanced when paired with anodal DCS as well as depolarizing current injections. In both cases, somatic spiking during the TBS was increased, suggesting that evoked somatic activity is the primary factor affecting LTP modulation. However, the boost of LTP with DCS was less than expected given the increase in spiking activity alone. In some cells, we also observed DCS-induced spiking, suggesting DCS also modulates LTP via induced network activity. The computational model reproduces these results and suggests that they are driven by both direct changes in postsynaptic spiking and indirect changes due to network activity.

CONCLUSION

DCS enhances synaptic plasticity by increasing postsynaptic somatic spiking, but we also find that an increase in network activity may boost but also limit this enhancement.

Active probing to highlight approaching transitions to ictal states in coupled neural mass models

The extraction of electrophysiological features that reliably forecast the occurrence of seizures is one of the most challenging goals in epilepsy research. Among possible approaches to tackle this problem is the use of active probing paradigms in which responses to stimuli are used to detect underlying system changes leading up to seizures. This work evaluates the theoretical and mechanistic underpinnings of this strategy using two coupled populations of the well-studied Wendling neural mass model. Different model settings are evaluated, shifting parameters (excitability, slow inhibition, or inter-population coupling gains) from normal towards ictal states while probing stimuli are applied every 2 seconds to the input of either one or both populations. The correlation between the extracted features and the ictogenic parameter shifting indicates if the impending transition to the ictal state may be identified in advance. Results show that not only can the response to the probing stimuli forecast seizures but this is true regardless of the altered ictogenic parameter. That is, similar feature changes are highlighted by probing stimuli responses in advance of the seizure including: increased response variance and lag-1 autocorrelation, decreased skewness, and increased mutual information between the outputs of both model subsets. These changes were mostly restricted to the stimulated population, showing a local effect of this perturbational approach. The transition latencies from normal activity to sustained discharges of spikes were not affected, suggesting that stimuli had no pro-ictal effects. However, stimuli were found to elicit interictal-like spikes just before the transition to the ictal state. Furthermore, the observed feature changes highlighted by probing the neuronal populations may reflect the phenomenon of critical slowing down, where increased recovery times from perturbations may signal the loss of a systems' resilience and are common hallmarks of an impending critical transition. These results provide more evidence that active probing approaches highlight information about underlying system changes involved in ictogenesis and may be able to play a role in assisting seizure forecasting methods which can be incorporated into early-warning systems that ultimately enable closing the loop for targeted seizure-controlling interventions.

Realistic modeling of mesoscopic ephaptic coupling in the human brain

Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and proposed as a substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to model mesoscopic ephaptic activity in the human brain and explore its trajectory during aging by characterizing the electric field generated by cortical dipoles using realistic finite element modeling. Extrapolating from electrophysiological measurements, we first observe that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant self-generated fields and to those produced by noninvasive transcranial brain stimulation, and therefore possibly able to modulate neuronal activity. Then, to evaluate the role of these fields in the human cortex in large MRI databases, we adapt an interaction approximation that considers the relative orientation of neuron and field to estimate the membrane potential perturbation in pyramidal cells. We use this approximation to define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from healthy subjects aged 16-83. Results reveal that ephaptic coupling, in the simplified mesoscopic modeling approach used here, significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. This study suggests that by providing the means for fast and direct interaction between neurons, ephaptic modulation may contribute to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology.

Selective recruitment of cortical neurons by electrical stimulation

Despite its critical importance in experimental and clinical neuroscience, at present there is no systematic method to predict which neural elements will be activated by a given stimulation regime. Here we develop a novel approach to model the effect of cortical stimulation on spiking probability of neurons in a volume of tissue, by applying an analytical estimate of stimulation-induced activation of different cell types across cortical layers. We utilize the morphology and properties of axonal arborization profiles obtained from publicly available anatomical reconstructions of the twelve main categories of neocortical neurons to derive the dependence of activation probability on cell type, layer and distance from the source. We then propagate this activity through the local network incorporating connectivity, synaptic and cellular properties. Our work predicts that (a) intracranial cortical stimulation induces selective activation across cell types and layers; (b) superficial anodal stimulation is more effective than cathodal at cell activation; (c) cortical surface stimulation focally activates layer I axons, and (d) there is an optimal stimulation intensity capable of eliciting cell activation lasting beyond the end of stimulation. We conclude that selective effects of cortical electrical stimulation across cell types and cortical layers are largely driven by their different axonal arborization and myelination profiles.

Brain stimulation is widely used to probe the neural system to learn about its properties, to normalize dysfunction (e.g., deep brain stimulation for Parkinsonian patients), or to manipulate brain activity, including enhancing memory and learning. Despite its critical importance in experimental and clinical neuroscience, at present there are no systematic methods to predict which neural elements of the brain will be activated by a given stimulation regime. To address this question, we propose a novel theoretical framework that models the effect of cortical stimulation on the spiking probability of a neuron based on its location, type and morphology. Our study predicts that short-lived superficial electrical stimulation has the ability to trigger spiking in layer IV pyramidal cells, and to evoke network activity that could persist for hundreds of milliseconds. It further predicts a much higher spiking response to anodal stimulation compared to cathodal one, as the existence of an optimal stimulation intensity, capable of inducing a maximal response in a population of cortical cells. The results of our study can be directly taken into account in planning future electrical stimulation experiments.

Modulations of dendritic Ca2+ spike with weak electric fields in layer 5 pyramidal cells

Weak electric fields (EFs) modulate input/output function of pyramidal cells. Dendritic Ca²⁺ spike is an important cellular mechanism for coupling synaptic inputs from different cortical layers, which plays a critical role in neuronal computation. This study aims to understand the effects of weak EFs on Ca²⁺ spikes initiated in the distal dendrites. We use a computational model to simulate dendritic Ca²⁺ spikes and backpropagating action potentials (APs) in layer 5 pyramidal cells. We apply uniform EFs (less than 20 mV/mm) to the model and examine how they affect the threshold for activation of Ca²⁺ spikes. We show that the effects of weak field on synaptically evoked Ca²⁺ spikes depend on the timing of synaptic inputs. When distal inputs coincide with the onset of EFs within a time window of several milliseconds, field-induced depolarization facilitates the initiation of Ca²⁺ spikes, while field-induced hyperpolarization suppresses dendritic APs. Sustained field-induced depolarization leads to the inactivation of Ca²⁺ channels and increases the threshold of Ca²⁺ spike. Sustained field-induced hyperpolarization de-inactivates Ca²⁺ channels and reduces the threshold of Ca²⁺ spike. By altering the threshold of backpropagation activated Ca²⁺ firing, field-induced depolarization increases the degree of coupling between inputs of the soma and distal dendrites, while field-induced hyperpolarization results in a decrease of coupling. The modulatory effects of weak EF are governed by the field direction with respect to the cell. Our study explains a fundamental link between field-induced polarization, dendritic Ca²⁺ spike, and somato-dendritic coupling. The findings are crucial to interpret how weak EFs achieve specific modulation of cellular activity.

Two Forms of Electrical Transmission Between Neurons

Electrical signaling is a cardinal feature of the nervous system and endows it with the capability of quickly reacting to changes in the environment. Although synaptic communication between nerve cells is perceived to be mainly chemically mediated, electrical synaptic interactions also occur. Two different strategies are responsible for electrical communication between neurons. One is the consequence of low resistance intercellular pathways, called "gap junctions", for the spread of electrical currents between the interior of two cells. The second occurs in the absence of cell-to-cell contacts and is a consequence of the extracellular electrical fields generated by the electrical activity of neurons. Here, we place present notions about electrical transmission in a historical perspective and contrast the contributions of the two different forms of electrical communication to brain function.

Ih interacts with somato-dendritic structure to determine frequency response to weak alternating electric field stimulation

Transcranial current stimulation (tCS) modulates brain dynamics using weak electric fields. Given the pathological changes in brain network oscillations in neurological and psychiatric illnesses, using alternating electric field waveforms that engage rhythmic activity has been proposed as a targeted, network-level treatment approach. Previous studies have investigated the effects of electric fields at the neuronal level. However, the biophysical basis of the cellular response to electric fields has remained limited. Here, we characterized the frequency-dependent response of different compartments in a layer V pyramidal neuron to exogenous electric fields to dissect the relative contributions of voltage-gated ion channels and neuronal morphology. Hyperpolarization-activated cation current (I_h) in the distal dendrites was the primary ionic mechanism shaping the model's response to electric field stimulation and caused subthreshold resonance in the tuft at 20 ± 4 Hz. In contrast, subthreshold I_h-mediated resonance in response to local sinusoidal current injection was present in all model compartments at 11 ± 2 Hz. The frequencies of both resonance responses were modulated by I_h conductance density. We found that the difference in resonance frequency between the two stimulation types can be explained by the fact that exogenous electric fields simultaneously polarize the membrane potentials at the distal ends of the neuron (relative to field direction) in opposite directions. Our results highlight the role of I_h in shaping the cellular response to electric field stimulation and suggest that the common model of tCS as a weak somatic current injection fails to capture the cellular effects of electric field stimulation. NEW & NOTEWORTHY Modulation of cortical oscillation by brain stimulation serves as a tool to understand the causal role of network oscillations in behavior and is a potential treatment modality that engages impaired network oscillations in disorders of the central nervous system. To develop targeted stimulation paradigms, cellular-level effects must be understood. We demonstrate that hyperpolarization-activated cation current (I_h) and cell morphology cooperatively shape the response to applied alternating electric fields.

And yet it moves: Recovery of volitional control after spinal cord injury

Preclinical and clinical neurophysiological and neurorehabilitation research has generated rather surprising levels of recovery of volitional sensory-motor function in persons with chronic motor paralysis following a spinal cord injury. The key factor in this recovery is largely activity-dependent plasticity of spinal and supraspinal networks. This key factor can be triggered by neuromodulation of these networks with electrical and pharmacological interventions. This review addresses some of the systems-level physiological mechanisms that might explain the effects of electrical modulation and how repetitive training facilitates the recovery of volitional motor control. In particular, we substantiate the hypotheses that: (1) in the majority of spinal lesions, a critical number and type of neurons in the region of the injury survive, but cannot conduct action potentials, and thus are electrically non-responsive; (2) these neuronal networks within the lesioned area can be neuromodulated to a transformed state of electrical competency; (3) these two factors enable the potential for extensive activity-dependent reorganization of neuronal networks in the spinal cord and brain, and (4) propriospinal networks play a critical role in driving this activity-dependent reorganization after injury. Real-time proprioceptive input to spinal networks provides the template for reorganization of spinal networks that play a leading role in the level of coordination of motor pools required to perform a given functional task. Repetitive exposure of multi-segmental sensory-motor networks to the dynamics of task-specific sensory input as occurs with repetitive training can functionally reshape spinal and supraspinal connectivity thus re-enabling one to perform complex motor tasks, even years post injury.

Morphology controls how hippocampal CA1 pyramidal neuron responds to uniform electric fields: a biophysical modeling study

Responses of different neurons to electric field (EF) are highly variable, which depends on intrinsic properties of cell type. Here we use multi-compartmental biophysical models to investigate how morphologic features affect EF-induced responses in hippocampal CA1 pyramidal neurons. We find that the basic morphologies of neuronal elements, including diameter, length, bend, branch, and axon terminals, are all correlated with somatic depolarization through altering the current sources or sinks created by applied field. Varying them alters the EF threshold for triggering action potentials (APs), and then determines cell sensitivity to suprathreshold field. Introducing excitatory postsynaptic potential increases cell excitability and reduces morphology-dependent EF firing threshold. It is also shown that applying identical subthreshold EF results in distinct polarizations on cell membrane with different realistic morphologies. These findings shed light on the crucial role of morphologies in determining field-induced neural response from the point of view of biophysical models. The predictions are conducive to better understanding the variability in modulatory effects of EF stimulation at the cellular level, which could also aid the interpretations of how applied fields activate central nervous system neurons and affect relevant circuits.

Using Biophysical Models to Understand the Effect of tDCS on Neurorehabilitation: Searching for Optimal Covariates to Enhance Poststroke Recovery

Stroke is a leading cause of worldwide disability, and up to 75% of survivors suffer from some degree of arm paresis. Recently, rehabilitation of stroke patients has focused on recovering motor skills by taking advantage of use-dependent neuroplasticity, where high-repetition of goal-oriented movement is at times combined with non-invasive brain stimulation, such as transcranial direct current stimulation (tDCS). Merging the two approaches is thought to provide outlasting clinical gains, by enhancing synaptic plasticity and motor relearning in the motor cortex primary area. However, this general approach has shown mixed results across the stroke population. In particular, stroke location has been found to correlate with the likelihood of success, which suggests that different patients might require different protocols. Understanding how motor rehabilitation and stimulation interact with ongoing neural dynamics is crucial to optimize rehabilitation strategies, but it requires theoretical and computational models to consider the multiple levels at which this complex phenomenon operate. In this work, we argue that biophysical models of cortical dynamics are uniquely suited to address this problem. Specifically, biophysical models can predict treatment efficacy by introducing explicit variables and dynamics for damaged connections, changes in neural excitability, neurotransmitters, neuromodulators, plasticity mechanisms, and repetitive movement, which together can represent brain state, effect of incoming stimulus, and movement-induced activity. In this work, we hypothesize that effects of tDCS depend on ongoing neural activity and that tDCS effects on plasticity may be also related to enhancing inhibitory processes. We propose a model design for each step of this complex system, and highlight strengths and limitations of the different modeling choices within our approach. Our theoretical framework proposes a change in paradigm, where biophysical models can contribute to the future design of novel protocols, in which combined tDCS and motor rehabilitation strategies are tailored to the ongoing dynamics that they interact with, by considering the known biophysical factors recruited by such protocols and their interaction.

The possible consequences for cognitive functions of external electric fields at power line frequency on hippocampal CA1 pyramidal neurons

The possible effects on cognitive processes of external electric fields, such as those generated by power line pillars and household appliances are of increasing public concern. They are difficult to study experimentally, and the relatively scarce and contradictory evidence make it difficult to clearly assess these effects. In this study, we investigate how, why and to what extent external perturbations of the intrinsic neuronal activity, such as those that can be caused by generation, transmission and use of electrical energy can affect neuronal activity during cognitive processes. For this purpose, we used a morphologically and biophysically realistic three-dimensional model of CA1 pyramidal neurons. The simulation findings suggest that an electric field oscillating at power lines frequency, and environmentally measured strength, can significantly alter both the average firing rate and temporal spike distribution properties of a hippocampal CA1 pyramidal neuron. This effect strongly depends on the specific and instantaneous relative spatial location of the neuron with respect to the field, and on the synaptic input properties. The model makes experimentally testable predictions on the possible functional consequences for normal hippocampal functions such as object recognition and spatial navigation. The results suggest that, although EF effects on cognitive processes may be difficult to occur in everyday life, their functional consequences deserve some consideration, especially when they constitute a systematic presence in living environments.

Modeling sequence and quasi-uniform assumption in computational neurostimulation

Computational neurostimulation aims to develop mathematical constructs that link the application of neuromodulation with changes in behavior and cognition. This process is critical but daunting for technical challenges and scientific unknowns. The overarching goal of this review is to address how this complex task can be made tractable. We describe a framework of sequential modeling steps to achieve this: (1) current flow models, (2) cell polarization models, (3) network and information processing models, and (4) models of the neuroscientific correlates of behavior. Each step is explained with a specific emphasis on the assumptions underpinning underlying sequential implementation. We explain the further implementation of the quasi-uniform assumption to overcome technical limitations and unknowns. We specifically focus on examples in electrical stimulation, such as transcranial direct current stimulation. Our approach and conclusions are broadly applied to immediate and ongoing efforts to deploy computational neurostimulation.

Computational study of synchrony in fields and microclusters of ephaptically coupled neurons

Neuronal hypersynchrony is implicated in epilepsy and other diseases. The low-frequency, spatially averaged electric fields from many thousands of neurons have been shown to promote synchrony. It remains unclear whether highly transient, spatially localized electric fields from single action potentials (ephaptic coupling) significantly affect spike timing of neighboring cells and in consequence, population synchrony. In this study, we simulated the extracellular potentials and the resulting coupling between neurons in the NEURON environment and generalized their connection rules to create an oscillator network model of a sheet of ephaptically coupled neurons. With the use of both models, we explained several aspects of epileptiform behavior not previously modeled by synaptically coupled networks. Importantly, reduction of neuron spacing induced synchronization via single-spike ephaptic coupling, agreeing with seizure suppression seen clinically and in vitro via extracellular volume adjustment. Further reduction of neuron spacing yielded locally synchronized clusters, providing a mechanism for recent in vitro observations of localized neuronal synchrony in the absence of synaptic and gap-junction coupling.

Endogenous field feedback promotes the detectability for exogenous electric signal in the hybrid coupled population

This paper presents the endogenous electric field in chemical or electrical synaptic coupled networks, aiming to study the role of endogenous field feedback in the signal propagation in neural systems. It shows that the feedback of endogenous fields to network activities can reduce the required energy of the noise and enhance the transmission of input signals in hybrid coupled populations. As a common and important nonsynaptic interactive method among neurons, particularly, the endogenous filed feedback can not only promote the detectability of exogenous weak signal in hybrid coupled neural population but also enhance the robustness of the detectability against noise. Furthermore, with the increasing of field coupling strengths, the endogenous field feedback is conductive to the stochastic resonance by facilitating the transition of cluster activities from the no spiking to spiking regions. Distinct from synaptic coupling, the endogenous field feedback can play a role as internal driving force to boost the population activities, which is similar to the noise. Thus, it can help to transmit exogenous weak signals within the network in the absence of noise drive via the stochastic-like resonance.

Effects of low frequency electric fields on synaptic integration in hippocampal CA1 pyramidal neurons: implications for power line emissions

The possible cognitive effects of low frequency external electric fields (EFs), such as those generated by power lines, are poorly understood. Their functional consequences for mechanisms at the single neuron level are very difficult to study and identify experimentally, especially in vivo. The major open problem is that experimental investigations on humans have given inconsistent or contradictory results, making it difficult to estimate the possible effects of external low frequency electric fields on cognitive functions. Here we investigate this issue with realistic models of hippocampal CA1 pyramidal neurons. Our findings suggest how and why EFs, with environmentally observed frequencies and intensities far lower than what is required for direct neural activation, can perturb dendritic signal processing and somatic firing of neurons that are crucially involved in cognitive tasks such as learning and memory. These results show that individual neuronal morphology, ion channel dendritic distribution, and alignment with the electric field are major determinants of overall effects, and provide a physiologically plausible explanation of why experimental findings can appear to be small and difficult to reproduce, yet deserve serious consideration.

Ephaptic coupling to endogenous electric field activity: why bother?

There has been a revived interest in the impact of electric fields on neurons and networks. Here, we discuss recent advances in our understanding of how endogenous and externally imposed electric fields impact brain function at different spatial (from synapses to single neurons and neural networks) and temporal scales (from milliseconds to seconds). How such ephaptic effects are mediated and manifested in the brain remains a mystery. We argue that it is both possible (based on available technologies) and worthwhile to vigorously pursue such research as it has significant implications on our understanding of brain processing and for translational neuroscience.

Neuronal spike initiation modulated by extracellular electric fields

Based on a reduced two-compartment model, the dynamical and biophysical mechanism underlying the spike initiation of the neuron to extracellular electric fields is investigated in this paper. With stability and phase plane analysis, we first investigate in detail the dynamical properties of neuronal spike initiation induced by geometric parameter and internal coupling conductance. The geometric parameter is the ratio between soma area and total membrane area, which describes the proportion of area occupied by somatic chamber. It is found that varying it could qualitatively alter the bifurcation structures of equilibrium as well as neuronal phase portraits, which remain unchanged when varying internal coupling conductance. By analyzing the activating properties of somatic membrane currents at subthreshold potentials, we explore the relevant biophysical basis of spike initiation dynamics induced by these two parameters. It is observed that increasing geometric parameter could greatly decrease the intensity of the internal current flowing from soma to dendrite, which switches spike initiation dynamics from Hopf bifurcation to SNIC bifurcation; increasing internal coupling conductance could lead to the increase of this outward internal current, whereas the increasing range is so small that it could not qualitatively alter the spike initiation dynamics. These results highlight that neuronal geometric parameter is a crucial factor in determining the spike initiation dynamics to electric fields. The finding is useful to interpret the functional significance of neuronal biophysical properties in their encoding dynamics, which could contribute to uncovering how neuron encodes electric field signals.

Electrical engram: how deep brain stimulation affects memory

Deep brain stimulation (DBS) is a surgical procedure involving implantation of a pacemaker that sends electric impulses to specific brain regions. DBS has been applied in patients with Parkinson's disease, depression, and obsessive-compulsive disorder (among others), and more recently in patients with Alzheimer's disease to improve memory functions. Current DBS approaches are based on the concept that high-frequency stimulation inhibits or excites specific brain regions. However, because DBS entails the application of repetitive electrical stimuli, it primarily exerts an effect on extracellular field-potential oscillations similar to those recorded with electroencephalography. Here, we suggest a new perspective on how DBS may ameliorate memory dysfunction: it may enhance normal electrophysiological patterns underlying long-term memory processes within the medial temporal lobe.