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.     

A new algorithm for voltage clamp by iteration: A learning control of a nonlinear neuronal system

Voltage-clamp of excitable membrane allows the measurement of membrane currents associated with electrical potential changes across the membrane. However, it has been impossible in practice to apply the conventional analog feedback voltageclamp circuits to single electrode voltage clamping in central neurons. The reason for this is that the feedback system becomes unstable because of the positive feedback required for compensation of capacitative loss through the wall of the microelectrode. Park et al. (1981) proposed a new iterative technique to solve this problem. It requires that the potential to be clamped repeats itself with little or no change. The amount of current needed to clamp the membrane potential is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Since the feedback loop is open in real time, the system has great stability, and this advantage can be exploited in single electrode preparations. The computation algorithm which calculates the current waveform based on the voltage deviation during the last trial is the central part of the iterative voltage-clamp system. In this paper, we propose a new algorithm, which has several theoretical and practical advantages over the original one proposed by Park et al. First, two parameters used in the new algorithm are predetermined by a current-clamp experiment. Second, the speed of convergence of the new algorithm is faster than that of the Park's original algorithm. This was shown by computer simulation of iterative voltage clamp of artificial membrane following Hodgkin-Huxley equations for squid axon membrane and Rall's compartment model for a neuron with dendrites. Finally, we offer proof that the new algorithm is certain to converge for the general cases of voltage-clamp experiments with active membrane properties, synaptic membranes, etc. Consequently, the new algorithm for iterative voltage clamp is very suitable for single electrode voltage clamp in the central neurons. The new algorithm has been successfully applied to voltage-clamp experiments on rubrospinal neurons of cats (Tsukahara, Murakami, Kawato, Oda, and Etoh, in preparation).     

Invariant visual object recognition: a model, with lighting invariance.

How are invariant representations of objects formed in the visual cortex? We describe a neurophysiological and computational approach which focusses on a feature hierarchy model in which invariant representations can be built by self-organizing learning based on the statistics of the visual input. The model can use temporal continuity in an associative synaptic learning rule with a short term memory trace, and/or it can use spatial continuity in Continuous Transformation learning. The model of visual processing in the ventral cortical stream can build representations of objects that are invariant with respect to translation, view, size, and in this paper we show also lighting. The model has been extended to provide an account of invariant representations in the dorsal visual system of the global motion produced by objects such as looming, rotation, and object-based movement. The model has been extended to incorporate top-down feedback connections to model the control of attention by biased competition in for example spatial and object search tasks. The model has also been extended to account for how the visual system can select single objects in complex visual scenes, and how multiple objects can be represented in a scene.     

Extended difference-of-Gaussians model incorporating cortical feedback for relay cells in the lateral geniculate nucleus of cat

A striking feature of the organization of the early visual pathway is the significant feedback from primary visual cortex to cells in the dorsal lateral geniculate nucleus (LGN). Despite numerous experimental and modeling studies, the functional role for this feedback remains elusive. We present a new firing-rate-based model for LGN relay cells in cat, explicitly accounting for thalamocortical loop effects. The established DOG model, here assumed to account for the spatial aspects of the feedforward processing of visual stimuli, is extended to incorporate the influence of thalamocortical loops including a full set of orientation-selective cortical cell populations. Assuming a phase-reversed push-pull arrangement of ON and OFF cortical feedback as seen experimentally, this extended DOG (eDOG) model exhibits linear firing properties despite non-linear firing characteristics of the corticothalamic cells. The spatiotemporal receptive field of the eDOG model has a simple algebraic structure in Fourier space, while the real-space receptive field, as well as responses to visual stimuli, are found by evaluation of an integral. As an example application we use the eDOG model to study effects of cortical feedback on responses to flashing circular spots and patch-grating stimuli and find that the eDOG model can qualitatively account for experimental findings.     

Corticothalamic interactions in the transfer of visual information

Thalamic function does not stand apart, as a discrete processing step, from the cortical circuitry. The thalamus receives extensive feedback from the cortex and this influences the firing pattern, synchronization and sensory response mode of relay cells. A crucial question concerns the extent to which the feedback simply controls the state and transmission mode of relay cells and the extent to which the feedback participates in the specific processing of sensory information. Using examples from experiments examining the influence of feedback from the visual cortex to the lateral geniculate nucleus (LGN), we argue that thalamic mechanisms are selectively focused by visually driven feedback to optimize the thalamic contribution to segmentation and global integration. This involves effects on both the temporal and spatial parameters characterizing the responses of LGN cells and includes, for example, motion-driven feedback effects from MT (middle temporal visual area) relayed via layer 6 of V1 (primary visual cortex).     

Adaptive control of an operator’s performance based on biological feedback using the parameters of spatial synchronization of brain cortex areas

The efficiency of an operator’s performance under the determined (D-activity) and stochastic (S-activity) conditions depends on the readiness and synchronization of the frontoparietal and parietooccipital brain cortex areas. The algorithm for the generation of the feedback signal and program of adaptive control based on parameters of these cortical areas’ spatial synchronization were developed. To develop the adaptive control based on this algorithm, two series of experiments on volunteers were performed. The results of the study showed a connection between the initial readiness estimated by Luscher’s test and the efficiency of S- and D-activities modeled by computer games. The objective signs of initial readiness for S- and D-activity were found using parameters of spatial synchronization of the studied cortical areas’ activity in different spectral bands. The possibility of developing adaptive control skills based on the algorithm of the feedback signal generation and maintenance of these skills for one month was also demonstrated. Adaptive control sessions were found to improve characteristics of S- and D-activity, modeled by computer games.     

Development of spatial coarse-to-fine processing in the visual pathway

The sequential analysis of information in a coarse-to-fine manner is a fundamental mode of processing in the visual pathway. Spatial frequency (SF) tuning, arguably the most fundamental feature of spatial vision, provides particular intuition within the coarse-to-fine framework: low spatial frequencies convey global information about an image (e.g., general orientation), while high spatial frequencies carry more detailed information (e.g., edges). In this paper, we study the development of cortical spatial frequency tuning. As feedforward input from the lateral geniculate nucleus (LGN) has been shown to have significant influence on cortical coarse-to-fine processing, we present a firing-rate based thalamocortical model which includes both feedforward and feedback components. We analyze the relationship between various model parameters (including cortical feedback strength) and responses. We confirm the importance of the antagonistic relationship between the center and surround responses in thalamic relay cell receptive fields (RFs), and further characterize how specific structural LGN RF parameters affect cortical coarse-to-fine processing. Our results also indicate that the effect of cortical feedback on spatial frequency tuning is age-dependent: in particular, cortical feedback more strongly affects coarse-to-fine processing in kittens than in adults. We use our results to propose an experimentally testable hypothesis for the function of the extensive feedback in the corticothalamic circuit.     

Top-Down Inputs Enhance Orientation Selectivity in Neurons of the Primary Visual Cortex during Perceptual Learning

Perceptual learning has been used to probe the mechanisms of cortical plasticity in the adult brain. Feedback projections are ubiquitous in the cortex, but little is known about their role in cortical plasticity. Here we explore the hypothesis that learning visual orientation discrimination involves learning-dependent plasticity of top-down feedback inputs from higher cortical areas, serving a different function from plasticity due to changes in recurrent connections within a cortical area. In a Hodgkin-Huxley-based spiking neural network model of visual cortex, we show that modulation of feedback inputs to V1 from higher cortical areas results in shunting inhibition in V1 neurons, which changes the response properties of V1 neurons. The orientation selectivity of V1 neurons is enhanced without changing orientation preference, preserving the topographic organizations in V1. These results provide new insights to the mechanisms of plasticity in the adult brain, reconciling apparently inconsistent experiments and providing a new hypothesis for a functional role of the feedback connections.     

Non-Invasive Electrical Brain Stimulation Montages for Modulation of Human Motor Function

Non-invasive electrical brain stimulation (NEBS) is used to modulate brain function and behavior, both for research and clinical purposes. In particular, NEBS can be applied transcranially either as direct current stimulation (tDCS) or alternating current stimulation (tACS). These stimulation types exert time-, dose- and in the case of tDCS polarity-specific effects on motor function and skill learning in healthy subjects. Lately, tDCS has been used to augment the therapy of motor disabilities in patients with stroke or movement disorders. This article provides a step-by-step protocol for targeting the primary motor cortex with tDCS and transcranial random noise stimulation (tRNS), a specific form of tACS using an electrical current applied randomly within a pre-defined frequency range. The setup of two different stimulation montages is explained. In both montages the emitting electrode (the anode for tDCS) is placed on the primary motor cortex of interest. For unilateral motor cortex stimulation the receiving electrode is placed on the contralateral forehead while for bilateral motor cortex stimulation the receiving electrode is placed on the opposite primary motor cortex. The advantages and disadvantages of each montage for the modulation of cortical excitability and motor function including learning are discussed, as well as safety, tolerability and blinding aspects.     

Human auditory cortical activation during self-vocalization

During speaking, auditory feedback is used to adjust vocalizations. The brain systems mediating this integrative ability have been investigated using a wide range of experimental strategies. In this report we examined how vocalization alters speech-sound processing within auditory cortex by directly recording evoked responses to vocalizations and playback stimuli using intracranial electrodes implanted in neurosurgery patients. Several new findings resulted from these high-resolution invasive recordings in human subjects. Suppressive effects of vocalization were found to occur only within circumscribed areas of auditory cortex. In addition, at a smaller number of sites, the opposite pattern was seen; cortical responses were enhanced during vocalization. This increase in activity was reflected in high gamma power changes, but was not evident in the averaged evoked potential waveforms. These new findings support forward models for vocal control in which efference copies of premotor cortex activity modulate sub-regions of auditory cortex.     

Modelling of cortical and thalamic 600 Hz activity by means of oscillatory networks

The purpose of this study is to investigate information processing in the primary somatosensory system with the help of oscillatory network modelling. Specifically, we consider interactions in the oscillatory 600 Hz activity between the thalamus and the cortical Brodmann areas 3b and 1. This type of cortical activity occurs after electrical stimulation of peripheral nerves such as the median nerve. Our measurements consist of simultaneous 31-channel MEG and 32-channel EEG recordings and individual 3D MRI data. We perform source localization by means of a multi-dipole model. The dipole activation time courses are then modelled by a set of coupled oscillators, described by linear second-order ordinary delay differential equations (DDEs). In particular, a new model for the thalamic activity is included in the oscillatory network. The parameters of the DDE system are successfully fitted to the data by a nonlinear evolutionary optimization method. To activate the oscillatory network, an individual input function is used, based on measurements of the propagated stimulation signal at the biceps. A significant feedback from the cortex to the thalamus could be detected by comparing the network modelling with and without feedback connections. Our finding in humans is supported by earlier animal studies. We conclude that this type of rhythmic brain activity can be modelled by oscillatory networks in order to disentangle feed forward and feedback information transfer.     

A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn

A theory is presented of the way in which the hypercolumns in primary visual cortex (V1) are organized to detect important features of visual images, namely local orientation and spatial-frequency. Given the existence in V1 of dual maps for these features, both organized around orientation pinwheels, we constructed a model of a hypercolumn in which orientation and spatial-frequency preferences are represented by the two angular coordinates of a sphere. The two poles of this sphere are taken to correspond, respectively, to high and low spatial-frequency preferences. In Part I of the paper, we use mean-field methods to derive exact solutions for localized activity states on the sphere. We show how cortical amplification through recurrent interactions generates a sharply tuned, contrast-invariant population response to both local orientation and local spatial frequency, even in the case of a weakly biased input from the lateral geniculate nucleus (LGN). A major prediction of our model is that this response is non-separable with respect to the local orientation and spatial frequency of a stimulus. That is, orientation tuning is weaker around the pinwheels, and there is a shift in spatial-frequency tuning towards that of the closest pinwheel at non-optimal orientations. In Part II of the paper, we demonstrate that a simple feed-forward model of spatial-frequency preference, unlike that for orientation preference, does not generate a faithful representation when amplified by recurrent interactions in V1. We then introduce the idea that cortico-geniculate feedback modulates LGN activity to generate a faithful representation, thus providing a new functional interpretation of the role of this feedback pathway. Using linear filter theory, we show that if the feedback from a cortical cell is taken to be approximately equal to the reciprocal of the corresponding feed-forward receptive field (in the two-dimensional Fourier domain), then the mismatch between the feed-forward and cortical frequency representations is eliminated. We therefore predict that cortico-geniculate feedback connections innervate the LGN in a pattern determined by the orientation and spatial-frequency biases of feed-forward receptive fields. Finally, we show how recurrent cortical interactions can generate cross-orientation suppression.     

A Simple Rule for Dendritic Spine and Axonal Bouton Formation Can Account for Cortical Reorganization after Focal Retinal Lesions

Lasting alterations in sensory input trigger massive structural and functional adaptations in cortical networks. The principles governing these experience-dependent changes are, however, poorly understood. Here, we examine whether a simple rule based on the neurons'' need for homeostasis in electrical activity may serve as driving force for cortical reorganization. According to this rule, a neuron creates new spines and boutons when its level of electrical activity is below a homeostatic set-point and decreases the number of spines and boutons when its activity exceeds this set-point. In addition, neurons need a minimum level of activity to form spines and boutons. Spine and bouton formation depends solely on the neuron''s own activity level, and synapses are formed by merging spines and boutons independently of activity. Using a novel computational model, we show that this simple growth rule produces neuron and network changes as observed in the visual cortex after focal retinal lesions. In the model, as in the cortex, the turnover of dendritic spines was increased strongest in the center of the lesion projection zone, while axonal boutons displayed a marked overshoot followed by pruning. Moreover, the decrease in external input was compensated for by the formation of new horizontal connections, which caused a retinotopic remapping. Homeostatic regulation may provide a unifying framework for understanding cortical reorganization, including network repair in degenerative diseases or following focal stroke.     

Top-Down Feedback in an HMAX-Like Cortical Model of Object Perception Based on Hierarchical Bayesian Networks and Belief Propagation

Hierarchical generative models, such as Bayesian networks, and belief propagation have been shown to provide a theoretical framework that can account for perceptual processes, including feedforward recognition and feedback modulation. The framework explains both psychophysical and physiological experimental data and maps well onto the hierarchical distributed cortical anatomy. However, the complexity required to model cortical processes makes inference, even using approximate methods, very computationally expensive. Thus, existing object perception models based on this approach are typically limited to tree-structured networks with no loops, use small toy examples or fail to account for certain perceptual aspects such as invariance to transformations or feedback reconstruction. In this study we develop a Bayesian network with an architecture similar to that of HMAX, a biologically-inspired hierarchical model of object recognition, and use loopy belief propagation to approximate the model operations (selectivity and invariance). Crucially, the resulting Bayesian network extends the functionality of HMAX by including top-down recursive feedback. Thus, the proposed model not only achieves successful feedforward recognition invariant to noise, occlusions, and changes in position and size, but is also able to reproduce modulatory effects such as illusory contour completion and attention. Our novel and rigorous methodology covers key aspects such as learning using a layerwise greedy algorithm, combining feedback information from multiple parents and reducing the number of operations required. Overall, this work extends an established model of object recognition to include high-level feedback modulation, based on state-of-the-art probabilistic approaches. The methodology employed, consistent with evidence from the visual cortex, can be potentially generalized to build models of hierarchical perceptual organization that include top-down and bottom-up interactions, for example, in other sensory modalities.     

CNV-like potentials on the cortical surface associated with conditioning in head-restrained rats

Head-restrained rats were conditioned to perform a CNV task: to press a lever in response to an imperative auditory stimulus (S2) given 1.5 sec after a warning stimulus (S1) for a drop of jelly food. With an electrode on the surface of the forelimb cortex, (1) sharp wave complexes immediately after S1 and S2, and (2) a negative slow potential (SP) between S1 and S2, on which early and late components were discernible, were recorded in association with performance of this task. With the electrode at a depth of 2 mm in the same cortical area, the corresponding field potential showed a long-lasting positive shift in addition to the components of the surface potential. These monopolar recordings were obtained with respect to a common reference at the frontal sinus. The surface-minus-depth potential (the transcortical potential), consequently, showed a surface-negative tonic wave, confirming Pirch's report (1980). During extinction of this conditioning, the SP between S1 and S2 disappeared, while the sharp waves following S1 and S2 remained with little modification, suggesting that the sharp waves are a kind of evoked potential (EP) elicited by the stimuli.Recording from 5 surface electrodes set in an array over the left hemisphere contralateral to the used forelimb during development of the conditioning revealed not only a spatial distribution of the SP but also a transition of the potentials. As the conditioning progressed, the negativity of the early SP component tended to increase, while that of the late component tended to decrease and was confined to the sensorimotor cortex. The similarities of the rat cortical surface potentials to the human and monkey CNV in their wave form and function suggests that the rat brain can produce electrical activity analogous to the human CNV.     

Studies of stimulus parameters for seizure disruption using neural network simulations

A large scale neural network simulation with realistic cortical architecture has been undertaken to investigate the effects of external electrical stimulation on the propagation and evolution of ongoing seizure activity. This is an effort to explore the parameter space of stimulation variables to uncover promising avenues of research for this therapeutic modality. The model consists of an approximately 800 mum x 800 mum region of simulated cortex, and includes seven neuron classes organized by cortical layer, inhibitory or excitatory properties, and electrophysiological characteristics. The cell dynamics are governed by a modified version of the Hodgkin-Huxley equations in single compartment format. Axonal connections are patterned after histological data and published models of local cortical wiring. Stimulation induced action potentials take place at the axon initial segments, according to threshold requirements on the applied electric field distribution. Stimulation induced action potentials in horizontal axonal branches are also separately simulated. The calculations are performed on a 16 node distributed 32-bit processor system. Clear differences in seizure evolution are presented for stimulated versus the undisturbed rhythmic activity. Data is provided for frequency dependent stimulation effects demonstrating a plateau effect of stimulation efficacy as the applied frequency is increased from 60 to 200 Hz. Timing of the stimulation with respect to the underlying rhythmic activity demonstrates a phase dependent sensitivity. Electrode height and position effects are also presented. Using a dipole stimulation electrode arrangement, clear orientation effects of the dipole with respect to the model connectivity is also demonstrated. A sensitivity analysis of these results as a function of the stimulation threshold is also provided.     

Mapping human brain networks with cortico-cortical evoked potentials

The cerebral cortex forms a sheet of neurons organized into a network of interconnected modules that is highly expanded in humans and presumably enables our most refined sensory and cognitive abilities. The links of this network form a fundamental aspect of its organization, and a great deal of research is focusing on understanding how information flows within and between different regions. However, an often-overlooked element of this connectivity regards a causal, hierarchical structure of regions, whereby certain nodes of the cortical network may exert greater influence over the others. While this is difficult to ascertain non-invasively, patients undergoing invasive electrode monitoring for epilepsy provide a unique window into this aspect of cortical organization. In this review, we highlight the potential for cortico-cortical evoked potential (CCEP) mapping to directly measure neuronal propagation across large-scale brain networks with spatio-temporal resolution that is superior to traditional neuroimaging methods. We first introduce effective connectivity and discuss the mechanisms underlying CCEP generation. Next, we highlight how CCEP mapping has begun to provide insight into the neural basis of non-invasive imaging signals. Finally, we present a novel approach to perturbing and measuring brain network function during cognitive processing. The direct measurement of CCEPs in response to electrical stimulation represents a potentially powerful clinical and basic science tool for probing the large-scale networks of the human cerebral cortex.     

Correction of Distortion in Flattened Representations of the Cortical Surface Allows Prediction of V1-V3 Functional Organization from Anatomy

Several domains of neuroscience offer map-like models that link location on the cortical surface to properties of sensory representation. Within cortical visual areas V1, V2, and V3, algebraic transformations can relate position in the visual field to the retinotopic representation on the flattened cortical sheet. A limit to the practical application of this structure-function model is that the cortex, while topologically a two-dimensional surface, is curved. Flattening of the curved surface to a plane unavoidably introduces local geometric distortions that are not accounted for in idealized models. Here, we show that this limitation is overcome by correcting the geometric distortion induced by cortical flattening. We use a mass-spring-damper simulation to create a registration between functional MRI retinotopic mapping data of visual areas V1, V2, and V3 and an algebraic model of retinotopy. This registration is then applied to the flattened cortical surface anatomy to create an anatomical template that is linked to the algebraic retinotopic model. This registered cortical template can be used to accurately predict the location and retinotopic organization of these early visual areas from cortical anatomy alone. Moreover, we show that prediction accuracy remains when extrapolating beyond the range of data used to inform the model, indicating that the registration reflects the retinotopic organization of visual cortex. We provide code for the mass-spring-damper technique, which has general utility for the registration of cortical structure and function beyond the visual cortex.