Does abnormal spinal reciprocal inhibition lead to co-contraction of antagonist motor units? A modeling study

It is suggested that co-contraction of antagonist motor units perhaps due to abnormal disynaptic I(a) reciprocal inhibition is responsible for Parkinsonian rigidity. A neural model of Parkinson's disease bradykinesia is extended to incorporate the effects of spindle feedback on key cortical cells and examine the effects of dopamine depletion on spinal activities. Simulation results show that although reciprocal inhibition is reduced in DA depleted case, it doesn't lead to co-contraction of antagonist motor neurons. Implications to Parkinsonian rigidity are discussed.     

The functional role of different neural activation profiles during precision grip: An artificial neural network approach

A dynamic and recurrent artificial neural network was used to investigate the functional properties of firing patterns observed in the primary motor (M1) and the primary somatosensory (S1) cortex of the behaving monkey during control of precision grip force. In the behaving monkey it was found that neurons in M1 and in S1 increase their firing activity with increasing grip force, as do the intrinsic and extrinsic hand muscles implicated in the task. However, some neurons also decreased their activity as a function of increasing force. The functional implication of these latter neurons is not clear and has not been elucidated so far. In order to explore their functional implication, we therefore simulated patterns of neural activity in artificial neural networks that represent cortical, spinal and afferent neural populations and tested whether particular activity profiles would emerge as a function of the input and of the connectivity of these networks. The functional implication of units with emergent or imposed decreasing activity was then explored.Decreasing patterns of activity in M1 units did not emerge from the networks. However, the same networks generated decreasing activity if imposed as target patterns. As indicated by the emerging weight space, M1 projection units with decreasing patterns are functionally less involved in driving alpha motoneurons than units with increasing profiles. Furthermore, these units did not provide significant fusimotor drive, whereas those with increasing profiles did. Fusimotor drive was a function of the (imposed) form of muscle spindle afferent activity: with gamma (fusimotor) drive, muscle spindle afferents provided signals other than muscle length (as observed experimentally). The network solutions thus predict a functional dichotomy between increasing and decreasing M1 neurons: the former primarily drive alpha and gamma motoneurons, the latter only weakly alpha motoneurons.     

Activity of precentral neurons during torque-triggered hand movements in awake primates.

In monkeys performing a handle-repositioning task involving primarily wrist flexion-extension (F-E) movements after a torque perturbation was delivered to the handle, single units were recorded extracellularly in the contralateral precentral cortex. Precentral neurons were identified by passive somatosensory stimulation, and were classified into five somatotopically organized populations. Based on electromyographic recordings, it was observed that flexors and extensors about the wrist joint were specifically involved in the repositioning of the handle, while many other muscles which act at the wrist and other forelimb joints were involved in the task in a supportive role. In precentral cortex, all neuronal responses observed were temporally correlated to both the sensory stimuli and the motor responses. Visual stimuli, presented simultaneously with torque perturbations, did not affect the early portion of cortical responses to such torque perturbations. In each of the five somatotopically organized neuronal populations, task-related neurons as well as task-unrelated ones were observed. A significantly larger proportion of wrist (F-E) neurons was related to the task, as compared with the other, nonwrist (F-E) populations. The above findings were discussed in the context of a hypothesis for the function of precentral cortex during voluntary limb movement in awake primates. This hypothesis incorporates a relationship between activities of populations of precentral neurons, defined with respect to their responses to peripheral events at or about single joints, and movements about the same joint.     

Cortical Resonance Frequencies Emerge from Network Size and Connectivity

Neural oscillations occur within a wide frequency range with different brain regions exhibiting resonance-like characteristics at specific points in the spectrum. At the microscopic scale, single neurons possess intrinsic oscillatory properties, such that is not yet known whether cortical resonance is consequential to neural oscillations or an emergent property of the networks that interconnect them. Using a network model of loosely-coupled Wilson-Cowan oscillators to simulate a patch of cortical sheet, we demonstrate that the size of the activated network is inversely related to its resonance frequency. Further analysis of the parameter space indicated that the number of excitatory and inhibitory connections, as well as the average transmission delay between units, determined the resonance frequency. The model predicted that if an activated network within the visual cortex increased in size, the resonance frequency of the network would decrease. We tested this prediction experimentally using the steady-state visual evoked potential where we stimulated the visual cortex with different size stimuli at a range of driving frequencies. We demonstrate that the frequency corresponding to peak steady-state response inversely correlated with the size of the network. We conclude that although individual neurons possess resonance properties, oscillatory activity at the macroscopic level is strongly influenced by network interactions, and that the steady-state response can be used to investigate functional networks.     

The Importance of Lateral Connections in the Parietal Cortex for Generating Motor Plans

Substantial evidence has highlighted the significant role of associative brain areas, such as the posterior parietal cortex (PPC) in transforming multimodal sensory information into motor plans. However, little is known about how different sensory information, which can have different delays or be absent, combines to produce a motor plan, such as executing a reaching movement. To address these issues, we constructed four biologically plausible network architectures to simulate PPC: 1) feedforward from sensory input to the PPC to a motor output area, 2) feedforward with the addition of an efference copy from the motor area, 3) feedforward with the addition of lateral or recurrent connectivity across PPC neurons, and 4) feedforward plus efference copy, and lateral connections. Using an evolutionary strategy, the connectivity of these network architectures was evolved to execute visually guided movements, where the target stimulus provided visual input for the entirety of each trial. The models were then tested on a memory guided motor task, where the visual target disappeared after a short duration. Sensory input to the neural networks had sensory delays consistent with results from monkey studies. We found that lateral connections within the PPC resulted in smoother movements and were necessary for accurate movements in the absence of visual input. The addition of lateral connections resulted in velocity profiles consistent with those observed in human and non-human primate visually guided studies of reaching, and allowed for smooth, rapid, and accurate movements under all conditions. In contrast, Feedforward or Feedback architectures were insufficient to overcome these challenges. Our results suggest that intrinsic lateral connections are critical for executing accurate, smooth motor plans.     

Parkinsonian tremor and simplification in network dynamics

We explore the behavior of richly connected inhibitory neural networks under parameter changes that correspond to weakening of synaptic efficacies between network units, and show that transitions from irregular to periodic dynamics are common in such systems. The weakening of these connections leads to a reduction in the number of units that effectively drive the dynamics and thus to simpler behavior. We hypothesize that the multiple interconnecting loops of the brain’s motor circuitry, which involve many inhibitory connections, exhibit such transitions. Normal physiological tremor is irregular while other forms of tremor show more regular oscillations. Tremor in Parkinson’s disease, for example, stems from weakened synaptic efficacies of dopaminergic neurons in the nigro-striatal pathway, as in our general model. The multiplicity of structures involved in the production of symptoms in Parkinson’s disease and the reversibility of symptoms by pharmacological and surgical manipulation of connection parameters suggest that such a neural network model is appropriate. Furthermore, fixed points that can occur in the network models are suggestive of akinesia in Parkinson’s disease. This model is consistent with the view that normal physiological systems can be regulated by robust and richly connected feedback networks with complex dynamics, and that loss of complexity in the feedback structure due to disease leads to more orderly behavior.     

Recurrent neural networks of integrate-and-fire cells simulating short-term memory and wrist movement tasks derived from continuous dynamic networks

Dynamic recurrent neural networks composed of units with continuous activation functions provide a powerful tool for simulating a wide range of behaviors, since the requisite interconnections can be readily derived by gradient descent methods. However, it is not clear whether more realistic integrate-and-fire cells with comparable connection weights would perform the same functions. We therefore investigated methods to convert dynamic recurrent neural networks of continuous units into networks with integrate-and-fire cells. The transforms were tested on two recurrent networks derived by backpropagation. The first simulates a short-term memory task with units that mimic neural activity observed in cortex of monkeys performing instructed delay tasks. The network utilizes recurrent connections to generate sustained activity that codes the remembered value of a transient cue. The second network simulates patterns of neural activity observed in monkeys performing a step-tracking task with flexion/extension wrist movements. This more complicated network provides a working model of the interactions between multiple spinal and supraspinal centers controlling motoneurons. Our conversion algorithm replaced each continuous unit with multiple integrate-and-fire cells that interact through delayed "synaptic potentials". Successful transformation depends on obtaining an appropriate fit between the activation function of the continuous units and the input-output relation of the spiking cells. This fit can be achieved by adapting the parameters of the synaptic potentials to replicate the input-output behavior of a standard sigmoidal activation function (shown for the short-term memory network). Alternatively, a customized activation function can be derived from the input-output relation of the spiking cells for a chosen set of parameters (demonstrated for the wrist flexion/extension network). In both cases the resulting networks of spiking cells exhibited activity that replicated the activity of corresponding continuous units. This confirms that the network solutions obtained through backpropagation apply to spiking networks and provides a useful method for deriving recurrent spiking networks performing a wide range of functions.     

A thalamo-cortical neural mass model for the simulation of brain rhythms during sleep

Cortico-thalamic interactions are known to play a pivotal role in many brain phenomena, including sleep, attention, memory consolidation and rhythm generation. Hence, simple mathematical models that can simulate the dialogue between the cortex and the thalamus, at a mesoscopic level, have a great cognitive value. In the present work we describe a neural mass model of a cortico-thalamic module, based on neurophysiological mechanisms. The model includes two thalamic populations (a thalamo-cortical relay cell population, TCR, and its related thalamic reticular nucleus, TRN), and a cortical column consisting of four connected populations (pyramidal neurons, excitatory interneurons, inhibitory interneurons with slow and fast kinetics). Moreover, thalamic neurons exhibit two firing modes: bursting and tonic. Finally, cortical synapses among pyramidal neurons incorporate a disfacilitation mechanism following prolonged activity. Simulations show that the model is able to mimic the different patterns of rhythmic activity in cortical and thalamic neurons (beta and alpha waves, spindles, delta waves, K-complexes, slow sleep waves) and their progressive changes from wakefulness to deep sleep, by just acting on modulatory inputs. Moreover, simulations performed by providing short sensory inputs to the TCR show that brain rhythms during sleep preserve the cortex from external perturbations, still allowing a high cortical activity necessary to drive synaptic plasticity and memory consolidation. In perspective, the present model may be used within larger cortico-thalamic networks, to gain a deeper understanding of mechanisms beneath synaptic changes during sleep, to investigate the specific role of brain rhythms, and to explore cortical synchronization achieved via thalamic influences.     

Physiological and pathological oscillatory networks in the human motor system.

Human brain functions are heavily contingent on neural interactions both at the single neuron and the neural population or system level. Accumulating evidence from neurophysiological studies strongly suggests that coupling of oscillatory neural activity provides an important mechanism to establish neural interactions. With the availability of whole-head magnetoencephalography (MEG) macroscopic oscillatory activity can be measured non-invasively from the human brain with high temporal and spatial resolution. To localise, quantify and map oscillatory activity and interactions onto individual brain anatomy we have developed the 'dynamic imaging of coherent sources' (DICS) method which allows to identify and analyse cerebral oscillatory networks from MEG recordings. Using this approach we have characterized physiological and pathological oscillatory networks in the human sensorimotor system. Coherent 8 Hz oscillations emerge from a cerebello-thalamo-premotor-motor cortical network and exert an 8 Hz oscillatory drive on the spinal motor neurons which can be observed as a physiological tremulousness of the movement termed movement discontinuities. This network represents the neurophysiological substrate of a discrete mode of motor control. In parkinsonian resting tremor we have identified an extensive cerebral network consisting of primary motor and lateral premotor cortex, supplementary motor cortex, thalamus/basal ganglia, posterior parietal cortex and secondary somatosensory cortex, which are entrained in the tremor or twice the tremor rhythm. This low frequency entrapment of motor areas likely plays an important role in the pathophysiology of parkinsonian motor symptoms. Finally, studies on patients with postural tremor in hepatic encephalopathy revealed that this type of tremor results from a pathologically slow thalamocortical and cortico-muscular coupling during isometric hold tasks. In conclusion, the analysis of oscillatory cerebral networks provides new insights into physiological mechanisms of motor control and pathophysiological mechanisms of tremor disorders.     

Neural Coding of Finger and Wrist Movements

Previous work (Schieber and Hibbard, 1993) has shown that single motor cortical neurons do not discharge specifically for a particular flexion-extension finger movement but instead are active with movements of different fingers. In addition, neuronal populations active with movements of different fingers overlap extensively in their spatial locations in the motor cortex. These data suggested that control of any finger movement utilizes a distributed population of neurons. In this study we applied the neuronal population vector analysis (Georgopoulos et al., 1983) to these same data to determine (1) whether single cells are tuned in an abstract, three-dimensional (3D) instructed finger and wrist movement space with hand-like geometry and (2) whether the neuronal population encodes specific finger movements. We found that the activity of 132/176 (75%) motor cortical neurons related to finger movements was indeed tuned in this space. Moreover, the population vector computed in this space predicted well the instructed finger movement. Thus, although single neurons may be related to several disparate finger movements, and neurons related to different finger movements are intermingled throughout the hand area of the motor cortex, the neuronal population activity does specify particular finger movements.     

Motor patterns during kicking movements in the locust

Locusts (Schistocerca gregaria) use a distinctive motor pattern to extend the tibia of a hind leg rapidly in a kick. The necessary force is generated by an almost isometric contraction of the extensor tibiae muscle restrained by the co-contraction of the flexor tibiae (co-contraction phase) and aided by the mechanics of the femoro-tibial joint. The stored energy is delivered suddenly when the flexor muscle is inhibited. This paper analyses the activity of motor neurons to the major hind leg muscles during kicking, and relates it to tibial movements and the resultant forces.During the co-contraction phase flexor tibiae motor neurons are driven by apparently common sources of synaptic inputs to depolarized plateaus at which they spike. The two excitatory extensor motor neurons are also depolarized by similar patterns of synaptic inputs, but with the slow producing more spikes at higher frequencies than the fast. Trochanteral depressors spike at high frequency, the single levator tarsi at low frequency, and common inhibitors 2 and 3 spike sporadically. Trochanteral levators, depressor tarsi, and a retractor unguis motor neuron are hyperpolarized.Before the tibia extends all flexor motor neurons are hyperpolarized simultaneously, two common inhibitors, and the levator trochanter and depressor tarsi motor neurons are depolarized. Later, but still before the tibial movement starts, the extensor tibiae and levator tarsi motor neurons are hyperpolarized. After the movement has started, the extensor motor neurons are hyperpolarized further and the depressor trochanteris motor neurons are also hyperpolarized, indicating a contribution of both central and sensory feedback pathways.Variations in the duration of the co-contraction of almost twenty-fold, and in the number of spikes in the fast extensor tibiae motor neuron from 2–50 produce a spectrum of tibial extensions ranging from slow and weak, to rapid and powerful. Flexibility in the networks producing the motor pattern therefore results in a range of movements suited to the fluctuating requirements of the animal.     

Effect of the topology and delayed interactions in neuronal networks synchronization

As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing (either evoked by external stimuli or internally generated) is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior.     

Red nucleus: role in motor control

Experimental reports in the past year have provided a better understanding of the motor functions of excitatory and inhibitory neurotransmitters in the red nucleus, and of the sensorimotor properties of single rubral neurons. These data fit well within the framework of a neural network model of the rubrocerebellar system.     

Associative neural network model for the generation of temporal patterns. Theory and application to central pattern generators.

Cyclic patterns of motor neuron activity are involved in the production of many rhythmic movements, such as walking, swimming, and scratching. These movements are controlled by neural circuits referred to as central pattern generators (CPGs). Some of these circuits function in the absence of both internal pacemakers and external feedback. We describe an associative neural network model whose dynamic behavior is similar to that of CPGs. The theory predicts the strength of all possible connections between pairs of neurons on the basis of the outputs of the CPG. It also allows the mean operating levels of the neurons to be deduced from the measured synaptic strengths between the pairs of neurons. We apply our theory to the CPG controlling escape swimming in the mollusk Tritonia diomedea. The basic rhythmic behavior is shown to be consistent with a simplified model that approximates neurons as threshold units and slow synaptic responses as elementary time delays. The model we describe may have relevance to other fixed action behaviors, as well as to the learning, recall, and recognition of temporally ordered information.     

Driving reservoir models with oscillations: a solution to the extreme structural sensitivity of chaotic networks

A large body of experimental and theoretical work on neural coding suggests that the information stored in brain circuits is represented by time-varying patterns of neural activity. Reservoir computing, where the activity of a recurrently connected pool of neurons is read by one or more units that provide an output response, successfully exploits this type of neural activity. However, the question of system robustness to small structural perturbations, such as failing neurons and synapses, has been largely overlooked. This contrasts with well-studied dynamical perturbations that lead to divergent network activity in the presence of chaos, as is the case for many reservoir networks. Here, we distinguish between two types of structural network perturbations, namely local (e.g., individual synaptic or neuronal failure) and global (e.g., network-wide fluctuations). Surprisingly, we show that while global perturbations have a limited impact on the ability of reservoir models to perform various tasks, local perturbations can produce drastic effects. To address this limitation, we introduce a new architecture where the reservoir is driven by a layer of oscillators that generate stable and repeatable trajectories. This model outperforms previous implementations while being resistant to relatively large local and global perturbations. This finding has implications for the design of reservoir models that capture the capacity of brain circuits to perform cognitively and behaviorally relevant tasks while remaining robust to various forms of perturbations. Further, our work proposes a novel role for neuronal oscillations found in cortical circuits, where they may serve as a collection of inputs from which a network can robustly generate complex dynamics and implement rich computations.     

On how network architecture determines the dominant patterns of spontaneous neural activity

In the absence of sensory stimulation, neocortical circuits display complex patterns of neural activity. These patterns are thought to reflect relevant properties of the network, including anatomical features like its modularity. It is also assumed that the synaptic connections of the network constrain the repertoire of emergent, spontaneous patterns. Although the link between network architecture and network activity has been extensively investigated in the last few years from different perspectives, our understanding of the relationship between the network connectivity and the structure of its spontaneous activity is still incomplete. Using a general mathematical model of neural dynamics we have studied the link between spontaneous activity and the underlying network architecture. In particular, here we show mathematically how the synaptic connections between neurons determine the repertoire of spatial patterns displayed in the spontaneous activity. To test our theoretical result, we have also used the model to simulate spontaneous activity of a neural network, whose architecture is inspired by the patchy organization of horizontal connections between cortical columns in the neocortex of primates and other mammals. The dominant spatial patterns of the spontaneous activity, calculated as its principal components, coincide remarkably well with those patterns predicted from the network connectivity using our theory. The equivalence between the concept of dominant pattern and the concept of attractor of the network dynamics is also demonstrated. This in turn suggests new ways of investigating encoding and storage capabilities of neural networks.     

Modeling perceptual learning with multiple interacting elements: A neural network model describing early visual perceptual learning

We introduce a neural network model of an early visual cortical area, in order to understand better results of psychophysical experiments concerning perceptual learning during odd element (pop-out) detection tasks (Ahissar and Hochstein, 1993, 1994a).The model describes a network, composed of orientation selective units, arranged in a hypercolumn structure, with receptive field properties modeled from real monkey neurons. Odd element detection is a final pattern of activity with one (or a few) salient units active. The learning algorithm used was the Associative reward-penalty (Ar-p) algorithm of reinforcement learning (Barto and Anandan, 1985), following physiological data indicating the role of supervision in cortical plasticity.Simulations show that network performance improves dramatically as the weights of inter-unit connections reach a balance between lateral iso-orientation inhibition, and facilitation from neighboring neurons with different preferred orientations. The network is able to learn even from chance performance, and in the presence of a large amount of noise in the response function. As additional tests of the model, we conducted experiments with human subjects in order to examine learning strategy and test model predictions.     

Hierarchical genetic algorithm versus static optimization-investigation of elbow flexion and extension movements

The applicability of static optimization (and, respectively, frequently used objective functions) for prediction of individual muscle forces for dynamic conditions has often been discussed. Some of the problems are whether time-independent objective functions are suitable, and how to incorporate muscle physiology in models. The present paper deals with a twofold task: (1) implementation of hierarchical genetic algorithm (HGA) based on the properties of the motor units (MUs) twitches, and using multi-objective, time-dependent optimization functions; and (2) comparison of the results of the HGA application with those obtained through static optimization with a criterion "minimum of a weighted sum of the muscle forces raised to the power of n". HGA and its software implementation are presented. The moments of neural stimulation of all MUs are design variables coding the problem in the terms of HGA. The main idea is in using genetic operations to find these moments, so that the sum of MUs twitches satisfies the imposed goals (required joint moments, minimal sum of muscle forces, etc.). Elbow flexion and extension movements with different velocities are considered as proper illustration. It is supposed that they are performed by two extensor muscles and three flexor muscles. The results show that HGA is a suitable means for precise investigation of motor control. Many experimentally observed phenomena (such as antagonistic co-contraction, three-phasic behavior of the muscles during fast movements) can find their explanation by the properties of the MUs twitches. Static optimization is also able to predict three-phasic behavior and could be used as practicable and computationally inexpensive method for total estimation of the muscle forces.     

Tracking Plasticity: Effects of Long-Term Rehearsal in Expert Dancers Encoding Music to Movement

Our knowledge of neural plasticity suggests that neural networks show adaptation to environmental and intrinsic change. In particular, studies investigating the neuroplastic changes associated with learning and practicing motor tasks have shown that practicing such tasks results in an increase in neural activation in several specific brain regions. However, studies comparing experts and non-experts suggest that experts employ less neuronal activation than non-experts when performing a familiar motor task. Here, we aimed to determine the long-term changes in neural networks associated with learning a new dance in professional ballet dancers over 34 weeks. Subjects visualized dance movements to music while undergoing fMRI scanning at four time points over 34-weeks. Results demonstrated that initial learning and performance at seven weeks led to increases in activation in cortical regions during visualization compared to the first week. However, at 34 weeks, the cortical networks showed reduced activation compared to week seven. Specifically, motor learning and performance over the 34 weeks showed the typical inverted-U-shaped function of learning. Further, our result demonstrate that learning of a motor sequence of dance movements to music in the real world can be visualized by expert dancers using fMRI and capture highly significant modeled fits of the brain network variance of BOLD signals from early learning to expert level performance.