Neural heterogeneity controls computations in spiking neural networks.

The brain is composed of complex networks of interacting neurons that express considerable heterogeneity in their physiology and spiking characteristics. How does this neural heterogeneity influence macroscopic neural dynamics, and how might it contribute to neural computation? In this work, we use a mean-field model to investigate computation in heterogeneous neural networks, by studying how the heterogeneity of cell spiking thresholds affects three key computational functions of a neural population: the gating, encoding, and decoding of neural signals. Our results suggest that heterogeneity serves different computational functions in different cell types. In inhibitory interneurons, varying the degree of spike threshold heterogeneity allows them to gate the propagation of neural signals in a reciprocally coupled excitatory population. Whereas homogeneous interneurons impose synchronized dynamics that narrow the dynamic repertoire of the excitatory neurons, heterogeneous interneurons act as an inhibitory offset while preserving excitatory neuron function. Spike threshold heterogeneity also controls the entrainment properties of neural networks to periodic input, thus affecting the temporal gating of synaptic inputs. Among excitatory neurons, heterogeneity increases the dimensionality of neural dynamics, improving the network's capacity to perform decoding tasks. Conversely, homogeneous networks suffer in their capacity for function generation, but excel at encoding signals via multistable dynamic regimes. Drawing from these findings, we propose intra-cell-type heterogeneity as a mechanism for sculpting the computational properties of local circuits of excitatory and inhibitory spiking neurons, permitting the same canonical microcircuit to be tuned for diverse computational tasks.

From monkeys to humans: observation-basedEMGbrain-computer interface decoders for humans with paralysis.

Objective. Intracortical brain-computer interfaces (iBCIs) aim to enable individuals with paralysis to control the movement of virtual limbs and robotic arms. Because patients' paralysis prevents training a direct neural activity to limb movement decoder, most iBCIs rely on 'observation-based' decoding in which the patient watches a moving cursor while mentally envisioning making the movement. However, this reliance on observed target motion for decoder development precludes its application to the prediction of unobservable motor output like muscle activity. Here, we ask whether recordings of muscle activity from a surrogate individual performing the same movement as the iBCI patient can be used as target for an iBCI decoder.Approach. We test two possible approaches, each using data from a human iBCI user and a monkey, both performing similar motor actions. In one approach, we trained a decoder to predict the electromyographic (EMG) activity of a monkey from neural signals recorded from a human. We then contrast this to a second approach, based on the hypothesis that the low-dimensional 'latent' neural representations of motor behavior, known to be preserved across time for a given behavior, might also be preserved across individuals. We 'transferred' an EMG decoder trained solely on monkey data to the human iBCI user after using Canonical Correlation Analysis to align the human latent signals to those of the monkey.Main results. We found that both direct and transfer decoding approaches allowed accurate EMG predictions between two monkeys and from a monkey to a human.Significance. Our findings suggest that these latent representations of behavior are consistent across animals and even primate species. These methods are an important initial step in the development of iBCI decoders that generate EMG predictions that could serve as signals for a biomimetic decoder controlling motion and impedance of a prosthetic arm, or even muscle force directly through functional electrical stimulation.

Macroscopic dynamics of neural networks with heterogeneous spiking thresholds.

Mean-field theory links the physiological properties of individual neurons to the emergent dynamics of neural population activity. These models provide an essential tool for studying brain function at different scales; however, for their application to neural populations on large scale, they need to account for differences between distinct neuron types. The Izhikevich single neuron model can account for a broad range of different neuron types and spiking patterns, thus rendering it an optimal candidate for a mean-field theoretic treatment of brain dynamics in heterogeneous networks. Here we derive the mean-field equations for networks of all-to-all coupled Izhikevich neurons with heterogeneous spiking thresholds. Using methods from bifurcation theory, we examine the conditions under which the mean-field theory accurately predicts the dynamics of the Izhikevich neuron network. To this end, we focus on three important features of the Izhikevich model that are subject here to simplifying assumptions: (i) spike-frequency adaptation, (ii) the spike reset conditions, and (iii) the distribution of single-cell spike thresholds across neurons. Our results indicate that, while the mean-field model is not an exact model of the Izhikevich network dynamics, it faithfully captures its different dynamic regimes and phase transitions. We thus present a mean-field model that can represent different neuron types and spiking dynamics. The model comprises biophysical state variables and parameters, incorporates realistic spike resetting conditions, and accounts for heterogeneity in neural spiking thresholds. These features allow for a broad applicability of the model as well as for a direct comparison to experimental data.

Estimating the dimensionality of the manifold underlying multi-electrode neural recordings.

It is generally accepted that the number of neurons in a given brain area far exceeds the number of neurons needed to carry any specific function controlled by that area. For example, motor areas of the human brain contain tens of millions of neurons that control the activation of tens or at most hundreds of muscles. This massive redundancy implies the covariation of many neurons, which constrains the population activity to a low-dimensional manifold within the space of all possible patterns of neural activity. To gain a conceptual understanding of the complexity of the neural activity within a manifold, it is useful to estimate its dimensionality, which quantifies the number of degrees of freedom required to describe the observed population activity without significant information loss. While there are many algorithms for dimensionality estimation, we do not know which are well suited for analyzing neural activity. The objective of this study was to evaluate the efficacy of several representative algorithms for estimating the dimensionality of linearly and nonlinearly embedded data. We generated synthetic neural recordings with known intrinsic dimensionality and used them to test the algorithms' accuracy and robustness. We emulated some of the important challenges associated with experimental data by adding noise, altering the nature of the embedding of the low-dimensional manifold within the high-dimensional recordings, varying the dimensionality of the manifold, and limiting the amount of available data. We demonstrated that linear algorithms overestimate the dimensionality of nonlinear, noise-free data. In cases of high noise, most algorithms overestimated the dimensionality. We thus developed a denoising algorithm based on deep learning, the "Joint Autoencoder", which significantly improved subsequent dimensionality estimation. Critically, we found that all algorithms failed when the intrinsic dimensionality was high (above 20) or when the amount of data used for estimation was low. Based on the challenges we observed, we formulated a pipeline for estimating the dimensionality of experimental neural data.

Continuous, multidimensional coding of 3D complex tactile stimuli by primary sensory neurons of the vibrissal system.

Across all sensory modalities, first-stage sensory neurons are an information bottleneck: they must convey all information available for an animal to perceive and act in its environment. Our understanding of coding properties of primary sensory neurons in the auditory and visual systems has been aided by the use of increasingly complex, naturalistic stimulus sets. By comparison, encoding properties of primary somatosensory afferents are poorly understood. Here, we use the rodent whisker system to examine how tactile information is represented in primary sensory neurons of the trigeminal ganglion (Vg). Vg neurons have long been thought to segregate into functional classes associated with separate streams of information processing. However, this view is based on Vg responses to restricted stimulus sets which potentially underreport the coding capabilities of these neurons. In contrast, the current study records Vg responses to complex three-dimensional (3D) stimulation while quantifying the complete 3D whisker shape and mechanics, thereby beginning to reveal their full representational capabilities. The results show that individual Vg neurons simultaneously represent multiple mechanical features of a stimulus, do not preferentially encode principal components of the stimuli, and represent continuous and tiled variations of all available mechanical information. These results directly contrast with proposed codes in which subpopulations of Vg neurons encode select stimulus features. Instead, individual Vg neurons likely overcome the information bottleneck by encoding large regions of a complex sensory space. This proposed tiled and multidimensional representation at the Vg directly constrains the computations performed by more central neurons of the vibrissotrigeminal pathway.

Unexpected complexity of everyday manual behaviors.

How does the brain control an effector as complex and versatile as the hand? One possibility is that neural control is simplified by limiting the space of hand movements. Indeed, hand kinematics can be largely described within 8 to 10 dimensions. This oft replicated finding has been construed as evidence that hand postures are confined to this subspace. A prediction from this hypothesis is that dimensions outside of this subspace reflect noise. To address this question, we track the hand of human participants as they perform two tasks-grasping and signing in American Sign Language. We apply multiple dimension reduction techniques and replicate the finding that most postural variance falls within a reduced subspace. However, we show that dimensions outside of this subspace are highly structured and task dependent, suggesting they too are under volitional control. We propose that hand control occupies a higher dimensional space than previously considered.

Long-term stability of cortical population dynamics underlying consistent behavior.

Animals readily execute learned behaviors in a consistent manner over long periods of time, and yet no equally stable neural correlate has been demonstrated. How does the cortex achieve this stable control? Using the sensorimotor system as a model of cortical processing, we investigated the hypothesis that the dynamics of neural latent activity, which captures the dominant co-variation patterns within the neural population, must be preserved across time. We recorded from populations of neurons in premotor, primary motor and somatosensory cortices as monkeys performed a reaching task, for up to 2 years. Intriguingly, despite a steady turnover in the recorded neurons, the low-dimensional latent dynamics remained stable. The stability allowed reliable decoding of behavioral features for the entire timespan, while fixed decoders based directly on the recorded neural activity degraded substantially. We posit that stable latent cortical dynamics within the manifold are the fundamental building blocks underlying consistent behavioral execution.

The dynamics of motor learning through the formation of internal models.

A medical student learning to perform a laparoscopic procedure or a recently paralyzed user of a powered wheelchair must learn to operate machinery via interfaces that translate their actions into commands for an external device. Since the user's actions are selected from a number of alternatives that would result in the same effect in the control space of the external device, learning to use such interfaces involves dealing with redundancy. Subjects need to learn an externally chosen many-to-one map that transforms their actions into device commands. Mathematically, we describe this type of learning as a deterministic dynamical process, whose state is the evolving forward and inverse internal models of the interface. The forward model predicts the outcomes of actions, while the inverse model generates actions designed to attain desired outcomes. Both the mathematical analysis of the proposed model of learning dynamics and the learning performance observed in a group of subjects demonstrate a first-order exponential convergence of the learning process toward a particular state that depends only on the initial state of the inverse and forward models and on the sequence of targets supplied to the users. Noise is not only present but necessary for the convergence of learning through the minimization of the difference between actual and predicted outcomes.

In vitro validation of in silico identified inhibitory interactions.

BACKGROUND: Understanding how neuronal signals propagate in local network is an important step in understanding information processing. As a result, spike trains recorded with multi-electrode arrays (MEAs) have been widely used to study the function of neural networks. Studying the dynamics of neuronal networks requires the identification of both excitatory and inhibitory connections. The detection of excitatory relationships can robustly be inferred by characterizing the statistical relationships of neural spike trains. However, the identification of inhibitory relationships is more difficult: distinguishing endogenous low firing rates from active inhibition is not obvious. NEW METHOD: In this paper, we propose an in silico interventional procedure that makes predictions about the effect of stimulating or inhibiting single neurons on other neurons, and thereby gives the ability to accurately identify inhibitory effects. COMPARISON: To experimentally test these predictions, we have developed a Neural Circuit Probe (NCP) that delivers drugs transiently and reversibly on individually identified neurons to assess their contributions to the neural circuit behavior. RESULTS: Using the NCP, putative inhibitory connections identified by the in silico procedure were validated through in vitro interventional experiments. CONCLUSIONS: Together, these results demonstrate how detailed microcircuitry can be inferred from statistical models derived from neurophysiology data.

Neural Networks for Modeling Neural Spiking in S1 Cortex.

Somatosensation is composed of two distinct modalities: touch, arising from sensors in the skin, and proprioception, resulting primarily from sensors in the muscles, combined with these same cutaneous sensors. In contrast to the wealth of information about touch, we know quite less about the nature of the signals giving rise to proprioception at the cortical level. Likewise, while there is considerable interest in developing encoding models of touch-related neurons for application to brain machine interfaces, much less emphasis has been placed on an analogous proprioceptive interface. Here we investigate the use of Artificial Neural Networks (ANNs) to model the relationship between the firing rates of single neurons in area 2, a largely proprioceptive region of somatosensory cortex (S1) and several types of kinematic variables related to arm movement. To gain a better understanding of how these kinematic variables interact to create the proprioceptive responses recorded in our datasets, we train ANNs under different conditions, each involving a different set of input and output variables. We explore the kinematic variables that provide the best network performance, and find that the addition of information about joint angles and/or muscle lengths significantly improves the prediction of neural firing rates. Our results thus provide new insight regarding the complex representations of the limb motion in S1: that the firing rates of neurons in area 2 may be more closely related to the activity of peripheral sensors than it is to extrinsic hand position. In addition, we conduct numerical experiments to determine the sensitivity of ANN models to various choices of training design and hyper-parameters. Our results provide a baseline and new tools for future research that utilizes machine learning to better describe and understand the activity of neurons in S1.

Cortical population activity within a preserved neural manifold underlies multiple motor behaviors.

Populations of cortical neurons flexibly perform different functions; for the primary motor cortex (M1) this means a rich repertoire of motor behaviors. We investigate the flexibility of M1 movement control by analyzing neural population activity during a variety of skilled wrist and reach-to-grasp tasks. We compare across tasks the neural modes that capture dominant neural covariance patterns during each task. While each task requires different patterns of muscle and single unit activity, we find unexpected similarities at the neural population level: the structure and activity of the neural modes is largely preserved across tasks. Furthermore, we find two sets of neural modes with task-independent activity that capture, respectively, generic temporal features of the set of tasks and a task-independent mapping onto muscle activity. This system of flexibly combined, well-preserved neural modes may underlie the ability of M1 to learn and generate a wide-ranging behavioral repertoire.

Neural Manifolds for the Control of Movement.

The analysis of neural dynamics in several brain cortices has consistently uncovered low-dimensional manifolds that capture a significant fraction of neural variability. These neural manifolds are spanned by specific patterns of correlated neural activity, the "neural modes." We discuss a model for neural control of movement in which the time-dependent activation of these neural modes is the generator of motor behavior. This manifold-based view of motor cortex may lead to a better understanding of how the brain controls movement.

Whisking mechanics and active sensing.

We describe recent advances in quantifying the three-dimensional (3D) geometry and mechanics of whisking. Careful delineation of relevant 3D reference frames reveals important geometric and mechanical distinctions between the localization problem ('where' is an object) and the feature extraction problem ('what' is an object). Head-centered and resting-whisker reference frames lend themselves to quantifying temporal and kinematic cues used for object localization. The whisking-centered reference frame lends itself to quantifying the contact mechanics likely associated with feature extraction. We offer the 'windowed sampling' hypothesis for active sensing: that rats can estimate an object's spatial features by integrating mechanical information across whiskers during brief (25-60ms) windows of 'haptic enclosure' with the whiskers, a motion that resembles a hand grasp.

Decoupling kinematics and mechanics reveals coding properties of trigeminal ganglion neurons in the rat vibrissal system.

Tactile information available to the rat vibrissal system begins as external forces that cause whisker deformations, which in turn excite mechanoreceptors in the follicle. Despite the fundamental mechanical origin of tactile information, primary sensory neurons in the trigeminal ganglion (Vg) have often been described as encoding the kinematics (geometry) of object contact. Here we aimed to determine the extent to which Vg neurons encode the kinematics vs. mechanics of contact. We used models of whisker bending to quantify mechanical signals (forces and moments) at the whisker base while simultaneously monitoring whisker kinematics and recording single Vg units in both anesthetized rats and awake, body restrained rats. We employed a novel manual stimulation technique to deflect whiskers in a way that decouples kinematics from mechanics, and used Generalized Linear Models (GLMs) to show that Vg neurons more directly encode mechanical signals when the whisker is deflected in this decoupled stimulus space.

Adaptive neuron-to-EMG decoder training for FES neuroprostheses.

OBJECTIVE: We have previously demonstrated a brain-machine interface neuroprosthetic system that provided continuous control of functional electrical stimulation (FES) and restoration of grasp in a primate model of spinal cord injury (SCI). Predicting intended EMG directly from cortical recordings provides a flexible high-dimensional control signal for FES. However, no peripheral signal such as force or EMG is available for training EMG decoders in paralyzed individuals. APPROACH: Here we present a method for training an EMG decoder in the absence of muscle activity recordings; the decoder relies on mapping behaviorally relevant cortical activity to the inferred EMG activity underlying an intended action. Monkeys were trained at a 2D isometric wrist force task to control a computer cursor by applying force in the flexion, extension, ulnar, and radial directions and execute a center-out task. We used a generic muscle force-to-endpoint force model based on muscle pulling directions to relate each target force to an optimal EMG pattern that attained the target force while minimizing overall muscle activity. We trained EMG decoders during the target hold periods using a gradient descent algorithm that compared EMG predictions to optimal EMG patterns. MAIN RESULTS: We tested this method both offline and online. We quantified both the accuracy of offline force predictions and the ability of a monkey to use these real-time force predictions for closed-loop cursor control. We compared both offline and online results to those obtained with several other direct force decoders, including an optimal decoder computed from concurrently measured neural and force signals. SIGNIFICANCE: This novel approach to training an adaptive EMG decoder could make a brain-control FES neuroprosthesis an effective tool to restore the hand function of paralyzed individuals. Clinical implementation would make use of individualized EMG-to-force models. Broad generalization could be achieved by including data from multiple grasping tasks in the training of the neuron-to-EMG decoder. Our approach would make it possible for persons with SCI to grasp objects with their own hands, using near-normal motor intent.

Long-Term Stability of Motor Cortical Activity: Implications for Brain Machine Interfaces and Optimal Feedback Control.

The human motor system is capable of remarkably precise control of movements--consider the skill of professional baseball pitchers or surgeons. This precise control relies upon stable representations of movements in the brain. Here, we investigated the stability of cortical activity at multiple spatial and temporal scales by recording local field potentials (LFPs) and action potentials (multiunit spikes, MSPs) while two monkeys controlled a cursor either with their hand or directly from the brain using a brain-machine interface. LFPs and some MSPs were remarkably stable over time periods ranging from 3 d to over 3 years; overall, LFPs were significantly more stable than spikes. We then assessed whether the stability of all neural activity, or just a subset of activity, was necessary to achieve stable behavior. We showed that projections of neural activity into the subspace relevant to the task (the "task-relevant space") were significantly more stable than were projections into the task-irrelevant (or "task-null") space. This provides cortical evidence in support of the minimum intervention principle, which proposes that optimal feedback control (OFC) allows the brain to tightly control only activity in the task-relevant space while allowing activity in the task-irrelevant space to vary substantially from trial to trial. We found that the brain appears capable of maintaining stable movement representations for extremely long periods of time, particularly so for neural activity in the task-relevant space, which agrees with OFC predictions. SIGNIFICANCE STATEMENT: It is unknown whether cortical signals are stable for more than a few weeks. Here, we demonstrate that motor cortical signals can exhibit high stability over several years. This result is particularly important to brain-machine interfaces because it could enable stable performance with infrequent recalibration. Although we can maintain movement accuracy over time, movement components that are unrelated to the goals of a task (such as elbow position during reaching) often vary from trial to trial. This is consistent with the minimum intervention principle of optimal feedback control. We provide evidence that the motor cortex acts according to this principle: cortical activity is more stable in the task-relevant space and more variable in the task-irrelevant space.

Multi-electrode stimulation in somatosensory cortex increases probability of detection.

OBJECTIVE: Brain machine interfaces (BMIs) that decode control signals from motor cortex have developed tremendously in the past decade, but virtually all rely exclusively on vision to provide feedback. There is now increasing interest in developing an afferent interface to replace natural somatosensation, much as the cochlear implant has done for the sense of hearing. Preliminary experiments toward a somatosensory neuroprosthesis have mostly addressed the sense of touch, but proprioception, the sense of limb position and movement, is also critical for the control of movement. However, proprioceptive areas of cortex lack the precise somatotopy of tactile areas. We showed previously that there is only a weak tendency for neighboring neurons in area 2 to signal similar directions of hand movement. Consequently, stimulation with the relatively large currents used in many studies is likely to activate a rather heterogeneous set of neurons. APPROACH: Here, we have compared the effect of single-electrode stimulation at subthreshold levels to the effect of stimulating as many as seven electrodes in combination. MAIN RESULTS: We found a mean enhancement in the sensitivity to the stimulus (d') of 0.17 for pairs compared to individual electrodes (an increase of roughly 30%), and an increase of 2.5 for groups of seven electrodes (260%). SIGNIFICANCE: We propose that a proprioceptive interface made up of several hundred electrodes may yield safer, more effective sensation than a BMI using fewer electrodes and larger currents.

Rewiring neural interactions by micro-stimulation.

Plasticity is a crucial component of normal brain function and a critical mechanism for recovery from injury. In vitro, associative pairing of presynaptic spiking and stimulus-induced postsynaptic depolarization causes changes in the synaptic efficacy of the presynaptic neuron, when activated by extrinsic stimulation. In vivo, such paradigms can alter the responses of whole groups of neurons to stimulation. Here, we used in vivo spike-triggered stimulation to drive plastic changes in rat forelimb sensorimotor cortex, which we monitored using a statistical measure of functional connectivity inferred from the spiking statistics of the neurons during normal, spontaneous behavior. These induced plastic changes in inferred functional connectivity depended on the latency between trigger spike and stimulation, and appear to reflect a robust reorganization of the network. Such targeted connectivity changes might provide a tool for rerouting the flow of information through a network, with implications for both rehabilitation and brain-machine interface applications.

Toward a biomimetic, bidirectional, brain machine interface.

The interest in Brain Machine Interface (BMI) systems has increased tremendously in recent times; many groups have become involved in this type of research, and progress has been quite encouraging. However, two fundamental limitations remain: 1) With a few notable exceptions, BMIs extract only kinematic information from the brain, ignoring the wealth of force or kinetic information also present in the primary motor cortex, and 2) most existing BMIs depend exclusively on natural vision to guide movement, lacking the rapid proprioceptive feedback that is critical for normal movement. The work reported here describes our efforts to address both of these limitations.

Toward the restoration of hand use to a paralyzed monkey: brain-controlled functional electrical stimulation of forearm muscles.

Loss of hand use is considered by many spinal cord injury survivors to be the most devastating consequence of their injury. Functional electrical stimulation (FES) of forearm and hand muscles has been used to provide basic, voluntary hand grasp to hundreds of human patients. Current approaches typically grade pre-programmed patterns of muscle activation using simple control signals, such as those derived from residual movement or muscle activity. However, the use of such fixed stimulation patterns limits hand function to the few tasks programmed into the controller. In contrast, we are developing a system that uses neural signals recorded from a multi-electrode array implanted in the motor cortex; this system has the potential to provide independent control of multiple muscles over a broad range of functional tasks. Two monkeys were able to use this cortically controlled FES system to control the contraction of four forearm muscles despite temporary limb paralysis. The amount of wrist force the monkeys were able to produce in a one-dimensional force tracking task was significantly increased. Furthermore, the monkeys were able to control the magnitude and time course of the force with sufficient accuracy to track visually displayed force targets at speeds reduced by only one-third to one-half of normal. Although these results were achieved by controlling only four muscles, there is no fundamental reason why the same methods could not be scaled up to control a larger number of muscles. We believe these results provide an important proof of concept that brain-controlled FES prostheses could ultimately be of great benefit to paralyzed patients with injuries in the mid-cervical spinal cord.