Spatial constancy mechanisms in motor control

The success of the human species in interacting with the environment depends on the ability to maintain spatial stability despite the continuous changes in sensory and motor inputs owing to movements of eyes, head and body. In this paper, I will review recent advances in the understanding of how the brain deals with the dynamic flow of sensory and motor information in order to maintain spatial constancy of movement goals. The first part summarizes studies in the saccadic system, showing that spatial constancy is governed by a dynamic feed-forward process, by gaze-centred remapping of target representations in anticipation of and across eye movements. The subsequent sections relate to other oculomotor behaviour, such as eye-head gaze shifts, smooth pursuit and vergence eye movements, and their implications for feed-forward mechanisms for spatial constancy. Work that studied the geometric complexities in spatial constancy and saccadic guidance across head and body movements, distinguishing between self-generated and passively induced motion, indicates that both feed-forward and sensory feedback processing play a role in spatial updating of movement goals. The paper ends with a discussion of the behavioural mechanisms of spatial constancy for arm motor control and their physiological implications for the brain. Taken together, the emerging picture is that the brain computes an evolving representation of three-dimensional action space, whose internal metric is updated in a nonlinear way, by optimally integrating noisy and ambiguous afferent and efferent signals.     

End-to-end neural system identification with neural information flow

Neural information flow (NIF) provides a novel approach for system identification in neuroscience. It models the neural computations in multiple brain regions and can be trained end-to-end via stochastic gradient descent from noninvasive data. NIF models represent neural information processing via a network of coupled tensors, each encoding the representation of the sensory input contained in a brain region. The elements of these tensors can be interpreted as cortical columns whose activity encodes the presence of a specific feature in a spatiotemporal location. Each tensor is coupled to the measured data specific to a brain region via low-rank observation models that can be decomposed into the spatial, temporal and feature receptive fields of a localized neuronal population. Both these observation models and the convolutional weights defining the information processing within regions are learned end-to-end by predicting the neural signal during sensory stimulation. We trained a NIF model on the activity of early visual areas using a large-scale fMRI dataset recorded in a single participant. We show that we can recover plausible visual representations and population receptive fields that are consistent with empirical findings.     

Exploiting the potential of three dimensional spatial wavelet analysis to explore nesting of temporal oscillations and spatial variance in simultaneous EEG-fMRI data

Synchronization of the activity in neural networks is a fundamental mechanism of brain function, putatively serving the integration of computations on multiple spatial and temporal scales. Time scales are thought to be nested within distinct spatial scales, so that whereas fast oscillations may integrate local networks, slow oscillations might integrate computations across distributed brain areas. We here describe a newly developed approach that provides potential for the further substantiation of this hypothesis in future studies. We demonstrate the feasibility and important caveats of a novel wavelet-based means of relating time series of three-dimensional spatial variance (energy) of fMRI data to time series of temporal variance of EEG. The spatial variance of fMRI data was determined by employing the three-dimensional dual-tree complex wavelet transform. The temporal variance of EEG data was estimated by using traditional continuous complex wavelets. We tested our algorithm on artificial signals with known signal-to-noise ratios and on empirical resting state EEG-fMRI data obtained from four healthy human subjects. By employing the human posterior alpha rhythm as an exemplar, we demonstrated face validity of the approach. We believe that the proposed method can serve as a suitable tool for future research on the spatiotemporal properties of brain dynamics, hence moving beyond analyses based exclusively in one domain or the other.     

Causal Inference for Spatial Constancy across Saccades

Our ability to interact with the environment hinges on creating a stable visual world despite the continuous changes in retinal input. To achieve visual stability, the brain must distinguish the retinal image shifts caused by eye movements and shifts due to movements of the visual scene. This process appears not to be flawless: during saccades, we often fail to detect whether visual objects remain stable or move, which is called saccadic suppression of displacement (SSD). How does the brain evaluate the memorized information of the presaccadic scene and the actual visual feedback of the postsaccadic visual scene in the computations for visual stability? Using a SSD task, we test how participants localize the presaccadic position of the fixation target, the saccade target or a peripheral non-foveated target that was displaced parallel or orthogonal during a horizontal saccade, and subsequently viewed for three different durations. Results showed different localization errors of the three targets, depending on the viewing time of the postsaccadic stimulus and its spatial separation from the presaccadic location. We modeled the data through a Bayesian causal inference mechanism, in which at the trial level an optimal mixing of two possible strategies, integration vs. separation of the presaccadic memory and the postsaccadic sensory signals, is applied. Fits of this model generally outperformed other plausible decision strategies for producing SSD. Our findings suggest that humans exploit a Bayesian inference process with two causal structures to mediate visual stability.     

Relative timing: from behaviour to neurons

Processing of temporal information is critical to behaviour. Here, we review the phenomenology and mechanism of relative timing, ordinal comparisons between the timing of occurrence of events. Relative timing can be an implicit component of particular brain computations or can be an explicit, conscious judgement. Psychophysical measurements of explicit relative timing have revealed clues about the interaction of sensory signals in the brain as well as in the influence of internal states, such as attention, on those interactions. Evidence from human neurophysiological and functional imaging studies, neuropsychological examination in brain-lesioned patients, and temporary disruptive interventions such as transcranial magnetic stimulation (TMS), point to a role of the parietal cortex in relative timing. Relative timing has traditionally been modelled as a ‘race’ between competing neural signals. We propose an updated race process based on the integration of sensory evidence towards a decision threshold rather than simple signal propagation. The model suggests a general approach for identifying brain regions involved in relative timing, based on looking for trial-by-trial correlations between neural activity and temporal order judgements (TOJs). Finally, we show how the paradigm can be used to reveal signals related to TOJs in parietal cortex of monkeys trained in a TOJ task.     

Coordinate transformations for eye and arm movements in the brain

Recent work on the coding of spatial information in the brain has significantly advanced our knowledge of sensory to motor transformations on several fronts. The encoding of information referenced to the retina (eye-centered) but modulated by eye position, called a gain field representation, has proved to be very common throughout parietal and occipital cortex. The use of an eye-centered representation as a working memory of spatial location is problematic if the eyes move during the memory period. Details regarding the manner in which the brain solves this problem are beginning to emerge. Finally, the discovery of eye-centered representations of ongoing or intended arm movements has changed the way we think about the order of operations in the sensory to motor coordinate transformation.     

A neural mechanism for coordinate transformation predicts pre-saccadic remapping

Whenever we shift our gaze, any location information encoded in the retinocentric reference frame that is predominant in the visual system is obliterated. How is spatial memory retained across gaze changes? Two different explanations have been proposed: Retinocentric information may be transformed into a gaze-invariant representation through a mechanism consistent with gain fields observed in parietal cortex, or retinocentric information may be updated in anticipation of the shift expected with every gaze change, a proposal consistent with neural observations in LIP. The explanations were considered incompatible with each other, because retinocentric update is observed before the gaze shift has terminated. Here, we show that a neural dynamic mechanism for coordinate transformation can also account for retinocentric updating. Our model postulates an extended mechanism of reference frame transformation that is based on bidirectional mapping between a retinocentric and a body-centered representation and that enables transforming multiple object locations in parallel. The dynamic coupling between the two reference frames generates a shift of the retinocentric representation for every gaze change. We account for the predictive nature of the observed remapping activity by using the same kind of neural mechanism to generate an internal representation of gaze direction that is predictively updated based on corollary discharge signals. We provide evidence for the model by accounting for a series of behavioral and neural experimental observations.     

Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.     

Do motoneurons encode the noncommutativity of ocular rotations?

As we look around, the orientation of our eyes depends on the order of the rotations that are carried out, a mathematical feature of rotatory motions known as noncommutativity. Theorists and experimentalists continue to debate how biological systems deal with this property when generating kinematically appropriate movements. Some believe that this is always done by neural commands to a simplified eye plant. Others have postulated that noncommutativity is implemented solely by the mechanical properties of the eyeball. Here we directly examined what the brain tells the muscles, by recording motoneuron activities as monkeys made eye movements. We found that vertical recti and superior/inferior oblique motoneurons, which drive sensory-generated torsional eye movements, do not modulate their firing rates according to the noncommutative-driven torsion during pursuit. We conclude that part of the solution for kinematically appropriate eye movements is found in the mechanical properties of the eyeball, although neural computations remain necessary and become increasingly important during head movements.     

Two-phase strategy of controlling motor coordination determined by task performance optimality

A quantitative model of optimal coordination between hand transport and grip aperture has been derived in our previous studies of reach-to-grasp movements without utilizing explicit knowledge of the optimality criterion or motor plant dynamics. The model’s utility for experimental data analysis has been demonstrated. Here we show how to generalize this model for a broad class of reaching-type, goal-directed movements. The model allows for measuring the variability of motor coordination and studying its dependence on movement phase. The experimentally found characteristics of that dependence imply that execution noise is low and does not affect motor coordination significantly. From those characteristics it is inferred that the cost of neural computations required for information acquisition and processing is included in the criterion of task performance optimality as a function of precision demand for state estimation and decision making. The precision demand is an additional optimized control variable that regulates the amount of neurocomputational resources activated dynamically. It is shown that an optimal control strategy in this case comprises two different phases. During the initial phase, the cost of neural computations is significantly reduced at the expense of reducing the demand for their precision, which results in speed-accuracy tradeoff violation and significant inter-trial variability of motor coordination. During the final phase, neural computations and thus motor coordination are considerably more precise to reduce the cost of errors in making a contact with the target object. The generality of the optimal coordination model and the two-phase control strategy is illustrated on several diverse examples.     

Local visual homing by matched-filter descent in image distances

In natural images, the distance measure between two images taken at different locations rises smoothly with increasing distance between the locations. This fact can be exploited for local visual homing where the task is to reach a goal location that is characterized by a snapshot image: descending in the image distance will lead the agent to the goal location. To compute an estimate of the spatial gradient in the distance measure, its value must be sampled at three noncollinear points. An animal or robot would have to insert exploratory movements into its home trajectory to collect these samples. Here we suggest a method based on the matched-filter concept that allows one to estimate the gradient without exploratory movements. Two matched filters – optical flow fields resulting from translatory movements in the horizontal plane – are used to predict two images in perpendicular directions from the current location. We investigate the relation to differential flow methods applied to the local homing problem and show that the matched-filter approach produces reliable homing behavior on image databases. Two alternative methods that only require a single matched filter are suggested. The matched-filter concept is also applied to derive a home-vector equation for a Fourier-based parameter method.     

Robust spatial working memory through homeostatic synaptic scaling in heterogeneous cortical networks

The concept of bell-shaped persistent neural activity represents a cornerstone of the theory for the internal representation of analog quantities, such as spatial location or head direction. Previous models, however, relied on the unrealistic assumption of network homogeneity. We investigate this issue in a network model where fine tuning of parameters is destroyed by heterogeneities in cellular and synaptic properties. Heterogeneities result in the loss of stored spatial information in a few seconds. Accurate encoding is recovered when a homeostatic mechanism scales the excitatory synapses to each cell to compensate for the heterogeneity in cellular excitability and synaptic inputs. Moreover, the more realistic model produces a wide diversity of tuning curves, as commonly observed in recordings from prefrontal neurons. We conclude that recurrent attractor networks in conjunction with appropriate homeostatic mechanisms provide a robust, biologically plausible theoretical framework for understanding the neural circuit basis of spatial working memory.     

A p-Adic model for the process of thinking disturbed by physiological and information noise

We develop a model of the process of thinking in the presence of noise (which is produced by the simultaneous action of a huge number of neurons in the brain as well as by external information and internal cognitive processes). Our model is based on Freud's idea on the splitting of cognitive processes into two (closely connected) domains: consciousness and subconsciousness. We represent the process of thinking as a random dynamical process in a space of ideas endowed with a non-Euclidean geometry (which differs extremely from the ordinary Euclidean geometry of spatial location of neurons in the brain). The so-called p-adic geometry on a space of ideas describes the ability of cognitive systems to form associations. We show that random dynamical thinking systems on a p -adic space of ideas still generate only deterministic ideas. We also study positive and negative effects of noise (in particular, creativeness and stress).     

Brain Systems for Probabilistic and Dynamic Prediction: Computational Specificity and Integration

A computational approach to functional specialization suggests that brain systems can be characterized in terms of the types of computations they perform, rather than their sensory or behavioral domains. We contrasted the neural systems associated with two computationally distinct forms of predictive model: a reinforcement-learning model of the environment obtained through experience with discrete events, and continuous dynamic forward modeling. By manipulating the precision with which each type of prediction could be used, we caused participants to shift computational strategies within a single spatial prediction task. Hence (using fMRI) we showed that activity in two brain systems (typically associated with reward learning and motor control) could be dissociated in terms of the forms of computations that were performed there, even when both systems were used to make parallel predictions of the same event. A region in parietal cortex, which was sensitive to the divergence between the predictions of the models and anatomically connected to both computational networks, is proposed to mediate integration of the two predictive modes to produce a single behavioral output.     

A Neural Population Model Incorporating Dopaminergic Neurotransmission during Complex Voluntary Behaviors

Assessing brain activity during complex voluntary motor behaviors that require the recruitment of multiple neural sites is a field of active research. Our current knowledge is primarily based on human brain imaging studies that have clear limitations in terms of temporal and spatial resolution. We developed a physiologically informed non-linear multi-compartment stochastic neural model to simulate functional brain activity coupled with neurotransmitter release during complex voluntary behavior, such as speech production. Due to its state-dependent modulation of neural firing, dopaminergic neurotransmission plays a key role in the organization of functional brain circuits controlling speech and language and thus has been incorporated in our neural population model. A rigorous mathematical proof establishing existence and uniqueness of solutions to the proposed model as well as a computationally efficient strategy to numerically approximate these solutions are presented. Simulated brain activity during the resting state and sentence production was analyzed using functional network connectivity, and graph theoretical techniques were employed to highlight differences between the two conditions. We demonstrate that our model successfully reproduces characteristic changes seen in empirical data between the resting state and speech production, and dopaminergic neurotransmission evokes pronounced changes in modeled functional connectivity by acting on the underlying biological stochastic neural model. Specifically, model and data networks in both speech and rest conditions share task-specific network features: both the simulated and empirical functional connectivity networks show an increase in nodal influence and segregation in speech over the resting state. These commonalities confirm that dopamine is a key neuromodulator of the functional connectome of speech control. Based on reproducible characteristic aspects of empirical data, we suggest a number of extensions of the proposed methodology building upon the current model.     

VSDI: a new era in functional imaging of cortical dynamics

During the last few decades, neuroscientists have benefited from the emergence of many powerful functional imaging techniques that cover broad spatial and temporal scales. We can now image single molecules controlling cell differentiation, growth and death; single cells and their neurites processing electrical inputs and sending outputs; neuronal circuits performing neural computations in vitro; and the intact brain. At present, imaging based on voltage-sensitive dyes (VSDI) offers the highest spatial and temporal resolution for imaging neocortical functions in the living brain, and has paved the way for a new era in the functional imaging of cortical dynamics. It has facilitated the exploration of fundamental mechanisms that underlie neocortical development, function and plasticity at the fundamental level of the cortical column.     

Tuning Properties of MT and MSTd and Divisive Interactions for Eye-Movement Compensation

The primate brain intelligently processes visual information from the world as the eyes move constantly. The brain must take into account visual motion induced by eye movements, so that visual information about the outside world can be recovered. Certain neurons in the dorsal part of monkey medial superior temporal area (MSTd) play an important role in integrating information about eye movements and visual motion. When a monkey tracks a moving target with its eyes, these neurons respond to visual motion as well as to smooth pursuit eye movements. Furthermore, the responses of some MSTd neurons to the motion of objects in the world are very similar during pursuit and during fixation, even though the visual information on the retina is altered by the pursuit eye movement. We call these neurons compensatory pursuit neurons. In this study we develop a computational model of MSTd compensatory pursuit neurons based on physiological data from single unit studies. Our model MSTd neurons can simulate the velocity tuning of monkey MSTd neurons. The model MSTd neurons also show the pursuit compensation property. We find that pursuit compensation can be achieved by divisive interaction between signals coding eye movements and signals coding visual motion. The model generates two implications that can be tested in future experiments: (1) compensatory pursuit neurons in MSTd should have the same direction preference for pursuit and retinal visual motion; (2) there should be non-compensatory pursuit neurons that show opposite preferred directions of pursuit and retinal visual motion.