Gerald P. Keith

Decoding the Cortical Transformations for Visually Guided Reaching in 3D Space

To explore the possible cortical mechanisms underlying the 3-dimensional (3D) visuomotor transformation for reaching, we trained a 4-layer feed-forward artificial neural network to compute a reach vector (output) from the visual positions of both the hand and target viewed from different eye and head orientations (inputs). The emergent properties of the intermediate layers reflected several known neurophysiological findings, for example, gain field-like modulations and position-dependent shifting of receptive fields (RFs). We performed a reference frame analysis for each individual network unit, simulating standard electrophysiological experiments, that is, RF mapping (unit input), motor field mapping, and microstimulation effects (unit outputs). At the level of individual units (in both intermediate layers), the 3 different electrophysiological approaches identified different reference frames, demonstrating that these techniques reveal different neuronal properties and suggesting that a comparison across these techniques is required to understand the neural code of physiological networks. This analysis showed fixed input-output relationships within each layer and, more importantly, within each unit. These local reference frame transformation modules provide the basic elements for the global transformation; their parallel contributions are combined in a gain field-like fashion at the population level to implement both the linear and nonlinear elements of the 3D visuomotor transformation.

Saccade-related remapping of target representations between topographic maps: a neural network study

The goal of this study was to explore how a neural network could solve the updating task associated with the double-saccade paradigm, where two targets are flashed in succession and the subject must make saccades to the remembered locations of both targets. Because of the eye rotation of the saccade to the first target, the remembered retinal position of the second target must be updated if an accurate saccade to that target is to be made. We trained a three-layer, feed-forward neural network to solve this updating task using back-propagation. The network’s inputs were the initial retinal position of the second target represented by a hill of activation in a 2D topographic array of units, as well as the initial eye orientation and the motor error of the saccade to the first target, each represented as 3D vectors in brainstem coordinates. The output of the network was the updated retinal position of the second target, also represented in a 2D topographic array of units. The network was trained to perform this updating using the full 3D geometry of eye rotations, and was able to produce the updated second-target position to within a 1° RMS accuracy for a set of test points that included saccades of up to 70°. Emergent properties in the networks hidden layer included sigmoidal receptive fields whose orientations formed distinct clusters, and predictive remapping similar to that seen in brain areas associated with saccade generation. Networks with the larger numbers of hidden-layer units developed two distinct types of units with different transformation properties: units that preferentially performed the linear remapping of vector subtraction, and units that performed the nonlinear elements of remapping that arise from initial eye orientation.

Intrinsic reference frames of superior colliculus visuomotor receptive fields during head-unrestrained gaze shifts.

A sensorimotor neurons receptive field and its frame of reference are easily conflated within the natural variability of spatial behavior. Here, we capitalized on such natural variations in 3-D eye and head positions during head-unrestrained gaze shifts to visual targets in two monkeys: to determine whether intermediate/deep layer superior colliculus (SC) receptive fields code visual targets or gaze kinematics, within four different frames of reference. Visuomotor receptive fields were either characterized during gaze shifts to visual targets from a central fixation position (32 U) or were partially characterized from each of three initial fixation points (31 U). Natural variations of initial 3-D gaze and head orientation (including torsion) provided spatial separation between four different coordinate frame models (space, head, eye, fixed-vector relative to fixation), whereas natural saccade errors provided spatial separation between target and gaze positions. Using a new statistical method based on predictive sum-of-squares, we found that in our population of 63 neurons (1) receptive field fits to target positions were significantly better than fits to actual gaze shift locations and (2) eye-centered models gave significantly better fits than the head or space frame. An intermediate frames analysis confirmed that individual neuron fits were distributed target-in-eye coordinates. Gaze position “gain” effects with the spatial tuning required for a 3-D reference frame transformation were significant in 23% (7/31) of neurons tested. We conclude that the SC primarily represents gaze targets relative to the eye but also carries early signatures of the 3-D sensorimotor transformation.

Visual–Motor Transformations Within Frontal Eye Fields During Head-Unrestrained Gaze Shifts in the Monkey

A fundamental question in sensorimotor control concerns the transformation of spatial signals from the retina into eye and head motor commands required for accurate gaze shifts. Here, we investigated these transformations by identifying the spatial codes embedded in visually evoked and movement-related responses in the frontal eye fields (FEFs) during head-unrestrained gaze shifts. Monkeys made delayed gaze shifts to the remembered location of briefly presented visual stimuli, with delay serving to dissociate visual and movement responses. A statistical analysis of nonparametric model fits to response field data from 57 neurons (38 with visual and 49 with movement activities) eliminated most effector-specific, head-fixed, and space-fixed models, but confirmed the dominance of eye-centered codes observed in head-restrained studies. More importantly, the visual response encoded target location, whereas the movement response mainly encoded the final position of the imminent gaze shift (including gaze errors). This spatiotemporal distinction between target and gaze coding was present not only at the population level, but even at the single-cell level. We propose that an imperfect visual–motor transformation occurs during the brief memory interval between perception and action, and further transformations from the FEFs eye-centered gaze motor code to effector-specific codes in motor frames occur downstream in the subcortical areas.

Functional organization within a neural network trained to update target representations across 3-D saccades

The goal of this study was to understand how neural networks solve the 3-D aspects of updating in the double-saccade task, where subjects make sequential saccades to the remembered locations of two targets. We trained a 3-layer, feed-forward neural network, using back-propagation, to calculate the 3-D motor error the second saccade. Network inputs were a 2-D topographic map of the direction of the second target in retinal coordinates, and 3-D vector representations of initial eye orientation and motor error of the first saccade in head-fixed coordinates. The network learned to account for all 3-D aspects of updating. Hidden-layer units (HLUs) showed retinal-coordinate visual receptive fields that were remapped across the first saccade. Two classes of HLUs emerged from the training, one class primarily implementing the linear aspects of updating using vector subtraction, the second class implementing the eye-orientation-dependent, non-linear aspects of updating. These mechanisms interacted at the unit level through gain-field-like input summations, and through the parallel “tweaking” of optimally-tuned HLU contributions to the output that shifted the overall population output vector to the correct second-saccade motor error. These observations may provide clues for the biological implementation of updating.

A method for mapping response fields and determining intrinsic reference frames of single-unit activity: applied to 3D head-unrestrained gaze shifts.

Natural movements towards a target show metric variations between trials. When movements combine contributions from multiple body-parts, such as head-unrestrained gaze shifts involving both eye and head rotation, the individual body-part movements may vary even more than the overall movement. The goal of this investigation was to develop a general method for both mapping sensory or motor response fields of neurons and determining their intrinsic reference frames, where these movement variations are actually utilized rather than avoided. We used head-unrestrained gaze shifts, three-dimensional (3D) geometry, and naturalistic distributions of eye and head orientation to explore the theoretical relationship between the intrinsic reference frame of a sensorimotor neurons response field and the coherence of the activity when this response field is fitted non-parametrically using different kernel bandwidths in different reference frames. We measure how well the regression surface predicts unfitted data using the PREdictive Sum-of-Squares (PRESS) statistic. The reference frame with the smallest PRESS statistic was categorized as the intrinsic reference frame if the PRESS statistic was significantly larger in other reference frames. We show that the method works best when targets are at regularly spaced positions within the response fields active region, and that the method identifies the best kernel bandwidth for response field estimation. We describe how gain-field effects may be dealt with, and how to test neurons within a population that fall on a continuum between specific reference frames. This method may be applied to any spatially coherent single-unit activity related to sensation and/or movement during naturally varying behaviors.

Cross-validated models of the relationships between neck muscle electromyography and three-dimensional head kinematics during gaze behavior

The object of this study was to model the relationship between neck electromyography (EMG) and three-dimensional (3-D) head kinematics during gaze behavior. In two monkeys, we recorded 3-D gaze, head orientation, and bilateral EMG activity in the sternocleidomastoid, splenius capitis, complexus, biventer cervicis, rectus capitis posterior major, and occipital capitis inferior muscles. Head-unrestrained animals fixated and made gaze saccades between targets within a 60° × 60° grid. We performed a stepwise regression in which polynomial model terms were retained/rejected based on their tendency to increase/decrease a cross-validation-based measure of model generalizability. This revealed several results that could not have been predicted from knowledge of musculoskeletal anatomy. During head holding, EMG activity in most muscles was related to horizontal head orientation, whereas fewer muscles correlated to vertical head orientation and none to small random variations in head torsion. A fourth-order polynomial model, with horizontal head orientation as the only independent variable, generalized nearly as well as higher order models. For head movements, we added time-varying linear and nonlinear perturbations in velocity and acceleration to the previously derived static (head holding) models. The static models still explained most of the EMG variance, but the additional motion terms, which included horizontal, vertical, and torsional contributions, significantly improved the results. Several coordinate systems were used for both static and dynamic analyses, with Fick coordinates showing a marginal (nonsignificant) advantage. Thus, during gaze fixations, recruitment within the neck muscles from which we recorded contributed primarily to position-dependent horizontal orientation terms in our data set, with more complex multidimensional contributions emerging during the head movements that accompany gaze shifts. These are crucial components of the late neuromuscular transformations in a complete model of 3-D head-neck system and should help constrain the study of premotor signals for head control during gaze behaviors.