Ronald E. Kettner

A neural network model of cortical activity during reaching

A neural network model that produces many of the directional and spatial response properties that have been observed for cortical neurons in monkeys moving toward targets in space is described. These include motor cortex units with broad tuning in a single preferred direction, approximately linear variation in activity for different hold positions, and approximate invariance in preferred direction for different starting points in space. Association cortex units in the model are sometimes irregular and reminiscent of neurons observed in visually responsive brain areas such as the posterior parietal cortex. The model is also compatible with population analyses performed on motor cortical neurons. Across network units, the distribution of preferred directions is uniformly distributed in directional space, and the degree of tuning and response magnitude vary from unit to unit. A population code used to predict accurately the direction of arm movements from a large population of coarsely tuned individual neurons allows predictions using a simulated population of unit responses obtained from the neural network model. This code works for different starting locations in space using the same parameters.

Predictive smooth pursuit of complex two-dimensional trajectories in monkey: Component interactions

Smooth pursuit eye movements were studied in monkeys tracking target spots that moved two-dimensionally. Complex target trajectories were created by applying either two or three sinusoids to horizontal and vertical axes in various combinations. The chance of observing predictable performance was increased by repeated training on each trajectory. Data analyses were based upon repeated presentations of each trajectory within sessions and on successive days. We wished to determine how accurately monkeys could pursue targets moving along these trajectories and to observe interactions among frequency components. At intermediate frequencies, tracking performance was smooth and consistent during repeated presentations with saccadic corrections that were well integrated with smooth pursuit. The mean gain for eight different sum-of-sines trajectories was 0.83 and the mean magnitude (absolute value) of the phase error was 6°. In light of the long delays that have been associated with the processing of visual information, these values indicate that the monkeys were pursuing predictively. Five factors influenced predictive pursuit performance: (1) there was a decline in performance with increasing frequency; (2) horizontal pursuit was better than vertical pursuit; (3) high-frequency components were tracked with higher gains and phase lags, while lower-frequency components were tracked with lower gains and phase leads; (4) the gain of sinusoidal pursuit was always reduced when a second sinusoid was applied to the same axis or, to a lessor extent, when a second sinusoid of higher frequency was applied to the orthogonal axis; (5) the phase of sinusoidal pursuit shifted from a phase lag to a phase lead when combined with a second sinusoid of higher frequency, but was not affected by the addition of a lower-frequency sinusoid. Findings 1 and 2 confirm, in monkeys, results reported for humans, and 3 extends to monkeys and to two-dimensional pursuit results based upon human subjects. All of these findings demonstrate that complex predictive tracking is controlled by a nonlinear and nonhomogeneous system that uses predictive strategies in concert with feedback control to generate good pursuit.

Predictive smooth pursuit of complex two-dimensional trajectories demonstrated by perturbation responses in monkeys

Two-dimensional sum-of-sines waveforms were pursued by the eye with very small phase delays compared with visual feedback delays estimated in the same monkeys. Processing delays in making smooth corrections averaged 90 msec after infrequent right-angle perturbations from a circular trajectory. These feedback delays were much larger than component phase delays during pursuit that averaged: 10 msec for sinusoids, 3 msec for circles, 20 msec for sum-of-two-sines trajectories, and 19 msec for sum-of-three-sines trajectories. This suggests that predictive control can play a strong role during tracking for a variety of simple and complex target trajectories.

Control of remembered reaching sequences in monkey

Motor and premotor cortex firing patterns from 307 single neurons were recorded while monkeys made rapid sequences of three reaching movements to remembered target buttons arrayed in two-dimensional space. A primary goal was to study and compare directionally tuned responses for each of three movement periods during 12 movement sequences that uniformly sampled the directional space in front of the monkey. The majority of neurons showed maximal responses during movements in a preferred direction with smaller increases during movements close to the preferred direction. These responses showed a statistically significant regression fit to a cosine function for 72% of the neurons examined. Comparisons among tuning directions computed separately for the first, second, and third movement periods suggested the near constancy of preferred direction across a rapidly executed series of movements even though these movements began at different starting points in space. Although directionally tuned neurons were only broadly tuned for a specific direction of movement, the neuronal ensemble carried accurate directional information. A population vector computed by summing vector contributions from the entire population of tuned neurons predicted movement direction with a mean accuracy of 20°. This population code made consistent predictions for each of the 36 movements that were studied using a single set of population parameters. Most of the remaining neurons (24%) that were not tuned during movement did show significant changes in activity during other aspects of task performance. Some nontuned neurons had nondirectional increases that were sustained during movement, while others showed identical phasic bursts during the three movement periods. These nontuned neurons may control stabilizations of the shoulder, trunk, and forearm during movement, or forearm movements during button pushing.

Modeling cerebellar flocculus and paraflocculus involvement in complex predictive smooth eye pursuit in monkeys.

Abstract: The role of flocculus and paraflocculus neurons in the cerebellar control of predictive eye movements was examined using two modeling techniques. The first study characterized the dependence of individual Purkinje‐cell firing patterns on oculomotor output, visual input, and response timing using multilinear regression techniques. Interestingly, no dependence on visual input was detected. Purkinje cell firing was explained by sensitivities to eye position and eye velocity alone. However, complex responses occurred when sensitivity vectors pointed in different directions. For example, some neurons showed a preference for circular pursuit in a particular rotation direction. Responses also tended to lead the eye during predictable pursuit and to lag during unpredictable, visually driven pursuit. This suggests that flocculus and paraflocculus neurons played a stronger role during predictive pursuit than visually driven pursuit. A second modeling study demonstrated how the flocculus/paraflocculus system might generate predictive pursuit. A biologically realistic neural network was simulated based on the known anatomy and physiology of this cerebellar system. It included mossy and climbing fibers with realistic responses, Purkinje cells acting on well‐characterized brain‐stem circuits, and granule, Golgi, basket, and stellate cells with appropriate connections. The network was able to learn new pursuit trajectories based on long‐term alterations in synaptic connectivity at parallel‐to‐Purkinje synapses. Interestingly, this model was able to generate predictive pursuit without visual input based only on eye‐motion input. Thus, both models provide complementary evidence for the generation of nonvisual predictive control by flocculus and paraflocculus neurons.

Kinematic model relating complex 2D smooth pursuit eye movements and Purkinje cell firing rate in cerebellar flocculus and paraflocculus of the rhesus monkey

Single-neuron responses from the flocculus and paraflocculus of the cerebellum were recorded from rhesus monkeys while they tracked targets moving along complex and simple 2D trajectories. Each neuron was analyzed using a multi-linear regression model that expressed the instantaneous firing rate of the neuron as a function of the instantaneous 2D position, velocity, and acceleration of the eye. In all cases, the model provided a good description of the data. In addition, the model explains why some neurons show relatively complex responses including a systematic preference for clockwise (CW) versus counterclockwise (CCW) circular target motions, while others low simpler responses. Most neurons had position and velocity preferred directions that were in alignment. These neurons had relatively simple response profiles with similar response amplitudes during CW versus CCW circular pursuit. Other neurons had position and velocity preferred directions that were not aligned and that differed by as much as 90/spl deg/. These neurons had more complex response properties including a preference for either CW or CCW circular pursuit. This suggests that neurons with simple responses receive inputs with similar spatial tuning properties, while complex responses result from inputs with different spatial tuning properties.

Primate Models for Understanding Brain Mechanisms of Cognitive Behavior

An approach to understanding cognitive brain function is described for behaviors that are best studied in primates. The approach begins with the development of an experimental paradigm that exhibits important aspects of the cognitive behavior, can be learned by a monkey, and allows quantification and experimental control. Behavioral and neural responses during task performance are then recorded and analyzed. Finally, biologically realistic neural network models of specific brain regions are created that generate appropriate behavioral and neural outputs. This approach is ambitious and depends on the combined efforts of many laboratories, but has a high payoff in providing a mechanistic explanation of cognitive function. To illustrate this approach, we discuss work that seeks to understand the neural basis of predictive control during smooth eye pursuit of visible, as well as imagined, targets in monkeys. This is a cognitive process that facilitates eye tracking based on the prediction of upcoming target motions from memory. Neural recording takes place in the flocculus/paraflocculus regions of the cerebellum and the frontal eye fields of the frontal lobe, regions that are involved in predictive eye pursuit. Mathematical modeling of neural/behavioral processing is done at several levels. Single-neuron-firing models are used to quantify single-neuron responses during task performance in terms of sensory, motor, and cognitive variables. Local-circuit models describe how these neural firing patterns might be processed using local synaptic and intracellular mechanisms. Finally, a neural network model is presented that describes how predictive eye tracking could be generated in the cerebellum.