A Theory of Geometric Constraints on Neural Activity for Natural Three-Dimensional Movement

Abstract

Although the orientation of an arm in space or the static view of an object may be represented by a population of neurons in complex ways, how these variables change with movement often follows simple linear rules, reflecting the underlying geometric constraints in the physical world. A theoretical analysis is presented for how such constraints affect the average firing rates of sensory and motor neurons during natural movements with low degrees of freedom, such as a limb movement and rigid object motion. When applied to nonrigid reaching arm movements, the linear theory accounts for cosine directional tuning with linear speed modulation, predicts a curl-free spatial distribution of preferred directions, and also explains why the instantaneous motion of the hand can be recovered from the neural population activity. For three-dimensional motion of a rigid object, the theory predicts that, to a first approximation, the response of a sensory neuron should have a preferred translational direction and a preferred rotation axis in space, both with cosine tuning functions modulated multiplicatively by speed and angular speed, respectively. Some known tuning properties of motion-sensitive neurons follow as special cases. Acceleration tuning and nonlinear speed modulation are considered in an extension of the linear theory. This general approach provides a principled method to derive mechanism-insensitive neuronal properties by exploiting the inherently low dimensionality of natural movements.

Statistical Encoding Model for a Primary Motor Cortical Brain-Machine Interface

“…The majority of the neurons we have studied here had firing rates that were linearly related to the kinematic variables. This linearity is not surprising, as it is consistent with the classical cosine shaped tuning curve (with respect to the direction of movement), and was thus anticipated by theoretical studies [5], [48]. However, a possibility that cannot be discounted based on our data is that the linearityresults froman underlying nonlinear relationship that is artificially linearized by being experimentally sampled in a narrow range of positions, velocities, and accelerations.…”

Functional Architecture of Eye Position Gain Fields in Visual Association Cortex of Behaving Monkey

“…If the principles governing multiple scales of functional architectures in early vision hold for this association cortex, then the large-scaled gain field functional architecture described here may serve as the scaffolding on which other sensory, attentional, and intentional maps may be embedded at finer columnar scales. These distributed multi-scaled representations of visual and eye position can be then combined to construct appropriate perceptual and motor signals in recipient cortical areas (Pouget and Sejnowski 1997;Siegel 1998;Zhang and Sejnowski 1999).…”

Computational approaches to motor control

“…In that model, the amount of neuromotor noise, which may originate from both central and peripheral sources, was assumed to scale with the magnitude of the motor command. Cosine tuning can also result from geometric constraints [13].…”