Spatial symmetries in vestibular projections to the uvula-nodulus

Foster, I.; Hanes, David A.; Barmack, Neal H.; McCollum, Gin

doi:10.1007/s00422-006-0136-y

Cited by 12 publications

(16 citation statements)

References 58 publications

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“…The next steps in the program we have described are to include in the model the (symmetry) structure of other projections in the vestibular system, for example the uvula-nodulus [7], to include the semicircular canals, and to make more direct contact with the biology. Two questions arise in this last step: Do the head motions we describe play some special role in the context of general periodic head motions (that is, do these motions appear frequently in animals), and can the classification of spatiotemporal symmetries of small amplitude motions near an upright head give a method for classifying types of head tremor?…”

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confidence: 99%

Spatiotemporal Symmetries in the Disynaptic Canal-Neck Projection

Golubitsky¹,

Shiau²,

Stewart³

2007

SIAM J. Appl. Math.

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Abstract. The vestibular system in almost all vertebrates, and in particular in humans, controls balance by employing a set of six semicircular canals, three in each inner ear, to detect angular accelerations of the head in three mutually orthogonal coordinate planes. Signals from the canals are transmitted to eight (groups of) neck motoneurons, which activate the eight corresponding muscle groups. These signals may be either excitatory or inhibitory, depending on the direction of head acceleration. McCollum and Boyle have observed that in the cat the relevant network of neurons possesses octahedral symmetry, a structure that they deduce from the known innervation patterns (connections) from canals to muscles. We rederive the octahedral symmetry from mathematical features of the probable network architecture, and model the movement of the head in response to the activation patterns of the muscles concerned. We assume that connections between neck muscles can be modeled by a "coupled cell network," a system of coupled ODEs whose variables correspond to the eight muscles, and that this network also has octahedral symmetry. The network and its symmetries imply that these ODEs must be equivariant under a suitable action of the octahedral group. It is observed that muscle motoneurons form natural "push-pull pairs" in which, for given movements of the head, one neuron produces an excitatory signal, whereas the other produces an inhibitory signal. By incorporating this feature into the mathematics in a natural way, we are led to a model in which the octahedral group acts by signed permutations on muscle motoneurons. We show that with the appropriate group actions, there are six possible spatiotemporal patterns of time-periodic states that can arise by Hopf bifurcation from an equilibrium representing an immobile head. Here we use results of Ashwin and Podvigina. Counting conjugate states, whose physiological interpretations can have significantly different features, there are 15 patterns of periodic oscillation, not counting left-right reflections or time-reversals as being different. We interpret these patterns as motions of the head, and note that all six types of pattern appear to correspond to natural head motions.

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confidence: 99%

Spatiotemporal Symmetries in the Disynaptic Canal-Neck Projection

Golubitsky¹,

Shiau²,

Stewart³

2007

SIAM J. Appl. Math.

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“…The same is true of the horizontal plane. However, these geometrical structures are hard-wired or have strong physiological substrates in the vestibular system and its projections, as analyzed using the mathematics of symmetry groups (Foster et al 2007; McCollum 2007; McCollum and Boyle 2004). These geometrical structures are spatial; the geometrical structure of gravitation is both spatial and temporal.…”

Section: Discussionmentioning

confidence: 99%

Phase-linking and the perceived motion during off-vertical axis rotation

2009

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Human off-vertical axis rotation (OVAR) in the dark typically produces perceived motion about a cone, the amplitude of which changes as a function of frequency. This perception is commonly attributed to the fact that both the OVAR and the conical motion have a gravity vector that rotates about the subject. Little-known, however, is that this rotating-gravity explanation for perceived conical motion is inconsistent with basic observations about self-motion perception: (a) that the perceived vertical moves toward alignment with the gravito-inertial acceleration (GIA) and (b) that perceived translation arises from perceived linear acceleration, as derived from the portion of the GIA not associated with gravity. Mathematically proved in this article is the fact that during OVAR these properties imply mismatched phase of perceived tilt and translation, in contrast to the common perception of matched phases which correspond to conical motion with pivot at the bottom. This result demonstrates that an additional perceptual rule is required to explain perception in OVAR. This study investigates, both analytically and computationally, the phase relationship between tilt and translation at different stimulus rates-slow (45°/s) and fast (180°/s), and the three-dimensional shape of predicted perceived motion, under different sets of hypotheses about self-motion perception. We propose that for human motion perception, there is a phase-linking of tilt and translation movements to construct a perception of one's overall motion path. Alternative hypotheses to achieve the phase match were tested with three-dimensional computational models, comparing the output with published experimental reports. The best fit with experimental data was the hypothesis that the phase of perceived translation was linked to perceived tilt, while the perceived tilt was determined by the GIA. This hypothesis successfully predicted the bottom-pivot cone commonly reported and a reduced sense of tilt during fast OVAR. Similar considerations apply to the hilltop illusion often reported during horizontal linear oscillation. Known response properties of central neurons are consistent with this ability to phase-link translation with tilt. In addition, the competing "standard" model was mathematically proved to be unable to predict the bottom-pivot cone regardless of the values used for parameters in the model.

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“…In addition, they are further bound into spatial systems by the symmetries of vestibular projections, which provide a logical structure in which the axes play equivalent roles and the two directions along each axis are joined into one axis (McCollum and Boyle 2004;Foster et al 2007;McCollum and Hanes 2010). For example, the right anterior and left posterior semicircular canals are joined into one axis in vestibular projections (Foster et al 2007). Natural units for angular velocity and acceleration could be defined, based on neuronal firing rates, but typically conventional units are imposed.…”

Section: Coordinatesmentioning

confidence: 98%

Face-infringement space: the frame of reference of the ventral intraparietal area

2012

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Experimental studies have shown that responses of ventral intraparietal area (VIP) neurons specialize in head movements and the environment near the head. VIP neurons respond to visual, auditory, and tactile stimuli, smooth pursuit eye movements, and passive and active movements of the head. This study demonstrates mathematical structure on a higher organizational level created within VIP by the integration of a complete set of variables covering face-infringement. Rather than positing dynamics in an a priori defined coordinate system such as those of physical space, we assemble neuronal receptive fields to find out what space of variables VIP neurons together cover. Section 1 presents a view of neurons as multidimensional mathematical objects. Each VIP neuron occupies or is responsive to a region in a sensorimotor phase space, thus unifying variables relevant to the disparate sensory modalities and movements. Convergence on one neuron joins variables functionally, as space and time are joined in relativistic physics to form a unified spacetime. The space of position and motion together forms a neuronal phase space, bridging neurophysiology and the physics of face-infringement. After a brief review of the experimental literature, the neuronal phase space natural to VIP is sequentially characterized, based on experimental data. Responses of neurons indicate variables that may serve as axes of neural reference frames, and neuronal responses have been so used in this study. The space of sensory and movement variables covered by VIP receptive fields joins visual and auditory space to body-bound sensory modalities: somatosensation and the inertial senses. This joining of allocentric and egocentric modalities is in keeping with the known relationship of the parietal lobe to the sense of self in space and to hemineglect, in both humans and monkeys. Following this inductive step, variables are formalized in terms of the mathematics of graph theory to deduce which combinations are complete as a multidimensional neural structure that provides the organism with a complete set of options regarding objects impacting the face, such as acceptance, pursuit, and avoidance. We consider four basic variable types: position and motion of the face and of an external object. Formalizing the four types of variables allows us to generalize to any sensory system and to determine the necessary and sufficient conditions for a neural center (for example, a cortical region) to provide a face-infringement space. We demonstrate that VIP includes at least one such face-infringement space.

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Spatial symmetries in vestibular projections to the uvula-nodulus

Cited by 12 publications

References 58 publications

Spatiotemporal Symmetries in the Disynaptic Canal-Neck Projection

Spatiotemporal Symmetries in the Disynaptic Canal-Neck Projection

Phase-linking and the perceived motion during off-vertical axis rotation

Face-infringement space: the frame of reference of the ventral intraparietal area

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