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ABSTRACT: Otolith end organs of vertebrates sense linear accelerations of the head and gravitation. The hair cells on their epithelia are responsible for transduction. In mammals, the striola, parallel to the line where hair cells reverse their polarization, is a narrow region centered on a curve with curvature and torsion. It has been shown that the striolar region is functionally different from the rest, being involved in a phasic vestibular pathway. We propose a mathematical and computational model that explains the necessity of this amazing geometry for the striola to be able to carry out its function. Our hypothesis, related to the biophysics of the hair cells and to the physiology of their afferent neurons, is that striolar afferents collect information from several type I hair cells to detect the jerk in a large domain of acceleration directions. This predicts a mean number of two calyces for afferent neurons, as measured in rodents. The domain of acceleration directions sensed by our striolar model is compatible with the experimental results obtained on monkeys considering all afferents. Therefore, the main result of our study is that phasic and tonic vestibular afferents cover the same geometrical fields, but at different dynamical and frequency domains.
Journal of Computational Neuroscience 04/2013; · 2.51 Impact Factor
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ABSTRACT: During locomotion, a top-down organization has been previously demonstrated with the head as a stabilized platform and gaze anticipating the horizontal direction of the trajectory. However, the quantitative assessment of the anticipatory sequence from gaze to trajectory and body segments has not been documented. The present paper provides a detailed investigation into the spatial and temporal anticipatory relationships among the direction of gaze and body segments during locomotion. Participants had to walk along several mentally simulated complex trajectories, without any visual cues indicating the trajectory to follow. The trajectory shapes were presented to the participants on a sheet of paper. Our study includes an analysis of the relationships between horizontal gaze anticipatory behavior direction and the upcoming changes in the trajectory. Our findings confirm the following: 1) The hierarchical ordered organization of gaze and body segment orientations during complex trajectories and free locomotion. Gaze direction anticipates the head orientation, and head orientation anticipates reorientation of the other body segments. 2) The influence of the curvature of the trajectory and constraints of the tasks on the temporal and spatial relationships between gaze and the body segments: Increased curvature resulted in increased time and spatial anticipation. 3) A different sequence of gaze movements at inflection points where gaze plans a much later segment of the trajectory.
Experimental Brain Research 09/2012; 223(1):65-78. · 2.39 Impact Factor
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ABSTRACT: The question of whether neural synchrony may be preserved in adult mammalian visual cortex despite abnormal postnatal visual experience was investigated by combining anatomical and computational approaches. Single callosal axons in visual cortex of early monocularly deprived (MD) adult cats were labeled anterogradely with biocytin in vivo and reconstructed in 3D. Spike propagation was then orthodromically simulated within each of these axons with NEURON software. Data were systematically compared to those previously obtained in normally reared (NR) adult cats with comparable approaches. The architecture of the callosal axons in MD animals differed significantly from the NR group, with longer branches and first nodes located deeper below the cortex. But, surprisingly, simulation of spike propagation demonstrated that transmission latencies of most spikes remained inferior to 2 ms, like the NR group. These results indicate that synchrony of neural activity may be preserved in adult visual cortex despite abnormal postnatal visual experience. According to the temporal binding hypothesis, this also indicates that the necessary timing for visual perception is present despite anatomical abnormalities in visual cortex.
Frontiers in Bioscience 01/2010; 15:681-707. · 3.52 Impact Factor
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ABSTRACT: Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations.
PLoS Computational Biology 08/2009; 5(7):e1000426. · 5.22 Impact Factor
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ABSTRACT: Numerous brain regions encode variables using spatial distribution of activity in neuronal maps. Their specific geometry is usually explained by sensory considerations only. We provide here, for the first time, a theory involving the motor function of the superior colliculus to explain the geometry of its maps. We use six hypotheses in accordance with neurobiology to show that linear and logarithmic mappings are the only ones compatible with the generation of saccadic motor command. This mathematical proof gives a global coherence to the neurobiological studies on which it is based. Moreover, a new solution to the problem of saccades involving both colliculi is proposed. Comparative simulations show that it is more precise than the classical one.
Biological Cybernetics 11/2007; 97(4):279-92. · 1.59 Impact Factor
