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Research in the vestibular field has revealed the existence of a central process, called ‘velocity storage’, that is activated by both visual and vestibular rotation cues and is modified by gravity, but whose functional relevance during natural motion has often been questioned. In this review, we explore spatial orientation in the context of a Bayesian model of vestibular information processing. In this framework, deficiencies/ambiguities in the peripheral vestibular sensors are compensated for by central processing to more accurately estimate rotation velocity, orientation relative to gravity, and inertial motion. First, an inverse model of semicircular canal dynamics is used to reconstruct rotation velocity by integrating canal signals over time. However, its low-frequency bandwidth is limited to avoid accumulation of noise in the integrator. A second internal model uses this reconstructed rotation velocity to compute an internal estimate of tilt and inertial acceleration. The bandwidth of this second internal model is also restricted at low frequencies to avoid noise accumulation and drift of the tilt/translation estimator over time. As a result, low-frequency translation can be erroneously misinterpreted as tilt. The time constants of these two integrators (internal models) can be conceptualized as two Bayesian priors of zero rotation velocity and zero linear acceleration, respectively. The model replicates empirical observations like ‘velocity storage’ and ‘frequency segregation’ and explains spatial orientation (e.g., ‘somatogravic’) illusions. Importantly, the functional significance of this network, including velocity storage, is found during short-lasting, natural head movements, rather than at low frequencies with which it has been traditionally studied.

Brainstem and cerebellar neurons implement an internal model to accurately estimate self-motion during externally generated (‘passive’) movements. However, these neurons show reduced responses during self-generated (‘active’) movements, indicating that predicted sensory consequences of motor commands cancel sensory signals. Remarkably, the computational processes underlying sensory prediction during active motion and their relationship to internal model computations during passive movements remain unknown. We construct a Kalman filter that incorporates motor commands into a previously established model of optimal passive self-motion estimation. The simulated sensory error and feedback signals match experimentally measured neuronal responses during active and passive head and trunk rotations and translations. We conclude that a single sensory internal model can combine motor commands with vestibular and proprioceptive signals optimally. Thus, although neurons carrying sensory prediction error or feedback signals show attenuated modulation, the sensory cues and internal model are both engaged and critically important for accurate self-motion estimation during active head movements. When seated in a car, we can detect when the vehicle begins to move even with our eyes closed. Structures in the inner ear called the vestibular, or balance, organs enable us to sense our own movement. They do this by detecting head rotations, accelerations and gravity. They then pass this information on to specialized vestibular regions of the brain. Experiments using rotating chairs and moving platforms have shown that passive movements – such as car journeys and rollercoaster rides – activate the brain’s vestibular regions. But recent work has revealed that voluntary movements – in which individuals start the movement themselves – activate these regions far less than passive movements. Does this mean that the brain ignores signals from the inner ear during voluntary movements? Another possibility is that the brain predicts in advance how each movement will affect the vestibular organs in the inner ear. It then compares these predictions with the signals it receives during the movement. Only mismatches between the two activate the brain’s vestibular regions. To test this theory, Laurens and Angelaki created a mathematical model that compares predicted signals with actual signals in the way the theory proposes. The model accurately predicts the patterns of brain activity seen during both active and passive movement. This reconciles the results of previous experiments on active and passive motion. It also suggests that the brain uses similar processes to analyze vestibular signals during both types of movement. These findings can help drive further research into how the brain uses sensory signals to refine our everyday movements. They can also help us understand how people recover from damage to the vestibular system. Most patients with vestibular injuries learn to walk again, but have difficulty walking on uneven ground. They also become disoriented by passive movement. Using the model to study how the brain adapts to loss of vestibular input could lead to new strategies to aid recovery.

Theories of cerebellar functions posit that the cerebellum implements internal models for online correction of motor actions and sensory estimation. As an example of such computations, an internal model resolves a sensory ambiguity where the peripheral otolith organs in the inner ear sense both head tilts and translations. Here we exploit the response dynamics of two functionally coupled Purkinje cell types in the vestibular part of the caudal vermis (lobules IX and X) to understand their role in this computation. We find that one population encodes tilt velocity, whereas the other, translation-selective, population encodes linear acceleration. We predict that an intermediate neuronal type should temporally integrate the output of tilt-selective cells into a tilt position signal.

In this study, the authors recorded from the cerebellum while monkeys experienced an illusory perception of self-motion, and found that the neurons encoded the erroneous linear acceleration. Their findings provide evidence that the cerebellum might be involved in the implementation of internal models, as previously hypothesized by theorists. A combination of theory and behavioral findings support a role for internal models in the resolution of sensory ambiguities and sensorimotor processing. Although the cerebellum has been proposed as a candidate for implementation of internal models, concrete evidence from neural responses is lacking. Using unnatural motion stimuli, which induce incorrect self-motion perception and eye movements, we explored the neural correlates of an internal model that has been proposed to compensate for Einstein's equivalence principle and generate neural estimates of linear acceleration and gravity. We found that caudal cerebellar vermis Purkinje cells and cerebellar nuclei neurons selective for actual linear acceleration also encoded erroneous linear acceleration, as would be expected from the internal model hypothesis, even when no actual linear acceleration occurred. These findings provide strong evidence that the cerebellum might be involved in the implementation of internal models that mimic physical principles to interpret sensory signals, as previously hypothesized.

Gravity sensing provides a robust verticality signal for three-dimensional navigation. Head direction cells in the mammalian limbic system implement an allocentric neuronal compass. Here we show that head-direction cells in the rodent thalamus, retrosplenial cortex and cingulum fiber bundle are tuned to conjunctive combinations of azimuth and tilt, i.e. pitch or roll. Pitch and roll orientation tuning is anchored to gravity and independent of visual landmarks. When the head tilts, azimuth tuning is affixed to the head-horizontal plane, but also uses gravity to remain anchored to the allocentric bearings in the earth-horizontal plane. Collectively, these results demonstrate that a three-dimensional, gravity-based, neural compass is likely a ubiquitous property of mammalian species, including ground-dwelling animals. Head direction neurons constitute the brain’s compass, and are classically known to indicate head orientation in the horizontal plane. Here, the authors show that head direction neurons form a three-dimensional compass that can also indicate head tilt, and anchors to gravity.

Path integration is a sensorimotor computation that can be used to infer latent dynamical states by integrating self-motion cues. We studied the influence of sensory observation (visual/vestibular) and latent control dynamics (velocity/acceleration) on human path integration using a novel motion-cueing algorithm. Sensory modality and control dynamics were both varied randomly across trials, as participants controlled a joystick to steer to a memorized target location in virtual reality. Visual and vestibular steering cues allowed comparable accuracies only when participants controlled their acceleration, suggesting that vestibular signals, on their own, fail to support accurate path integration in the absence of sustained acceleration. Nevertheless, performance in all conditions reflected a failure to fully adapt to changes in the underlying control dynamics, a result that was well explained by a bias in the dynamics estimation. This work demonstrates how an incorrect internal model of control dynamics affects navigation in volatile environments in spite of continuous sensory feedback.

The central nervous system (CNS) achieves fine motor control by generating predictions of the consequences of the motor command, often called forward models of the movement. These predictions are used centrally to detect not-self generated sensations, to modify ongoing movements, and to induce motor learning. However, finding a neuronal correlate of forward models has proven difficult. In the oculomotor system, we can identify neuronal correlates of forward models vs. neuronal correlates of motor commands by examining neuronal responses during smooth pursuit at eccentric eye positions. During pursuit, torsional eye movement information is not present in the motor command, but it is generated by the mechanic of the orbit. Importantly, the directionality and approximate magnitude of torsional eye movement follow the half angle rule. We use this rule to investigate the role of the cerebellar flocculus complex (FL, flocculus and ventral paraflocculus) in the generation of forward models of the eye. We found that mossy fibers (input elements to the FL) did not change their response to pursuit with eccentricity. Thus, they do not carry torsional eye movement information. However, vertical Purkinje cells (PCs; output elements of the FL) showed a preference for counter-clockwise (CCW) eye velocity [corresponding to extorsion (outward rotation) of the ipsilateral eye]. We hypothesize that FL computes an estimate of torsional eye movement since torsion is present in PCs but not in mossy fibers. Overall, our results add to those of other laboratories in supporting the existence in the CNS of a predictive signal constructed from motor command information.

Sensory signals undergo substantial recoding when neural activity is relayed from sensors through pre-thalamic and thalamic nuclei to cortex. To explore how temporal dynamics and directional tuning are sculpted in hierarchical vestibular circuits, we compared responses of macaque otolith afferents with neurons in the vestibular and cerebellar nuclei, as well as five cortical areas, to identical three-dimensional translational motion. We demonstrate a remarkable spatio-temporal transformation: otolith afferents carry spatially aligned cosine-tuned translational acceleration and jerk signals. In contrast, brainstem and cerebellar neurons exhibit non-linear, mixed selectivity for translational velocity, acceleration, jerk and position. Furthermore, these components often show dissimilar spatial tuning. Moderate further transformation of translation signals occurs in the cortex, such that similar spatio-temporal properties are found in multiple cortical areas. These results suggest that the first synapse represents a key processing element in vestibular pathways, robustly shaping how self-motion is represented in central vestibular circuits and cortical areas.

Parametric roll is an amplification of the roll motion due to the periodic variation of the restoring moment in waves. This phenomenon is mostly observed in head and following seas and is the cause of several accidents occurred on container vessels during recent decades. One of the second generation intact stability criteria, currently under finalization and validation by the IMO, requires computing the maximum roll angle with regard to parametric roll. Both proposed methods are relatively complex to implement and require tools that naval architects are not accustomed to. In this paper, we propose an easier alternative method providing the amplitude of parametric roll for any loading condition at any speed, based on energy considerations and assuming a linear GZ. The implementation of this easy method in the corresponding second generation intact stability criterion provides almost the same value of KG max than the on-degree-of-freedom time simulation proposed by the future regulation.

The granular layer is the input layer of the cerebellar cortex. It receives information through mossy fibers, which contact local granular layer interneurons (GLIs) and granular layer output neurons (granule cells). GLIs provide one of the first signal processing stages in the cerebellar cortex by exciting or inhibiting granule cells. Despite the importance of this early processing stage for later cerebellar computations, the responses of GLIs and the functional connections of mossy fibers with GLIs in awake animals are poorly understood. Here, we recorded GLIs and mossy fibers in the macaque ventral-paraflocculus (VPFL) during oculomotor tasks, providing the first full inventory of GLI responses in the VPFL of awake primates. We found that while mossy fiber responses are characterized by a linear monotonic relationship between firing rate and eye position, GLIs show complex response profiles characterized by \"eye position fields\" and single or double directional tunings. For the majority of GLIs, prominent features of their responses can be explained by assuming that a single GLI receives inputs from mossy fibers with similar or opposite directional preferences, and that these mossy fiber inputs influence GLI discharge through net excitatory or inhibitory pathways. Importantly, GLIs receiving mossy fiber inputs through these putative excitatory and inhibitory pathways show different firing properties, suggesting that they indeed correspond to two distinct classes of interneurons. We propose a new interpretation of the information flow through the cerebellar cortex granular layer, in which mossy fiber input patterns drive the responses of GLIs not only through excitatory but also through net inhibitory pathways, and that excited and inhibited GLIs can be identified based on their responses and their intrinsic properties.