Simulation of adaptive mechanisms in the vestibulo-ocular reflex

The vestibulo-ocular reflex (VOR), which stabilizes the eyes in space during head movements, can undergo adaptive modification to maintain retinal stability in response to natural or experimental challenges. A number of models and neural sites have been proposed to account for this adaptation but these do not fully explain how the nervous system can detect and correct errors in both gain and phase of the VOR. This paper presents a general error correction algorithm based on the multiplicative combination of three signals (retinal slip velocity, head position, head velocity) directly relevant to processing of the VOR. The algorithm is highly specific, requiring the combination of particular sets of signals to achieve compensation. It is robust, with essentially perfect compensation observed for all gain (0.25X–4.0X) and phase (-180°–+180°) errors tested. Output of the model closely resembles behavioral data from both gain and phase adaptation experiments in a variety of species. Imposing physiological constraints (no negative activation levels or changes in the sign of unit weights) does not alter the effectiveness of the algorithm. These results suggest that the mechanisms implemented in our model correspond to those implemented in the brain of the behaving organism. Predictions concerning the nature of the adaptive process are specific enough to permit experimental verification using electrophysiological techniques. In addition, the model provides a strategy for adaptive control of any first order mechanical system.     

Cross axis VOR induced by pursuit training in monkeys: further properties of adaptive responses

We have shown recently in alert monkeys that repeated interaction between the pursuit and vestibular systems in the orthogonal plane induces adaptive changes in the VOR. To examine further properties of adaptive cross axis VOR induced by pursuit training, sinusoidal whole body rotation was applied either in the pitch or yaw plane while presenting a target spot that moved orthogonally to the rotation plane with either 90 degrees phase-lead or 90 degrees phase-lag to the chair signal. After one hour of training at 0.5 Hz (+/- 10 degrees), considerable phase-shift was observed in orthogonal eye movement responses consistent with the training paradigms by identical chair rotation in complete darkness, with further lead at lower frequencies and lag at higher frequencies. However, gains (eye/chair) induced by phase- shift pursuit training was different during pitch and yaw rotation. Although frequency tuning was maintained during pitch in the phase-shift paradigms, it was not maintained during yaw, resulting in higher gains at lower stimulus frequencies compared to the gains during yaw. This difference may reflect otolith contribution during pitch rotation. To understand further the nature of signals that induce adaptive cross axis VOR, we examined interaction of pursuit, whole field-visual pattern and vestibular stimuli. Magnitudes of the cross axis VOR with a spot alone on one hand and with a spot and pattern moving together in the same plane on the other during chair rotation were similar, and when one of the two visual stimuli was stationary during chair rotation, our well trained monkeys did not induce the cross axis VOR. These results suggest that the cross axis VOR induced by pursuit training shares common mechanisms with the cross axis VOR induced by whole field-slip stimuli and that if conflicting information is given between the two visual stimuli, adaptive changes are inhibited. Horizontal GVPs were recorded in the cerebellar floccular lobe during pitch rotation coupled with horizontal pursuit stimuli. These GVPs did not respond to pitch in the dark before training, but responded after 60 min of pursuit training with eye velocity sensitivities similar to those before training. Adaptive change in the VOR was specific to smooth eye movements but not to saccades in our paradigms.     

Decorrelation control by the cerebellum achieves oculomotor plant compensation in simulated vestibulo-ocular reflex

We introduce decorrelation control as a candidate algorithm for the cerebellar microcircuit and demonstrate its utility for oculomotor plant compensation in a linear model of the vestibulo-ocular reflex (VOR). Using an adaptive-filter representation of cerebellar cortex and an anti-Hebbian learning rule, the algorithm learnt to compensate for the oculomotor plant by minimizing correlations between a predictor variable (eye-movement command) and a target variable (retinal slip), without requiring a motor-error signal. Because it also provides an estimate of the unpredicted component of the target variable, decorrelation control can simplify both motor coordination and sensory acquisition. It thus unifies motor and sensory cerebellar functions.     

Cerebellar Motor Learning: When Is Cortical Plasticity Not Enough?

Classical Marr-Albus theories of cerebellar learning employ only cortical sites of plasticity. However, tests of these theories using adaptive calibration of the vestibulo–ocular reflex (VOR) have indicated plasticity in both cerebellar cortex and the brainstem. To resolve this long-standing conflict, we attempted to identify the computational role of the brainstem site, by using an adaptive filter version of the cerebellar microcircuit to model VOR calibration for changes in the oculomotor plant. With only cortical plasticity, introducing a realistic delay in the retinal-slip error signal of 100 ms prevented learning at frequencies higher than 2.5 Hz, although the VOR itself is accurate up to at least 25 Hz. However, the introduction of an additional brainstem site of plasticity, driven by the correlation between cerebellar and vestibular inputs, overcame the 2.5 Hz limitation and allowed learning of accurate high-frequency gains. This “cortex-first” learning mechanism is consistent with a wide variety of evidence concerning the role of the flocculus in VOR calibration, and complements rather than replaces the previously proposed “brainstem-first” mechanism that operates when ocular tracking mechanisms are effective. These results (i) describe a process whereby information originally learnt in one area of the brain (cerebellar cortex) can be transferred and expressed in another (brainstem), and (ii) indicate for the first time why a brainstem site of plasticity is actually required by Marr-Albus type models when high-frequency gains must be learned in the presence of error delay.     

Depression of the vestibulo-ocular and optokinetic responses by intrafloccular microinjection of GABA-A and GABA-B agonists in the rabbit

The functional implication of the cerebellar flocculus in regulation of the VOR and OKR gain has mostly been studied by lesion experiments, and the hypotheses derived from these experiments are not always in line with one another. In the present study, a reversible method was used to inhibit floccular Purkinje cells. The GABA-A agonist muscimol or the GABA-B agonist baclofen were bilaterally injected into the flocculus of rabbits, and the effects of these injections on the gain of the VOR and OKR were studied. Both drugs induced a reduction by at least 50% of the gain of the VOR in light and darkness, and of the OKR. Although GABA-A and GABA-B receptors are known to have different cerebellar localizations, muscimol and baclofen injections resulted in quantitatively similar effects. It is suggested that these GABA-agonists cause either direct or indirect inhibition of floccular Purkinje cells, thus reducing modulation of the firing rate of these neurons by afferent mossy and climbing fibers. Because the flocular Purkinje cells act out of phase with the vestibular neurons which drive the oculomotor neurons, a reduced output of floccular Purkinje cells would result in a reduction of the VOR and OKR gain. These experiments provide strong evidence that the cerebellar flocculus has a positive influence on the basic VOR and OKR gain.     

Bio-inspired adaptive feedback error learning architecture for motor control

This study proposes an adaptive control architecture based on an accurate regression method called Locally Weighted Projection Regression (LWPR) and on a bio-inspired module, such as a cerebellar-like engine. This hybrid architecture takes full advantage of the machine learning module (LWPR kernel) to abstract an optimized representation of the sensorimotor space while the cerebellar component integrates this to generate corrective terms in the framework of a control task. Furthermore, we illustrate how the use of a simple adaptive error feedback term allows to use the proposed architecture even in the absence of an accurate analytic reference model. The presented approach achieves an accurate control with low gain corrective terms (for compliant control schemes). We evaluate the contribution of the different components of the proposed scheme comparing the obtained performance with alternative approaches. Then, we show that the presented architecture can be used for accurate manipulation of different objects when their physical properties are not directly known by the controller. We evaluate how the scheme scales for simulated plants of high Degrees of Freedom (7-DOFs).     

A model of the cerebellum in adaptive control of saccadic gain

 We review data showing that the cerebellum is required for adaptation of saccadic gain to repeated presentations of dual-step visual targets and thus, presumably, for providing adaptive corrections for the brainstem saccade generator in response to any error created by the open-loop saccadic system. We model the adaptability of the system in terms of plasticity of synapses from parallel fibers to Purkinje cells in cerebellar cortex, stressing the integration of cerebellar cortex and nuclei in microzones as the units for correction of motor pattern generators. We propose a model of the inferior olive as an error detector, and use a ‘window of eligibility’ to insure that error signals that elicit a corrective movement are used to adjust the original movement, not the secondary movement. In a companion paper we simulate this large, realistic network of neural-like units to study the complex spatiotemporal behavior of neuronal subpopulations implicated in the control and adaptation of saccades. Received: 25 November 1994/Accepted in revised form: 6 February 1996     

Neural network models of velocity storage in the horizontal vestibulo-ocular reflex

The vestibulo-ocular reflex (VOR) produces compensatory eye movements by utilizing head rotational velocity signals from the semicircular canals to control contractions of the extraocular muscles. In mammals, the time course of horizontal VOR is longer than that of the canal signals driving it, revealing the presence of a central integrator known as velocity storage. Although the neurons mediating VOR have been described neurophysiologically, their properties, and the mechanism of velocity storage itself, remain unexplained. Recent models of integration in VOR are based on systems of linear elements, interconnected in arbitrary ways. The present study extends this work by modeling horizontal VOR as a learning network composed of nonlinear model neurons. Network architectures are based on the VOR arc (canal afferents, vestibular nucleus (VN) neurons and extraocular motoneurons) and have both forward and lateral connections. The networks learn to produce velocity storage integration by forming lateral (commissural) inhibitory feedback loops between VN neurons. These loops overlap and interact in a complex way, forming both fast and slow VN pathways. The networks exhibit some of the nonlinear properties of the actual VOR, such as dependency of decay rate and phase lag upon input magnitude, and skewing of the response to higher magnitude sinusoidal inputs. Model VN neurons resemble their real counterparts. Both have increased time constant and gain, and decreased spontaneous rate as compared to canal afferents. Also, both model and real VN neurons exhibit rectification and skew. The results suggest that lateral inhibitory interactions produce velocity storage and also determine the properties of neurons mediating VOR. The neural network models demonstrate how commissural inhibition may be organized along the VOR pathway.     

The vestibulo-ocular reflex and velocity storage in spinocerebellar ataxia 8

The autosomal dominant spinocerebellar ataxias (SCAs) are a group of neurodegenerative diseases characterized by progressive instability of posture and gait, incoordination, ocular motor dysfunction, and dysarthria due to degeneration of cerebellar and brainstem neurons. Among the more than 20 genetically distinct subtypes, SCA8 is one of several wherein clinical observations indicate that cerebellar dysfunction is primary, and there is little evidence for other CNS involvement. The aim of the present work was to study the decay of the horizontal vestibulo-ocular reflex (VOR) after a short period of constant acceleration to understand the pathophysiology of the VOR due to cerebellar Purkinje cell degeneration in SCA8. The VOR was recorded in patients with genetically defined SCA8 during rotation in the dark. Moderate to severely affected patients had a qualitatively intact VOR, but there were quantitative differences in the gain and dynamics compared to normal controls. During angular velocity ramp rotations, there was a reversal in the direction of the VOR that was more pronounced in SCA8 compared to controls. Modeling studies indicate that there are significant changes in the velocity storage network, including abnormal feedback of an eye position signal into the network that contributes to this reversal. These and other results will help to identify features that are diagnostic for SCA subtypes and provide new information about selective vulnerability of neurons controlling vestibular reflexes.     

Distributed parallel processing in the vertical vestibulo-ocular reflex: Learning networks compared to tensor theory

The vestibulo-ocular reflex (VOR) is capable of producing compensatory eye movements in three dimensions. It utilizes the head rotational velocity signals from the semicircular canals to control the contractions of the extraocular muscles. Since canal and muscle coordinate frames are not orthogonal and differ from one another, a sensorimotor transformation must be produced by the VOR neural network. Tensor theory has been used to construct a linear transformation that can model the three-dimensional behavior of the VOR. But tensor theory does not take the distributed, redundant nature of the VOR neural network into account. It suggests that the neurons subserving the VOR, such as vestibular nucleus neurons, should have specific sensitivity-vectors. Actual data, however, are not in accord. Data from the cat show that the sensitivity-vectors of vestibular nucleus neurons, rather than aligning with any specific vectors, are dispersed widely. As an alternative to tensor theory, we modeled the vertical VOR as a three-layered neural network programmed using the back-propagation learning algorithm. Units in mature networks had divergent sensitivity-vectors which resembled those of actual vestibular nucleus neurons in the cat. This similarity suggests that the VOR sensorimotor transformation may be represented redundantly rather than uniquely. The results demonstrate how vestibular nucleus neurons can encode the VOR sensorimotor transformation in a distributed manner.     

Impairment of LTD and cerebellar learning by Purkinje cell-specific ablation of cGMP-dependent protein kinase I

The molecular basis for cerebellar plasticity and motor learning remains controversial. Cerebellar Purkinje cells (PCs) contain a high concentration of cGMP-dependent protein kinase type I (cGKI). To investigate the function of cGKI in long-term depression (LTD) and cerebellar learning, we have generated conditional knockout mice lacking cGKI selectively in PCs. These cGKI mutants had a normal cerebellar morphology and intact synaptic calcium signaling, but strongly reduced LTD. Interestingly, no defects in general behavior and motor performance could be detected in the LTD-deficient mice, but the mutants exhibited an impaired adaptation of the vestibulo-ocular reflex (VOR). These results indicate that cGKI in PCs is dispensable for general motor coordination, but that it is required for cerebellar LTD and specific forms of motor learning, namely the adaptation of the VOR.     

Motor deficits in neurofibromatosis type 1 mice: the role of the cerebellum

Neurofibromatosis type 1 (NF1) is an autosomal dominantly inherited disease, characterized by various neurocutaneous symptoms, cognitive impairments and problems in fine and gross motor performance. Although cognitive deficits in NF1 have been attributed to increased release of the inhibitory neurotransmitter γ-amino butyric acid (GABA) in the hippocampus, the origin of the motor deficits is unknown. Cerebellar Purkinje cells, the sole output neurons of the cerebellar cortex, are GABAergic neurons and express neurofibromin at high levels, suggesting an important role for the cerebellum in the observed motor deficits in NF1. To test this, we determined the cerebellar contribution to motor problems in Nf1(+/-) mice, a validated mouse model for NF1. Using the Rotarod, a non-specific motor performance test, we confirmed that, like NF1 patients, Nf1(+/-) mice have motor deficits. Next, to evaluate the role of the cerebellum in these deficits, mice were subjected to cerebellum-specific motor performance and learning tests. Nf1(+/-) mice showed no impairment on the Erasmus ladder, as step time and number of missteps were not different. Furthermore, when compensatory eye movements were tested, no performance deficits were found in the optokinetic reflex and vestibulo-ocular reflex in the dark (VOR) or in the light (VVOR). Finally, Nf1(+/-) mice successfully completed short- and long-term VOR adaptation paradigms, tests that both depend on cerebellar function. Thus, despite the confirmed presence of motor performance problems in Nf1(+/-) mice, we found no indication of a cerebellar component. These results, combined with recent clinical data, suggest that cerebellar function is not overtly affected in NF1 patients.     

An adaptive and predictive control strategy for an activated sludge process

This paper focuses on the development of a simple adaptive and predictive control algorithm, used to regulate the effluent quality of an activated sludge treatment process. This control algorithm is based on the development of a linear incremental second order model which takes distinctively into account the main disturbances on the process. The model is employed to predict the effluent pollution over a finite horizon. Then, the control inputs are computed from the predictions and the desired output set point. The simulations conducted with a non linear process model showed that such a control strategy could improve the process performances by minimizing the effluent pollution and the energetic cost of the system.     

Neural recordings and behavioral observations in the monkey vestibulo-ocular reflex constrain the cellular mechanisms for cerebellum-dependent behavioral learning

Recordings from the cerebellum under behavioral conditions that cause learning in the vestibulo-ocular reflex (VOR) constrain the cellular mechanisms that could mediate learning. Analysis of the complex-spike responses of Purkinje cells demonstrates a mismatch between the properties of cerebellar long-term depression (LTD) in vitro and the signals available to guide learning in vivo. To resolve this mismatch, it may be necessary to assume that there are multiple cellular mechanisms of VOR learning, including both depression and potentiation.     

Adaptive feedback control models of the vestibulocerebellum and spinocerebellum

We extend the cerebellar learning model proposed by Kawato and Gomi (1992) to the case where a specific region of the cerebellum executes adaptive feed-back control as well as feedforward control. The model is still based on the feedback-error-learning scheme. The proposed adaptive feedback control model is developed in detail as a specific neural circuit model for three different regions of the cerebellum and the learning of the corresponding representative movements: (i) the flocculus and adaptive modification of the vestibulo-ocular reflex and optokinetic eye-movement responses, (ii) the vermis and adaptive posture control, and (iii) the intermediate zones of the hemisphere and adaptive control of locomotion. As a representative example, simultaneous adaptation of the vestibulo-ocular reflex and the optokinetic eye-movement response was successfully simulated while the Purkinje cells receive copies of motor commands through recurrent neural connections as well as vestibular and retinal-slip parallel-fiber inputs.     

Neural adaptive control for vibration suppression in composite fin-tip of aircraft

In this paper, we present a neural adaptive control scheme for active vibration suppression of a composite aircraft fin tip. The mathematical model of a composite aircraft fin tip is derived using the finite element approach. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes very accurately. Piezo-electric actuators and sensors are placed at optimal locations such that the vibration suppression is a maximum. Model-reference direct adaptive neural network control scheme is proposed to force the vibration level within the minimum acceptable limit. In this scheme, Gaussian neural network with linear filters is used to approximate the inverse dynamics of the system and the parameters of the neural controller are estimated using Lyapunov based update law. In order to reduce the computational burden, which is critical for real-time applications, the number of hidden neurons is also estimated in the proposed scheme. The global asymptotic stability of the overall system is ensured using the principles of Lyapunov approach. Simulation studies are carried-out using sinusoidal force functions of varying frequency. Experimental results show that the proposed neural adaptive control scheme is capable of providing significant vibration suppression in the multiple bending modes of interest. The performance of the proposed scheme is better than the H(infinity) control scheme.     

Selective engagement of plasticity mechanisms for motor memory storage

The number and diversity of plasticity mechanisms in the brain raises a central question: does a neural circuit store all memories by stereotyped application of the available plasticity mechanisms, or can subsets of these mechanisms be selectively engaged for specific memories? The uniform architecture of the cerebellum has inspired the idea that plasticity mechanisms like cerebellar long-term depression (LTD) contribute universally to memory storage. To test this idea, we investigated a set of closely related, cerebellum-dependent motor memories. In mutant mice lacking Ca(2+)/calmodulin-dependent protein kinase IV (CaMKIV), the maintenance of cerebellar LTD is abolished. Although memory for an increase in the gain of the vestibulo-ocular reflex (VOR) induced with high-frequency stimuli was impaired in these mice, memories for decreases in VOR gain and increases in gain induced with low-frequency stimuli were intact. Thus, a particular plasticity mechanism need not support all cerebellum-dependent memories, but can be engaged selectively according to the parameters of training.     

On-line adaptive control of a fed-batch fermentation of Saccharomyces cerevisiae

The feasibility of applying an adaptive control technique to a fermentation process is investigated. The nonlinear, time-variant parameters of a fermentation process were estimated on-line as a series of linearized describing matrices. The matrices were used to update a suboptimal feedback law which controlled the process in real time over the linear region. Experiments were performed on a small-scale fully instrumented fermenter with the online, real-time adaptive control package. Results are presented for both single- and multivariable control, and indicate successful control of yeast cell growth.     

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate versus current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.