Henrietta L. Galiana

Original Contribution: Dynamic feedback to the superior colliculus in a neural network model of the gaze control system

The role of the superior colliculus (SC) has been explored in the context of the gaze control system, with the conclusion that recent data place it inside the control loop calculating gaze error. A neural network proposed for the SC achieves both spatial and temporal integration of gaze signals. When placing the SC inside a gaze control loop, linear time-space transformations can be achieved even with restricted feedback on the edges of the map. The proposed gaze control model can reproduce all of the properties of previous head-fixed models. However, for the first time, a collicular mechanism is shown to provide plausible explanations for conflicting results upon electrical stimulation of rostral versus caudal sites on the colliculus, and can generate reasonable trajectories for both eye and head platforms in the head-free condition. The key assumption is the distribution of a common motor (gaze) error to the platforms contributing to the movement.

The use of system identification techniques in the analysis of oculomotor burst neuron spike train dynamics.

The objective of system identification methods is to construct a mathematical model of a dynamical system in order to describe adequately the input-output relationship observed in that system. Over the past several decades, mathematical models have been employed frequently in the oculomotor field, and their use has contributed greatly to our understanding of how information flows through the implicated brain regions. However, the existing analyses of oculomotor neural discharges have not taken advantage of the power of optimization algorithms that have been developed for system identification purposes. In this article, we employ these techniques to specifically investigate the “burst generator” in the brainstem that drives saccadic eye movements. The discharge characteristics of a specific class of neurons, inhibitory burst neurons (IBNs) that project monosynaptically to ocular motoneurons, are examined. The discharges of IBNs are analyzed using different linear and nonlinear equations that express a neurons firing frequency and history (i.e., the derivative of frequency), in terms of quantities that describe a saccade trajectory, such as eye position, velocity, and acceleration. The variance accounted for by each equation can be compared to choose the optimal model. The methods we present allow optimization across multiple saccade trajectories simultaneously. We are able to investigate objectively how well a specific equation predicts a neurons discharge pattern as well as whether increasing the complexity of a model is justifiable. In addition, we demonstrate that these techniques can be used both to provide an objective estimate of a neurons dynamic latency and to test whether a neurons initial firing rate (expressed as an initial condition) is a function of a quantity describing a saccade trajectory (such as initial eye position).

A nystagmus strategy to linearize the vestibulo-ocular reflex

Two important aspects of the vestibulo-ocular reflex (VOR) are addressed. First, the linear range of ocular responses is much more extensive than expected from the characteristics of central pathways (CNS), and this is shown to result directly from early convergence of fast and slow premotor signals in the central processes, associated with significant and intermittent changes in functional connectivity (effective structural modulation). Second, the presence of such structural modulation implies that responses must be analyzed using transient analysis techniques, rather than previous steady state approaches, in order to properly evaluate reflex dynamics. Simulation results with a recent model of the VOR are used to illustrate the arguments. Relying on known interconnections between saccadic burst circuits in the brainstem, and the ocular premotor areas of the vestibular nuclei, a viable strategy for the timing of nystagmus events is proposed. The strategy easily reproduces the characteristic changes in vestibular nystagmus with the amplitude of head velocities, and with the frequency of passive head oscillation.<<ETX>>

NARMAX representation and identification of ankle dynamics

Representation and identification of a parallel pathway description of ankle dynamics as a model of the nonlinear autoregressive, moving average exogenous (NARMAX) class is considered. A nonlinear difference equation describing this ankle model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to ankle dynamics and its properties investigated via continuous-time simulations of experimental conditions. Simulation results show that 1) the outputs of the NARMAX model match closely those generated using continuous-time methods and 2) NARMAX identification methods applied to ankle dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental human ankle data models with high cross-validation variance accounted for.

A bootstrap method for structure detection of NARMAX models

Many systems may be described by NARMAX models using only a few terms. However, depending on the order of the system the number of candidate terms can become very large. Selection of a subset of these candidate terms is necessary for an efficient system description. This is an unresolved issue in system identification for over-parameterized models. Therefore, in this paper, we develop a bootstrap structure detection (BSD) algorithm as a means of determining the structure of highly over-parameterized models. The performance of this BSD technique was evaluated by using it to estimate the structure of a (1) simple NARMAX model, (2) moderately over-parameterized NARMAX model and (3) highly over-parameterized NARMAX model. The results demonstrate that the BSD algorithm is a robust method for detecting the structure of NARMAX models. This method provides accurate estimates of parameter statistics without relying on assumptions made by traditional procedures and yields a parsimonious description of the system.

Providing distinct vergence and version dynamics in a bilateral oculomotor network

Given reported interactions between vergence and version dynamics, ocular reflexes cannot be properly modelled as separate independent subsystems. Using a model structure compatible with known anatomy, we show that a single bilateral system can produce results consistent with observed data both at the central and ocular levels. This model provides for both vergence and conjugate integrators in a single controller, and explains the observed modulation on abducens interneurons and mesencephalic vergence cells during vergence responses. Reported interactions between version and vergence would then be a natural consequence of a shared premotor network. Major implications include: the need to record both eyes in a protocol, since cross-talk is always possible; and adaptation to monocular changes could be distributed in all motor projections to both eyes.

A bilateral model integrating vergence and the vestibulo-ocular reflex

The majority of previous modelling studies of vergence and the vestibulo-ocular reflex (VOR) have postulated arbitrary structures mainly on the basis of input-output behavioural relationships. Such models were developed following traditional schemes of oculomotor organization, based upon the notion of independence between different oculomotor subsystems. This impedes the simulation of complex binocular interactions and associated central activities. In contrast to preceding studies, the mathematical model for binocular control presented here was developed fully on physiological and anatomical grounds which reflect the organization and functional properties of known vergence and VOR premotor centres. Computer simulations show the model properly simulates the mainobserved characteristics in the discharge of several premotor and motor nuclei during slow vergence and the VOR in the dark. In particular, the model reproduces the activity profiles of abducens internuclear neurons, secondary vestibular cells, tonic prepositus hypoglossi neurons and ocular motoneurons during vergence and the VOR. It also simulates the activity of mesencephalic neurons whose discharge is modulated by vergence parameters alone. It is shown that given recent neurophysiological and behavioural findings, ocular reflexes cannot be properly modelled as separate independent subsystems whereas a single, unified modelling approach can produce results consistent with observed data. This study also shows how changes in the functional activity of shared pathways in a single two-sided structure produce vergence and conjugate integrators whose function relies on coupled loops across the brainstem: separate, dedicated operators are not necessary to replicate data. This provides evidence that challenges previous studies supporting the existence of separate vergence and conjugate integrators to transform velocity to position signals in the brainstem. A major implication of this study is that it questions the validity of testing conjugate and vergence systems independently, neglecting potential interactions.

Modelling non-linearities in the vestibulo-ocular reflex (VOR) after unilateral or bilateral loss of peripheral vestibular function

Abstract. We recorded the vestibulo-ocular reflex (VOR) in 18 normal subjects, 50 patients with unilateral loss of vestibular function and 18 patients with bilateral loss of vestibular function. The unilateral cases had either partial loss (i.e. vestibular neuronitis or Menieres disease) or total loss (i.e. vestibular nerve section), whereas bilateral cases had only partial loss (i.e. due to ototoxicity or to suspected microangiopathy, secondary to severe kidney disease). Tests were performed at 1/6-Hz passive head rotation in the dark, with peak head velocities ranging from 125 to 190°/s. We report on the distinct VOR non-linearities observed in unilateral versus bilateral patients: whereas unilateral patients all exhibit an asymmetric hypofunction with decreasing VOR gain at higher head velocities, bilateral patients have a more severe but symmetric hypofunction associated with increasing VOR gain at higher head velocities. We present a model study that can duplicate the nature of these characteristics, based mainly on peripheral non-linear semicircular canal characteristics and secondary central compensation. Theoretical analyses point to the importance of clinical test parameters (rotation speed and frequency) in the determination of a functional VOR and the detection of reflex non-linearities, so that test protocols can seriously bias the evaluation of adequate functional recovery.

Head-shaking Nystagmus (HSN): the Theoretical Explanation and the Experimental Proof

Head-shaking nystagmus (HSN) is induced by oscillating the head at high frequency in the horizontal plane. This test is used in the clinic to detect the presence of a unilateral loss of vestibular function. HSN has been described as monophasic with fast-phase direction towards either side, or biphasic with the direction of fast phases reversing after a few seconds. Loss of vestibular function amplifies existing non-linearities in the vestibular system, so that imposed sinusoids can induce biases which are the source of HSN. Fifty-one patients suffering from loss of peripheral vestibular function (43 partial, 11 total unilateral tests) were exposed to whole-body sinusoidal stimulation, with increasing head velocities (90-220°/s) at 1/6Hz, to explore the consistency of per-rotatory induced biases. A bias was induced in all cases, but it wandered on either side, healthy or pathologic, unless test head velocities were larger than ~180°/s. Given this condition, the slow-phase bias was located towards the pathologic side for all patients with significant bias (>5°/s). These observations demonstrate that the sign and amplitude of the bias is variable and is not correlated with the lesioned side, unless high head velocities are imposed. This explains why the direction of the initial phase of HSN in the clinic seems so labile. Subsequent monophasic or biphasic characteristics of HSN are simply the reflection of interactions between two main time constants associated with ?velocity storage? and ?gaze holding? in the vestibular central processes.

Transient analysis of vestibular nystagmus

The significance of a nystagmus-dependent, transient component in the overall slow-phase response of the vestibulo-ocular reflex (VOR) is brought into focus. First, a simulated example is presented that shows how this transient component can bias current algorithms for the estimation of VOR parameters. Second, new algorithms are proposed that are able to estimate VOR parameters regardless of the presence of transients. Third, the new algorithms are applied to experimental data, and the results are compared with those from current algorithms. The results clearly show that the transient component can significantly alter the apparent VOR time constant, particularly when the reflex has been lesioned. The algorithms open new areas of research on the possible role of nystagmus in enhancing the compensatory function of the VOR.