Parametric classification of segments in ocular nystagmus

Automatic Classification of the Vestibulo-Ocular Reflex Nystagmus: Integration of Data Clustering and System Identification

The vestibulo-ocular reflex (VOR) plays an important role in our daily activities by enabling us to fixate on objects during head movements. Modeling and identification of the VOR improves our insight into the system behavior and improves diagnosis of various disorders. However, the switching nature of eye movements (nystagmus), including the VOR, makes dynamic analysis challenging. The first step in such analysis is to segment data into its subsystem responses (here slow and fast segment intervals). Misclassification of segments results in biased analysis of the system of interest. Here, we develop a novel three-step algorithm to classify the VOR data into slow and fast intervals automatically. The proposed algorithm is initialized using a K-means clustering method. The initial classification is then refined using system identification approaches and prediction error statistics. The performance of the algorithm is evaluated on simulated and experimental data. It is shown that the new algorithm performance is much improved over the previous methods, in terms of higher specificity.

A sparse matrix approach for simultaneous quantification of nystagmus and saccade

The vestibulo-ocular reflex (VOR) consists of two intermingled non-linear subsystems; namely, nystagmus and saccade. Typically, nystagmus is analysed using a single sufficiently long signal or a concatenation of them. Saccade information is not analysed and discarded due to insufficient data length to provide consistent and minimum variance estimates. This paper presents a novel sparse matrix approach to system identification of the VOR. It allows for the simultaneous estimation of both nystagmus and saccade signals. We show via simulation of the VOR that our technique provides consistent and unbiased estimates in the presence of output additive noise.

Automatic classification and robust identification of vestibulo-ocular reflex responses: from theory to practice: introducing GNL-HybELS

The Vestibulo-Ocular Reflex (VOR) stabilizes images of the world on our retinae when our head moves. Basic daily activities are thus impaired if this reflex malfunctions. During the past few decades, scientists have modeled and identified this system mathematically to diagnose and treat VOR deficits. However, traditional methods do not analyze VOR data comprehensively because they disregard the switching nature of nystagmus; this can bias estimates of VOR dynamics. Here we propose, for the first time, an automated tool to analyze entire VOR responses (slow and fast phases), without a priori classification of nystagmus segments. We have developed GNL-HybELS (Generalized NonLinear Hybrid Extended Least Squares), an algorithmic tool to simultaneously classify and identify the responses of a multi-mode nonlinear system with delay, such as the horizontal VOR and its alternating slow and fast phases. This algorithm combines the procedures of Generalized Principle Component Analysis (GPCA) for classification, and Hybrid Extended Least Squares (HybELS) for identification, by minimizing a cost function in an optimization framework. It is validated here on clean and noisy VOR simulations and then applied to clinical VOR tests on controls and patients. Prediction errors were less than 1 deg for simulations and ranged from .69 deg to 2.1 deg for the clinical data. Nonlinearities, asymmetries, and dynamic parameters were detected in normal and patient data, in both fast and slow phases of the response. This objective approach to VOR analysis now allows the design of more complex protocols for the testing of oculomotor and other hybrid systems.

Multi-input GNL-HybELS: an automated tool for the analysis of oculomotor dynamics during visual-vestibular interactions

The eyes play a major role in our everyday activities. Eye movements are controlled by the oculomotor system, which enables us to stay focused on visual targets, switch visual attention, and compensate for external perturbations. This system's response to isolated visual or vestibular stimuli has been studied for decades, but what seems to be more critical is to know how it would respond to a combination of these stimuli, because in most natural situations, multiple stimuli are present. It is now believed that sensory fusion does not affect the dynamics of oculomotor modalities, despite studies suggesting otherwise. However, these interactions have not been studied in mathematical detail due to the lack of proper analysis tools and poor stimulus conditions. Here we propose an automated tool to analyze oculomotor responses without a-priori classification of nystagmus segments, where visual and vestibular stimuli are uncorrelated. Our method simultaneously classifies and identifies the responses of a multi-input multi-mode system. We validated our method on simulations, estimating sensory delays, semicircular canal time constant, and dynamics in both slow and fast phases of the response. Using this method, we can now investigate the effect of sensory fusion on the dynamics of oculomotor subsystems. With the analysis power of our new method, clinical protocols can now be improved to test these subsystems more efficiently and objectively.

GNL-HybELS: an algorithm to classify and identify VOR responses simultaneously

The Vestibulo-Ocular Reflex (VOR) stabilizes the images of the world on the retinae when the head is in motion. Basic daily activities such as walking or driving depend on the proper functioning of this reflex. For several decades, scientists have developed methods to model and identify this system mathematically. However, traditional methods cannot analyze VOR data comprehensively because they disregard pieces of data (fast phases) which biases estimated reflex dynamics. Here we propose, for the first time, an automated tool to analyze entire VOR responses (slow and fast phases), without apriori classification of nystagmus segments.

Simultaneous identification of oculomotor subsystems using a hybrid system approach: introducing hybrid extended least squares

The oculomotor system plays an essential role in our daily activities. It keeps the images of the world steady on the retina and enables us to track visual targets, or switch between targets. The modeling and identification of this system is key in the diagnosis and treatment of various diseases and lesions. Today, clinical protocols incorporate mathematical techniques to test the functionality of patients' oculomotor modalities through the analysis of the patients' responses to various stimuli. We have developed a new tool for simultaneous identification of the two modes of oculomotor responses, using hybrid extended least squares (HybELS), a novel identification method tailored for hybrid autoregressive moving average with exogenous input models. Previously, modified extended least squares (MELS) was proposed for the identification of vestibular nystagmus dynamics, one mode at a time. It involved searching for segment initial conditions (ICs) to avoid biased results. HybELS identifies both modes simultaneously, and does not require estimation of ICs. Results on experimental vestibuloocular reflex (VOR) data show that HybELS proves to be more robust than MELS with respect to identification of complex models. Furthermore, it is notably less computationally expensive than MELS. In the multi-input case, HybELS outperforms other tested methods, including MELS, both in parameter estimation and prediction error.

A Hybrid Extended Least Squares method (HybELS) for Vestibulo-Ocular Reflex identification

The Vestibulo-Ocular Reflex (VOR) plays an essential role in the majority of daily activities by keeping the images of the world steady on the retina when either the environment or the body is moving. The modeling and identification of this system plays a key role in the diagnosis and treatment of various diseases and lesions, and their associated syndromes. Today, clinical protocols incorporate mathematical techniques for testing the functionality of patients' VORs through the analysis of the patients' responses to various stimuli. We have developed a new tool for simultaneous identification of the two modes of the horizontal VOR, using a novel algorithm. This algorithm, HybELS (Hybrid Extended Least Squares), is a regression-based identification method tailored for hybrid ARMAX (AutoRegressive Moving Average with eXogenous inputs) models, which can also be used for the identification of other neural systems. In the context of the VOR, MELS (Modified Extended Least Squares) has been proposed previously for the identification of vestibular nystagmus dynamics, one mode at a time. It also involved searching for segment initial conditions to avoid biased results. Our hybrid approach identifies the two modes simultaneously, and does not require estimation of initial conditions, since it takes advantage of state continuity in the transitions between fast and slow phases. The results on experimental VOR in the dark show that HybELS outperforms MELS in several aspects: It proves to be more robust than MELS with respect to the system order used for identification, while resulting in more accurate estimates in almost all contexts as well. Furthermore, due to the hybrid nature of the method, its calculations are algebraically more compact, and HybELS turns out to be much less computationally expensive than MELS.

Improved algorithm for classification of ocular nystagmus

An improved algorithm for classification of nystagmus was designed allowing the sorting of response segments even in severely non-linear patients and subjects with abnormally large phase shifts. The algorithm employs a model-based approach that was developed by Rey and Galiana. The improved classification algorithm consists of two essential stages. In the first stage the eye velocity response is classified to obtain initial estimates of the slow phase eye velocity intervals. In the second stage, the slow phase estimates are used to identify a response phase shift and nonlinearity, and compensate for their effects. Multiple tests on simulated data and experimental data obtained from clinical subjects are presented. The results of the tests demonstrate that the algorithm is able to analyze the patient data with a high accuracy even in the presence of noise, eye-blinks and other artifacts.

A Least-Squares Parameter Estimation Algorithm for Switched Hammerstein Systems With Applications to the VOR

A "Multimode" or "switched" system is one that switches between various modes of operation. When a switch occurs from one mode to another, a discontinuity may result followed by a smooth evolution under the new regime. Characterizing the switching behavior of these systems is not well understood and, therefore, identification of multimode systems typically requires a preprocessing step to classify the observed data according to a mode of operation. A further consequence of the switched nature of these systems is that data available for parameter estimation of any subsystem may be inadequate. As such, identification and parameter estimation of multimode systems remains an unresolved problem. In this paper, we 1) show that the NARMAX model structure can be used to describe the impulsive-smooth behavior of switched systems, 2) propose a modified extended least squares (MELS) algorithm to estimate the coefficients of such models, and 3) demonstrate its applicability to simulated and real data from the Vestibulo-Ocular Reflex (VOR). The approach will also allow the identification of other nonlinear bio-systems, suspected of containing "hard" nonlinearities.

Comparison of linear vs. non-linear methods for analysing the vestibulo-ocular reflex (VOR)

The vestibulo-ocular reflex (VOR) is traditionally evaluated by the gain (sensitivity) and offset (bias) of nystagmus slow phases during sinusoidal, passive, head rotation in the dark. The analysis methods used are typically only truly applicable to linear systems, but are widely used despite the fact that the VOR has been known to be non-linear since the 19th century. We show here that the parameters obtained by linear methods, with data derived from a non-linear system, can be very noisy and unreliable. The questions are: under what conditions can linear approximations be tolerated, or justified, and can an analysis approach be devised which inherently tolerates non-linearities? Using both simulated and experimental data, it is found that assuming linear analysis methods can produce variable VOR gains and erroneous estimates of the VOR bias. changing with the selected oscillation protocol. Examples of' parameter distortions in bias and VOR gain are first given using simulated data relating slow phase eye velocity to head velocity, at different peak velocities. The relevance of these distortions is then illustrated with selected examples from a database of recordings on normals and unilateral vestibular patients, during rotations in the dark 1/6 Hz and maximum speeds of 90 to 180 degrees/s. More consistent estimates of the gain and bias can be found by properly correcting for phase differences between head and eve velocity, and allowing for non-linear reflex properties. Special indices are suggested to decide whether a particular subject's VOR should be considered non-linear, in order to select the appropriate representation in each case, before estimating VOR characteristics. Selecting the appropriate model (linear or non-linear) will contribute to a better unmasking of parametric trends in the VOR, when comparing normal vs. acute-lesioned subjects, or acute vs, compensated patients. These results have many implications for the design of clinical vestibular protocols and in the evaluation of patient functional deficits.

Vestibulo-ocular reflex (VOR) biases in normal subjects and patients with compensated vestibular loss

The properties of the vestibulo-ocular reflex (VOR) were examined during sinusoidal passive head rotation in the dark at 1/6 Hz, in 9 normal subjects and 14 unilateral vestibular patients. Rotation speeds ranged from 90 to 180 degrees/s. The bias (offset of slow-phase velocity from zero) and gain in the VOR were estimated by using a polynomial (cubic) fit between head and slow-phase eye velocity, thereby allowing for possible non-linearities in the reflex. The gain in the VOR in this context refers to the linear components of the fit, and so predicts sensitivity only at low head velocities. The aim of the study was to verify previous theoretical predictions that VOR bias could vary with the rotation parameters, that this bias could be used to detect the side of a vestibular lesion even at low frequency rotation, and make non-linearities more obvious. Confirming these predictions, the VOR bias in a given test is never equal to any spontaneous nystagmus, even if present before rotation. The range of values for the gain in the VOR (as defined above) in normals and compensated unilateral vestibular patients overlap, so that they cannot be statistically separated into two response sets.(ABSTRACT TRUNCATED AT 250 WORDS)

A nystagmus strategy to linearize the vestibulo-ocular reflex

This paper addresses two important aspects of the vestibulo-ocular reflex (VOR). 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 inter-connections 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.