Modeling and quality assessment of nystagmus eye movements recorded using an eye-tracker

Abstract

Mathematical modeling of nystagmus oscillations is a technique with applications in diagnostics, treatment evaluation, and acuity testing. Modeling is a powerful tool for the analysis of nystagmus oscillations but quality assessment of the input data is needed in order to avoid misinterpretation of the modeling results. In this work, we propose a signal quality metric for nystagmus waveforms, the normalized segment error (NSE). The NSE is based on the energy in the error signal between the observed oscillations and a reconstruction from a harmonic sinusoidal model called the normalized waveform model (NWM). A threshold for discrimination between nystagmus oscillations and disturbances is estimated using simulated signals and receiver operator characteristics (ROC). The ROC is optimized to find noisy segments and abrupt waveform and frequency changes in the simulated data that disturb the modeling. The discrimination threshold, 𝜖 , obtained from the ROC analysis, is applied to real recordings of nystagmus data in order to determine whether a segment is of high quality or not. The NWM parameters from both the simulated dataset and the nystagmus recordings are analyzed for the two classes suggested by the threshold. The optimized 𝜖 yielded a true-positive rate and a false-positive rate of 0.97 and 0.07, respectively, for the simulated data. The results from the NWM parameter analysis show that they are consistent with the known values of the simulated signals, and that the method estimates similar model parameters when performing analysis of repeated recordings from one subject.

Analysing nystagmus waveforms: a computational framework

“…Their high resolution, greater linearity, improved sampling rates and noise reduction properties are particularly important for examining nystagmus waveforms, which can vary from cycle to cycle. Advances in signal calibration of a moving eye 64 , 65 , together with new techniques for noise reduction of the data 66 , will no doubt assist in the analysis of a nystagmus time series. Moreover, targeted studies on nystagmus feature extraction 9 , 20 , 35 , 67 and modelling of nystagmus waveforms (see “ Mechanisms underlying the waveform complexity ” section) will improve our understanding of the mechanisms underpinning the oscillations.…”

Waveform characterisation and comparison of nystagmus eye-tracking signals

“…The model used to describe the various nystagmus waveform morphologies is referred to as the normalised waveform model (Rosengren et al 2020). The normalised waveform model is used to parametrise the different observed nystagmus oscillations, as well as to assess the quality of the observed signal.…”

“…and a h , f 1 h and f h are the amplitude, frequency and phase of each harmonic h, respectively. The advantage of this model is that it allows for a normalisation of the amplitude, frequency and phase, leading to a robust description of different signal segments (Rosengren et al 2020). A metric called the normalised segment error (NSE) has previously been introduced to evaluate the goodness of fit between the observed signal and the signal model.…”

“…If the two waveforms have a similar feature vector, the WDI between them will be close to zero. Since there is little energy above 50 Hz, all signals were downsampled to 100 Hz (Rosengren et al 2020). If the frequency of the nystagmus oscillation is too high, there may not be parameters values for higher order harmonics, in which case these parameter values are set to zero.…”

“…In this work, a sinusoidal model referred to as the normalised waveform model (Rosengren et al 2020) is used to model the nystagmus waveforms Each waveform is divided and modelled in short segments and the model parameters are then clustered together. The clustering is done in relation to predefined template waveform morphologies and requires the use of a waveform distance measure.…”