Optimisation and Computational Methods to Model the Oculomotor System with Focus on Nystagmus

Abstract

Infantile nystagmus is a condition that causes involuntary, bilateral and conjugate oscillations of the eyes, which are predominately restricted to the horizontal plane. In order to investigate the cause of nystagmus, computational models and nonlinear dynamics techniques have been used to model and analyse the oculomotor system. Computational models are important in making predictions and creating a quantitative framework for the analysis of the oculomotor system. Parameter estimation is a critical step in the construction and analysis of these models. A preliminary parameter estimation of a nonlinear dynamics model proposed by Broomhead et al. [1] has been shown to be able to simulate both normal rapid eye movements (i.e. saccades) and nystagmus oscillations. The application of nonlinear analysis to experimental jerk nystagmus recordings, has shown that the local dimensions number of the oscillation varies across the phase angle of the nystagmus cycle. It has been hypothesised that this is due to the impact of signal dependent noise (SDN) on the neural commands in the oculomotor system. The main aims of this study were: (i) to develop parameter estimation methods for the Broomhead et al. [1] model in order to explore its predictive capacity by fitting it to experimental recordings of nystagmus waveforms and saccades; (ii) to develop a stochastic oculomotor model and examine the hypothesis that noise on the neural commands could be the cause of the behavioural characteristics measured from experimental nystagmus time series using nonlinear analysis techniques. In this work, two parameter estimation methods were developed, one for fitting the model to the experimental nystagmus waveforms and one to saccades. By using the former method, we successfully fitted the model to experimental nystagmus waveforms. This fit allowed to find the specific parameter values that set the model to generate these waveforms. The types of the waveforms that we successfully fitted were asymmetric pseudo-cycloid, jerk and jerk with extended foveation. The fit of other types of nystagmus waveforms were not examined in this work. Moreover, the results showed which waveforms the model can generate almost perfectly and the waveform characteristics of a number of jerk waveforms which it cannot exactly generate. These characteristics were on a specific type of jerk nystagmus waveforms with a very extreme fast phase. The latter parameter estimation method allowed us to explore whether the model can generate horizontal saccades of different amplitudes with the same behaviour as observed experimentally. The results suggest that the model can generate the experimental saccadic velocity profiles of different saccadic amplitudes. However, the results show that best fittings of the model to the experimental data are when different model parameter values were used for different saccadic amplitude. Our parameter estimation methods are based on multi-objective genetic algorithms (MOGA), which have the advantage of optimising biological models with a multi-objective, high-dimensional and complex search space. However, the integration of these models, for a wide range of parameter combinations, is very computationally intensive for a single central processing unit (CPU). To overcome this obstacle, we accelerated the parameter estimation method by utilising the parallel capabilities of a graphics processing unit (GPU). Depending of the GPU model, this could provide a speedup of 30 compared to a midrange CPU. The stochastic model that we developed is based on the Broomhead et al. [1] model, with signal dependent noise (SDN) and constant noise (CN) added to the neural commands. We fitted the stochastic model to saccades and jerk nystagmus waveforms. It was found that SDN and CN can cause similar variability to the local dimensions number of the oscillation as found in the experimental jerk nystagmus waveforms and in the case of saccade generation the saccadic variability recorded experimentally. However, there are small differences in the simulated behaviour compared to the nystagmus experimental data. We hypothesise that these could be caused by the inability of the model to simulate exactly key jerk waveform characteristics. Moreover, the differences between the simulations and the experimental nystagmus waveforms indicate that the proposed model requires further expansion, and this could include other oculomotor subsystem(s).