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.