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. We have developed GNL-HybELS (Generalized NonLinear Hybrid Extended Least Squares), a tool to simultaneously classify and identify the responses of a multi-mode nonlinear system with delay, such as the horizontal VOR. This algorithm combines Generalized Principle Component Analysis (GPCA) for classification, and Hybrid Extended Least Squares (HybELS) for identification. The method was validated on noisy simulation data and tested on experimental data. GNL-HybELS classifies and identifies dynamic parameters, nonlinearity, and delay of a multi-mode (hybrid) system, with high accuracy and robustness, with rms prediction errors between 1.3-2.6 deg for measured data. It enables researchers and clinicians to analyze VOR responses reliably, and therefore, can pave the way for more precise diagnoses and treatments for lesions and diseases of the vestibular system. It can also be readily applied to other neural systems that exhibit switching or multi-mode behavior.