Orthonormal (Fourier and Walsh) models of time-varying evoked potentials in neurological injury

Abstract

Estimation of time-varying changes in evoked potentials (EP's) has important applications, such as monitoring high-risk neurosurgical procedures. We test the hypothesis that injury related changes in EP signals may be modeled by orthonormal basis functions. We evaluate two models of time-varying EP signals: the Fourier series model (FSM) and the Walsh function model (WFM). We estimate the Fourier and Walsh coefficients with the aid of an adaptive least-mean-squares technique. Results from computer simulations illustrate how selection of model order and of the adaptation rate of the estimator affect the signal-to-noise ratio (SNR). The FSM results in a somewhat higher steady-state SNR than does the WFM; however, the WFM is less computationally complex than is the FSM. We apply these two orthonormal functions to evaluate transient response to hypoxic hypoxia in anesthetized cats. Trends of the first five frequencies (Fourier) and sequencies (Walsh) show that the lower frequencies and sequencies may be sensitive indicators of hypoxic neurological injury.