Methodological Framework for Estimating the Correlation Dimension in HRV Signals

Abstract

This paper presents a methodological framework for robust estimation of the correlation dimension in HRV signals. It includes (i) a fast algorithm for on-line computation of correlation sums; (ii) log-log curves fitting to a sigmoidal function for robust maximum slope estimation discarding the estimation according to fitting requirements; (iii) three different approaches for linear region slope estimation based on latter point; and (iv) exponential fitting for robust estimation of saturation level of slope series with increasing embedded dimension to finally obtain the correlation dimension estimate. Each approach for slope estimation leads to a correlation dimension estimate, calledD^2,D^2⊥, andD^2max.D^2andD^2maxestimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, andD^2⊥with 1%. The three approaches are applied to HRV signals of pregnant women before spinal anesthesia for cesarean delivery in order to identify patients at risk for hypotension.D^2keeps the 81% of accuracy previously described in the literature whileD^2⊥andD^2maxapproaches reach 91% of accuracy in the same database.