Complexity and Nonlinearity in Short-Term Heart Period Variability: Comparison of Methods Based on Local Nonlinear Prediction

Abstract

This paper evaluates the paradigm that proposes to quantify short-term complexity and detect nonlinear dynamics by exploiting local nonlinear prediction. Local nonlinear prediction methods are classified according to how they judge similarity among patterns of L samples (i.e., according to different definitions of the cells utilized to discretize the phase space) and examined in connection with different types of surrogate data: 1) phase-randomized or Fourier transform based, FT; 2) amplitude-adjusted FT, AAFT; 3) iteratively-refined AAFT, IAAFT, preserving distribution IAAFT-1; 4) IAAFT preserving power spectrum, IAAFT-2. The methods were applied on ad-hoc simulations and on a large database of short heart period variability series (approximately 300 cardiac beats) recorded in healthy young subjects during experimental conditions inducing a sympathetic activation (head-up tilt, infusion of nitroprusside, or handgrip), a parasympathetic activation (low dose administration of atropine or infusion of phenylephrine), a complete parasympathetic blockade (high dose administration of atropine), or during controlled respiration at different breathing rates. As to complexity analysis we found that: 1) although complexity indexes derived from different methods were different in terms of absolute values, changes due to experimental conditions were consistently detected; 2) complexity was significantly decreased by all the experimental conditions provoking a sympathetic activation and by controlled respiration at slow breathing rates. As to detection of nonlinearities we found that: 1) IAAFT-1 and IAAFT-2 surrogates performed similarly in all protocols; 2) FT and IAAFT surrogates detected about the same percentage of nonlinear dynamics in all protocols; 3) AAFT surrogates were inappropriate with all the methods and should be dismissed in future applications; 4) methods based on overlapping cells with variable size were characterized by a larger rate of false detections of nonlinear dynamics; 5) short-term heart period variability at rest was mostly linear; 6) controlled respiration at slow breathing rates increased nonlinear components, while the separate activation of the two branches of the autonomic nervous system (i.e., sympathetic or parasympathetic) was ineffective at this regard.

Assessing causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods

“…The GA approach performs an explicit representation off in which nonlinear relationships are assumed and weighed by a set of coefficients to be estimated from the data. The most used LA approach evaluatesf from the k-Euclidean nearest neighbours of z PCQC1 (n), implementing either locally constant models or locally linear models that perform, respectively, a zeroth order LA (LA0) and a first-order LA (LA1) of f. Nonlinear prediction methods based on GA, LA0 and LA1 have been formalized in the past (Farmer & Sidorowich 1987;Korenberg 1989;Sugihara & May 1990), and recently developed to perform self-prediction, cross-prediction and mixed prediction over short and noisy bivariate time series (Porta et al 2007;Wang et al 2007;Faes et al 2008a,b). We refer to appendix A for a detailed description of the algorithms implemented in this study to perform linear and nonlinear prediction.…”

“…The degree of predictability of the series y can be quantified by taking the squared correlation between its original values, y(n), and predicted values,ŷ ðnÞ, yielding the index r 2 y (Porta et al 2007). This index ranges between 0 and 1, indicating, respectively, full unpredictability and full predictability of y.…”

“…Hence, measures of predictability can be defined as the maximum of the squared correlation obtained varying within a prescribed range the number P and Q of samples used for prediction. Accordingly, the time series are described with the embedding yielding the maximum predictability (Porta et al 2007). This choice prevents the use of large values for P and Q, which in short time series could be associated with an illconditioned model identification.…”

“…This choice prevents the use of large values for P and Q, which in short time series could be associated with an illconditioned model identification. When a single series is predicted only from its past values through a self-prediction approach, the maximum self-predictability (SP) is taken as a measure of regularity (Porta et al 2007) SP y Z max PZ1; . ; P max QZK1 SP y ðPÞ; SP x Z max PZ1; .…”

Measurement fidelity of heart rate variability signal processing: The devil is in the details

“…Geometric (e.g., triangular shapes of Lorenz plots) and nonlinear methods (e.g., detrended fluctuation analysis, approximate entropy) can also be used to analyze HRV (Pincus, 1995;Porta et al, 2001Porta et al, , 2007Richman and Moorman, 2000;Task Force, 1996;Voss et al, 2009). However, these methods largely depend on the precision of equipment (i.e., obtain appropriate number of RR intervals), recording length (i.e., preferably 24 h for geometric methods), and capability of these advanced analyses in software programs.…”