Symbolic Dynamics - a Powerful Tool in Non-Invasive Biomedical Signal Processing∗ A. Voss1, N. Wessel3, V. Baier1, K.J. Osterziel2, J. Kurths3, R. Dietz2, A. Schirdewan2
[email protected] University of Applied Sciences Jena Faculty of Medical Engineering Carl-Zeiss-Promenade 2 07745 Jena Germany.
Abstract The aim of this paper is to discuss the ability of symbolic dynamics as a nonlinear approach to analyze heart rate and blood pressure variability for an improved characterization of different cardiovascular regulations and dysregulations. Heart rate variability (HRV) and blood pressure variability (BPV) reflect the complex interactions of many different control loops of the cardiovascular system. In relation to the complexity of the sinus node activity modulation system, a more predominantly non-linear behavior has to be assumed. In this way the detailed description and classification of dynamic changes using time and frequency measures is often not sufficient. Therefore, we have introduced new methods of non-linear dynamics, especially from symbolic dynamics to distinguish between different states of the autonomic interactions. We demonstrate that parameters obtained from symbolic dynamics are useful for risk stratification after myocardial infarction, for characterization of different cardiovascular diseases and for phenotyping in genetic studies.
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Introduction
Symbolic dynamics is a useful tool in several fields of complexity analysis in science. We have applied symbolic dynamics mainly to characterize the dynamics of heart rate (HRV) and blood pressure variability (BPV). Symbols represent now either levels of time differences or differences in systolic blood pressure between successive beats. Physiological data very often show complex structures which cannot be quantified or interpreted with linear methods. The disadvantage of the linear parameters is the limited information about the underlying dynamic system, whereas the ‘classical’ nonlinear description suffers from the curse of dimensionality. In addition, often there are not enough data points within the time series to get a reliable estimate of these nonlinear measures. Therefore, we favor measures of complexity that quantify the systems dynamic even in rather short time series - like the symbolic dynamics.
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This work was supported by the Deutsche Forschungsgemeinschaft DFG under Grant No. Vo505/2-1, Vo505/2-3, the Federal Ministry of Education, Science, Research and Technology and by anonymous contributions.
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Method
Symbolic dynamics is based on a coarse-graining of the dynamics of a signal. The time series (in our cases the ecg or the non-invasive recorded blood pressure curve) are transformed into symbol sequences with symbols from a given alphabet. Some detailed information is lost but the coarse dynamic behavior remains and can be analyzed. Depending on the time series we have to define the type and number of symbols. Long time series allow a higher number of symbols (a higher resolution of the analysis) than short time series. For instance, the heart rate time series RR1,...,RRn is transformed into a symbol sequence s1,...,sn with symbols from the alphabet {0,1,2,3}, where µ denotes the mean of all NNintervals and a is a constant equal to 0.1. In this way some detailed information is lost, but the more general dynamic behavior can be analyzed.
Elektrocardiogram RR1
RR2
RR3
RR4
RR5
RR6
RR n: nth RR interval length symbol definition µ < (1+a)* µ
