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1 2008

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Entropia w badaniach zaburzeń rytmu serca

Graff B., Graff G., Kolesiak A.

Matematyka Stosowana : matematyka dla społeczeństwa

2008

Nr 9

46-56

Artykuł prezentuje zastosowanie Approximate Entropy, będącej miarą stopnia złożoności szeregów czasowych, do analizy zmienności rytmu serca.

Healthy human heart rate is characterized by oscillations observed in intervals between consecutive heartbeats (RR intervals). Conventional methods of heart rate variability analysis measure the overall magnitude of RR interval fluctuations around its mean value or the magnitude of fluctuations in predetermined frequencies. The new methods of chaos theory and nonlinear dynamics provide powerful tools, which allow to predict clinical outcome in patients with cardiovascular diseases. The main aim of our article is to present Approximate Entropy (ApEn), a measure of system regularity and complexity, introduced by Pincus in 1991. ApEn estimation used for clinical purposes is applied for finite number of records, divided in vectors, and depends on two fixed parameters m and r. Then Approximate Entropy may be interpreted as the average of negative natural logarithms of conditional probability, that two vectors of length m + 1 are similar (we define here r-similarity), if two vectors of the length m are similar. The article provides a formal mathematical description of ApEn and presents a simple algorithm for its assessment. The choice of input parameters m and r is also discussed. In vast majority of publications r depends on standard deviation (SD) of average of all records, when individual features of heart rhythm are taken into account. The fraction of r, equal to 0, 2SD, and m = 2 are usually chosen on the basis of previous findings of good statistical validity. With the above set of parameters we can avoid the influence of outliers and do not loose too much information. ApEn has also some disadvantages - the main is counting self similarities. To reduce this kind of bias some improvements of the methods based on Pincus’ algorithm were developed. For example Sample Entropy (SampEn), which has similar algorithm but does not count self-matches, was proposed and easily applied to clinical time-series. In the article we present also an application of ApEn in predicting atrial fibrillation (AF), a type of arrhythmia which is the most common sustained heart rhythm disturbance. Both ApEn and SampEn decrease before the spontaneous onset of AF. What is more, ApEn is not sensitive to ectopy beats and therefore can be assessed fully automatically. The potential application of ApEn is the possibility to detect an increased vulnerability to AF before the onset of arrhythmia during continuous heart rate recording, for example for patients with implantable pacemakers. The recognition of the higher risk of AF would be followed by immediate pacemaker reprogramming to prevent an episode of arrhythmia. It would result not only in better quality of life of the patient but also in decreased number of hospitalization and cost of treatment.