PVC detection by the heart-beat interval data—Markov chain approach

Abstract

In the Markov chain approach, a sequence of heart beat intervals (R-R wave intervals) is automatically transformed into a three-symbol sequence. The symbols may be thought of as S-R-L for short, regular, and long heart beat intervals, respectively. The probability that an observed sequence was generated by each of a set prototype model characteristic of different cardiac arrhythmias is computed. That prototype corresponding to the largest probability of generating the observed sequence is classified as the disorder. If the R-R interval symbol sequence is in fact a Markov chain this procedure has the lowest probability of classification error performance. An explicit formula for the probability of classification error for the two alternative hypothesis test situation is developed. The probability of classification error is demonstrated to be exponentially bounded with n, the number of R-R intervals used for classification purposes. Tests of the Markov chain approach and the analysis of the probability of classification error were performed on clinical test data from patients with atrial fibrillation and atrial fibrillation with occasional PVC's and on simulated R-R interval data using models derived from the patient data. The occurrence of PVC's in atrial fibrillation could be successfully distinguished from the atrial fibrillation alone situation by the Markov chain approach. The simulation study results were consistent with the theoretical analysis of classification error performance. The probability of misclassification for n fixed is dependent upon the similarity of the prototypic models as measured by the difference between the self entropies of the models. Clinically satisfactory classification performance to distinguish between atrial fibrillation and atrial fibrillation with occasional PVC's may require n = 400 R-R intervals.