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. Jf the R-R interval symbol sequence is in fact a Markovchain this procedurehas the lowestprobability 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 atria1 fibrillation and atria1 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 atria1 fibrillation could be successfully distinguished from the atria1 fibrillation alone situation by the Markovchainapproach.
The simulation study results wereconsistent with the theoretical analysis of classification error performance. The probability of misclassification for II fixedisdependentupon the similarity of the prototypicmodels 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.
An application of the Markov chain approach (I) to the automatic classification of cardiac arrhythmias to the problem of PVC detection is reported. Discussion of the clinical importance of PVC detection and alternative approaches have appeared in this journal (2, 3). The particular situation considered was that of distinguishing