Verhulst map measures: new biomarkers for heart rate classification

Recording, monitoring, and analyzing biological signals has received significant attention in medicine. A fundamental phase for understanding a bio-system under various conditions is to process the corresponding bio-signal appropriately. To this effect, different conventional and nonlinear approaches have been proposed. However, since the non-stationary properties of the bio-signals are not revealed by traditional linear methods, nonlinear dynamical techniques play a crucial role in examining the behavior of a bio-system. This work proposes new bio-markers based on the chaotic nature of the biomedical signals. These measures were introduced using the Verhulst map, a simple tool for characterizing the morphology of the reconstructed phase space. For this purpose, we extracted the features from the heart rate (HR) signals of six groups of meditators and non-meditators. For a typical classification problem, the performance of some conventional classifiers, including the k-nearest neighbor, support vector machine, and Naïve Bayes, was appraised separately. In addition, the competence of a hybrid classification strategy was inspected using majority voting. The results indicated a maximum accuracy, F1-score, and sensitivity of 100%. These findings reveal that the proposed framework is eminently capable of analyzing and classifying the HR signals of the groups. In conclusion, the Verhulst diagram-based measures are simple and based on the dynamics of the bio-signals, which can be served for quantifying different signals in medical systems.