Exploratory Study of the Cardiac Dynamic Trajectory in the Embedding Space

Abstract

In this paper, the topological and dynamical properties of the heart sounds are assessed. The signal is preprocessed and projected into an embedding subspace, which is more suitable to detect the irregularities and the unstable trajectories registered during the cardiac murmurs than the original heart sound signal.We present a method for heart murmur classification divided into five major steps: a) signal is divided into heart beats; b) entropy gradient envelogram is computed from the pre-processed signal; c) the orbital trajectories are reconstructed using the embedding theory; d) n orbits in the embedding subspace are extracted (per heart beat); e) the median of the n orbits is used as an input to K-Nearest Neighbors (KNN) classifier.The experimental results achieved are in agreement with the current state of art for heart murmur classification. IntroductionHeart sound auscultation using a traditional stethoscope is the simplest, fastest and cheapest method for heart examination. Although the importance of the traditional auscultation methods has decreased due to its inherent restrictions. The phonocardiogram (PCG) has preserved its importance in pediatric cardiology, cardiology, and internal diseases, evaluating congenital cardiac defects. The phonocardiogram is divided into heart cycle (S11) components such as: S1 (first heart sound) and S2 (second heart sound) [1]. These establish the boundaries of the other two fundamental components of a heart cycle: the systole (S21), and the diastole (S12). The S1 and S2 are generated by the opening and closing of the heart valves, in pathogenic situations additional sounds such as S3, S4 or murmurs are listened [1]. Heart murmurs are turbulence phenomena characterized by momentum diffusion, high momentum convection, and rapid variation of pressure and velocity both in space and time [1]. The automatic detection of heart murmurs strongly depends on the extraction of an appropriate set of features, which are hopefully capable of splitting the data into two or more categories: normal and different types of abnormal cases.Ahlstrom proposed a set of 207 features composed by Shannon energy, wavelet coefficients, fractal dimensions and recurrence quantification analysis. A subset of 14 features was derived using a Pudil's sequential floating forward selection algorithm. Using a neural network classifier, this subset achieved 86% of accuracy [2]. Delgado-Trejos compared three types of features: spectral, perceptual and fractal features. Using a K-nearest neighbor's classifier they observed that fractal features provide the best accuracy (97, 17%) followed by spectral (95, 28%) and perceptual features (88,7%). This fact it is explained by the presence of long-range (fractal) correlation along with distinct classes of non-linear interactions [3]. The feature set described in our previous work [4] is a combination of time-frequency domain, perceptual and fractal analysis. We also proposed: 1) the dimension correlation curve; 2) the exponential decay of the false nearest...