Higher order dynamic mode decomposition: From fluid dynamics to heart disease analysis.

In this work, we study in detail the performance of Higher Order Dynamic Mode Decomposition (HODMD) technique when applied to echocardiography images. HODMD is a data-driven method generally used in fluid dynamics and in the analysis of complex non-linear dynamical systems modeling several complex industrial applications. In this paper we apply HODMD, for the first time to the authors knowledge, for patterns recognition in echocardiography, specifically, echocardiography data taken from several mice, either in healthy conditions or afflicted by different cardiac diseases. We exploit the HODMD advantageous properties in dynamics identification and noise cleaning to identify the relevant frequencies and coherent patterns for each one of the diseases. The echocardiography datasets consist of video loops taken with respect to a long axis view (LAX) and a short axis view (SAX), where each video loop covers at least three cardiac cycles, formed by (at most) 300 frames each (called snapshots). The proposed algorithm, using only a maximum quantity of 200 snapshots, was able to capture two branches of frequencies, representing the heart rate and respiratory rate. Additionally, the algorithm provided a number of modes, which represent the dominant features and patterns in the different echocardiography images, also related to the heart and the lung. Six datasets were analyzed: one echocardiography taken from a healthy subject and five different sets of echocardiography taken from subjects with either Diabetic Cardiomyopathy, Obesity, SFSR4 Hypertrophy, TAC Hypertrophy or Myocardial Infarction. The results show that HODMD is robust and a suitable tool to identify characteristic patterns able to classify the different pathologies studied.