Abstract
Two distinct operational procedures are proposed for diagnosis and tracking of heart disease evolution (in particular atrial fibrillations). The first procedure, based on the application of non-linear dynamic methods (strange attractors, skewness, kurtosis, histograms, Lyapunov exponent, etc.) analyzes the electrical activity of the heart (electrocardiogram signals). The second procedure, based on multifractalization through Markovian and non-Markovian-type stochasticizations in the framework of the scale relativity theory, reconstructs any type of EKG signal by means of harmonic mappings from the usual space to the hyperbolic one. These mappings mime various scale transitions by differential geometries, in Riemann spaces with symmetries of SL(2R)-type. Then, the two operational procedures are not mutually exclusive, but rather become complementary, through their finality, which is gaining valuable information concerning fibrillation crises. As such, the author’s proposed method could be used for developing new models for medical diagnosis and evolution tracking of heart diseases (patterns dynamics, signal reconstruction, etc.).
Highlights
It tends tends to increase during the first atrial fibrillation crisis, with a maximum of around 110 to increase during the first atrial fibrillation crisis, with a maximum of around 110 bpm
Diagnostics and evolution of atrial fibrillation by applying non-linear dynamics method skewness and kurtosis values are in accordance with pulse rate distributions
Diagnostics and evolution of atrial fibrillation by applying non-linear dynamics method skewness and kurtosis values are in accordance with pulse rate distributions from the histograms of the analyzed ECG signal
Summary
For the evaluation of heart-rate variability, many time series analysis methods were applied to EKG: autocorrelation function, power spectrum, fractal dimensions, Hurst exponent, Lyapunov exponent, reconstructed phase-space analysis, bifurcation. For the evaluation of heart-rate variability, many time series analysis 2methods were applied to EKG: autocorrelation function, power spectrum, fractal dimensions, Hurst exponent, Lyapunov exponent, reconstructed phase-space analysis, bifurcation analysis, detrended detrended fluctuation fluctuation analysis, analysis, recurrence recurrence plot, plot, sample sample entropy, entropy,approximate approximate analysis, entropy, Kolmogorov–Sinai entropy, etc. EKGsignals signals analysis, while the second one is based on the reconstruction of EKG signals. Can be assimilated, both functionally and structurally, to a multifractal object.,the the dynamics dynamicswhich which govern govern such such an an object object can can be be described described using using the the scale scale relativity relativity theory, theory, under under its itsvarious variousmodels models(be In this paper could facilitate implementation of such methods clinical practice
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