Contribution to the Modeling of Non-Stationary Biomedical Signals

Abstract

This thesis explores the application of fractional-order calculus to the modeling of nonstationary biomedical signals, with a particular focus on electrocardiogram (ECG) signals. Traditional ECG models based on integer-order differential equations, such as the widely used McSharry model, provide a solid foundation for synthetic ECG generation but often fall short in capturing the long-memory and complex dynamics inherent in physiological signals. To address these limitations, this work extends classical models by incorporating fractional differential equations (FDEs), which enable the representation of memory and hereditary properties intrinsic to biological systems. The proposed fractional-order ECG model integrates fractional derivatives into the McSharry framework, enhancing its flexibility and accuracy while preserving essential morphological features of the PQRST complex. The Predictor-Corrector method is employed for numerically solving the fractional differential equations, and Genetic Algorithms are utilized for robust parameter optimization. This hybrid approach allows for precise tuning of model parameters, resulting in synthetic ECG signals that closely fit real physiological data. Extensive numerical simulations were conducted and validated against clinical ECG recordings from the MIT-BIH Arrhythmia Database. The fractional-order model demonstrated a significant improvement over the classical integer-order model, achieving a 48.40% reduction in mean squared error (MSE) and a 23.18% increase in compression efficiency across five distinct heartbeat types. The optimized fractional orders (alpha) consistently ranged between 0.96 and 0.99, indicating that subtle deviations from integer order substantially enhance model performance. In addition to fractional modeling, this thesis contributes novel methodologies including the integration of Hopf bifurcation dynamics into the ECG generation process to simulate realistic cardiac rhythms and the application of the Grey Wolf Optimizer for efficient parameter estimation. These advancements further improve the fidelity of synthetic ii iii ECG signals and broaden the scope of arrhythmia simulation. Overall, the findings underscore the potential of fractional-order models combined with advanced optimization techniques to advance biomedical signal processing. This framework facilitates more accurate simulation, analysis, and classification of complex non-stationary physiological signals, with significant implications for computational cardiology, personalized healthcare, and the development of automated diagnostic tools.