Fractal Models for Simulating Biomedical Signals

In the article, two fractal models: Fractal Brownian Motion (FBM) and Fractal Gaussian Noise (FGN) for simulating biomedical signals are presented, investigated and analysed. These models reflect the complex and nonlinear dynamics of cardiac activity and may be useful in the study of various cardiovascular diseases and conditions. The main characteristics of biomedical signals, such as self-similarity, fractal dimension, long-term dependence and scale invariance, depend on the Hurst parameter, and its values vary between 0 and 1. If the value of this parameter is between 0.5 and 1.0, then the investigated signal has a positive correlation and shows persistence. Understanding and properly estimating the Hurst parameter can provide important information about the behaviour of complex systems and signals, such as the biomedical signals. In this paper, the FBM is simulated by applying the Random Midpoint Displacement algorithm and the FGN by the Paxson algorithm. A comparative analysis and evaluation of the presented algorithms was made regarding the following two aspects: accuracy of the simulated signals and the required processing time for simulating signals of different lengths. Based on the comparative analysis and evaluation of the presented algorithms, the better algorithm will be determined, which can be used in the study and analysis of real biomedical signals, such as the cardiac signals (RR time series).