Mathematical Modeling of Different Heart Rhythms to Diagnose Chronic Heart Disease

In this chapter, it is explored that the possibility that ECG recordings belong to class of multifractal process for which a large number of scaling exponents are required to characterize their scaling structures. There are many recent studies which proved that the healthy heartbeat demonstrates regular cardiac rhythm based on Homeostasis principals since physiologically, our body system tries to reduce heart rate variability (HRV). We use the BIDMC Congestive Heart Failure database including long term ECG recordings from 11 men, aged 22 to 71, and 4 women, aged 54 to 63 with severe congestive heart failure and the MIT-BIH Arrhythmia database that contains 48 half-hour excerpts of two-channel ambulatory ECG recordings, obtained from 47 subjects studied by the BIH Arrhythmia Laboratory between 1975 and 1979. We compare these two chronic heart diseases with the control people in the MIT-BIH Normal Sinus Rhythm database which includes 18 long-term ECG recordings of 5 men, aged 26 to 45, and 13 women, aged 20 to 50 without significant arrhythmia. The vibration analysis such as power spectral densities (PSD) analysis has been performed for differentiating the time series. Multifractal spectrum analysis has evaluated the multifractal dynamics of heartbeat interval signals to distinguish between patients with severe congestive heart failure and normal signals with arrhythmia. The fractal complexity of each heart beat is determined using the Higuchi algorithm, and the signals are then contrasted over various time intervals [1]. According to our analysis, when multifractal analysis and scaling exponent were used as a classifier, the three classes were well separated. In addition, multifractal analysis revealed that we have a narrow range of exponents for arrhythmia and congestive heart failure subjects and as a result, a clear loss of multifractality for them. We continue the analysis of heartbeat interval time series by estimating the power law scaling exponents for healthy subjects and compare them with scaling exponents of patients with congestive heart failure and arrhythmia. Then we apply multifractal analysis to study the multifractal structure and complex dynamics of these three groups of signals. Our findings provide a comprehensive framework for diagnostic and classifying different patients with cardiac disease such as arrhythmia and congestive heart failure and differentiate them with normal people without heart disease which is crucial in finding the best diagnostic and controlling strategy in fight against chronic heart disease.