Nonlinear dynamics and modeling of heart and brain signals

Abstract

The theory of nonlinear dynamic systems provides new ways to handle complex dynamic systems. Chaos theory offers new concepts, algorithms and methods for processing, enhancing and analyzing the measured signals. In recent years, researchers have been applying the concepts of chaos theory to bio-signal analysis. In this work, the complex dynamics of the heart (Electrocardiogram (ECG)) and the brain (Electroencephalogram (EEG)) signals are analyzed in detail using the tools of chaos theory. In the modern world, every year several thousands of people die of cardiac problems. This makes the automatic analysis and the assessment of risk for these problems a critical task. Analyses using the conventional linear methods are often found to produce inconclusive results. Therefore in this work we propose and apply unconventional methods of nonlinear dynamics to analyze ECG and EEG signals. In the case of ECG, the heart rate variability (HRV) signal is analyzed using various complexity measures that are basing on symbolic dynamics. These complexity measures with the parameters in the frequency domain serve to be a promising way to get a more precise definition of individual risk. This is done in two stages: (i) feature extraction and (ii) classification. A feature library with more than ten features extracted from the HRV signal is developed for eight different cardiac health states. The measures are then validated with neural network and fuzzy classifiers for their ability to do more precise classification. A classification accuracy of about 80-95% is achieved in our work. In EEG analysis, the search for the hidden information for identification of seizures has a long history. In this work, an effort is made to analyze the normal and epileptic EEGs using the chaos theory. In this work, emphasis is made on the extraction and selection of key and relevant features that distinguish EEG (on the same subject) with and without the epileptic seizures. The features extracted include chaotic invariants and information theory features. Results obtained are promising and clear differences are seen in the extracted features between normal and epileptic EEGs. At present, new biomedical signal processing algorithms are usually evaluated by applying them to signals acquired from real patients. Most cases, the signals are of short duration for the evaluator to decide on the accuracy and reliability of the given algorithm. To facilitate this evaluation, it is required to generate longer duration signals from these short duration signals while preserving the characteristics of the signal. In this work, we have proposed linear and nonlinear techniques to model the HRV and EEG signals from their respective short duration data. From the models, longer duration signals are synthesized for further analysis. Results of these generated signals show that the models can generate the HRV and EEG signals that approximate the real HRV and EEG signals. The HRV signal models are useful in the prediction of the heart rate signals and subsequently help in the analysis and diagnosis of cardiac abnormalities. The modeling of EEG signals can be a very useful tool in the prediction of seizures. In this work, we have also proposed a new nonlinear model architecture using pipelined recurrent neural network (PRNN) to model the HRV and EEG signals. The new architecture performs better in terms of prediction error (measured as normalized root mean square error (NRMSE)) and signal to noise ratio (SNR). The signals modeled using the proposed architecture is able to successfully model the inherent nonlinear characteristics of the experimental signals. From the results it can be clearly seen that the proposed architecture clearly outperforms the linear models. This is due to the nonlinear model¿s inherent ability to model the underlying nonlinearity of the system under investigation.