Research On Time Irreversibility Of Heart Rate Variability

The heart beat of healthy human is a typical multi-input complex system. On the basis of idiopathic sinus rhythm, it is also controlled harmoniously by autonomic nervous system which including sympathetic nervous, parasympathetic nervous and other aspects. Human heart rates fluctuate from beat to beat in a complex manner which is called HRV (heart rate variability). As a noninvasive diagnosis method, the analysis of HRV is widely used in the assessment of cardiac sympatho-vagal modulation activity.As the cardiac system which generates HRV is in nonlinearity, the methods deriving from nonlinear dynamic analysis should be adopted for HRV analysis. At present, in terms of nonlinear analysis of HRV signal, it is still dominated by power-law analysis and entropy analysis. As a unique method of nonlinear analysis, time-irreversibility test is introduced by some scholars into the HRV analysis recently, which reveals some characteristics of the cardiac dynamic systems.However, most of those researches are still limited to the exploration of irreversible measurements which is used to prove the opinion that "HRV signals derived from healthy subjects is time irreversible". Even though it is applied to HRV in pathological state (e.g. Congestive Heart Failure, CHF) by some researchers, it is hard to get consistent results. And the objective of our research is to find some time-irreversible measurements which are sensitive to different physiological and pathological states, in order to reveal the underlying features of cardiac system and achieve unanimous conclusion and diagnostic standard. In this paper, we mainly did the following works:(1) Base on the concept of multi-scale analysis, we presented a (Pm%, Gm%) space to indicate the irreversibility of time series. which is called MSTI method. It is concluded from numerical verification that the method will be more reliable than single-scale method when applied to the reconstruction of time-reversibility in dynamic systems including delays. And the cardiac dynamic system is actually such a system, in which regulations are usually per-formed via multiple feedback loops incorporating different delays. When the (Pm%, Gm%) space was applied to the HRV of healthy subjects, results from data surrogating test verified that time irreversibility is a general characteristic of RR intervals of healthy populations, which provides a strong evidence on the argument that heart rate variability is nonlinear. Furthermore, an obvious phenomenon can be observed that almost all the points are located in the region of Quadrant I of the (Pm%, Gm%) space and in linear distribution. When we applied the MSTI method to synthetic RR sequences, there is a significant difference from real signals. Therefore, we suggest that the method should be used as an evaluating tool in the modeling of physiologic series. And the reason for the explanation of the disagreements of previous studies was found while the method is used to analyze the RR intervals of CHF patients. Finally, we applied the MSTI method to the data collected from11healthy youth during daytime and nighttime respectively. The results show that irreversible dynamics detected in RR intervals of healthy population appeared in a tendency that stronger in nighttime than in daytime.(2) In consideration of embedding the series in a m-dimensional phase space (m>2), we proposed the high-dimensional time irreversibility (HDTI) analysis. Our test valuates m-dimensional irreversibility by checking the asymmetry of the distribution of points obtained by projecting the m-dimensional reconstructed dynamics onto multiple2-dimensional planes, and then integrating the results on all planes. Comparing with the MSTI method, the HDTI method is also an effective way to distinguish the synthetic series from the physiological ones and can reveal the circadian variations of irreversible dynamics in healthy human as well. Moreover, the influence of the aging on irreversible dynamics can be reflected by the HDTI method when the analyzed data length reaches5000, whereas the influence of the disease can be reflected with shorter data length (about1000). Furthermore, when the method was applied to the extreme short (about4-7minutes,512points) RR intervals of healthy human during and after exercise, we found that the measurement of irreversibility varies linearly with the tendency of heart rate, which reflects the changes of cardiac sympatho-vagal modulations from equilibrium to non-equilibrium, and then recovering from non-equilibrium to equilibrium gradually.(3) Symbolic dynamics is an important and effective method in nonlinear science and there is few research ever reported on symbolic irreversible analysis of HRV. In this paper, we introduced the theory of symbolic dynamics to study time irreversibility of HRV, aiming to explore the nonlinear characteristics and complexity of cardiac systems from another aspect. We proposed a method called equiprobable-symbollise, which produces symbols equiprobability according to probability distribution of the original series. Five indices were presented to measure the symbolic irreversible dynamics, and then we evaluated the performance of different symbolized methods by using these indices when applied to numerical data. As a result, equiprobable-symbollise method was proved to be the most effecitve one. The conclusions achieved from this method are consistent with the MSTI and HDTI method:the RR intervals of healthy youth are more likely to be irreversible, and such an irreversibility will decrease with aging or heart disease; for healthy population, irreversible dynamics exist a rhythm and vary for RR intervals in daytime and nighttime, and a stronger irreversibility was detected in nighttime.While equiprobable-symbollise method was applied to the circadian data, all of the above mentioned five indices was proved to be very sensitive to the changes of the characteristics of the cardiac dynamic systems from daytime to nighttime, even with the data length of only500. And the difference reflected by the measurements keep almost unchanged along with the increasing of data length. Furthermore, the measurement of the difference entropy seems to be much more sensitive than other indices in distinguishing CHF populations from the healthy. It is concluded from our researches that the symbolic-irreversibility analysis based on equiprobable-symbollise shows more superiority than the above mentioned methods.(4) Artificial neural network, inspired by biological nervous systems, is composed of simple elements operating in parallel and open up very broad vistas in the field of pattern recognition. Considering that the information delivered by any single HRV index is inadequate and it is very difficult to completely classify the CHF patients from healthy people by using a single index. In order to combine linear and nonlinear method together for HRV analysis, a variety of indices assembly was designed as the feature parameters of artificial neutral network. During the process of selecting the network and training, by using the mean performance and mean epochs of10-fold cross-validation over10times, the feature vector, architecture, as well as the weights and bias of the BP network were determined. When the selected model was applied to16samples (which include10healthy samples and6CHF ones) and11RR sequences of healthy youth, just one sample derived from a CHF patient can not been diagnosed. The results showed that the selected model exhibits perfect generalization ability. It is to be noted that, the symbolic irreversibility index is selected in the feature vector of the final model, which further proving the importance of time irreversibility method in the analysis of HRV.