心率变异性的时间不可逆性研究
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摘要
健康人的心跳是一个典型的多输入的复杂系统,它在自发窦性节律的基础上,同时受自主神经系统——交感神经、副交感神经等多种因素的协调控制,因而呈现复杂的变异性,即心率变异性(heart rate variability, HRV)。作为评价自主神经系统的活动水平的一种无创性手段,对HRV的分析在评价心交感神经与迷走神经活动水平方面有着广泛的应用。
由于产生HRV的心脏动力系统是非线性的,因此对HRV的分析应该采用非线性动力学分析法。目前在HRV的非线性分析方面,仍以幂律分析和熵分析为主；作为一种独特的非线性分析手段,时间不可逆性分析近来也被一些学者应用到HRV的分析中来,并且揭示了心脏动力系统的一些性质。但是这方面的研究仍停留在提出各种时间不可逆性测度并用其证明来自于健康个体的HRV具有时间不可逆性这一点上,即便是有些研究将其应用到了病理状态下,如充血性心力衰竭(congestive heart failure, CHF),却还有不一致的结论。本研究的目的就在于：寻找能恰当反映心脏动力系统在不同的生理病理状态下区别的时间不可逆性测度以揭示心脏动力系统本质,进而在临床应用中得到一致结论并形成诊断标准。为此,我们进行了如下工作：
(1)基于多尺度思想,提出用(Pm%, Gm%)平面来直观地展示时间序列的不可逆性。我们称其为多尺度时间不可逆性(MSTI)分析法。通过数值仿真,我们确认该方法在重构具有时间延迟特性的动力系统的时间不可逆性时会更可靠,而心脏动力系统正是一个带有多级延迟、多级反馈控制模式的系统；当我们将(Pm%, Gm%)平面应用于健康人的HRV分析中时,替代数据检验的结果证明“健康人的RR间期序列普遍具有时间不可逆性”,这一点为“健康人的心率变异性是非线性的”的论点提供了有力的证据；同时发现一个值得深思的现象：这些点基本都落入第一象限并呈线性分布；当我们将MSTI法应用于人造序列时,该方法可以很明显地区分人造序列和真实生理序列,因此,该方法可以作为一个测试生理信号模型的工具；而当我们将其应用于来自于CHF患者的RR间期序列上时,我们找到了解释前人研究结果不一致的本质原因；最后,应用该方法对自行采集的11位健康年轻人的白天清醒和夜间睡眠时的RR间期序列分析的结果表明,健康年轻人HRV的时间不可逆性展现出了“夜间增强,日间减弱”的规律。
(2)基于高维相空间重构的思想,提出将相空间重构图向多个2维平面投影,在每个投影平面上进行时间不可逆性分析,然后将多个平面上的分析结果综合考虑的方法。我们称之为高维的时间不可逆性(HDTI)分析法。相比于MSTI分析法,该方法同样能有效地区分人造序列和真实生理序列,以及展现健康人心脏动力系统特性的昼夜节律。而比MSTI分析法更具优势的是,在所分析的数据长度达到5000点时,HDTI方法还能揭示出年龄老化对健康人HRV的时间不可逆性的影响；且在较短的数据长度下(1000点),就能检测出疾病对HRV时间不可逆性的影响；而当我们将该方法应用于运动中和运动后的短时(约4-7分钟,数据长度为512点)的RR间期序列的分析中时,发现不可逆性测度值与心率的线性趋势项密切相关,其变化趋势正好反映了运动前、中、后交感迷走神经之间的这种从平衡态到非平衡态、再从非平衡态逐渐恢复到平衡态的过程。
(3)鉴于符号动力学是非线性科学中一种重要而有效的理论方法,但目前鲜有对HRV进行符号化时间不可逆性分析的研究,因此,我们尝试利用符号动力学的原理与方法来探索HRV序列的时间不可逆性,目的在于从另一个角度来探索心脏动力系统的非线性特性及其复杂程度。为此我们做了如下一些工作：提出以序列概率分布的m等分位点作为符号划分依据的等概率符号化法；提出了5个衡量符号序列时间不可逆性的参数；利用仿真数据,比较了不同符号化方法与序列的时间不可逆研究结合的效果,结果表明等概率符号化的效果最优；利用基于等概率符号化的时间不可逆性测度来分析HRV,得到了与前述两种方法(MSTI和HDTI)一致的结论,即：来自于健康年轻人的RR间期序列最倾向于具有时间不可逆性,而随着年龄的老化以及疾病的出现,这种可能性会降低；健康年轻人的RR间期序列的时间不可逆性具有昼夜差异,夜间睡眠时不可逆性增强。等概率符号化时间不可逆性分析中的5个测度,在数据长度仅为500点的时,就都敏感地捕捉到了健康年轻人夜间睡眠和白天清醒时的心脏动力学特性的变化,而且,这些测度所反映出来的昼夜差异随着所考察的数据长度的增加变化很小；另外,其中的分布差异熵测度在区分健康人和CHF患者的RR间期序列时具有较强的敏感性。相比于前述两种方法,等概率符号化时间不可逆性方法在分析心率变异性信号上更显优势。
(4)人工神经网络是由大量并行工作的神经元组成的智能仿生模型,它在模式识别领域已经展示出了广阔的应用前景。鉴于单一心率变异性指标所表达出来的信息具有片面性,很难用一个单一的指标来完全分类CHF患者和健康人的不足。因此,为了联合HRV的线性和非线性动力学分析方法,我们设计了多种指标组合来作为人工神经网络的输入特征向量。在网络的选择与训练过程中,我们以10次10折交叉验证的平均性能和平均迭代步数作为选择标准,确定了用于CHF诊断的智能模型的输入特征向量组合、网络结构和网络参数。当我们使用该模型对预留的16例样本数据(其中包括10例健康样本和6例CHF患者样本)和自行采集的11位健康年轻人的HRV序列进行分类时,仅有一例CHF患者没有被诊断出来,模型展现出了较好的泛化能力。需要指出的是,在最终确定的模型输入特征向量组合中,就有我们提出的符号化时间不可逆性指标,因此进一步证明了时间不可逆性分析在HRV的分析中起着不可忽视的作用。
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.
由于产生HRV的心脏动力系统是非线性的,因此对HRV的分析应该采用非线性动力学分析法。目前在HRV的非线性分析方面,仍以幂律分析和熵分析为主；作为一种独特的非线性分析手段,时间不可逆性分析近来也被一些学者应用到HRV的分析中来,并且揭示了心脏动力系统的一些性质。但是这方面的研究仍停留在提出各种时间不可逆性测度并用其证明来自于健康个体的HRV具有时间不可逆性这一点上,即便是有些研究将其应用到了病理状态下,如充血性心力衰竭(congestive heart failure, CHF),却还有不一致的结论。本研究的目的就在于：寻找能恰当反映心脏动力系统在不同的生理病理状态下区别的时间不可逆性测度以揭示心脏动力系统本质,进而在临床应用中得到一致结论并形成诊断标准。为此,我们进行了如下工作：
(1)基于多尺度思想,提出用(Pm%, Gm%)平面来直观地展示时间序列的不可逆性。我们称其为多尺度时间不可逆性(MSTI)分析法。通过数值仿真,我们确认该方法在重构具有时间延迟特性的动力系统的时间不可逆性时会更可靠,而心脏动力系统正是一个带有多级延迟、多级反馈控制模式的系统；当我们将(Pm%, Gm%)平面应用于健康人的HRV分析中时,替代数据检验的结果证明“健康人的RR间期序列普遍具有时间不可逆性”,这一点为“健康人的心率变异性是非线性的”的论点提供了有力的证据；同时发现一个值得深思的现象：这些点基本都落入第一象限并呈线性分布；当我们将MSTI法应用于人造序列时,该方法可以很明显地区分人造序列和真实生理序列,因此,该方法可以作为一个测试生理信号模型的工具；而当我们将其应用于来自于CHF患者的RR间期序列上时,我们找到了解释前人研究结果不一致的本质原因；最后,应用该方法对自行采集的11位健康年轻人的白天清醒和夜间睡眠时的RR间期序列分析的结果表明,健康年轻人HRV的时间不可逆性展现出了“夜间增强,日间减弱”的规律。
(2)基于高维相空间重构的思想,提出将相空间重构图向多个2维平面投影,在每个投影平面上进行时间不可逆性分析,然后将多个平面上的分析结果综合考虑的方法。我们称之为高维的时间不可逆性(HDTI)分析法。相比于MSTI分析法,该方法同样能有效地区分人造序列和真实生理序列,以及展现健康人心脏动力系统特性的昼夜节律。而比MSTI分析法更具优势的是,在所分析的数据长度达到5000点时,HDTI方法还能揭示出年龄老化对健康人HRV的时间不可逆性的影响；且在较短的数据长度下(1000点),就能检测出疾病对HRV时间不可逆性的影响；而当我们将该方法应用于运动中和运动后的短时(约4-7分钟,数据长度为512点)的RR间期序列的分析中时,发现不可逆性测度值与心率的线性趋势项密切相关,其变化趋势正好反映了运动前、中、后交感迷走神经之间的这种从平衡态到非平衡态、再从非平衡态逐渐恢复到平衡态的过程。
(3)鉴于符号动力学是非线性科学中一种重要而有效的理论方法,但目前鲜有对HRV进行符号化时间不可逆性分析的研究,因此,我们尝试利用符号动力学的原理与方法来探索HRV序列的时间不可逆性,目的在于从另一个角度来探索心脏动力系统的非线性特性及其复杂程度。为此我们做了如下一些工作：提出以序列概率分布的m等分位点作为符号划分依据的等概率符号化法；提出了5个衡量符号序列时间不可逆性的参数；利用仿真数据,比较了不同符号化方法与序列的时间不可逆研究结合的效果,结果表明等概率符号化的效果最优；利用基于等概率符号化的时间不可逆性测度来分析HRV,得到了与前述两种方法(MSTI和HDTI)一致的结论,即：来自于健康年轻人的RR间期序列最倾向于具有时间不可逆性,而随着年龄的老化以及疾病的出现,这种可能性会降低；健康年轻人的RR间期序列的时间不可逆性具有昼夜差异,夜间睡眠时不可逆性增强。等概率符号化时间不可逆性分析中的5个测度,在数据长度仅为500点的时,就都敏感地捕捉到了健康年轻人夜间睡眠和白天清醒时的心脏动力学特性的变化,而且,这些测度所反映出来的昼夜差异随着所考察的数据长度的增加变化很小；另外,其中的分布差异熵测度在区分健康人和CHF患者的RR间期序列时具有较强的敏感性。相比于前述两种方法,等概率符号化时间不可逆性方法在分析心率变异性信号上更显优势。
(4)人工神经网络是由大量并行工作的神经元组成的智能仿生模型,它在模式识别领域已经展示出了广阔的应用前景。鉴于单一心率变异性指标所表达出来的信息具有片面性,很难用一个单一的指标来完全分类CHF患者和健康人的不足。因此,为了联合HRV的线性和非线性动力学分析方法,我们设计了多种指标组合来作为人工神经网络的输入特征向量。在网络的选择与训练过程中,我们以10次10折交叉验证的平均性能和平均迭代步数作为选择标准,确定了用于CHF诊断的智能模型的输入特征向量组合、网络结构和网络参数。当我们使用该模型对预留的16例样本数据(其中包括10例健康样本和6例CHF患者样本)和自行采集的11位健康年轻人的HRV序列进行分类时,仅有一例CHF患者没有被诊断出来,模型展现出了较好的泛化能力。需要指出的是,在最终确定的模型输入特征向量组合中,就有我们提出的符号化时间不可逆性指标,因此进一步证明了时间不可逆性分析在HRV的分析中起着不可忽视的作用。
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.
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