基于熵测度的短时心脏动力学分析
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摘要
心血管疾病的无创无损早期检测是目前生物医学领域面临的重大挑战,心脏动力学分析是克服该挑战的有效手段之一。熵测度是一类常用的心脏动力学分析工具,其在分析有限长度含噪生理序列方面具有显著优势。
本文旨在探究短时心脏动力学分析用于心血管疾病无创无损早期检测的潜在价值。定义了分析熵测度统计性能的定量指标,对比研究了现有熵测度的稳定性和一致性。提出了分布熵算法及其对应的多尺度和多变量形式,验证了它们分析短时序列时的统计性能。基于分布熵分析,系统研究了短时心脏动力特征在老年人群和心衰患者中的变化规律。所做主要工作如下：
(1)引入调整因子λ,定义了物理模糊隶属函数,提出了改进的模糊熵测度族。仿真试验结果表明：改进的模糊熵测度族相比原始算法具有显著提高的稳定性,其一致性与原始算法相当；λ的取值与时间序列的噪声水平相关,当λ较大时,隶属函数会过高地估计噪声水平,影响算法的一致性；折中考虑算法的稳定性和一致性,对λ的取值范围作了经验规定。
(2)定义了定量评价熵测度统计性能的分辨能力指数和可靠水平指数,建立了算法统计性能的科学评价体系。通过耦合宽带噪声模型、耦合MIX(p)模型、耦合Henon映射和耦合Rossler系统,对比研究了互熵和多变量熵的统计性能,结果表明：互熵仅对线性随机过程有效,而对非线性混沌系统难以获得客观结果；相比多变量熵,互熵的参数依赖性较高；低频趋势会对多变量熵分析结果造成影响；多尺度分析时,互熵和多变量熵的统计性能均无显著改善。
(3)建立了分布熵测度及对应的多变量和多尺度形式。提出经典熵测度统计性能难以获得进一步提升的根源在于它们仅对序列的相空间特征进行了局部评估,基于向量间的距离分布特征,提出了相空间的全局度量算法,建立了分布熵测度；定义了多变量联合相空间重构算法,建立了多变量分布熵测度,对分布熵和多变量分布熵的统计性能进行了定量分析。结果表明：相比样本熵和改进的模糊熵,分布熵的一致性和稳定性显著提高；当时间序列仅具有50个有效采样点时,分布熵也具有相当优越的统计性能；多变量分布熵能够有效挖掘多通道序列间的耦合性,相比多变量样本熵和改进的多变量模糊熵,多变量分布熵的统计性能显著提高。
(4)研究了短时心脏电动力学特征随年龄的变化趋势,揭示了老年人群自主神经功能的退化规律。试验结果表明：短时心动周期序列的分布熵值和改进的模糊熵值在不同年龄人群间具有显著差异,而经典熵测度不能有效区分不同年龄人群间的差异；相比改进的模糊熵,分布熵结果随年龄的变化趋势更为显著；当年龄超过40岁时,短时心动周期序列原始尺度上的分布熵开始显著降低,年龄超过70岁后,这种降低趋势不再继续,分布熵在较低水平上维持不变；高时间尺度上的分布熵结果在不同年龄人群间无显著差异。
(5)率先研究了年龄对短时心脏机械动力学特征和心脏电-机械耦合特征的影响,为无创无损检测心血管疾病提供了新的有益思路。试验结果表明：健康年轻人群中,短时心脏舒张间期序列的分布熵与短时心动周期序列相当,心动周期-舒张间期的多变量分布熵较高,即两者之间存在显著耦合；年龄超过40岁后,短时舒张间期序列的分布熵显著低于短时心动周期序列,它们的耦合性也显著降低,且随年龄的增加耦合性继续降低,提示老龄化可能引发心脏机械功能的退化,影响心脏的收缩或舒张运动。
(6)基于短时心脏动力学分析,构建了无创无损心衰检测指标。临床试验表明：短时电动力学特征、短时机械动力学特征和电-机械耦合特征在心衰患者中均显著下降；与年龄造成的影响不同,心衰同时造成高尺度上各动力学特征的降低；短时电动力学特征用于检测心衰的敏感性和特异性分别为92.31%和96.00%；短时机械动力学特征和电-机械耦合特征能够提供独立于电动力学特征之外的有益信息,基于上述全部短时动力学特征所建立的心衰检测指标,其敏感性和特异性分别达到96.15%和100%。
The early noninvasive and nondestructive detection of cardiovascular diseases is a contemporary challenge in the field of biomedicine. Concepts from cardiac dynamics appear to provide it promising methods through the assessment of the integrated behaviors of the cardiovascular signals on a system level. Entropy measures are commonly applied in cardiac dynamics. They have been shown to be very promising in the dynamical analysis of physiological series with finite length and various noises.
This dissertation aimed to probe deeply into the significance of short-term cardiac dynamics in the noninvasive and nondestructive detection of cardiovascular diseases. Briefly, quantitative indices for the evaluation of statistical abilities were defined first and the stability as well as the consistency of conventional entropy measures were compared. Then this dissertation established a novel distribution entropy measure and its multiscale and multivariate counterparts. Their statistical abilities were also examined rigorously. Finally, the significance of short-term cardiac dynamical features estimated by distribution entropy was explored with real-world cardiovascular data. Main works in this dissertation are listed as follows.
(1) A physical fuzzy membership function was defined by introducing an adjustable factor λ; a refined family of fuzzy entropy was developed accordingly. Simulation results indicated that the refined algorithms had clearly improved stability in comparison with the original ones. Their consistency was highly comparable with the original algorithms. The value of λ depended on the noise level of the time-series; the noise level would be over-estimated by relatively large λ, which could consequently affect the consistency. Its value could thus be selected empirically by a compromise between the stability and consistency.
(2) Systematically methods for the evaluation of the statistical abilities of entropy measures were established. Prior to the evaluation, a distinguishability index and a reliability index was defined. This work then implemented elaborate tests on the consistency of both cross entropies and multivariate entropies through4distinctly different theoretical models-coupled broadband noise model, coupled MIX(p) process, coupled Henon map, and coupled Rossler system. Results indicated that cross entropies failed to work in nonlinear chaotic systems although they could work relatively well in linear stochastic processes. Multivariate entropies could, however, work well in both; they were also less dependent on input parameters in comparison with cross entropies. However, the low-frequency trend in time-series could affect the performances of both multivariate entropy measures. Their abilities could not be further improved by multiscale analysis.
(3) A novel distribution entropy and its multivariate and multiscale counterparts were developed. It indicated in this dissertation that conventional entropy measures did not fully characterize the information carried in the state space, which accounted much for their inconsistency and instability. This work developed a novel distribution entropy metric by integrating the information carried therein. Besides, it established a joint procedure for multivariate state-space reconstruction. The multivariate distribution entropy was developed accordingly. Their stability and consistency were subsequently examined quantitatively and rigorously. Results showed distribution entropy a very robust metric for assessing the complexity. In comparison with both sample entropy and refined fuzzy entropy, it had significantly improved consistency and stability. It was also very stable in data sets in as small as50data points. Besides, multivariate distribution entropy inherited the advantages of distribution entropy, indicating by far better performances in assessing the multivariate complexity of simulation models compared to conventional algorithms.
(4) Aging effects on the short-term cardiac electrodynamical features were investigated in this dissertation, which should probably be a new dynamical picture of the autonomic control. Results indicated that both the distribution entropy and the refined fuzzy entropy had significant differences among different aging groups. However, conventional measures failed to captures these differences. In comparison with refined fuzzy entropy, distribution entropy showed more significant varying patterns with aging. The distribution entropy of short-term heartbeat interval data at the first scale declined significantly in group with age>40year. But for old people whose ages were70year and above, the distribution entropy did not reduce further; it maintained in a relatively low level. By comparison, no significant variation was captured in distribution entropy at higher scales.
(5) This dissertation had explored, for the first time, the aging effects on the short-term cardiac mechano-dynamical features and the electromechanical coupling, which should provide valuable tools for the noninvasive and nondestructive detection of cardiovascular diseases. Results showed that distribution entropy of short-term cardiac diastolic period was highly comparable with that of heartbeat interval data in healthy young adults. The multivariate distribution entropy of heart rate-diastolic period was relative large, showing a tight coupling between them. The distribution entropy of the cardiac diastolic period was significantly lower than that of heartbeat interval data. Their coupling was also declined and this declining tendency maintained with aging. Those results suggested a possible mechanism of aging induced damage in cardiac mechanic function which should affect the contraction and relaxation of the heart.
(6) Noninvasive and nondestructive indices for the detection of heart failure were established by short-term cardiac dynamics. Clinical trials showed that the electrodynamical, mechano-dynamical features and the electro-mechanical coupling at the first scale all significantly depressed in heart failure patients. Additionally, these features were also distinctly declined at higher scales, which were different from the affects of aging. There was a certain merit of short-term cardiac electrodynamical features in HF detection. However, the short-term cardiac mechano-dynamical features and the electro-mechanical coupling could indeed be capable of providing additional valuable information in this specific task. The index constructed by all dynamical features resulted obviously improved performances with sensitivity of96.15%and specificity of100%, in comparison with that developed by solely electrodynamical features, whose sensitivity and specificity was92.31%and96.00%, respectively.
本文旨在探究短时心脏动力学分析用于心血管疾病无创无损早期检测的潜在价值。定义了分析熵测度统计性能的定量指标,对比研究了现有熵测度的稳定性和一致性。提出了分布熵算法及其对应的多尺度和多变量形式,验证了它们分析短时序列时的统计性能。基于分布熵分析,系统研究了短时心脏动力特征在老年人群和心衰患者中的变化规律。所做主要工作如下：
(1)引入调整因子λ,定义了物理模糊隶属函数,提出了改进的模糊熵测度族。仿真试验结果表明：改进的模糊熵测度族相比原始算法具有显著提高的稳定性,其一致性与原始算法相当；λ的取值与时间序列的噪声水平相关,当λ较大时,隶属函数会过高地估计噪声水平,影响算法的一致性；折中考虑算法的稳定性和一致性,对λ的取值范围作了经验规定。
(2)定义了定量评价熵测度统计性能的分辨能力指数和可靠水平指数,建立了算法统计性能的科学评价体系。通过耦合宽带噪声模型、耦合MIX(p)模型、耦合Henon映射和耦合Rossler系统,对比研究了互熵和多变量熵的统计性能,结果表明：互熵仅对线性随机过程有效,而对非线性混沌系统难以获得客观结果；相比多变量熵,互熵的参数依赖性较高；低频趋势会对多变量熵分析结果造成影响；多尺度分析时,互熵和多变量熵的统计性能均无显著改善。
(3)建立了分布熵测度及对应的多变量和多尺度形式。提出经典熵测度统计性能难以获得进一步提升的根源在于它们仅对序列的相空间特征进行了局部评估,基于向量间的距离分布特征,提出了相空间的全局度量算法,建立了分布熵测度；定义了多变量联合相空间重构算法,建立了多变量分布熵测度,对分布熵和多变量分布熵的统计性能进行了定量分析。结果表明：相比样本熵和改进的模糊熵,分布熵的一致性和稳定性显著提高；当时间序列仅具有50个有效采样点时,分布熵也具有相当优越的统计性能；多变量分布熵能够有效挖掘多通道序列间的耦合性,相比多变量样本熵和改进的多变量模糊熵,多变量分布熵的统计性能显著提高。
(4)研究了短时心脏电动力学特征随年龄的变化趋势,揭示了老年人群自主神经功能的退化规律。试验结果表明：短时心动周期序列的分布熵值和改进的模糊熵值在不同年龄人群间具有显著差异,而经典熵测度不能有效区分不同年龄人群间的差异；相比改进的模糊熵,分布熵结果随年龄的变化趋势更为显著；当年龄超过40岁时,短时心动周期序列原始尺度上的分布熵开始显著降低,年龄超过70岁后,这种降低趋势不再继续,分布熵在较低水平上维持不变；高时间尺度上的分布熵结果在不同年龄人群间无显著差异。
(5)率先研究了年龄对短时心脏机械动力学特征和心脏电-机械耦合特征的影响,为无创无损检测心血管疾病提供了新的有益思路。试验结果表明：健康年轻人群中,短时心脏舒张间期序列的分布熵与短时心动周期序列相当,心动周期-舒张间期的多变量分布熵较高,即两者之间存在显著耦合；年龄超过40岁后,短时舒张间期序列的分布熵显著低于短时心动周期序列,它们的耦合性也显著降低,且随年龄的增加耦合性继续降低,提示老龄化可能引发心脏机械功能的退化,影响心脏的收缩或舒张运动。
(6)基于短时心脏动力学分析,构建了无创无损心衰检测指标。临床试验表明：短时电动力学特征、短时机械动力学特征和电-机械耦合特征在心衰患者中均显著下降；与年龄造成的影响不同,心衰同时造成高尺度上各动力学特征的降低；短时电动力学特征用于检测心衰的敏感性和特异性分别为92.31%和96.00%；短时机械动力学特征和电-机械耦合特征能够提供独立于电动力学特征之外的有益信息,基于上述全部短时动力学特征所建立的心衰检测指标,其敏感性和特异性分别达到96.15%和100%。
The early noninvasive and nondestructive detection of cardiovascular diseases is a contemporary challenge in the field of biomedicine. Concepts from cardiac dynamics appear to provide it promising methods through the assessment of the integrated behaviors of the cardiovascular signals on a system level. Entropy measures are commonly applied in cardiac dynamics. They have been shown to be very promising in the dynamical analysis of physiological series with finite length and various noises.
This dissertation aimed to probe deeply into the significance of short-term cardiac dynamics in the noninvasive and nondestructive detection of cardiovascular diseases. Briefly, quantitative indices for the evaluation of statistical abilities were defined first and the stability as well as the consistency of conventional entropy measures were compared. Then this dissertation established a novel distribution entropy measure and its multiscale and multivariate counterparts. Their statistical abilities were also examined rigorously. Finally, the significance of short-term cardiac dynamical features estimated by distribution entropy was explored with real-world cardiovascular data. Main works in this dissertation are listed as follows.
(1) A physical fuzzy membership function was defined by introducing an adjustable factor λ; a refined family of fuzzy entropy was developed accordingly. Simulation results indicated that the refined algorithms had clearly improved stability in comparison with the original ones. Their consistency was highly comparable with the original algorithms. The value of λ depended on the noise level of the time-series; the noise level would be over-estimated by relatively large λ, which could consequently affect the consistency. Its value could thus be selected empirically by a compromise between the stability and consistency.
(2) Systematically methods for the evaluation of the statistical abilities of entropy measures were established. Prior to the evaluation, a distinguishability index and a reliability index was defined. This work then implemented elaborate tests on the consistency of both cross entropies and multivariate entropies through4distinctly different theoretical models-coupled broadband noise model, coupled MIX(p) process, coupled Henon map, and coupled Rossler system. Results indicated that cross entropies failed to work in nonlinear chaotic systems although they could work relatively well in linear stochastic processes. Multivariate entropies could, however, work well in both; they were also less dependent on input parameters in comparison with cross entropies. However, the low-frequency trend in time-series could affect the performances of both multivariate entropy measures. Their abilities could not be further improved by multiscale analysis.
(3) A novel distribution entropy and its multivariate and multiscale counterparts were developed. It indicated in this dissertation that conventional entropy measures did not fully characterize the information carried in the state space, which accounted much for their inconsistency and instability. This work developed a novel distribution entropy metric by integrating the information carried therein. Besides, it established a joint procedure for multivariate state-space reconstruction. The multivariate distribution entropy was developed accordingly. Their stability and consistency were subsequently examined quantitatively and rigorously. Results showed distribution entropy a very robust metric for assessing the complexity. In comparison with both sample entropy and refined fuzzy entropy, it had significantly improved consistency and stability. It was also very stable in data sets in as small as50data points. Besides, multivariate distribution entropy inherited the advantages of distribution entropy, indicating by far better performances in assessing the multivariate complexity of simulation models compared to conventional algorithms.
(4) Aging effects on the short-term cardiac electrodynamical features were investigated in this dissertation, which should probably be a new dynamical picture of the autonomic control. Results indicated that both the distribution entropy and the refined fuzzy entropy had significant differences among different aging groups. However, conventional measures failed to captures these differences. In comparison with refined fuzzy entropy, distribution entropy showed more significant varying patterns with aging. The distribution entropy of short-term heartbeat interval data at the first scale declined significantly in group with age>40year. But for old people whose ages were70year and above, the distribution entropy did not reduce further; it maintained in a relatively low level. By comparison, no significant variation was captured in distribution entropy at higher scales.
(5) This dissertation had explored, for the first time, the aging effects on the short-term cardiac mechano-dynamical features and the electromechanical coupling, which should provide valuable tools for the noninvasive and nondestructive detection of cardiovascular diseases. Results showed that distribution entropy of short-term cardiac diastolic period was highly comparable with that of heartbeat interval data in healthy young adults. The multivariate distribution entropy of heart rate-diastolic period was relative large, showing a tight coupling between them. The distribution entropy of the cardiac diastolic period was significantly lower than that of heartbeat interval data. Their coupling was also declined and this declining tendency maintained with aging. Those results suggested a possible mechanism of aging induced damage in cardiac mechanic function which should affect the contraction and relaxation of the heart.
(6) Noninvasive and nondestructive indices for the detection of heart failure were established by short-term cardiac dynamics. Clinical trials showed that the electrodynamical, mechano-dynamical features and the electro-mechanical coupling at the first scale all significantly depressed in heart failure patients. Additionally, these features were also distinctly declined at higher scales, which were different from the affects of aging. There was a certain merit of short-term cardiac electrodynamical features in HF detection. However, the short-term cardiac mechano-dynamical features and the electro-mechanical coupling could indeed be capable of providing additional valuable information in this specific task. The index constructed by all dynamical features resulted obviously improved performances with sensitivity of96.15%and specificity of100%, in comparison with that developed by solely electrodynamical features, whose sensitivity and specificity was92.31%and96.00%, respectively.
引文
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