分形理论在心音信号的分析与识别中的应用研究
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摘要
心音信号是人体最重要的声信号之一，它包含着心脏各部分的生理和病理信息，是心脏及心血管系统机械运动状况的反映。在心血管疾病尚未发展到足以产生临床及病理改变时，心音中出现的杂音和畸变就是重要的诊断信息。因此，准确地分析和识别心音信号对心血管系统疾病的诊断具有重要的意义。
论文将分形理论引入到心音信号的研究中，以分形维数为基础进行心音信号的分析与识别，为心血管疾病提供一种新的无损诊断方法。首先对两种分形维数估算方法：方差分形维数法和二进盒维数法进行研究，并通过实验对两种估算方法进行验证和比较；接着对心音信号的分形特征进行研究，并对正常心音和病态心音的分形维数进行比较；然后给出心音信号分形维数轨迹的构造算法，讨论时间窗口参数对心音信号分形维数轨迹产生的影响，并分析心音信号分形维数轨迹的特征；最后结合心音信号分形维数轨迹的特征和心音信号的时域特性，提出一种基于分形维数轨迹的心音信号自动分段算法，给出了分段算法的策略和具体步骤，并用大量病例对分段算法的性能进行了验证。
研究结果表明，心音信号存在无标度区间，具有明显的分形特征；分形维数能够定量地描述心音信号的复杂程度，显著地区分正常心音和病态心音；基于分形维数轨迹的心音信号自动分段算法无需依赖任何参考信号，准确率高，鲁棒性强，具有良好的分段效果。
Heart sound is one of the most important voice signals of human body. It includes physiology and pathologic information of each part of heart, and reflects the mechanical movement condition of the heart and the cardiovascular system. When the cardiovascular diseases haven't developed to be good enough to produce clinical and pathologic change, murmur and aberration of heart sound is important information for diagnosis. Therefore, correct analysis and recognition of heart sound is significant to the diagnosis of cardiovascular diseases.
This paper introduces fractal theory to the study of heart sound, and makes analysis and recognition of heart sound on the basis of fractal dimension, and provides a new noninvasive diagnostic for cardiovascular diseases. Firstly, this paper studies two kinds of fractal dimension estimation methods: variance fractal dimension and binary box-counting dimension, and verifies and compares the two methods. Next, it studies the fractal characteristic of heart sound, and draws a parallel between fractal dimension of normal and morbid heart sound. Then, this paper presents construction method of fractal dimension trajectory of heart sound, and discusses how time window parameters affect 'fractal dimension trajectory of heart sound, and analyses the characteristics of fractal dimension trajectory. Finally, a new automatic segmentation algorithm of heart sound is put forward by combining fractal dimension trajectory and time characteristics of heart sound, and the strategies and steps of segmentation are given, and the algorithm is tested with a large number of normal and abnormal heart sound data.
The results show heart sound has non-scaling span and obvious fractal characteristics. Fractal dimension can quantitatively express the complexity of heart sound, and evidently distinguish normal and morbid heart sound. Automatic segmentation algorithm of heart sound based on fractal dimension trajectory is of high accuracy and robust without other signal as reference, and segment results are good.
论文将分形理论引入到心音信号的研究中，以分形维数为基础进行心音信号的分析与识别，为心血管疾病提供一种新的无损诊断方法。首先对两种分形维数估算方法：方差分形维数法和二进盒维数法进行研究，并通过实验对两种估算方法进行验证和比较；接着对心音信号的分形特征进行研究，并对正常心音和病态心音的分形维数进行比较；然后给出心音信号分形维数轨迹的构造算法，讨论时间窗口参数对心音信号分形维数轨迹产生的影响，并分析心音信号分形维数轨迹的特征；最后结合心音信号分形维数轨迹的特征和心音信号的时域特性，提出一种基于分形维数轨迹的心音信号自动分段算法，给出了分段算法的策略和具体步骤，并用大量病例对分段算法的性能进行了验证。
研究结果表明，心音信号存在无标度区间，具有明显的分形特征；分形维数能够定量地描述心音信号的复杂程度，显著地区分正常心音和病态心音；基于分形维数轨迹的心音信号自动分段算法无需依赖任何参考信号，准确率高，鲁棒性强，具有良好的分段效果。
Heart sound is one of the most important voice signals of human body. It includes physiology and pathologic information of each part of heart, and reflects the mechanical movement condition of the heart and the cardiovascular system. When the cardiovascular diseases haven't developed to be good enough to produce clinical and pathologic change, murmur and aberration of heart sound is important information for diagnosis. Therefore, correct analysis and recognition of heart sound is significant to the diagnosis of cardiovascular diseases.
This paper introduces fractal theory to the study of heart sound, and makes analysis and recognition of heart sound on the basis of fractal dimension, and provides a new noninvasive diagnostic for cardiovascular diseases. Firstly, this paper studies two kinds of fractal dimension estimation methods: variance fractal dimension and binary box-counting dimension, and verifies and compares the two methods. Next, it studies the fractal characteristic of heart sound, and draws a parallel between fractal dimension of normal and morbid heart sound. Then, this paper presents construction method of fractal dimension trajectory of heart sound, and discusses how time window parameters affect 'fractal dimension trajectory of heart sound, and analyses the characteristics of fractal dimension trajectory. Finally, a new automatic segmentation algorithm of heart sound is put forward by combining fractal dimension trajectory and time characteristics of heart sound, and the strategies and steps of segmentation are given, and the algorithm is tested with a large number of normal and abnormal heart sound data.
The results show heart sound has non-scaling span and obvious fractal characteristics. Fractal dimension can quantitatively express the complexity of heart sound, and evidently distinguish normal and morbid heart sound. Automatic segmentation algorithm of heart sound based on fractal dimension trajectory is of high accuracy and robust without other signal as reference, and segment results are good.
引文
[1] 王衍文，王海滨，程敬之．心音信号的识别与分类．生物医学工程学杂志，1999，16(3)：382
[2] 何飞燕．心音的分析．中国医学物理学杂志，2004，21(4)：239
[3] 陈剑，郭兴明，肖守中．心音信号识别的意义及其方法的研究．2004，27(2)：87～89
[4] M. Abella, J. Formolo, D. G. Penney. Comparison of the acoustic properties of six popular stethoscopes. J. Acoust. Soc. Am, 1992, 91: 2224～2228
[5] Durand LG, Pibarot P. Digital Signal Processing of the Phonocardiogram: Review of the Most Recent Advancements. Critical Reviews in Biomedical Engineering, 1995, 23(3/4): 163～219
[6] Balster DA, Chan DP, Rowland DG; et al. Digital acoustic analysis of precordial innocent versus ventricular septal defect murmurs in children. Am. J. Cardiol, 1997, 79(11): 1552～1555
[7] J. R. Bulgrin, B. J. Rubal, C. R. Thompson, et al. Comparison of short-time Fourier, wavelet and time-domain analyses of intracardiac sounds. Biomedical Sciences Instrumentation, 1993, 29: 465～472
[8] Donnerstein, R. L. Continuous spectral analysis of heart murmurs for evaluating stenotic cardiac lesions. Am. J. Cardiol, 1989, 64(10): 625～630
[9] Nygaard H, Thuesen L, Hasenkam JM, et al. Assessing the severity of aortic valve stenosis by spectral analysis of cardiac murmurs (spectral vibrocardiography). Part Ⅰ: Technical aspects. Heart Valve Dis, 1993, 2(4): 454～467
[10] Nygaard H, Thuesen L, Terp K, et al. Assessing the severity of aortic valve stenosis by spectral analysis of cardiac murmurs (spectral vibrocardiography). Part Ⅱ: Clinical aspects. Heart Valve Dis. 1993, 2(4): 468～475
[11] Nandagopal, Bogner, Mazumdar. Spectral analysis of second heart sound in normal children by selective linear prediction coding. Medical and biological engineering and computing. 1984, 22: 229～239
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[13] Akey M, Semmlow J L, et al. Noninvasive detection of coronary stenoses before and after angioplasty using eigenvector methods. IEEE Transactions on Biomedical Engineering, 1990, 37(11): 1095～1104
[14] 王海滨，陈欣根．心音信号的特征矢量辨识分析．第四军医大学学报，1993，14(3)：186～188
[15] Burhan Ergen, Yetkin Tatar. The analysis of heart sound based on linear and high order statistical methods. Proceeding of the 23rd Annual IEEE-EMBS, 2001, 2139～2140
[16] B. El. ASIR, L. KHADRA, A. H. Al - ABBASI, et al. Time-frequency Analysis of Heart Sounds. Digital Signal Processing Applications, 1996, 2: 553～558
[17] Sava H, Durand L G. Automatic detection of cardiac cycle based on an adaptive time-frequency analysis of the phonocardiogram. The 19th Annual International Conference of the IEEE-EMBS, 1997: 1316～1319
[18] Liang Huiying, Sakari L, Iiro H. A heart sound segmentation algorithm using wavelet decomposition and reconstruction. The 19th Annual International Conference of the IEEE-EMBS, 1997: 1630～1633
[19] 周静，杨永明．心音信号的时—频分析．重庆大学学报，2004，27(4)：159～162
[20] 于云之，聂邦畿．心音的临床意义及研究现状．现代医学仪器与应用，1997，9(3)：9～12
[21] Voss A, Mix A, Hubner T. Diagnosing Aortic Valve Stenosis by Parameter Extraction of Heart Sound Signals. Annals of Biomedical Engineering, 2005, 33(9): 1167～1174
[22] 李勇，高小榕，郭爱雯．基于连续小波变化的心音信号的时频分析．清华大学学报，2001，41(3)：77～80
[23] 赵玲，李桥，邵庆余，等．正常与异常心音信号比较研究．中国医学物理学杂志，2000，17(3)：154～156
[24] 童基均，汪亚明，李光等．心音的非线性时间序列分析．传感技术学报，2005，3：15～17
[25] 刘毅，张彩明，邵庆余等．基于小波变换的心音信号分析研究．计算机应用研究，2004，5：5～53
[26] M. El-Segaier, O. Lilja, S. Lukkarinen, et al. Computer-Based Detection and Analysis of Heart Sound and Murmur. Annals of Biomedical Engineering, 2005, 3(7): 937～942
[27] Djebbari A, Bereksi Reguig. Short-time Fourier transform analysis of the phonocardiogram signal. The 7th IEEE International Conference on Electronics, Circuits and Systems, 2002, 2: 844～847
[28] 张玉华，邵庆余，朱兴雷等．心音三维分析研究．山东医科大学学报，1999，37(3)：195～198
[29] Ahmd Zuri. The general interference characteristics of the wigner-ville distribution and its effect on time frequency representation of a signal. ICEMSP, 1999
[30] I. Y. Kim, S. M. Lee, H. S. Yeo, et al. Feature extraction for heart sound recognition based on time-frequency analysis. Proceeding of the First joint EMBS/BMES Conference, Atlanta. GA. USA, 1999: 960
[31] Jung Jun Lee, Sang Min Lee, In Young Kim, et al. Comparison between short time Fourier and Wavelet Transform for feature extraction of heart sound. IEEE Transactions on Signal Processing, 1999, 45(9): 1547～1550
[32] 李桥，赵玲，邵庆余等．应用小波变换进行心音三维时频分析的研究．中国医学物理学杂志，2001，48(2)：110～112
[33] 刘毅，李桥，邵庆余等．心音信号小波变换分析研究．山东医科大学学报，2000，38(2)：139～141，143
[34] 全海燕，王威廉．基于小波多分辨率分析的第一第二心音提取．北京生物医学工程，2004，23(1)：64～66
[35] 胡晓，王威廉．基于小波变换心音定位．生物医学工程与临床，2002，6(4)： 181～184
[36] 张建．瞬时频率分析及其在心音信号处理中的应用：[硕士学位论文]．汕头：汕头大学，2000，9
[37] 赵治栋．基于舒张期心音信号分析与特征提取的冠心病无损诊断研究：[博士学位论文]．杭州：浙江大学，2004，5
[38] Lehner R J, Rangayyan R M. Athree-channel microcomputer system for segmentation and characterization of the phonocardiogram. IEEE Trans on Biomedical Engineering, 1987, 34(6): 485～489
[39] Groch MW, Domnanovich JR, Erwin WD. A new heart sounds gating devices for medical Imaging. IEEE Trans on Biomedical Engineering, 1992, 39: 307～310
[40] Gerbarg D S. Analysis of phonocardiogram by a digital computer. Circulation Research, 1962, 11: 569～576
[41] 王文辉，施民．便携式心音分析仪的研制．中国医疗器械杂志，1994，18(1)：9～13
[42] 吴效明，岑人经．心音信号检测的一种新方法．生物医学工程学杂志，1996，13(4)：349～352
[43] 王衍文，王海滨，程敬之．一种基于Choi-Williams分布的心音信号检测方法．声学技术，1998，17(2)：63～68
[44] H. Liang, S. Lukkarinen, I. Hartimo. Heart sound segmentation algorithm based on heart sound envelogram. Computers in Cardiology, 1997, 24: 105～108
[45] T Oskiper, R Watrous. Detection of the First Heart Sound using a Time-delay Neural Network. Computers in Cardiology, 2002, 29: 537～540
[46] Zaiton Sharif, Shaparas Daliman, et al. An expert system approach for classification of heart sounds and murmurs. International Symposium on Signal Processing and its Application(ISSPA), Kuala Lumpur, Malaysia, 2003: 739～742
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[2] 何飞燕．心音的分析．中国医学物理学杂志，2004，21(4)：239
[3] 陈剑，郭兴明，肖守中．心音信号识别的意义及其方法的研究．2004，27(2)：87～89
[4] M. Abella, J. Formolo, D. G. Penney. Comparison of the acoustic properties of six popular stethoscopes. J. Acoust. Soc. Am, 1992, 91: 2224～2228
[5] Durand LG, Pibarot P. Digital Signal Processing of the Phonocardiogram: Review of the Most Recent Advancements. Critical Reviews in Biomedical Engineering, 1995, 23(3/4): 163～219
[6] Balster DA, Chan DP, Rowland DG; et al. Digital acoustic analysis of precordial innocent versus ventricular septal defect murmurs in children. Am. J. Cardiol, 1997, 79(11): 1552～1555
[7] J. R. Bulgrin, B. J. Rubal, C. R. Thompson, et al. Comparison of short-time Fourier, wavelet and time-domain analyses of intracardiac sounds. Biomedical Sciences Instrumentation, 1993, 29: 465～472
[8] Donnerstein, R. L. Continuous spectral analysis of heart murmurs for evaluating stenotic cardiac lesions. Am. J. Cardiol, 1989, 64(10): 625～630
[9] Nygaard H, Thuesen L, Hasenkam JM, et al. Assessing the severity of aortic valve stenosis by spectral analysis of cardiac murmurs (spectral vibrocardiography). Part Ⅰ: Technical aspects. Heart Valve Dis, 1993, 2(4): 454～467
[10] Nygaard H, Thuesen L, Terp K, et al. Assessing the severity of aortic valve stenosis by spectral analysis of cardiac murmurs (spectral vibrocardiography). Part Ⅱ: Clinical aspects. Heart Valve Dis. 1993, 2(4): 468～475
[11] Nandagopal, Bogner, Mazumdar. Spectral analysis of second heart sound in normal children by selective linear prediction coding. Medical and biological engineering and computing. 1984, 22: 229～239
[12] Durand L G., de Guise J, Cloutier G., et al. Evaluation of FFT-based modem parametric methods for the spectral analysis of bioprosthetic valve sounds. IEEE Transactions on Biomedical Engineering, 1986, 33(6): 572～591
[13] Akey M, Semmlow J L, et al. Noninvasive detection of coronary stenoses before and after angioplasty using eigenvector methods. IEEE Transactions on Biomedical Engineering, 1990, 37(11): 1095～1104
[14] 王海滨，陈欣根．心音信号的特征矢量辨识分析．第四军医大学学报，1993，14(3)：186～188
[15] Burhan Ergen, Yetkin Tatar. The analysis of heart sound based on linear and high order statistical methods. Proceeding of the 23rd Annual IEEE-EMBS, 2001, 2139～2140
[16] B. El. ASIR, L. KHADRA, A. H. Al - ABBASI, et al. Time-frequency Analysis of Heart Sounds. Digital Signal Processing Applications, 1996, 2: 553～558
[17] Sava H, Durand L G. Automatic detection of cardiac cycle based on an adaptive time-frequency analysis of the phonocardiogram. The 19th Annual International Conference of the IEEE-EMBS, 1997: 1316～1319
[18] Liang Huiying, Sakari L, Iiro H. A heart sound segmentation algorithm using wavelet decomposition and reconstruction. The 19th Annual International Conference of the IEEE-EMBS, 1997: 1630～1633
[19] 周静，杨永明．心音信号的时—频分析．重庆大学学报，2004，27(4)：159～162
[20] 于云之，聂邦畿．心音的临床意义及研究现状．现代医学仪器与应用，1997，9(3)：9～12
[21] Voss A, Mix A, Hubner T. Diagnosing Aortic Valve Stenosis by Parameter Extraction of Heart Sound Signals. Annals of Biomedical Engineering, 2005, 33(9): 1167～1174
[22] 李勇，高小榕，郭爱雯．基于连续小波变化的心音信号的时频分析．清华大学学报，2001，41(3)：77～80
[23] 赵玲，李桥，邵庆余，等．正常与异常心音信号比较研究．中国医学物理学杂志，2000，17(3)：154～156
[24] 童基均，汪亚明，李光等．心音的非线性时间序列分析．传感技术学报，2005，3：15～17
[25] 刘毅，张彩明，邵庆余等．基于小波变换的心音信号分析研究．计算机应用研究，2004，5：5～53
[26] M. El-Segaier, O. Lilja, S. Lukkarinen, et al. Computer-Based Detection and Analysis of Heart Sound and Murmur. Annals of Biomedical Engineering, 2005, 3(7): 937～942
[27] Djebbari A, Bereksi Reguig. Short-time Fourier transform analysis of the phonocardiogram signal. The 7th IEEE International Conference on Electronics, Circuits and Systems, 2002, 2: 844～847
[28] 张玉华，邵庆余，朱兴雷等．心音三维分析研究．山东医科大学学报，1999，37(3)：195～198
[29] Ahmd Zuri. The general interference characteristics of the wigner-ville distribution and its effect on time frequency representation of a signal. ICEMSP, 1999
[30] I. Y. Kim, S. M. Lee, H. S. Yeo, et al. Feature extraction for heart sound recognition based on time-frequency analysis. Proceeding of the First joint EMBS/BMES Conference, Atlanta. GA. USA, 1999: 960
[31] Jung Jun Lee, Sang Min Lee, In Young Kim, et al. Comparison between short time Fourier and Wavelet Transform for feature extraction of heart sound. IEEE Transactions on Signal Processing, 1999, 45(9): 1547～1550
[32] 李桥，赵玲，邵庆余等．应用小波变换进行心音三维时频分析的研究．中国医学物理学杂志，2001，48(2)：110～112
[33] 刘毅，李桥，邵庆余等．心音信号小波变换分析研究．山东医科大学学报，2000，38(2)：139～141，143
[34] 全海燕，王威廉．基于小波多分辨率分析的第一第二心音提取．北京生物医学工程，2004，23(1)：64～66
[35] 胡晓，王威廉．基于小波变换心音定位．生物医学工程与临床，2002，6(4)： 181～184
[36] 张建．瞬时频率分析及其在心音信号处理中的应用：[硕士学位论文]．汕头：汕头大学，2000，9
[37] 赵治栋．基于舒张期心音信号分析与特征提取的冠心病无损诊断研究：[博士学位论文]．杭州：浙江大学，2004，5
[38] Lehner R J, Rangayyan R M. Athree-channel microcomputer system for segmentation and characterization of the phonocardiogram. IEEE Trans on Biomedical Engineering, 1987, 34(6): 485～489
[39] Groch MW, Domnanovich JR, Erwin WD. A new heart sounds gating devices for medical Imaging. IEEE Trans on Biomedical Engineering, 1992, 39: 307～310
[40] Gerbarg D S. Analysis of phonocardiogram by a digital computer. Circulation Research, 1962, 11: 569～576
[41] 王文辉，施民．便携式心音分析仪的研制．中国医疗器械杂志，1994，18(1)：9～13
[42] 吴效明，岑人经．心音信号检测的一种新方法．生物医学工程学杂志，1996，13(4)：349～352
[43] 王衍文，王海滨，程敬之．一种基于Choi-Williams分布的心音信号检测方法．声学技术，1998，17(2)：63～68
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