改進(jìn)排列熵方法及其在心率變異復(fù)雜度分析中的應(yīng)用_圖文

1、中國(guó)組織工程研究與臨床康復(fù)第14卷第52期 20101224出版Journal of Clinical Rehabilitative Tissue Engineering Research December 24, 2010 Vol.14 No.52 ISSN 1673-8225 CN 21-1539/R CODEN: Z LKHAH 9781 1Key Laboratory of Image Processing & Image Communication of Jiangsu Province, School of Geography and Biomedical Informat

2、ion, Nanjing University of Posts & Telecommunications, Nanjing 210003, Jiangsu Province, China; 2Institute for Biomedical Electronic Engineering, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, Jiangsu Province, ChinaMa Qian-li, Doctor, Masters supervisor, Key L

3、aboratory of Image Processing & Image Communication of Jiangsu Province, School of Geography and Biomedical Information, Nanjing University of Posts & Telecommunications, Nanjing 210003, Jiangsu Province, ChinamaqlCorrespondence to: Bian Chun-hua, Doctor, Associate professor, Masters supervi

4、sor, Institute for Biomedical Electronic Engineering, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, Jiangsu Province, Chinabch Supported by: the National Natural Science Foundation of China, No. 60501003* Received: 2010-09-16 Accepted: 2010-11-11改進(jìn)排列熵方法及其在心率變異復(fù)雜度分

5、析中的應(yīng)用*馬千里1,卞春華2Application of modified permutation entropy in heart rate variability analysisMa Qian-li1, Bian Chun-hua2AbstractBACKGROUND: Heart rate variability (HRV contains important information about regulation of cardiovascular system. Various nonlinear dynamics methods and complexity measure

6、have been used for HRV analysis. Recently-proposed permutation entropy is a new complexity measure, which has been widely used due to its conceptual and computational simplicity. OBJECTIVE: To improve the equal-state processing method of permutation entropy based on the characteristics of HRV using

7、same symbol in the permutation symbolic series to represent the equal-states, and to investigate the value of the modified permutation entropy applied to the analysis of HRV via clinically collected data.METHODS: HRV data were from MIT-BIH Fantasia database and BIDMC Congestive Heart Failure (CHF da

8、tabase on PhysioNet. The databases consisted of three groups, i.e. healthy young, healthy elderly and CHF patients. The data were analyzed using permutation entropy and modified permutation entropy methods. One-way analysis of variance and t-test were utilized for statistical analysis.RESULTS AND CO

9、NCLUSION: Both types of the equal-state processing methods of permutation entropy were failed to effectively distinguish three groups, especially between healthy young and healthy elderly groups. In contrast, the modified permutation entropy was able to distinguish three groups effectively, even whe

10、n applied to short-term heart rate variability data (500 RR intervals, approximately 6-7 minutes. Modified permutation entropy can greatly improve the ability to distinguish the HRV signal under different physiological and pathological conditions. It can characterize the complexity of HRV more effec

11、tively than permutation entropy.Ma QL, Bian CH.Application of modified permutation entropy in heart rate variability analysis.Zhongguo Zuzhi Gongcheng Yanjiu yu Linchuang Kangfu. 2010;14(52: 9781-9785. 摘要背景:心率變異信號(hào)蘊(yùn)含著有關(guān)心血管系統(tǒng)調(diào)節(jié)的重要信息,很多非線性動(dòng)力學(xué)方法和復(fù)雜性測(cè)度已被用于心率變異信號(hào)的分析。排列熵是近年提出的一種新的熵測(cè)度,具有概念簡(jiǎn)單,計(jì)算簡(jiǎn)潔等優(yōu)點(diǎn),在很多領(lǐng)域得到

12、了廣泛的應(yīng)用。目的:針對(duì)心率變異信號(hào)特點(diǎn),對(duì)排列熵方法進(jìn)行等值狀態(tài)處理的改進(jìn),在排列符號(hào)序列中以相同符號(hào)代表等值狀態(tài);通過(guò)臨床數(shù)據(jù)實(shí)驗(yàn),考察改進(jìn)排列熵方法在心率變異性信號(hào)分析中的應(yīng)用價(jià)值。方法:心率變異信號(hào)取自PhysioNet中MIT-BIH Fantasia數(shù)據(jù)庫(kù)和BIDMC Congestive Heart Failure(CHF數(shù)據(jù)庫(kù),分為年輕健康人、老年健康人和充血性心力衰竭患者3組。應(yīng)用排列熵和改進(jìn)排列熵方法對(duì)3組數(shù)據(jù)分別進(jìn)行分析,通過(guò)單因素方差分析和t檢驗(yàn)對(duì)結(jié)果進(jìn)行統(tǒng)計(jì)分析。結(jié)果與結(jié)論:排列熵的兩種等值狀態(tài)處理方法均無(wú)法對(duì)3組數(shù)據(jù)作出有效區(qū)分,尤其是年輕健康人和老年健康人兩組數(shù)據(jù)

13、;而改進(jìn)排列熵方法可以對(duì)3組數(shù)據(jù)作出非常有效的區(qū)分,即使是在短時(shí)的心率變異性分析中(500個(gè)RR間期,67 min。提示改進(jìn)排列熵方法可以有效提高生理、病理心率變異信號(hào)的區(qū)分度,比排列熵方法更有效的表征心率變異信號(hào)的復(fù)雜性。關(guān)鍵詞:心電圖;心率變異性;衰老;充血性心力衰竭;復(fù)雜性;排列熵doi:10.3969/j.issn.1673-8225.2010.52.023馬千里,卞春華.改進(jìn)排列熵方法及其在心率變異復(fù)雜度分析中的應(yīng)用J.中國(guó)組織工程研究與臨床康復(fù),2010, 14(52:9781-9785. 0 引言健康心臟跳動(dòng)的節(jié)律不是平穩(wěn)而是時(shí)刻變化的,受

14、到很多內(nèi)外因素的影響,造成逐次心跳間期之間存在著微小的時(shí)間差異即心率變異,其蘊(yùn)含著有關(guān)心血管系統(tǒng)調(diào)節(jié)的重要信息1。大量研究表明,自主神經(jīng)系統(tǒng)兩支交感神經(jīng)和副交感神經(jīng)與心率變異性之間存在著重要的聯(lián)系:當(dāng)交感神經(jīng)控制增強(qiáng)或副交感神經(jīng)功能受損時(shí),心率變異性降低,易促發(fā)心肌缺血、心功能紊亂等心臟疾病甚至導(dǎo)致死亡2-4。心率還受到諸多其他因素如運(yùn)動(dòng)、呼吸、血壓、體溫及精神緊張的影響而變化,晝夜生物節(jié)律和腎素-血管緊張素系統(tǒng)等因素也參與調(diào)節(jié)5。這些因素使得心率變異序列表現(xiàn)出高度的非平穩(wěn)性和復(fù)雜性。因此,除了常規(guī)的線性分析手段外,很多非線性動(dòng)力學(xué)方法和復(fù)雜性測(cè)度,如李亞普諾夫指數(shù)、關(guān)聯(lián)維、多重分形和熵測(cè)度等

15、也被用于心率變異序列的分析,這些研究對(duì)揭示心率變異和心血管調(diào)節(jié)的潛在規(guī)律和生理本質(zhì)起到了促進(jìn)作用6-16。熵是度量時(shí)間馬千里,等. 改進(jìn)排列熵方法及其在心率變異復(fù)雜度分析中的應(yīng)用 P .O. Box 1200, Shenyang 110004 9782www.CRTER .org1南京郵電大學(xué)地理與生物信息學(xué)院,圖像處理與圖像通信江蘇省重點(diǎn)實(shí)驗(yàn)室,江蘇省南京市 210003;2南京大學(xué)電子科學(xué)與工程學(xué)院,生物醫(yī)學(xué)電子工程研究所,江蘇省南京市 210093馬千里,男,1978年生,安徽省淮南市人,漢族,2006年南京大學(xué)畢業(yè),博士,碩士生導(dǎo)師,主要從事信號(hào)與信息處理研究。maql通訊作者:卞春華

16、,博士,副教授,碩士生導(dǎo)師,南京大學(xué)電子科學(xué)與工程學(xué)院,生物醫(yī)學(xué)電子工程研究所,江蘇省南京市 210093bch中圖分類號(hào):R318文獻(xiàn)標(biāo)識(shí)碼:B文章編號(hào):1673-8225 (201052-09781-04收稿日期:2010-09-16 修回日期:2010-11-11 (20100916014/G ·A=k v v v P P P m H 1ln (1(=m m H H P P 序列復(fù)雜性的一種有效方法,為區(qū)分規(guī)則(周期信號(hào)、隨機(jī)信號(hào)和混沌信號(hào),近20年來(lái)提出了多種熵測(cè)度,以從不同角度量化其復(fù)雜度,并具有一定的抗噪聲、干擾能力,包括Kolmogorov 熵、近似熵、符號(hào)序列熵等6,

17、 16-19。而B(niǎo)andt 等20近年提出的排列熵(permutationentropy ,PE 方法具有概念簡(jiǎn)單,計(jì)算簡(jiǎn)潔等優(yōu)點(diǎn),在很多領(lǐng)域得到了廣泛的應(yīng)用。PE 方法假設(shè)系統(tǒng)輸出值是連續(xù)的,因此忽略序列中兩值相等的情況。假如遇到相等的情況,Bandt 等20提出根據(jù)前后順序確定排列值,或加入隨機(jī)噪聲消除相等的值。這種處理方法在某些系統(tǒng)中是有效的21-25。而在心率變異性分析中,由于心電信號(hào)采樣頻率的限制,得到的RR 間期是離散的,分辨力有限(例如:在 250 Hz 心電采樣率下,RR 間期的分辨力為 4 ms,此時(shí)出現(xiàn)等值的可能性較大。因此,本文提出了改進(jìn)排列熵(modified perm

18、utation entropy ,mPE方法,在排序符號(hào)化過(guò)程中加入對(duì)等值數(shù)據(jù)的處理,將等值的RR 間期以相同的排列符號(hào)值替代。實(shí)驗(yàn)證明,改進(jìn)排列熵方法對(duì)提高心率變異信號(hào)復(fù)雜動(dòng)力學(xué)分析的準(zhǔn)確性是有效的。1 實(shí)驗(yàn)方法1.1 排列熵算法 設(shè)一離散時(shí)間序列為x(i, i = 1, 2, , n,對(duì)其中任意一個(gè)元素x(i進(jìn)行相空間重構(gòu),得到X (i = x (i, x (i+l, , x (i +(m-1l (1式中m 和l 分別為嵌入維數(shù)和延遲時(shí)間。將X(i的m 個(gè)重構(gòu)分量x(i, x(i+l, , x(i+(m-1l按照升序重新進(jìn)行排列,即x (i+(j 1-1l x (i+(j 2-1l x (

19、i+(j m -1l (2如果存在x(i+(j k1-1l = x(i+(j k2-1l,此時(shí)就按j 值的大小來(lái)進(jìn)行排序,也就是當(dāng)j k1 < j k2時(shí),有x(i+(j k1-1l x(i+(j k2-1l。所以,任意一個(gè)向量X(i"都可以得到一組符號(hào)序列A (g = j 1, j 2, , j m (3其中g(shù)=1, 2, , k ,且k m!,m 個(gè)不同的符號(hào)j1, j2, , jm一共有m!種不同的排列,也就是一共有m!種不同的符號(hào)序列。計(jì)算每一種符號(hào)序列出現(xiàn)的概率P 1, P 2, , P k ,此時(shí),時(shí)間序列x(i, i = 1, 2, , n的k 種不同符號(hào)序列的排

20、列熵就可以按照Shannon 信息熵的形式定義為(4當(dāng)P v =1/m!時(shí),H P (m就達(dá)到了最大值ln(m!。可見(jiàn),H P (m值與嵌入維數(shù)m 值有關(guān),為了方便起見(jiàn),通常將H P (m進(jìn)行標(biāo)準(zhǔn)化處理:(5H P 值的大小表示時(shí)間序列x(i, i = 1, 2, , n的隨機(jī)程度:H P 的值越小,說(shuō)明時(shí)間序列越規(guī)則,反之則時(shí)間序列越接近隨機(jī)。 1.2 改進(jìn)排列熵算法 原始的排列熵算法對(duì)于序列中相等值的處理如前文所述是根據(jù)在序列中出現(xiàn)的前后次序賦予不同的符號(hào)。Bandt 等20也提出了另外一種方法,即在原始時(shí)間序列上加入微小噪聲干擾,以消除等值情況。這兩種方法在時(shí)間序列的取值是連續(xù)的,或離散

21、的但分辨力很高的情況下是有效的,因?yàn)闀r(shí)間序列本身出現(xiàn)等值的概率就很小。但在分辨力較低的情況下,等值出現(xiàn)的概率可能較高,或者等值本身就表示了系統(tǒng)的一個(gè)特征狀態(tài),如本文研究的心率變異序列。如果此時(shí)忽略或者人為消除等值的狀態(tài),有可能無(wú)法準(zhǔn)確描述系統(tǒng)的復(fù)雜性。因此,在改進(jìn)排列熵算法中,相等的值將用相同的符號(hào)表示。同前文,對(duì)重構(gòu)分量排序得到x (i+(j1-1l x (i+(j 2-1l x (i+(j m -1l該向量X(i對(duì)應(yīng)的符號(hào)序列一般定義為A(j k =k 。若其中出現(xiàn)等值的情況x(i+(j k1-1l = x(i+(j k2-1l,則使用相同符號(hào)定義,即A(j k1= A(j k2=k1。由

22、此,得到符號(hào)序列A (g = s 1,s 2, , s m 。與排列熵方法構(gòu)造的排列符號(hào)序列不同,該序列中允許出現(xiàn)相同的符號(hào)。其后按照前文馬千里,等. 改進(jìn)排列熵方法及其在心率變異復(fù)雜度分析中的應(yīng)用 ISSN 1673-8225 CN 21-1539/R CODEN: ZLKHAH9783www.CRTER .org方法計(jì)算改進(jìn)排列熵mPE 。2 實(shí)驗(yàn)數(shù)據(jù)本文使用PhysioNet 國(guó)際標(biāo)準(zhǔn)數(shù)據(jù)庫(kù)測(cè)試mPE 分析方法。測(cè)試使用的心率變異信號(hào)取自MIT-BIH Fantasia 數(shù)據(jù)庫(kù)和BIDMC Congestive Heart Failure(CHF數(shù)據(jù)庫(kù)26-28。Fantasia 數(shù)據(jù)庫(kù)

23、中包括40個(gè)健康樣本:20位年輕人(2134歲和20位老年人(6885歲的長(zhǎng)時(shí)心電記錄。所有人在進(jìn)行心電信號(hào)采集時(shí)保持仰臥休息狀態(tài),竇性心率,觀看Fantasia 影片(Disney, 1940出品幫助保持清醒。心電信號(hào)采樣頻率為250 Hz(對(duì)應(yīng)心率變異信號(hào)的分辨力為4 ms,采集時(shí)間為120 min 。數(shù)據(jù)庫(kù)中給出了從連續(xù)心電信號(hào)自動(dòng)檢測(cè)得到的R 波波峰的時(shí)間標(biāo)注,從而獲得心跳間期時(shí)間序列27。BIDMC CHF 數(shù)據(jù)庫(kù)是充血性心力衰竭病理數(shù)據(jù),該數(shù)據(jù)庫(kù)包含來(lái)自15例嚴(yán)重充血性心力衰竭(NYHA34級(jí)患者的長(zhǎng)程心電記錄,其中男性11例(年齡2271歲,女性4例(年齡5463歲。每個(gè)記錄包含

24、大約20 h 的兩導(dǎo)心電信號(hào),采樣頻率為250 Hz 。同時(shí)提供了自動(dòng)檢測(cè)的R 波標(biāo)記,并經(jīng)過(guò)人工修正28。3 實(shí)驗(yàn)結(jié)果首先,使用原始排列熵對(duì)實(shí)驗(yàn)數(shù)據(jù)進(jìn)行了分析。圖1a 為在相等狀態(tài)出現(xiàn)時(shí)根據(jù)出現(xiàn)次序賦以不同符號(hào)的處理方法(記為PE1,可以直觀的看到,這種處理方法對(duì)于病理生理的狀態(tài)完全沒(méi)有區(qū)分。使用增加隨機(jī)噪聲的方法(記為PE2人為去除相等狀態(tài),所加隨機(jī)噪聲為高斯白噪聲,幅度為2 ms ,結(jié)果見(jiàn)圖1b 。PE2方法對(duì)3組數(shù)據(jù)的區(qū)分結(jié)果有所改善,但仍不夠敏感。對(duì)這兩種分析方法的結(jié)果進(jìn)行單因素方差分析(ANOVA,見(jiàn)表1。PE2的ANOVA 分析雖然給出了P < 0.01的結(jié)果,表示3組總體

25、上有顯著區(qū)分,但從圖1b 中可以看出,年輕、年老兩組數(shù)據(jù)并沒(méi)有顯著區(qū)分(t 檢驗(yàn),P > 0.05。使用改進(jìn)排列熵方法對(duì)3組心率變異信號(hào)進(jìn)行分析,結(jié)果見(jiàn)圖2。年輕、年老、CHF 3組數(shù)據(jù)可以得到很好的區(qū)分,并且隨著所分析數(shù)據(jù)長(zhǎng)度的增加,區(qū)分度不斷增大。使用ANOVA 方法對(duì)分析結(jié)果進(jìn)行統(tǒng)計(jì)分析,見(jiàn)表1。與PE1和PE2方法比較,3組數(shù)據(jù)的mPE 分析差異具有顯著性意義。其次,使用不同的嵌入維數(shù)(m=37計(jì)算排列熵與改進(jìn)排列熵,結(jié)果見(jiàn)圖3所示。排列熵在所計(jì)算的嵌入維數(shù)范圍內(nèi)都無(wú)法有效區(qū)分3組數(shù)據(jù)。改進(jìn)排列熵在嵌入維數(shù)m=3時(shí)區(qū)分度最好,隨著嵌入維數(shù)的增加,區(qū)分度降低。ANOVA 分析的結(jié)果

26、見(jiàn)表2。Figure 2 Modified permutation entropy analysis of heart ratevariability data in three groups 圖2 各組數(shù)據(jù)的改進(jìn)排列熵分析1.9 1.7 1.5 1.3m P E500 1 000 2 000 4 000 8 000 NCHF:congestive heart failure馬千里,等. 改進(jìn)排列熵方法及其在心率變異復(fù)雜度分析中的應(yīng)用 P .O. Box 1200, Shenya ng 110004 9784www.CRTER .org4 討論心率變異信號(hào)蘊(yùn)含著有關(guān)心血管系統(tǒng)調(diào)節(jié)的重要信息,很

27、多非線性動(dòng)力學(xué)方法和復(fù)雜性測(cè)度已被用于心率變異信號(hào)的分析。心率變異信號(hào)的復(fù)雜性反映心血管系統(tǒng)的生理、病理狀態(tài),其研究主要基于各種熵測(cè)度。而大多數(shù)的熵測(cè)度在計(jì)算時(shí)均需要人為設(shè)置參數(shù)劃分幅值區(qū)間進(jìn)行符號(hào)化,具有主觀性,并且應(yīng)用于不同樣本,參數(shù)設(shè)置可能會(huì)有差異,給實(shí)際應(yīng)用帶來(lái)一定的難度。排列熵是近年提出的一種新的熵測(cè)度,具有概念簡(jiǎn)單,計(jì)算簡(jiǎn)潔等優(yōu)點(diǎn)。排列熵方法按照幅值大小的排序進(jìn)行符號(hào)化,不需要設(shè)置任何參數(shù),因此具有較好的魯棒性,在很多領(lǐng)域得到了廣泛的應(yīng)用,但國(guó)內(nèi)外目前使用排列熵進(jìn)行心率變異信號(hào)復(fù)雜性的研究還很少29-30。另一方面,國(guó)內(nèi)外各領(lǐng)域目前對(duì)于排列熵的研究與應(yīng)用均假設(shè)等值狀態(tài)出現(xiàn)的概率很小

28、,對(duì)結(jié)果沒(méi)有影響,對(duì)等值狀態(tài)的處理方法即Bandt 提出的根據(jù)前后順序確定排列值,或加入隨機(jī)噪聲消除相等的值兩種方法。但在分析實(shí)際采集的精度較低的離散化數(shù)據(jù)時(shí),等值狀態(tài)出現(xiàn)的概率較大,使用這兩種方法處理等值狀態(tài)可能會(huì)使分析結(jié)果與系統(tǒng)實(shí)際狀態(tài)存在較大偏差。而本文通過(guò)對(duì)來(lái)自于國(guó)際標(biāo)準(zhǔn)數(shù)據(jù)庫(kù)的3組心率變異數(shù)據(jù)的研究分析則證實(shí)了這一問(wèn)題,前述兩種對(duì)等值狀態(tài)的處理方法無(wú)法對(duì)年輕、年老和充血性心力衰竭3種心率變異信號(hào)作出有效區(qū)分,即無(wú)法準(zhǔn)確表征生理、病理狀態(tài)對(duì)心血管調(diào)節(jié)復(fù)雜性的影響。因此本文針對(duì)心率變異信號(hào)特點(diǎn),對(duì)排列熵方法進(jìn)行等值狀態(tài)處理的改進(jìn),在排列符號(hào)序列中增加相同符號(hào)代表等值狀態(tài),提出了改進(jìn)排列熵

29、算法。實(shí)驗(yàn)結(jié)果表明改進(jìn)排列熵可以對(duì)年輕、年老和充血性心力衰竭3種心率變異信號(hào)作出非常有效的區(qū)分,比排列熵方法更有效的表征心率變異信號(hào)的復(fù)雜性。5 參考文獻(xiàn)1Task Force of the European Society of Cardiology and The North American Society of Pacing and Electrophysiology. Heart Rate Variability, Standards of Measurement, Physiological Interpretation,and Clinical Use. Circulation.

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