Mode entropy and dynamical analysis of irregularity for HFECG

ARTICLESChinese Science Bulletin 2004 Vol. 49 No.17 1886- 1890the irregular analysis of the time series of short termphysiology signals, such as heart rate signals, blood pres-Mode entropy and dynamicalsure signals, male sex hormone excretion curve and theanalysis of irregularity forElectroencephalogram!- ; the research reports involvingApEn in the ECG wavy analysis have not been seen so far.HFECGAccording to this work, ApEn cannot be applied to thestudy of irregularity of SBS wave patterns due to its defi-ciency in statistical methodology.XU Yinlin'2, NING Xinbao', CHEN Ying'ApEn describes the production rate of new informa-& WANG Jun'tion, so a frequent appearance of similar wave segments1. State Key Laboratory of Modem Acoustics and Department of Elec-will lead to a reduction in the ApEn value. In a time seriestronic Science and Engineering, Institute for Biomedical ElectronicEngineering, Nanjing University, Nanjing 210093, Chinaof wavy signal, all the continual m data points can form a2. College of Physics Science and Technology. Nanjing Normal Univer-vector with m-dimensions. Statistically speaking, whatsity, Nanjing 210097, ChinaApEn reflects is the conditional probability of seeingCorrespondence should be addressed to Ning Xinbao (0),The ECG with frequency components exceeding 100{0 (z≤0).Hz is called high frequency electrocardiogram (HFECG).In the time field, the high frequency wavelets named(5) The average over i of the natural logarithms of“notches" and“slurs", etc. are presented on the basal SBSC"(r) iswave. The swing of these minor waves is not too big, onlyscores of microvolt, and occupies only 5% of the wholeN-m+1E InC"(r).ECG signal's varying range. Nevertheless they are break-ing points with high frequency components. Many re(6) The ModEn of the series is given assearchesl9 131 found that the amount and shape of theseModEn(m,r,N)=φ"-1-φ" m≥1.(1)wavelets are directly related to the health or disease ofThe ModEn value is obviously related to the assign-heart. In clinical trials, it has been confirmed that thement of m and r. When calculating ApEn, Pincus takes mHFECG can reveal the increments of these small compo-= 2,r= 0.1- -0.2* std in practices (the std is the standardnents of the transmission block of the ventricle's left anddeviation of a time series of N data points, named stdright bundle, myocardial ischemia, myocardial damage(ApEn)), that is equivalent to our taking m = 2, r = .and some other heart diseases. In addition, it is important0.1- -0.2*std in the computation of ModEn (the std is thefor the early stage diagnosis because of the sensitivity ofstandard deviation of increment series of data points,the tiny component to heart disease.The number and the shape of the tiny components innamed std(ModEn)).It can be noticed from the above definition thatHFECG directly affect the irregularity of HFECG In thisModEn (2, r, N) reflects the difference in the time seriesresearch, we used ModEn to achieve a quantitative analy-between the“probability" of the segments (modes) of twosis on this irregularity. In order to simulate the process ofapproximate points and that of the segments (modes) ofmyocardial ischemia, an animal model is designed, usingthree approximate points. It reveals the likelihood of cre-6 rabbits. Separately ligating the branch of left ventricle ofating a new mode, as the vector dimension increases fromcoronary artery of the rabbit hear, we made the rabbits'2 to 3, i.e. it displays the irregularity of the curve. More-hearts lacking blood and crocking up step by step in aover, the mode approximations of vectors in the ModEncomparatively short time. In the experiment, pathologicalcalculation only focus on the shape approximation amongchanges of the rabbit heart will be revealed by analyzingthe vectors but not the absolute value of their elements.the dynamical changes of ModEn of HFECG in each pe-Thereby ModEn is effectively restraining the low fre-riod.quency component by the differential (increment) in prac-1 The definition of ModEn and comparison withtice. This is the maximal diference between ModEn andApEnApEn.The definition of ModEn is similar to that ofFirst we use Logistic Mapping to check up andApEnI214- 16. As for a time series of N+1 points:compare ApEn and ModEn. The Logistic Mapping is{u(i):1≤i≤N+1}.given by the following expression:x+1= Rx(1-x).(1) Construct an increment series with N data points:d(i)=[u(i+1)-u(i)] i=1→N .If parameter R is controlled, the periodic time series(2) Pick up any m data points from the series to makeor the chaos series of different irregularity can be given!4.In the process of acquiring the Logistic time series, wean m-dimension vector:need to cancel the first 500 unsteady transitional serialX(i)=[d(),d(i+ ),.-,.(i+m-1).points, and then calculate the ApEn (m, r, N) and ModEn(3) Define the difference between two such vectors(m, r,N), in which m is 2 and N is 2000. Table lgives thearelated results.Table 1 signifies that when R = 3.5, the logistic se-L[X(), X()]=. max .[d(i+k)-d(j+k)].k=0- m-quence is the time series fluctuating quickly with the pe-(4) Give the tolerance r, count the appearance pro-riod 4, and both the ApEn and ModEn values equal zero;portion of vectors, which are approximate to X(), andTable 1 Comparison between ApEn and ModEn of Logistic Mappingdefine the function C"(r) asR r= 0.2 std (ApEn) ApEn r = 0.2 std (ModEn) ModEn3.50.041900.0828C"(r)=-1 N-+I0(r- L4).3.6020050.08670.4988N-m局3.7中国煤化工D.07570.64973.8YHCNMH G1842-0.08800.8969Here the 0(z) is the Heviside function:3.90.9467Chinese Science Bulletin Vol. 49 No. 17 September 20041887ARTICLESwhen R= 3.6- 3.9, the Logistic sequence is a chaos seriesfew in a short-term. However, algorithm of ModEn iswith increasing irregularity, and both ApEn and ModEnbased on the distance of each data points but not on thevalue increase with R simultaneously. Thus, both algo-absolute value of the data points within a vector. In an-rithms of ApEn and ModEn are able to describe the rela-other word, it just refers to the shape of a vector for thetive complexity of quickly fluctuating series.determination of whether any two vectors in the series areThen, we superimpose the Logistic Mapping seriesapproximate. In this case, there are still many approxi-to the sine wave sequence, which is fluctuating slowly andmate vectors no matter whether the fluctuation of wave isheavily:slow or quick, manifesting a significant statistics.u, = 1000* sin(2ri/1000) + 10* x;(R)2 Experimental results and analysis of MIi=1→2000(3The experimental subjects are 6 purebred rabbits ofIn the above expression, the amplitude proportion ofNew Zealand numbered from No. 1 to No.6, aged aboutthe sine wave to the Logistic Mapping series is basically12 month and weighted from 2.3 to 2.7 kg. First, a drug,the same as that of the ingredient fluctuating slowly to theurethane with 20% density, was injected into veins ontiny component in the HFECG. The increment is:their ears in a dosage of 5 mL/kg. Then, the rabbits' tra-d;=u:+1-M;(4cheas were dissected and conected to a respirator whilethey are anesthetic. Opening the thoracic cavities andDisplayed in Fig. 2 are the superimposition curves ofseparately ligating the branches of left ventricles of coro-formulae (3) and (4). It almost cannot catch the vision fornary arteries of the rabbits' hearts, different degrees of MIthe tiny components superimposing on the sine wave frommodels are completed so as to create different pathologicFig. 2(a), but after dealing with the increment, Fig. 2(b)conditions through the factitious intervention. 12-leadreflects that the slowly varying part of the signal is greatlysynchronous HFECG signals are continuously recordedcompressed and the quickly varying small part is relatively,under each condition. Experimental device was NHE-distinctly boosted up.2000 ECG workstation. The sample frequency ofWe compare algorithms of ApEn with that of ModEnHFECG's data sets was I kHz. Data sets are treated byin the signal u; again. The results indicate that ApEn loseswavelet filtering (the wavelet function is bior6.8) tostatistical stability in a short-term of SBS signals. To illus-remove respiration waves and 50 Hz noises. Data setstrate the short-term astringency of the value of ApEn andwere divided into 3 states in period of time:ModEn, taking N from 2000 to 2900 with interval 100, weState A (a normal one state, just as a contrast inget 10 values of ApEn and ModEn. The averages and theanalysis). The rabbits are anesthetic and sutured as soon asscattered scopes (i.e. standard deviation) of 10 ApEns andthe thoracic cavities were opened. The data was recordedModEns areevery other 1- -2 min. Every recording span lasted for oneApEn =0.2606111.18%minute. State A lasted 10 min.ModEn = 0.8556土0.67%State B. The rabbits' thoracic cavities were openedBy the above two equations, ApEn is dispersive andfor the second time. We ligated the branches in 1/3 under-not convergent in measuring the complexity of such su- side of left ventricles of coronary arteries of their heartsperimposition signal because of the deficiency of the sta-and then sutured the thoracic cavities. HFECG's data setstistical method of ApEn, i.e. ApEn loses statistical stabilitywere recorded when the signals were stable.when signal fluctuating is t0o large and the amount ofState C. The rabbits' thoracic cavities are opened forapproximate vectors with useful tiny components is toothe third time. We ligated the branches in 1/3 upside of left1000a)|(b)15|0500-10-1000-11000 15002000中国煤化工1500MHCNMHGFig.2. The superposing curve of the sine wave and the Logistic Mapping. (a) Absolute value curve: (b) increment value curve.1888Chinese Science Bulletin Vol. 49 No. 17 September 2004ARTICLESventricles of coronary arteries of the their hearts and su-Therefore, all dynamic curves of ModEn rose rapidly andtured the thoracic cavities again. In the same way,obviously, predicting that ModEn is extremely sensitive toHFECG's data sets were recorded.he changes of those tiny components caused by low-In states B and C, HFECG's data sets were recordedgrade ischemia. Thus, the application significance of theevery other 1- -2 min. Both states lasted for 45一60 min.ModEn is shown in the early stage diagnosis of heart dis-Dynamical values of ModEn of 6 rabbits in the threeease.states were computed (Fig. 3).Furthermore, in state B, the growth of ModEn is notIn computing the value of ModEn of all leads'monotonous but circuitous. It implies that the heart keepsHFECG we just picked the 6 chest leads' one nearest tomaking adjustment itself to abate slight myocardialheart because limbs leads had smaller signals to noiseischemia. In physiology, a branch of another coronaryratio, which brought difficulty to our right analysis. Weartery rather than the coronary artery with infarct com-have analyzed all data of 6 rabbits and found somepletely or partially may repay to supply blood for the heart.phenomena as follows:The final values of ModEn of the four rabbits (No. 1, No.In state B, after being ligated, small blog in the car-2, No. 5 and No. 6), who had delicate physical conditionsdiac muscles and small block of transmitting function(dull and not lively), tended to increase after the adjust-bring on the asymmetry of local myocardial structure.ment, while the other two rabbits (No. 3 and No.4), whoThey influence tiny components with high frequency.had stronger physical conditions (lively and active), gen-1.1No. 1No.2State C.9State B0.9pN^内是0.7-0.5 State A0.5-State AN51503050709110 130Time/min0.8.8-No. 3No.40.70.7}0.60.66.5-↓W~M.5十0.4- StateA[StateA0.3+.3L0.2100412016No, 5No.6tmsA90.9-圣0.7|是0.71 State B0.5. LStateA0.33060200中国煤化工160Fig. 3. The dynamic values of ModEn of HFECJMYHCNMHGChinese Science Bulletin Vol. 49 No. 17 September 20041889ARTICLESerally relieved myocardial ischemia catabatic by their re-2. Pincus, s. M.. Approximate entropy as a measure of system com-paying effort. Their ultimate results of ModEn tend to beplexity, Proc. Natl. Acad. Sci. USA, 1991, 88: 2297- 2301.reposeful, even to come bake to the healthy level.3. Pincus, S. M., Approximate entropy (ApEn) as a complexity meas-In state C, the values of ModEn for the rabbits (No. 1,ure, Chaos, 1995, 5: 110-117.No.2, No.3 and No.4), rise up again because of heavy4. Pincus, s. M.. Goldberger, A. L.. Physiological time series analysis:myocardial ischemia caused by the second ligation, re-what does regularity quantify? Am. J. Physiol, 1994, 266: H1643vealing a serious and irreversible lack of blood in rabbits'- H1656.hearts, and the miocardial infarction aggravates, while the5. Pincus, s. M., Mulligan, T. Iranmanesh, A. et al., Older males se-second ligations causes the full putrescence in wide areasxrete luteinizing hormone and testosterone more irregularly, andof the hearts of rabbits (No. 5 and No.6). These bearts arejointly more asynchronously. than younger males, Proc. Natl. Acad.found to be dark red in the later dissection. It indicatesSci. USA, 1996 , 93: 14100- -14105.that the structure of cardiac muscles returns to be in as. Joydeep, B., Complexity analysis of spontaneous EEG, Actabalanced state again. In this case the high frequency com-Neurobiol. Exp.. 2000, 60: 495- 501.ponents of HFECG reduce and make the values of ModEn7. Dante, R. C, Unhealthy surprises, Nature, 2002. 419: 263.decrease sharply.Although rabbits are different from human, the re-8. Madalena, C., Ary, L, Goldberger, A. L. et al, Multiscale entropypaying in the designed experiment using rabbits shouldanalysis of complex physiologic time series, Phys. Rev. Lett. 2002,also appear in human, only taking a longer time. The dy-89: 068102.namic variety of ModEn of rabbits' HFECG in periods in9. Ning, X. B. Shen, Z. Y, Shen, D. C. et al., The data acquisition &the experiment can also reveal the physiological processanalysis of high frequency electrocardiogram (HFECG), J. of Nan-of pathological changes in human. Thereby, it can guidejing Univ.in Chinese), 1991, 27: 273- -284.clinical research on human heart disease, which is just the10. Langner, P. H. Geelowitz, D. B.. Briller, s. A., Wide band re-aim of our experiment.cording of the electrocardiogram and coronary disease, American3 ConclusionsHeart Joumal, 1973, 86: 308.1. Vanderark, C. R.. Reynolds, E. W.. Genesis of high frequencyBoth of the algorithms of ModEn based on incrementnotching of QRS complex in an in virro cardiac model, Circulation,and Pincus’ ApEn can reflect the complexity of the1975, 51: 257--262.quickly fluctuating signals. Thus, they are both adapted to12. Flowers, N. C, Horan, L. G, Tolleson, W. J. et al., Localization ofthe complex research of most short-term physiologicalthe site of myocardial scarring in man by high-frequency compo-series. However as for the SBS signals mixed with usefulnents, Circulation, 1969, 40 927- -934.tiny high-frequency-components, for instance, the HFECGsignal that is closely related to early heart disease, analysis13. Zhu, W. P, Economides, A., Preliminary observation on the genesisof high frequency components of the epicardial ECG in the isolatedof ModEn is more effective than that of ApEn. The resultsof animal experiments reveal that there are obvious dy-rat heart under conditions of graded ischemia, Medical &namical changes of ModEn in the case of MI. The ModEnBiological Engineering & computing, 1991, 29 (Suppl): 986.rises circuitously while the heart is in low-grade myocar-4. Yang. F. s.. Liao, W. C., Approximate Entropy: A complexitydial ischemia. It reflects an altemant influence of patho-measure suitable for short data, Chinese J. of Medical Instrumenta-logical changes and repaying, showing that ModEn is ex-tion (in Chinese), 1997, 21:283- -286.tremely sensitive to the changes in those tiny components15. Hong. B.. Tang, Q. Y. Yang, F s.. ApEn and Cross-ApEn Property,caused by low-grade myocardial ischemia. Therefore,Fast Algorithm and Preliminary Application to the Study of EEGModEn shows its applied significance in the early stageand Cognition, Signal Processing (in Chinese), 1999, 15: 100-diagnosis of heart disease, as well as a practical sense in10the research into myocardial ischemia.16. Wang. Z. Z., Ning, X. B.. Zhang, Y. et al, Distribution of corelaReferencestion dimensions of synchronous 12- lead ECG signals, Chinese Sci.Buletin, 2000, 45: 1628- -1632.1. Eckmann, J. P., Ruelle, D., Ergodic theory of chaos and strange at-tractors, Rev. Moderm Phys., 1985, S7:617- 654.(Received February 5, 2004; accepted April 21, 2004)中国煤化工MHCNMHG1 890Chinese Science Bulletin Vol. 49 No. 17 September 2004