Detecting the Fetal Electrocardiogram by Wavelet Theory-Based Methods

Transcription

1 Vol. 7, No. 3, Septemer Detecting the Fetl Electrocrdiogrm y Wvelet Theory-Bsed Methods F. MOCHIMARU, Y. FUJIMOTO Deprtment of Ostetrics nd Gynecology, Hirtsuk City Hospitl, Hirtsuk City, Jpn Y. ISHIKAWA Ishikw Medicl Clinic, Sitm City, Jpn Summry Accurte detection of fetl hert signls during pregnncy hs the potentil to provide specific informtion on possile fetl crdic diseses. By nlyzing stndrd ECG recordings derived from leds plced on the mternl domen, we determined tht fetl signls hve very low power reltive to tht of the mternl ECG, nd they re mixed with severl sources of interference. We took noninvsive fetl electrocrdiogrms from the mternl domen, extrcted the fetl QRS complex, P wve nd T wve from the mternl electrocrdiogrm wveforms, nd identified the fetures of those wveforms. The wveform of the fetl ECG is morphologiclly similr to tht of the dult ECG in the continuous wvelet trnsform, which is method for nlyzing time-dependent signls in oth time nd frequency domins. We showed tht the oserved wveforms were not noise, ut were ctully the fetl ECG. Our high-frequency, high-resolution ECG llows the fetl P wve nd T wve to e monitored. We think this will ecome powerful tool for dignosing nd treting fetl rrhythmis. Key Words Wvelet trnsforms, fetl ECG, wvelet-sed detrending, wvelet-sed denoising, Lipschitz exponents Introduction Just s n electrocrdiogrm is useful in dignosing crdic diseses in children nd dults, the nlysis of the fetl electrocrdiogrm (FECG) could e relile method for dignosing crdic diseses, especilly fetl rrhythmis. During delivery, ccurte recordings cn e mde y plcing n electrode on the fetl sclp. However, during pregnncy other methods should e used due to the inccessiility of the fetus. Idelly, the FECG recorded from the mternl domen is highly desirle, noninvsive method. However, FECG signls hve very low power reltive to tht of the mternl ECG (MECG) due to severl sources of interference. Potentil recordings tken on the mternl domen re ffected not only y lrge seline fluctutions (cused y severl ioelectric phenomen), ut lso y vrious types of noise (intrinsic noise from recorder, noise from electrode-skin contct, etc.). This mkes it difficult to discriminte etween FECG wveforms nd extrneous noise. With lrge seline fluctutions, we used wveletsed multiresolution nlysis (MRA) to exclude those trends. We lso used MRA to remove noise. Furthermore, to prove tht the oserved wveforms were not due to noise ut ctully were FECG wveforms, we used the mthemticl chrcteriztion of singulrities with Lipschitz exponents. While erlier reserchers [1,2] studied only those peks thought to e the fetl QRS complex, not the ctul FECG wveforms, our technique llows ll of the ECG wveforms to e oserved, such s the P wve, QRS complex, nd T wve. Through continuous wveform nlysis (CWT) [1], i.e., nlysis of the

2 186 Vol. 7, No. 3, Septemer 2002 time nd frequency domin, the wveforms thought to e the cquired FECG showed form very similr to tht of dult ECG wveforms. Therey, we hve shown tht the QRS complex under the CWT hs gourd shpe. The min structurl T4 component of the T wve is horizontlly elongted spindle shpe t frequencies less thn the low frequency prt of the QRS complex, forming the se of the gourd shpe. If the T wve is flttened nd lowered, this se will exist directly under the QRS, nd if the T wve is strong, it will e displced fter the QRS complex [3]. Mterils nd Methods Mternl nd Fetl ECG Using the nked eye, it is lmost impossile to recognize the dmixture of the fetl ECG wveform in stndrd ECG leds from tht of pregnnt womn. When performing fetl ECG with the wrist leds plced over the mternl domen on oth sides of the uterine fundus, the mplitude of the mternl QRS complex will e reduced y 90% compred to stndrd led plcement, nd the fetl QRS will e esier to decipher. For the purposes of this pper, we positioned the leds s stted ove. We used high-frequency high-resolution ECG (HFHR-ECG) [3] with smpling rtes from 5 to 20 khz to store the time frmes on computer for further nlysis. The FECG recordings were performed on 27-yer-old womn during the 38 th week of pregnncy. Continuous Wvelet Trnsformtion Wvelet theory is designed to provide good time resolution nd poor frequency resolution t high frequencies, nd good frequency resolution nd poor time resolution t low frequencies. This pproch is useful for ECG signls, i.e., signls, with high frequency components for short durtions, nd low frequency components for long durtions. From one-dimensionl input signl f(t), in this cse the ECG signl, the continuous wvelet trnsformtion is two-dimensionl function of scle prmeter ( ~1/frequency > 0) nd trnsltion prmeter ( = time locliztion t which the signl is nlyzed). There re severl wvelet functions (mother wvelets Ψ(t) with Ψ (t) conjugte complex) ville with different properties. Here, Gor-8 Power wvelets [4] were used s the mternl wvelets for the CWT. Some other methods of wvelet nlysis were used to check the results; the Duechies method [5] ws used for discrete wvelet trnsforms nd the Wickerhuser methods [6] were used for wvelet pcket trnsforms with the est sis lgorithm. All nlyses were performed using "Wvelet Anlysis nd Spectrum Anlysis Softwre: MEM" [7]. Wvelet Trnsform Bsed Detrending For this pper, detrending ccording to the Jensen method [8] ws pplied to dt in which the smples hd lrge seline fluctutions. Therefore, we performed MRA up to the 12 th level of the rw ECG dt using Duechies20 wvelets. The 12 th order pproximtion function (f12) consists of slow vritions nd ws removed from the rw ECG for further dt processing. Wvelet Trnsform Bsed Noise Removl There is no universl method to reduce noise. Becuse ptterns of noise distriution (the proilty distriution function of noise) re different, i.e., Gussin distriution white noise, nd uniform distriution white noise, denoising is lwys trde-off [9]. Our ECG dt with MRA show tht there were severl types of noise. To remove these noises, we pplied wvelet trnsform-sed denoising of the detrended dt y multiresolution nlysis up to the 12 th levels using Coiflet24 wvelets. Denoising ws performed ccording to different criteri. In so clled hrd-thresholding, wvelet coefficients on some or ll scles tht re elow certin threshold re elieved to e noise nd they re set to zero. In so clled soft -thresholding, dditionlly, coefficients on ll coefficients ove this threshold re reduced y the vlue of the threshold. Generlly, we used the hrd thresholding to remove noise, which loclized some levels, nd soft thresholding to remove the noise uniformly.weighted stndrd devitions of the wvelet coefficients t ech resolution level in MRA [7] were used s the thresholds t ech resolution level. For exmple, if the stndrd devition of the wvelet coefficient of level 7 is σ7nd the weighting fctor is s7, the threshold is given y λ7= σ7 s7. We selected weighting fctors which mde the cost of the informtioncost-function (e.g., informtion entropy, Guss- Mrkov entropy, theoreticl dimension [6,7]) s smll

3 Vol. 7, No. 3, Septemer s possile, nd lso mde the coefficient of determintion (squre of the correltion coefficient) s lrge s possile. Lipschitz Exponents We cquired the modulus mxim (locl extrem) [10] from the fst dydic trnsformtion of the denoised ECG signl y using the qudrtic spline wvelet of Mllt [4] nd Crmon et l. [11]. Although only the mxim re determined y this method, since the fetl nd mternl QRS hve opposite orienttions, we lso determined the minim, nd took the verticl direction into considertion. In the following, the Lipschitz exponent is clculted from the decy of the modulus mxim mplitude y the slope of the decy curve less 0.5 [4].Although this method hs poor frequency resolution, it is excellent for detecting frctl structure nd singulrities; singulrity with Lipschitz exponent < 0 is elieved to e relted to noise. However, if there re high-power peks, such s the mternl QRS nd mternl T wve present in the vicinity of the fetl ECG wveform, the fetl wveform will e influenced nd the Lipschitz exponents nd other spects will chnge s well. Thus, the modulus mxim technique is not suited for detecting complex morphologicl chrcteristics. Results Wvelet Trnsform-Bsed Detrending A typicl mternl ECG from the second lim led tht includes the fetl ECG is superimposed on slow vritions (Figure 1), which re removed y pplying multiresolution nlysis (Figure 1). Figure 1. Mternl ECG (modified led II, smpling rte 10 khz) tht includes the fetl ECG (38 th week of pregnncy). The mternl hert rte ws 92 ets/min nd the fetl hert rte ws 143 ets/min. Pnel ) Multiresolution nlysis with Duechies20 wvelet efore detrending. The 12 th order pproximtion function f12 (with fj-1= fj + gj)is thought to consist of slow vritions. Pnel ) The Multi resolution nlysis of the dt fter detrending, i.e., fter removl of f12 from the rw ECG signl. This post-detrending ECG shows no seline fluctutions. Also note tht f12 is essentilly flt.

4 188 Vol. 7, No. 3, Septemer 2002 c Figure 2. Denoising of portion of Figure 1. Pnel ) Multiresolution nlysis with Coiflet24 wvelets. Lrge mounts of noise re seen t level 7 nd elow. We removed this noise y using indices such s the coefficient of determintion nd informtion cost functions, nd used the stndrd devition of the wvelet coefficients for ech level s threshold weighting fctors. We used weighting fctors of 4.0 times the stndrd devition for levels 1 to 3, 2.5 times the stndrd devition for levels 4 nd 5, 2.0 times for level 6, 1.5 times for level 7, nd 0.6 times for level 8 (coefficient of determintion RR 2 = 0.976, informtion entropy = 16.69, theoreticl dimension = 12387). Pnel ) Multiresolution nlysis with Coiflet24 wvelets fter hrd-threshold denoising. The noise t the g7 level is reduced nd wve motion is only visile t the loctions of the mternl nd the fetl QRS complex (informtion entropy =16.28 nd theoreticl dimension = were lower thn efore). Pnel c) Comprison of signls efore nd fter Coiflet24 denoising. The light gry line is the signl efore denoising, nd the thick lck line is the signl fter denoising. Note tht the direction of the fetl QRS complex is opposite tht of the mternl QRS. The hevy line is the post-denoising dt nd the light gry line is the pre-denoising dt. Wvelet Trnsform-Bsed Denoising The ECG wveform is shown in Figures 2,, nd c efore nd fter denoising. The orienttion of the fetl QRS is the opposite of the mternl QRS; this indictes tht when the fetus is in the norml position in the uterus, the orienttion of the fetl hert is opposite tht of the mternl hert. High levels of noise re seen in the dt under the eighth level, nd the dt under the third level is thought to e meningless (no effect is seen in the CWT).

5 Vol. 7, No. 3, Septemer d Figure 3. Lipschitz exponent nlysis of portion of the dt in Figure 1 fter denoising. Fst dydic trnsformtion (pnel ), modulus mxim (pnel ). Anlysis of one mternl nd two fetl QRS complexes (modulus mxim in pnel c nd Lipschitz exponent in pnel d). The slope of the fetl grphs essentilly mtches the mternl chnges from scle 8 to scle 6. Lipschitz exponent of the mternl QRS complex = 0.65 (slope of the curve in pnel d 0.5). c Lipschitz Exponents Figure 3 shows the fst dydic trnsformtion nd the modulus mxim of the denoised ECG. The sections enclosed in roken squres re peks due to the mternl QRS nd the sections enclosed in roken circles re thought to e due to the fetl QRS. The slope of the grphs of the two fetl QRS essentilly mtches the chnges in the mternl QRS from scle -8 to scle -6. However, fter tht point, it is either flt or flling slightly. Noise y definition is loclized nd, thus, singulrity cused y noise does not hve long-term rnge. Consequently, the two smll peks in the ECG of Figure 3c, which hve singulrity similr to the mternl QRS complex, re not noise ut the fetl QRS complexes.

6 190 Vol. 7, No. 3, Septemer 2002 Figure 4. ECG (modified led II) nd continuous wvelet trnsform using Gor 8 Power wvelets. The QRS complex in the mternl ECG wveform hs nrrow, elongted gourd shpe, nd the fetl QRS complex hs nrrow, elongted ter shpe. Fetl ECG The mternl QRS complexes in Figure 4 hve nrrow, elongted gourd shpe. The fetl QRS complexes re shifted to higher frequencies nd hve nrrow, elongted ter shpe. In mximum resolution CWT (Figure 5), the fetl QRS complexes hve gourdshped fetures too nd knots corresponding to the P wve nd the T wve tht cn e seen in the CWT of typicl ECGs [3]. To show the effect of noise, CWT of the rw ECG efore denoising is performed. In Figure 6, fetl P wve nd fetl T wve cn e recognized, s well s the fetl QRS. Since the fetl QRS on the right is close to the mternl QRS t the center of the figure, they influence ech other nd the shpe is deformed reltive to the typicl form [3]. Noise is visile s horizontl frequency nd etween 50 nd 200 Hz. In ddition to contour plot, the CWT is shown s three-dimensionl CWT imge (Figure 6). We cn infer tht the fetl P wve nd fetl T wve cn e seen in the fetl QRS complex t the left of the imge: If it were possi- Figure 5. ECG (dt of Figure 2c fter denoising) nd continuous wvelet trnsform using Gor 8 Power wvelets. The mternl QRS complex nd the min structurl components (T3 nd T4) of the mternl T wve re clerly seen. The second fetl ECG wveform, which is not ffected y the mternl QRS complex, is typicl for continuous wvelet trnsform nd the positions of the fetl P wve nd fetl T wve cn e inferred from the imge. le to remove the noise in the vicinity of the fetl P wve, we might e le to extrpolte even more structurl detils. We performed hrd denoising on the dt from Figure 6. The CWT fter denoising (Figures 7) re quite similr. The positions of the fetl P wve nd fetl T wve cn e inferred from the morphologicl fetures of the CWT [3] of the fetl ECG. By tking the projection of this positions (i.e., y drwing verticl lines in the CWT imge), we cn determine the position of the fetl P wve nd fetl T wve in the rw ECG. Superposition of the Fetl nd Mternl QRS Complexes We investigted techniques for detecting the comintion of the fetl, with the mternl QRS complex. A specil sitution occurs for the fetl QRS complex superimposed y the mternl QRS complex (Figure 8). As result, the q nd s lines tht cn e seen in typicl CWT [3] re not visile, nd the ends re rounded. However, it is not cler whether or not the form of the

7 Vol. 7, No. 3, Septemer Figure 6. Pre-denoising rw ECG (modified led VF) nd continuous wvelet trnsform using Gor 8 Power wvelets. From the contour plot (pnel ), the fetl ECG wveform is typicl ECG wveform fter CWT, nd thus, the positions of the fetl P wve nd fetl T wve cn e inferred [3]. The fetures of the other fetl ECG wveforms re similr. From the three-dimensionl imge, while we cn infer tht the fetl P nd T wve cn e seen in the fetl QRS complex t the left of the imge nd we could hope to extrpolte even more structurl detil ssuming we were le to remove the noise close to the fetl P wve. Figure 7. Post-denoising ECG (modified led VF) nd continuous wvelet trnsform using Gor 8 Power wvelets shown s contour plot (pnel ) nd three-dimensionl imge (pnel ). Compred to the pre-denoising dt (Figure 6), the noise in the rnge shown y the rrows t the ends of the grph hs een lrgely removed. We used indices such s the coefficient of determintion nd informtion cost functions, nd used the stndrd devition of the wvelet coefficients for ech level s threshold weighting fctor (coefficient of determintion RR 2 = 0.964, informtion entropy = 1.46, theoreticl dimension = 867, nd Guss- Mrkov entropy = ).

8 192 Vol. 7, No. 3, Septemer 2002 mternl QRS complex hs een chnged y the overlpping fetl QRS complex. Therefore, we studied the chnges in the form of the mternl QRS complex under multiresolution nlysis with Coiflet24 wvelets ccording to whether or not n dded fetl QRS complex is present (Figure 8). The section elieved to e superposed y the fetl QRS complex hs lrge wve motion, which is not seen in the section without superposed fetl QRS complex. If we consider this in conjunction with the fct tht fetl QRS wve motion ppers in the vicinity of g7, g8, nd f8, this cn e seen s proof of the superimposition of the fetl QRS complex on the mternl QRS complex. Similr phenomen were oserved using Duechies20 nd Spline24 wvelets s well. Figure 8. Pre-denoising ECG (modified led II) which includes the mternl QRS complex ( ), fetl QRS complex ( ), nd mternl QRS complex ( ) superimposed with fetl QRS complex (?). Pnel ) Continuous wvelet trnsform using Gor 8 Power wvelets. As result of the superposition of the fetl nd mternl QRS complex, the q nd s lines (high frequency prts of the mternl QRS complex) tht cn e seen in typicl CWT exmple re not visile, nd the ends re rounded. Pnel ) Multi resolution nlysis using Coiflet24 wvelets up to mximum resolution level of 8. The superposition of the fetl nd mternl QRS complex on the g7 level ( ) shows lrge wve motion unlike the mternl QRS complex without superimposed fetl QRS complex ( ). Discussion In order to fully exhiit its cpilities, high-frequency smpling is necessry to provide wvelet trnsform; this hs een descried s mthemticl microscope for the nturl sciences. The smpling frequency used in conventionl ECGs is 250 Hz (which is close to resolution of 1 Byte/s = 2 8 /s = 256 /s ). If orthonorml wvelets re used nd we ssume tht we will use numer of wvelet coefficients up to the numer tht hs mening for multiresolution nlysis, then we cn only perform nlysis up to 8 levels for Hr wvelets nd up to 4 levels for Duechies 20 wvelets. Khmene et l. [2] cquired fetl ECGs t 500 Hz from the mternl domen, nd performed wvelet nlyses using the modulus mxim. However, even if the modulus mxim (the qudrtic spline wvelets) re used, this is not n dequte smpling frequency to extrct the singulr points or to clculte the Lipschitz exponent, which expresses the chrcteristics of the singulr points. Mllt [4] strts the Lipschitz exponent clcultion from scle 3, where distortion in the verticl direction ecomes smller. Therefore, t 500 Hz the mximum scle tht cn e used for the clcultion is 5 nd no one cn gurntee tht the locl mxim of the fetl nd mternl QRS complexes remin within the rnge of these scles. In the Khmene et l. [2] pper, the nlysis with the modulus mxim ws limited to scle 5, nd they did not ctully clculte the Lipschitz exponent. Furthermore, to perform multiresolution nlysis for mny wvelets, meningful nlyses t 500 Hz re limited to 4 levels, or t the most 5 levels, due to the numer of wvelet coefficients. It

9 Vol. 7, No. 3, Septemer is difficult to fully extrct the informtion nd chrcteristics from fetl ECG in n nlyses which uses these insufficient scles (smpling rte t 500 Hz). Actully, their nlysis does not identify the FECG P wve nd T wve; it even hs prolems in discriminting the FECG-QRS complex from noise. In our experience, the FECG-QRS will e oscured in the QRS of the MECG two or three times in 10 seconds period, nd it is difficult to extrct the fetl QRS oscured in the mternl QRS with the modulus mxim or fst dydic wvelet trnsformtion. To demonstrte tht the cquired ECG wveform includes the FECG wveforms nd tht those signls re not noise ut re the FECG P wve, QRS complex nd T wve, we performed the following functions. We clculted the Lipschitz exponent, nlyzed the morphologicl fetures of the FECG using the continuous wvelet trnsform, nd performed wvelet pcket nlysis using est sis lgorithm with informtion entropy s the cost. Conclusion Anlysis of the FECG could e relile method for dignosing crdic diseses, especilly fetl rrhythmis. The HFHR-ECG cn e noninvsively recorded from the mternl domen nd llows the fetl P wve, QRS complex nd T wve to e monitored. We elieve tht it will ecome powerful tool for dignosis nd tretment of fetl rrhythmis. Acknowledgment We thnk Professor Emeritus Motokzu Hori for his thoughtful review nd his comments. References [1] Kntz H, Schreier T. Nonliner time series nlysis. Cmridge: Cmridge University Press, 1997: [2] Khmene A, Neghdripour S. A new method for the extrction of fetl ECG from the composite dominl signl. IEEE Trns Biomed Eng. 2000; 47: [3] Ishikw Y, Mochimru F. Wvelet theory-sed nlysis of high-frequency, high-resolution electrocrdiogrms: new concept for clinicl uses. Prog Biomed Res. 2002; 7: [4] Mllt S. Wvelet Tour of Signl Processing, 2 nd edition. Sn Diego: Acdemic Press. 1998: , [5] Duechies I. Ten Lectures on Wvelets. Phildelphi: SIAM Press. 1992: 195. [6] Wickerhuser MV. Adpted Wvelet Anlysis from Theory to Softwre. Ntick: AK Peters. 1994: [7] Ishikw Y. Wvelet Anlysis for Clinicl Medicine (in Jpnese) with MEM Softwre on CD-ROM. Tokyo: Medicl Puliction (IGAKU-SHUPPAN). 2000: , [8] Jensen A, L Cour-Hro A. Ripples in Mthemtics. Berlin: Springer. 2000: [9] Jnsen M. Noise Reduction y Wvelet Thresholding. New York: Springer. 2000: [10] D Fontour Cost F, Cesr RM Jr. Shpe Anlysis nd Clssifiction. New York: CRC Press. 2000: [11] Crmon R, Hwng W-L, Torresni B, et l. Prcticl Time- Frequency Anlysis. Gor nd Wvelet Trnsforms with n Implementtion in S (Wvelet Anlysis nd its Applictions, Volume 9). Sn Diego: Acdemic Press. 1998: Contct Fumio Mochimru, MD Deprtment of Ostetrics nd Gynecology Hirtsuk City Hospitl Minmihr, Hirtsuk City, Kngw Jpn Telephone: Fx: E-mil: KmMF2169@ol.com