Assessment of cardiac time intervals by wavelet transform of the impedance cardiogram

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1 Technology nd Helth Cre 24 (2016) S803 S809 DOI /THC IOS Press S803 Assessment of crdic time intervls by wvelet trnsform of the impednce crdiogrm Rodion Stepnov,, Sergey Podtev, Andrey Dumler,b nd Sergey Chuginov,b Institute of Continuous Medi Mechnics, Perm, Russi b Deprtment of Introduction into Internl Diseses, Perm Stte Medicl Acdemy, Perm, Russi Abstrct. BACKGROUND: Impednce crdiogrphy (ICG) is n inexpensive, noninvsive technique for estimting hemodynmic prmeters. ICG cn be used to obtin the ejection frction of the left trium nd to monitor systolic time intervls. Trditionl ICG technique does not enble unmbiguous detection of the left ventricle ejection time (LVET) nd the time reltionships between specific mrker points. OBJECTIVE: This work ims to pprobte new pproch for ICG signl processing using wvelet trnsform (WT) nd to investigte the possibilities of this pproch for determintion of the prmeters which re relted to the stroke volume (SV), in prticulr LVET. METHODS: Thorcic tetrpolr polyrheocrdiogrphy method for simultneous registrtion of ECG, ICG nd phonocrdiogrms hs been used. A control group consisted of eight helthy men ged yers. In ddition, four ptients with essentil hypertension prticipted in the study. Wvelet representtion of the ICG dt produced locl mxim in two dimensionl distribution of the wvelet coefficient. Ech extremum point ws chrcterized by the mplitude, scle nd time, which determine SV. RESULTS: LVET ws defined s the scle corresponding to the E-wve mximum relted to the systolic phse of the crdic cycle. Also, we defined the initil systolic time intervl (ISTI) s the time intervl between R pek in the ECG nd E-wve mximum on the wvelet plne. During functionl test LVET nd ISTI vlues defined by WT demonstrted proper hemodynmic response to loding for the control group nd ptients with essentil hypertension. CONCLUSION: The proposed pproch demonstrtes the bility of ICG-WT technique for dequte ssessment of SV prmeters, including crdic time intervls. Keywords: Impednce crdiogrphy, wvelet trnsform, hemodynmic prmeters 1. Introduction Impednce crdiogrphy (ICG) is inexpensive, noninvsive technique for ssessment of hemodynmic prmeters. ICG cn be used to obtin left tril ejection frction nd to monitor systolic time intervls. The principle underlying the rheogrphy method is bsed on chnges in the electricl resistnce of prticulr re of the body to high-frequency lternting current proportionl to blood volume vritions in the re t ny given time point in time. ICG cn be used to obtin one of the key Corresponding uthor: Rodion Stepnov, Institute of Continuous Medi Mechnics, Ak. Korolev str 1, Perm, Russi. Tel.: ; E-mil: rodion@icmm.ru /16/$35.00 c 2016 IOS Press nd the uthors. All rights reserved This rticle is published online with Open Access nd distributed under the terms of the Cretive Commons Attribution Non- Commercil License.

2 S804 R. Stepnov et l. / Assessment of crdic time intervls by wvelet trnsform of the impednce crdiogrm Fig. 1. Chrcteristic ECG, dz/dt nd PCG signls, where B is the strt of ejection of blood by the left ventricle, C is the mjor upwrd deflection occurring during systole, O is relted to the distolic phse, nd X is the closure of the ortic vlve. hemodynmic prmeters: stroke volume (SV). The crdic dysfunctions cn be detected by recognition of different ICG ptterns. This llows one the sustin monitoring of hemodynmic prmeters during screening dignostics or intensive cre. However further crdic evlution is needed. Doppler echocrdiogrphy [1] is procedure tht uses ultrsound technology to exmine the hert or blood vessels, but it demnds considerbly less time nd skills to produce ccurte ssessment. There re severl chrcteristic points which re usully considered to describe the ICG wveform [2]. These points re used to distinguish the physiologicl prticulrities of crdic cycles. Figure 1 shows the so clled B, X, C nd R points, E nd O wves. The points B nd X correspond to the first nd second hert sounds. They re simultneous with the mximl deflection t the pex nd the closure of the ortic vlve, respectively. In some cses the identifiction of the B point loction is difficult. It my hppen tht the chrcteristic upstroke provides mrker of B point which is not sufficiently pronounced [3]. The C point is defined by the pek of dz/dt curve, which reflects the mximl derivtive in the impednce. Ultrsound method mesurements confirm tht the C point my be relted to the mximl velocity of the hert ejection [4]. For ICG the first mximum (i.e. E-wve) is relted to the systolic phse of the crdic cycle, nd the second mximum with smller mplitude (O-wve) is relted to the distolic phse. The mplitude of the E-wve is proportionl to the SV, nd the mplitude of the O-wve correltes to chnge in the volume of the left uricle during short-term distolic phse. In some cses the mplitude of the O-wve proves to be n importnt dignostic prmeter [5,6]. Following the Kubicek formul [7], the stroke volume SV is proportionl to the ejection time nd the mximum vlue of the first derivtive of the recorded impednce Z(t) during the given cycle. The left ventricle ejection time (LVET) is defined s the time intervl of left ventriculr ejection, which occurs between the opening of the ortic vlve nd its subsequent closure. However, s stted in some studies [8], there is evidence tht ICG does not enble the detection of the onset of the ortic

3 R. Stepnov et l. / Assessment of crdic time intervls by wvelet trnsform of the impednce crdiogrm S805 vlve opening nd closing process. Most of the ICG lgorithms for LVET computtion exhibit very low correltion coefficients nd very high systemtic estimtion errors nd dispersions [9]. The objective of this work is demonstrtion of the wvelet trnsform for processing nd interprettion of the impednce crdiogrm wveforms nd n investigtion the possibilities of this pproch to determine the prmeters of the SV, in prticulr LVET. Also we mesured initil systolic time intervl (ISTI) dely between electricl nd mechnicl pumping ctivities of the hert [10]. We note tht ISTI is not prticulrly different from the electro-mechnicl dely. We evluted the ISTI nd LVET depending on the hert rte in response to posturl test. 2. Mesurement nd its processing lgorithm 2.1. Mesuring technique The control group ws composed of eight helthy men ged yers. In ddition, four ptients with essentil hypertension prticipted in the study. We used the method of computer thorcic tetrpolr polyrheocrdiogrphy for simultneous registrtion ECG, ICG nd phonocrdiogrms [11]. During the polyrheocrdiogrm registrtion done for six people (three subjects from the control group nd three ptients) the functionl test (isometric lod) ws performed. Ptients legs were held rised t n ngle of degrees to the horizontl in order to crete sttic force. Another six people pssed the thorcic tetrpolr polyrheocrdiogrphy without the functionl test for comprison nlysis Wvelet trnsform The fundmentl ide of wvelet trnsforms is tht decomposition should be done with bse functions which hve finite resolution in the physicl nd spectrl spces. Hence, the wvelet coefficients represent the locl spectrl chrcteristics of signl. Continuous wvelet trnsform of the nlyzing function S(t) is given by convolution w S (, b) = 1 ( t S(t )ϑ ) b dt, (1) where w S (, b) is the wvelet coefficient of the scle, nd t the position b nd ϑ(t) it is the nlyzing (mother) wvelet. The function S cn be reconstructed using the inverse trnsform (see, e.g. [12]) S(t) = 1 C ϑ ( t t ϑ The reconstruction Eq. (2) exists on condition tht C ϑ = 1 2 ) w S (, t ) ddt 2. (2) ˆϑ(ω) 2 dω <. (3) ω

4 S806 R. Stepnov et l. / Assessment of crdic time intervls by wvelet trnsform of the impednce crdiogrm Fig. 2. 2D distribution of wvelet coefficients (top) nd nlysing signl (bottom). The red/blue colours denote positive/negtine vlues. The white re corresponds to the vlues of wvelet coefficients which re less thn 10% of mximum vlue. The chrcteristic C points re shown by green points. Here, ˆϑ(ω) = ϑ(t)e iωt dt is the Fourier trnsform of the nlyzing wvelet ϑ(t). Let us define the wvelet trnsform of the nlysing function G(t), which is derivtion of the mesuredfunction S(t), s follows w G (, b) = 1 Eqution (4) cn be differentited by prts w G (, b) = 1 ( t G(t )ϑ ) b dt. (4) ( t S(t )ξ ) b dt, (5) where ξ(t) = ϑ (t) is the differentiting wvelet. This mens tht wvelet trnsform of the nlyzing function G(t) cn be obtined s the wvelet trnsform of the mesured signl S(t) using new wvelet fmily ξ(t). The dvntge of the originl wvelet differentition lgorithm [13] is combintion of filtering nd differentiting procedures to process the rheocrdiogrm. We hve chosen the so-clled Mexicn ht ϑ(t) =(1 t 2 )exp( t 2 /2) s the nlyzing wvelet, which provides high resolution in time in order to seprte chrcteristic points (see Fig. 1). However the spectrl resolution is better with the wvelet Morle ϑ(t) =exp( t2 2 +2πit), which is usully used for frequency filtering. 3. Results The wvelet coefficients of the impednce derivtive re shown in Fig. 2 s two dimensionl distribution. This distribution consists of lternted structures which correspond to locl mxim nd minim.

5 R. Stepnov et l. / Assessment of crdic time intervls by wvelet trnsform of the impednce crdiogrm S807 Fig. 3. Chrcteristic vritions of the wvelet coefficient E w (mplitude of E-wve) during the posturl test for helthy prticipnts (red points) nd for the ptient with essentil hypertension (blck squres). The most pronounced mxim (mrked by points) represent E peks in ech crdic cycle. Our method cn be used to define the time moment t E, the scle E nd mplitude w E for ech extremum point (mrket by green point) in the 2D domin. It is considerbly different from the nlysis of n ordinl signl, which dels with the mplitude nd time of the E-pek. The wvelet coefficient mp gives three relevnt prmeters (insted of two) tht re not ffected by the noise nd breth modultion of Z. The interprettion of these prmeters is importnt to be justified. First of ll we consider n mplitude w E. We hve performed n isometric functionl test (legs re lifted t n ngle of degrees to the horizontl) for verifiction conformity w E nd stroke volume. The corresponding hemodynmic responses for two typicl prticipnts re shown in Fig. 3. For the helthy prticipnt (25 yer old mn) the stroke volume increses simultneously with linerly incresing index w E tht chrcterizes the mximl velocity of hert ejection. The mplitude w E restores its norml vlue within few minutes fter the end of the test. This behviour ccomplishes proper hemodynmic response to loding known s n evidence of the Frnk-Strling mechnism. Chnges in the crdic output were not found during the isometric stress for ptients with the essentil hypertension. A typicl vrition in w E is shown Fig. 3 for 55 yer old mn, who ws given the following dignosis: diltion of the left trium nd concentric left ventriculr hypertrophy nd coronry rtery disese. Compenstory mechnisms did not work in this cse becuse no direct dpttion to hemodynmic stress ws observed. Secondly, we check whether the scle w of ech extremum point with mplitude E w chrcterizes n extension of E wve in time. It cn be used for estimtion of LVET. Figure 4() shows tht the wvelet estimte is well correlted with the RR intervls. The correltion coefficient clculted over 163 crdic circles is 0.7 for helthy subjects nd 0.6 for the ptient with hypertension. Another subjects showed similr correltion in rnge between 0.6 nd 0.7. We hve lso compred w with time intervl between the first nd second hert sounds. We hve determined it using the phonogrm recorded simultneously with the impednce crdiogrm. The third prmeter extrcted from the E wve mximum is the initil systolic time intervl. We define the ISTI s the time intervl between the R pek in the electrocrdiogrm nd the time t E of E w for ech crdic circle. ISTI is defined in helthy humns nd the ptient with hypertension t vrious hert rtes.

6 S808 R. Stepnov et l. / Assessment of crdic time intervls by wvelet trnsform of the impednce crdiogrm () (b) Fig. 4. Time nd scle of wvelet E wve mximum for helthy subjects (red) nd the ptient with hypertension (blck): w (LVET estimte) vs RR intervls (), ISTI vs RR intervl (b). Figure 4(b) shows typicl dependence of ISTI on the RR intervls. The bsolute shortening of ISTI for the ptient with hypertension cn be ttributed to compenstory rection nd incresed myocrdil contrctility. Also we hve observed the shortening of the ISTI with incresing hert rte in response to n exercise stimulus in the sme spirit s in [10]. It is interesting tht ISTI hs different slopes for helthy subjects (ISTI 0.14RR) nd the ptient with hypertension (ISTI 0.1RR). Another tests demonstrte more sctter distribution of points thn it is shown in Fig. 4(b). However tking into ccount the errors we hve estimted the slope 0.15 ± 0.1 for helthy subjects nd 0.1 ± 0.3 for the ptient with hypertension. It is worthy of note tht the vribility of prments for ptients studied t rest (no lod) is not enough to obtin dependencies shown in Figs 3 nd Conclusions Our results tht re represented grpficlly cn serve s demonstrtion of the cpbilities of the method proposed. It is obvious tht n dditionl sttisticl dt is necessry for convincing conclusions. However, the proposed pproch demonstrtes tht ICG-WT technologies cn provide dequte ssessment of crdic time intervls, including LVET nd ISTI. Our method cn be used in clinicl prctice for erly dignostics of crdiovsculr system remodelling in the course of different pthologies. It is shown tht the wvelet trnsform is not only s common tool for filtrtion, but it cn lso be used to study the corresponding time-frequency ICG structure defined by wvelet coefficients. Acknowledgment The work ws supported by the Russin Science Foundtion under project References [1] Bour J, Kellett J. Impednce crdiogrphy A rpid nd cost-effective screening tool for crdic disese [Review]. Europen journl of internl medicine. 2008; 19(6):

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