科研費報告書収録論文(課題番号:17206043/研究代表者:金井浩/粘弾性特性に関する断層像の非侵襲的描出による心筋拡張特性の体系的解明

Kanai Hiroshi

English

application/pdf学術論文 (Article)科研費報告書収録論文(課題番号:17206043/研究代表者:金井浩/粘弾性特性に関する断層像の非侵襲的描出による心筋拡張特性の体系的解明)1351444 bytesjournal articl

Kanai, Hiroshi

Tohoku University Repository (TOUR) / 東北大学機関リポジトリ

In Vivo Viscoelasticity Estimation of MyocardiumHiroshi KanaiDepartment of Electronic Engineering, Graduate School of Engineering, Tohoku University,Sendai 980-8579, Japan. Email: hkanai@ecei.tohoku.ac.jpAbstract— Though myocardial viscoelasticity is essential in theevaluation of heart diastolic properties, it has never been non-invasively measured in vivo. By the ultrasonic measurement ofthe myocardial motion, we have already found that some pulsivewaves are spontaneously excited by aortic-valve closure (AVC)at end-systole (T0). In this study, a sparse sector scan at asufficiently high frame rate clearly reveals wave propagation alongthe heart wall. The propagation time of the wave along the heartwall is very small, namely, several milliseconds, and cannot bemeasured by conventional equipment. From the measured phasevelocity, we estimate the myocardial viscoelasticity in vivo. In invivo experiments applied to 6 healthy subjects, 3 patients withhypertrophic cardiomyopathy (HCM), and 3 patients with aorticstenosis (AS), the propagation of the pulsive wave was clearlyvisible in all subjects. For the frequency component up to 90 Hz,the typical propagation speed is about several m/s and rapidlydecreased around the time of AVC. For the healthy subject, thetypical value of elasticity was about 24-30 kPa and did not changearound the time of AVC. The typical transient values of viscositydecreased rapidly from 400 Pa·s to 70 Pa·s around the time ofAVC. The measured shear elasticity and viscosity in this study arecomparable to those obtained for the human tissues using audiofrequency in in vitro experiments reported in the literature. Themethod cannot be easily applied to these patients because therewere inhomogeneities in the phase velocities due to the diseasedmyocardium. By applying the measurement of the phase velocityto each of 5 layers set in the heart wall, the phase velocity in themiddle layer was lower than those in the LV- and RV-sides of theheart wall, which will corresponds to the change in myocardialfiber orientations. This method offers potential for in vivo imagingof the spatial distribution of the passive mechanical propertiesof the myocardium, which cannot be obtained by conventionalechocardiography, CT, or MRI.I. INTRODUCTIONConventional ultrasonography, computer tomography (CT),and magnetic resonant imaging (MRI) enable clinical visu-alization of cross-sectional images of the human heart, buttheir imaging is restricted to large motion (> 1 mm) and lowfrequency components (< 30 Hz). The tissue Doppler imaging(TDI) technique enables determination of motion distributionof the myocardium in real time. Even in current measurement,however, the sampling frequency of the motion of the heartwall is low (at most 200 Hz [1]), that is, the sampling periodis 5 ms, which is too long to detect the propagation time ofthe wave.To measure the original vibrations of the heart sounds,we have already developed a method to transcutaneouslymeasure the heart-wall vibrations as a waveform at one pointor multiple points preset along an ultrasonic beam in the heartwall [2]. We found that there is a steep dip in the pulse whichoccurs exactly at the time of AVC (T0) [3] as shown in Fig.1. This notch has been also measured by the TDI approach todetermine the time of AVC (T0).As shown in the upper figure of Fig. 1, use of the sparsesector scan [3] has allowed us to simultaneously measureheart-wall motion at 160 points at a sufficiently high framerate to measure the propagation of the notch pulse along theinterventricular septum (IVS). From consecutively obtainedspatial distributions of the phase value of the vibration wave,our study [4] has revealed for the first time that the steep dipof the notch pulse propagates along the IVS from the base tothe apex, and its phase velocity is determined. By analyzingvarious frequency components up to 90 Hz, the propagationspeed shows the frequency dispersion.                                                                                                                                                         ventricleaortic valve(open)root of aortic valveleft ventricleapex sideIVS1 cmPCGrightECGbase side716101215111314 numberbeam25619 834LVRVIVSLAUS probe chestAo valveRAAoscanarea0000 200 400 600 1000 1200time from R−wave [ms] 8000.05 m/sdiastolesystoleT0heart soundsecondisovolumicrelaxation periodPCGECG0.05 m/svelocity on RV−side of IVSvelocity on LV−side of IVSFig. 1. upper: A cross-sectional image measured by conventional echocar-diography in a healthy young male (subject A). The upper-right illustrationshows the scanning range of the ultrasonic beams in this imaging. The arrowsshow the directions of the 16 ultrasonic beams used to measure the vibrationsat about 160 points in the heart wall. lower: In vivo measurement resultsfor the healthy man at two points set along the 13th ultrasonic beam. Eachwaveform for six consecutive cardiac cycles is overlaid.This study shows that this dispersion characteristic agreeswith the theoretical one of the Lamb wave which propagatesin the viscoelastic plate immersed in fluid. By introducing the10950-7803-9383-X/05/$20.00 (c) 2005 IEEE 2005 IEEE Ultrasonics SymposiumAuthorized licensed use limited to: TOHOKU UNIVERSITY. Downloaded on February 4, 2009 at 21:42 from IEEE Xplore.  Restrictions apply.single Voigt model into the equation of the Lamb wave andfitting the derived theoretical phase velocity to the measureddispersion, the myocardial viscoelastic properties are deter-mined noninvasively for the first time.+pivibration−pi/2phase60 mmapex side base sidePCG0ECG+pi+pi/235 mmIVSRVphasefittedphase LV−pi0Ao−valveAo−valveAo−valveAo−valveroot ofsubject−Asubject−Bsubject−C subject−Dsubject−Esubject−FFig. 2. Spatial distributions of color-coded phase values for 60-Hz componentof the notch pulse in Fig. 1 for 6 healthy young subjects (A-F). The analyzedtime corresponds to AVC (T0).II. PROPAGATION OF PULSIVE WAVE ALONG HEARTWALLUsing a sparse sector scan in 16 directions, multiple pointswere preset at 770-µm intervals in the heart wall along eachof 16 ultrasonic beams, and the vibrations at about 160 pointswere simultaneously measured as waveforms with a samplingfrequency of 450 Hz by the phased tracking method [3].Since the wavelength of the detected pulsive wave is about100 mm for a 30-Hz component and is comparable to thesize of the whole heart, its propagation phenomenon cannotbe clearly visualized by showing the spatial distribution of theinstantaneous amplitude of the pulsive wave. Therefore, usingthe method in [3], 2-D spatial distribution of the instantaneousphase values of the measured wave is shown in Fig. 2. Forthis imaging, the short-time Fourier transform is applied to thepulsive wave at each point in Fig. 1 after the pulsive wave ismultiplied by the Hanning window with a short length of 35ms. The phase value is detected for each frequency componentfrom 10 Hz to 90 Hz, and then color-coded based on the upper-right circular figure. Figure 2 shows the phase distributionsfor a 60-Hz component along the IVS at a time of AVC (T0)for 6 healthy young subjects. For 3 patients with HCM, and3 patients with AS, the results are shown in Fig. 3.From the consecutively obtained cross-sectional 2-D im-ages, a motion picture is presented. It can be seen that a fewpulsive waves are radiated from the root of aortic valve andpropagate along the IVS. The delay due to the propagation ofthe pulse from the root to the apex is several milliseconds,which has not been recognized at all by any other clinicaltechnique.PCGphase75 mm−pi/2IVS0phase+pi+pi/2fittedphaseECGRVvibration+pi0−piapex side30 mmLVbase sideAo−valveAo−valve(d)(f)(c)(e)(b)(a)Fig. 3. Spatial distributions of color-coded phase values for 40-Hz or 60-Hzcomponents of the notch pulse in Fig. 1 for 3 patients with HCM (a)-(c), and3 patients with AS (d)-(f). The analyzed time corresponds to AVC (T0).III. ESTIMATION OF VISCOELASTICITY USING LAMBWAVE AND VOIGT MODELSTo determine the instantaneous phase velocity of the pulsivewave, if the straight line with a constant gradient k [rad/m]is spatially fit to the instantaneous spatial distribution of themeasured phase in each cross-sectional image in Fig. 2, theinstantaneous phase velocity for the frequency component f0 isdetermined by 2πf0/k. However, since there is initially somespatial distribution of the phase which is independent of thepropagation, the wavelength and thus the wave number k donot correspond to the actual phase velocity.Therefore, in this study, based on the definition of thephase velocity, the distance ∆x between two consecutivelyobtained phase distributions is determined. For this, the phasedistribution θ(x; t) at a time t is compared with the shiftedphase distribution θ(x+∆x; t−∆T ) obtained at a time t−∆T .Regarding the phenomenon of the wave propagation alongthe viscoelastic plate with thickness 2h, there are three kindsof plate wave. In the parasternal longitudinal-axis view, thedirection (−y) of each ultrasonic beam is almost perpendicularto the IVS, and the detected motion is along each beam (y-direction in Fig. 4). The pulsive wave propagates along the IVS(x-direction). The vibrations at the RV-side and those at theLV-side are almost parallel (asymmetric). The wavelength λ isabout 100 mm for the 30-Hz component and 40−65 mm forthe 90-Hz component. The thickness 2h of the IVS is about 1010960-7803-9383-X/05/$20.00 (c) 2005 IEEE 2005 IEEE Ultrasonics SymposiumAuthorized licensed use limited to: TOHOKU UNIVERSITY. Downloaded on February 4, 2009 at 21:42 from IEEE Xplore.  Restrictions apply.mm in healthy adults. Thus, the thickness is sufficiently thin.The separate in vivo experiments show that the longitudinalcomponent with x-displacement also propagates along the IVS(x-direction). The propagation speed of the shear componentis seen to be close to that of the longitudinal component.Thus, there is a likelihood of coupling between the SV-component and the longitudinal component. Given these facts,the detected vibration signal can be modeled by a Lamb wavewith asymmetric mode in Fig. 4.RVLVxIVS−displacementy−displacementbaseapexy=−hyxy=+hzy=0Fig. 4. Lamb wave with asymmetric mode of plate waves in the viscoelasticplate with thickness 2h. The SV-wave component (y-displacement) andlongitudinal component (x-displacement) are coupled, and the Lamb wavethen propagates along the x-direction.For the IVS, the blood in RV and LV should be considered.Thus, the model of the Lamb wave propagating along theviscoelastic plate immersed in blood, is employed in thepresent study. Let us define the wave number of the Lambwave by kL. By referring to [5, Eq. (4.24)], the function,termed f(kL, kp, ks), which should be zero, is given byf(kL, kp, ks) = 4k2Lηβ cosh(ηh) sinh(βh)−(2k2L − k2s )2 sinh(ηh) cosh(βh)−ρbηk4sρmηbcosh(ηh) cosh(βh) = 0, (1)where kp and ks are the wave numbers of the primary waveand the secondary wave, respectively. Using the wave numberkb in blood, η=√k2L − k2p, β=√k2L − k2s , and ηb=√k2L − k2b.ρm and ρb are the myocardium density and the blood density,respectively, and ρm can be approximated by ρb=1.1×103kg/m3. The thickness 2h of the IVS is determined from theB-mode image.By introducing a single Voigt dash-pot model in the fre-quency range up to 90 Hz, the Lame´ elastic constants λ andµ become complex values as λ=λ1+j ωλ2 and µ=µ1+j ωµ2,respectively [6]. Since λ is about 103 times larger than µ forsoft tissue due to non-compressibility [6], kp is approximatedby kb. Since kL is close to ks, η ≈ kL and ηb ≈ kL. Therefore,f(kL, kp, ks) of Eq. (1) is approximated byf ′(cL, µ, ω) = 4k3Lβ cosh(kLh) sinh(βh))−(2k2L − k2s )2 sinh(kLh) cosh(βh)−k4s cosh(kLh) cosh(βh) = 0, (2)where kL=ω/cL(µ, ω) and ks=ω√ρm/µ. Thus, f ′(cL, µ, ω)depends on both the phase velocity cL(µ, ω) of the Lambwave and the Lame´ elastic constant µ=µ1+j ωµ2, that is, theelasticity µ1 and the viscosity µ2 are estimated so that thetheoretical value of the phase velocity cL(µ, ω) of the Lambwave is to be close to the measured the dispersion of the phasevelocity cphase(ω).0 00time from R−wave [ms]TT −8 msLV−side (13th)RV−side (13th)LV−side (9th)RV−side (9th)T +10 msPCG0.05 m/sECG380360IR periodsystole0000340 400012345670 20 40 60 80 100phase velocity [m/s]frequency [Hz]T − 4 msT − 2 msT       msT + 2 msT + 4 msT + 6 msT + 8 msT +10 ms000000000T − 8 msT − 6 ms08Fig. 5. Measured instantaneous phase velocity values {cphase} and fittedtheoretical curves ĉL(µ̂, f) for the frequency components from 10 Hz to 90Hz during the period from T0−8 ms to T0+10 ms in left upper figure.IV. In Vivo EXPERIMENTAL RESULTSFor subject A, by analyzing the period from T0−8 ms toT0+10 ms for each frequency component from 10 Hz to 90Hz, the instantaneous phase velocity cphase(ω) was obtainedas in Fig. 5. There is large dispersion among the instantaneousphase velocities {cphase(ω)}, and they rapidly decrease for allfrequency components in this short period around the time ofAVC (T0).The estimated elasticity µ1 is about 24−30 kPa and does notchange around the time of AVC. The instantaneous viscosityµ2 of the myocardium rapidly decreases from about 400 Pa·sto 70 Pa·s. This would be due to the rapid decrease in theLV inner pressure from about 120 mmHg to several mmHg,which is caused by relaxation of the myocardium.0100200300400500−5 0 5 10subject Asubject Bsubject Csubject Dsubject Eviscosity [Pa s]0time around aortic valve closure (T ) [ms]Fig. 6. Transient of the viscosity parameters {µ2} measured during theperiod from T0−8 ms to T0+10 ms for five healthy young male subjects.For the other four subjects, B−E, the same measurementand analysis were applied, and similar transient characteristicsof the viscosity were obtained as shown in Fig. 6.Using the estimated Lame´ constant µ̂, the phase velocityĉL(µ̂, f) is obtained. The results are shown by the solid linesin Fig. 5 for each time t. The estimates {ĉL(µ̂, f)} well fitthe measured dispersion characteristics cphase(f).10970-7803-9383-X/05/$20.00 (c) 2005 IEEE 2005 IEEE Ultrasonics SymposiumAuthorized licensed use limited to: TOHOKU UNIVERSITY. Downloaded on February 4, 2009 at 21:42 from IEEE Xplore.  Restrictions apply.V. PHASE VELOCITY FOR EACH LAYER OF IVSFor patients with HCM, parallel alignment of muscle cellsbecomes irregular (myocardial disarray). In literature, theanisotropy of the speed of sound and the elastic properties havebeen measured in in vitro experiments. In the actual heart wall,along the radial axis (the thickness direction) of the LV, themyocardial fiber orientation changes gradually. In this study,for subject D, the IVS was divided into 5 layers along theultrasonic beams and for each layer the phase velocity of theLamb wave was determined as shown in Fig. 7. The phasevelocity decreased during the short period just after the AVC(T0). The phase velocity in the middle layer was lower thanthose in the LV-side and RV-side of the heart wall. This resultwill corresponds to the change in myocardial fiber orientations.velocity [m/s]0.01 m/svelocity [m/s]transmural 5 layerstime from AVC [ms]at LV−sidevibrationat RV−sidevibration2nd heart sound−20 0 203403.5−40504100015 20LV−side time from AVC [ms]middle02RV−side234LV−side  middle  2.5t=T0+1.7 mst=T0+15 ms RV−sideFig. 7. The phase velocity of each of 5 layers set in the IVS for healthysubject D.VI. DISCUSSIONThe elastic values and viscosity values obtained in thepresent study are compared with those reported for the my-ocardium and soft tissues in the literature using audio or lowerfrequency components up to 10 kHz as shown in Fig. 8. Exceptfor those of the present study, all data were measured in invitro experiments. Roughly speaking, the elasticity is largefor very low frequency less than 10 Hz and for frequencyhigher than 1 MHz. In [12], the experimental results for pigkidney showed that the elasticity increases with frequency inthe frequency range from 0.01 Hz to 20 Hz. The viscositydata are well fitted to µ2=626.7×f−0.722 [Pa·s], which showsthat the viscosity decreases with the increase in frequency f .By considering the frequency dependency and the freshness ofthe specimen in Fig. 8, the elasticity and viscosity measuredin the present study are close to those measured for the samefrequency range in the literature.VII. CONCLUSIONSWe measured rapid and minute vibrations simultaneously atmultiple points in the IVS. Clear propagation of the pulsivewave along the IVS was recognized. From the dispersioncanine aorta3 old5 young120 mmHg20 mmHg beef muscle [7]human muscle [6](thoracic) [11](thoracic)[10]canine LV [9]12−18hrs after deathcow muscle [13]25hrs after death cow muscle [13]cow muscle [13]5hrs after deathpig kidney [12]bovinemyocardium [8]parallelmyocardium [8]bovineperpendicularhuman aortathis study1elasticity [kPa]frequency [Hz]10000100010010110000100010010626.7           Pa sf −0.722pig kidney [12]5hrs after deathcow muscle [13]20 mmHg120 mmHgparallelbovinemyocardium [8]perpendicularcanine aorta(thoracic) [11]canine LV [9]25hrs after death cow muscle [13]cow muscle [13]12−18hrs after deathbeef muscle [7]human muscle [6]3 old5 younghuman aorta(thoracic)[10]this study1viscosity [Pa s]frequency [Hz]10000100101100001000100010010Fig. 8. The elastic values {µ1} and viscosity values {µ2} reported for themyocardium and soft tissues in the literature using audio or lower frequencycomponents up to 10 kHz.of the phase velocities, the myocardial viscoelasticity wasdetermined noninvasively for the first time. This method offerspotential for in vivo imaging of the spatial distribution ofthe passive mechanical properties of the myocardium andits rapid change during the IR period, which would enabledirect assessment of diastolic properties based on myocardialrelaxation in heart failure.The author is grateful to Prof. Emeritus Motonao Tanakaand Prof. Yoshiro Koiwa of Tohoku University.REFERENCES[1] G. R. Sutherland, et al., J. Am. Soc. Echocardiogr., vol. 17, pp. 788-802,2004.[2] H. Kanai, et al., IEEE Trans. UFFC., vol. 43, pp. 791-810, 1996.[3] H. Kanai and Y. Koiwa, Ultrasound Med. Biol., vol. 27, pp. 481-498,2001.[4] H. Kanai, 2004 IEEE International Ultrason. Sympo. Proc., pp. 482-485,2004.[5] T. Kundo, Ultrasonic Nondestructive Evaluation, New York: CRC Press,2003.[6] H. L. Oestreicher, J. Acoust. Soc. Am., vol. 23, pp. 707-714, 1951.[7] S. Catheline, et al., J. Acoust. Soc. Am., vol. 105, pp. 2941-2950, 1999.[8] P.-K. Choi, et al., The IEICE Trans., vol. J84-A, pp. 1439-1443, 2001.(inJapanese)[9] G. H. Templeton and L. R. Nardizzi, J. Appl. Physiol., vol. 36, pp.123-127, 1974.[10] B. M. Learoyd, M. G. Taylor, Circ. Res., vol. 18, pp. 278-292, 1966.[11] B. S. Gow and M. G. Taylor, Circ. Res. vol. 23, pp. 111-122, 1968.[12] S. Nasseri, et al., Rheol. Acta, vol. 41, pp. 180-192, 2002.[13] E. R. Fitzgerald, et al., J. Acoust. Soc. Am., vol. 29, pp. 61-64, 1957.10980-7803-9383-X/05/$20.00 (c) 2005 IEEE 2005 IEEE Ultrasonics SymposiumAuthorized licensed use limited to: TOHOKU UNIVERSITY. Downloaded on February 4, 2009 at 21:42 from IEEE Xplore.  Restrictions apply.

In vivo viscoelasticity estimation of myocardium

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In vivo viscoelasticity estimation of myocardium

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