Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268

Detection of harmonic ultrasound scattered frommicrobubbles with ultrasound transducer for harmonic

imaging having double peak type frequency characteristics

Shinichi Takeuchi, Toshio Sato, Shiro Wakui, Norimichi Kawashima *Biomedical Engineering Department, Faculty of Engineering, Biomedical Engineering Center, Toin Uni�ersity of Yokohama,

1614 Kurogane-cho, Aoba-Ku, Yokohama 225-8502, Japan

Received 28 September 2001; accepted 12 November 2001

Abstract

Ultrasound transducer with double peak type frequency characteristics was proposed for contrast harmonicimaging. It can transmit ultrasound in a fundamental mode and receive the second harmonic signal from tissues ormicrobubble contrast agents. The transducer has been made by stacking a piezoelectric ceramic vibrator and asubvibrating plate on the backing block made of ferrite rubber with an acoustic absorption. Glass subvibrating plate(0.4 mm thick) was found suitable for this ultrasound transducer. The second harmonic component contained in thescattered waves from microbubbles coated with surfactant was detected experimentally with a trial manufacturedultrasound transducer with double peak type frequency characteristics. The results confirmed that the transducer cantransmit ultrasound to microbubbles, excite the second harmonic component based on the nonlinear behavior ofmicrobubbles and detect the second harmonic component. It was also found that the second harmonic componentcan be detected most effectively when burst waves with cycles from 5 to 10 were applied to the ultrasound transducer.© 2002 Elsevier Science B.V. All rights reserved.

Keywords: Contrast harmonic imaging; Ultrasound transducer; Double peak type frequency characteristics; Microbubbles; Secondharmonic component

www.elsevier.com/locate/colsurfb

1. Introduction

Recent reports have dealt with new ultrasoundimaging methods and blood flow measuring meth-ods using harmonic components based on thenonlinear behavior of microbubbles [1–3]. Thesetechniques are regarded as contrast harmonic

imaging methods. Stronger harmonic componentsare radiated from microbubbles than those fromthe surrounding blood or the surrounding tissue.It is then useful for observation of vascular sys-tems or perfusion [4] of microbubbles to makeultrasound diagnostic images using these contrastharmonic imaging system.

A new ultrasound transducer with double peaktype frequency characteristics suitable for the con-trast harmonic imaging system was developed in

* Corresponding author. Tel./fax: +81-45-974-5607.E-mail address: kawasima@cc.toin.ac.jp (N. Kawashima).

0927-7765/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.

PII: S 0927 -7765 (01 )00325 -3

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268258

this study. While the conventional ultrasoundtransducers have a sensitivity at a fundamentalfrequency and at frequencies odd times the funda-mental frequency, they show no sensitivity atfrequencies even times the fundamental frequency.Thus, it is difficult for the conventional ultra-sound transducers to detect the second harmoniccomponents at frequency twice the fundamentalfrequency. On the contrary, the proposed ultra-sound transducer with double peak type fre-quency characteristics has a structure in which asubvibrating plate is stacked on a piezoelectricceramic vibrator, and it can transmit ultrasoundto microbubbles and can receive the second har-monic components from microbubbles with a sin-gle transducer simultaneously. The ultrasoundtransducer with a glass subvibrating plate with athickness of 0.42 mm on the PZT vibrator with athickness of 0.31 mm was proposed and trialmanufactured based on a design with numericalcalculations. The second harmonic componentcontained in the scattered waves from microbub-bles coated with surfactant was detected experi-mentally with the trial manufactured ultrasoundtransducer. As a result, it was confirmed that thetransducer can transmit ultrasound to the mi-crobubbles, excite the second harmonic compo-nent based on the nonlinear behavior of themicrobubbles and detect the second harmoniccomponent.

Microbubbles coated with surfactants ofsodium stearate, sodium palmitate, saponine, etc.were used in this study. The diameter of mi-crobubbles was in the range of 0.7–6 �m with theaverage diameter of 1.63 �m and the size for mostbubbles of 0.87 �m. The shell elasticity parameter,Sp, of microbubbles was estimated to be 3.0 N/mand their shell friction parameter, Sf, was esti-mated to be 0.07 �N s/m [5,6]. These parametersare important to understand the acoustic behaviorof microbubbles.

When the voltage applied to the trial manufac-tured ultrasound transducer was changed, the ra-tio of second harmonic level to fundamental levelincreased with increase of applied voltage ranging70–100 V. However, the increasing tendency inthe ratio diminished above 100 V of appliedvoltage. It was also found that the second har-

monic component can be detected most effectivelyin the range of 5–10 cycles of applied tone bursts.

2. Experimental

2.1. Microbubbles

Most of microbubbles used as ultrasound con-trast agents are coated with membrane to keepthe lifetime long. The microbubbles used in thisstudy are also coated with surfactant membraneto keep their lifetime long. These microbubbleswere prepared by mixing sodium stearate solutioncontaining 30 wt% sodium palmitate with saponinsolution and then adding a 10 wt% solution ofcalcium chloride solution to the mixture afterfiltering to adjust the size distribution of mi-crobubbles. The size distribution of microbubblesand the frequency characteristics of ultrasoundattenuation in the microbubble dispersion aremeasured to estimate the properties of microbub-bles. The size (diameter) distribution of microbub-bles is measured by Coulter multisizer. Themeasuring system of the frequency characteristicsof ultrasound attenuation in the microbubble dis-persion is shown in Fig. 1. The microbubbledispersion container is inserted between the trans-mitting and receiving ultrasound probes in de-

Fig. 1. Measurement system of the frequency characteristics ofultrasound attenuation in the microbubble dispersion.

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268 259

gassed water for measurement. Ultrasound pulseradiates from the ultrasound probe, propagatesthrough sample dispersion of microbubbles andreceived by the receiving ultrasound probe, re-ceiver and oscilloscope. The frequency character-istics of attenuation constant were calculated fromthe received data.

The property of microbubbles with shell is ef-fected by their shell parameters. The shell parame-ters can be estimated by the curve fitting methodbetween the simulated frequency characteristics ofattenuation constant obtained by numerical calcu-lations and the measured frequency characteristicsof attenuation constant, because the attenuationconstant is a function of the shell parameters Sp

and Sf. The shell parameters describing the me-chanical properties of surfactant coated mi-crobubbles were estimated concerning with thismeasured size distribution. The shell elasticityparameter, Sp, is expressed by Eq. (1) and theshell friction parameter, Sf, is expressed by Eq.(2). Furthermore, the attenuation constant of ul-trasound propagation in microbubble dispersionis expressed by Eq. (3).

The shell elasticity parameter, Sp, is expressedby Eq. (1) with Young’s modulus E, Poisson’sratio, �, and the thickness of membrane, t [7].

Sp=Et

1−�(1)

The shell friction parameter, Sf, is expressed byEq. (2) with the effective mass of bubbles, m,(=4�r3), the damping constant by friction inmembrane, �f, and the angular frequency of illu-minating ultrasound, �, [8].

Sf=�fm� (2)

Furthermore, the attenuation constant of ultra-sound propagation in microbubble dispersion isexpressed by Eq. (3) [9,10].

�=4.34��

0

�en(r) dr fRC2 = fR

2 +2Sp

m�

�e=4�r2(�/kr)

[( fR/f )2−1]2+�2

�=�r+�t+�v+Sf

2�fm(3)

Fig. 2. Basic structure of the ultrasound transducer withdouble peak type frequency characteristics for harmonic imag-ing.

where � is the attenuation constant, �e is theextinction cross section, r is the radius of mi-crobubble, fR is the resonant frequency of freebubble with radius r, fRC is the resonant frequencyof a bubble of radius r with coated membrane, f isthe measuring frequency, k is the wave number, mis the effective mass, � is the total damping con-stant, �r is the damping constant based on theacoustic radiation, �t is the damping constantbased on the thermal conduction, �v is the damp-ing constant based on shear viscosity and n(r) isthe size distribution of bubbles.

2.2. Ultrasound transducer with double peak typefrequency characteristics

An ultrasound transducer with double peaktype frequency characteristics for harmonic imag-ing is proposed and developed to transmit theultrasound into microbubbles in human body andto detect the second harmonic components con-tained in the scattered waves from microbubbles.The basic structure of the ultrasound transducer isdescribed in this section. The transducer has astructure shown in Fig. 2 in which a subvibratingplate is placed on a PZT vibrator adhered on aferrite rubber backing.

Since the acoustic impedance of piezoelectricceramic vibrator is larger than that of the back-ing, the subvibrating plate and acoustic load, the

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268260

piezoelectric ceramic vibrator resonates at �/2resonance mode. On the other hand, since theacoustic impedance of the subvibrating plate issmaller than that of the piezoelectric ceramic vi-brator and larger than that of the acoustic load,the subvibrating plate resonates at �/4 resonancemode. When the �/2 resonance frequency of thepiezoelectric ceramic vibrator is different from the�/4 resonance frequency of the subvibrating plate,double peaks are seen in the frequency character-istics of transfer function or transmitting andreceiving sensitivities. The peak on the lower fre-quency side of the double peaks is used to trans-mit ultrasound to microbubbles and excite thesecond harmonic component, whereas the peakon the higher frequency side is used to receive thesecond harmonic component. The thicknesses ofpiezoelectric ceramic vibrator and the subvibrat-ing plate were then determined as follows:

Thickness of the piezoelectric ceramic vibrator

=12×

Sound speed of the piezoelectric ceramic vibratorFrequency of the second harmonic component

(4)

Thickness of the subvibrating plate

=14×

Sound speed of the subvibrating plateFrequency of the fundamental component

(5)

The proposed ultrasound transducer is detaildesigned with numerical calculation by the equiv-alent circuit approach. The proposed transducer isexpressed by a four terminals F parameters matrixwith Mason’ s equivalent circuit [11] for piezoelec-tric ceramic vibrator shown in Fig. 3 and theequivalent circuit for subvibrating circuit shownin Fig. 4. Furthermore, the frequency characteris-tics of transmitting and receiving sensitivities arecalculated referring to the transfer function bySittig [12,13]. The effects are examined of thethickness of piezoelectric ceramic vibrator, acous-tic impedance and the thickness of subvibratingplate, output impedance of transmitting circuit,and input impedance of receiving circuit on thetransmitting and receiving sensitivities and the

Fig. 3. Mason’s equivalent circuit of thickness mode piezoelec-tric vibrator.

desirable structure of the proposed ultrasoundtransducer is considered.

When the backing of acoustic impedance ZB isconnected between one pair of acoustic terminalsin Mason’s equivalent circuit of piezoelectric ce-ramic vibrator, the four terminals F parametersmatrix between the other pair of acoustic termi-nals and the pair of electric terminal in Mason’sequivalent circuit is expressed by Eq. (6). Further-more, the equivalent circuit of subvibrating plateis also expressed by Eq. (7) with the one-dimen-sional transmission line model.

Fig. 4. Equivalent circuit for the subvibrating plate of ultra-sound transducer with double peak type frequency characteris-tics with one-dimensional transmission line.

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Fig. 5. Equivalent circuit with F parameter matrix of the ultrasound transducer with double peak type frequency characteristics.

�A0 B0

C0 D0

n=

1�Q

�1 j�2/�C0

j�C0 0n

�cos �+ jzb sin � Z0(zb cos �+ j sin �

j sin �/Z0 2(cos �−1)+ jzb sin �

n(6)

where Q=cos �−1+ jzb sin �, zb=ZB/Zo

�As Bs

Cs Ds

n=�cos �s jZs sin �s

j sin �s/Zs cos �s

n(7)

The F parameter matrix of two pairs of portsequivalent circuit for the proposed ultrasoundtransducer with double peak type frequency char-acteristics is described by cascading the F parame-ter matrices of two pairs of port equivalent circuitsfor piezoelectric ceramic vibrator, subvibratingplate and adhesive layer and so on. The equivalentcircuit of ultrasound transmitting and receivingsystem with this proposed ultrasound transducer isshown in Fig. 5. The transmitting circuit is ex-pressed by Thevenin’s equivalent circuit consistingof a constant voltage source, Vs, and internalimpedance, Zs, and the receiving circuit is expressedby load impedance, Zl. The transfer function of thissystem F(t) can be expressed by Eq. (8) [12].Furthermore, the frequency characteristics oftransmitting sensitivity, T( f ), (electric to acoustic)and the frequency characteristics of receiving sensi-

tivity, R( f ), (acoustic to electric) are expressed byEqs. (9) and (10), respectively. Parameters A, B, C,and D in the transfer function, F( f ), of Eq. (8), inthe transmitting sensitivity, T( f ), of Eq. (9) and inthe receiving sensitivity, R( f ), of Eq. (10) mean theelements of cascaded F parameters of piezoelectricceramic vibrator, subvibrating plate, etc.

F( f )

=2ZmZl

[AZm+B+Zs(CZm+D)][AZm+B+Zl(CZm+D)] (8)

T( f )=Zm

Zs(CZm+D)+AZm+B(9)

R( f )=2Zl

Zl(CZm+D)+AZm+B(10)

2.3. Detection of harmonic components generatedin water with proposed ultrasound transducer

When ultrasound propagates in water, the sec-ond harmonic components are generated in waterwithout microbubbles. The second harmonic com-ponents generated in water affect the estimation ofthe second harmonic components from microbub-bles. The detection of second harmonic compo-nents generated in water with the ultrasoundtransducer was conducted before the detection ofsecond harmonic components from microbubbles.

Measuring system of received spectrum by needletype hydrophone as receiver and trail manufac-tured ultrasound transducer as transmitter to esti-mate the ultrasound transmission performance ofthe trial manufactured ultrasound transducer is

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268262

shown in Fig. 6. The ultrasound transducer withdouble peak type frequency characteristics wasused for imaging of diagnostic image with onlyhigher harmonic components based on the nonlin-ear behavior of tissues and microbubble contrastagents. A tone burst wave was then applied to thetrial manufactured ultrasound transducer. Toneburst wave can be defined in a required frequencyrange so that no harmonic components are con-tained in the wave transmitted from the ultra-sound transducer. The tone burst wave with tencycles, a pulse repetition frequency of 1 kHz andan amplitude of 500 mV from the signal generatorwas amplified by the power amplifier with a gainof 50 dB and applied to the trial manufacturedultrasound transducer.

The experimental system to estimate the secondharmonic component detection performance ofthe trial manufactured transducer is shown in Fig.7. The ultrasound pulse radiated from the trialmanufactured ultrasound transducer was reflectedfrom a brass cubic block with 50 mm sides andthe reflected ultrasound was received with thesame trial manufactured ultrasound transducer inwater. The distance between the trial manufac-tured ultrasound transducer and the reflectingface of the brass cubic block was 100 mm. Thereceived spectrum is calculated from measuredultrasound waves by Fast Fourier Transform(FFT). The ultrasound propagation distance inthis experiment is twice the distance in the experi-ment in Fig. 6.

Fig. 7. Measurement system of reflected spectrum from brasscubic block reflector illuminated with ultrasound by the trialmanufactured ultrasound transducer with double peak typefrequency characteristics (distance between the trial manufac-tured ultrasound transducer and the brass reflector: 100 mm).

2.4. Detection of harmonic components scatteredfrom microbubbles with proposed ultrasoundtransducer

The transfer function of the trial manufacturedultrasound transducer should have the doublepeak type frequency characteristics with peaks atabout 3.5 and 7 MHz. The peak at 3.5 MHz isused for transmission of ultrasound to microbub-bles and that at 7 MHz is used for detection ofthe second harmonic components contained in thescattered wave from microbubbles. These func-tions of trial manufactured transducers are confi-rmed experimentally. The measuring system usedin this experiment is shown in Fig. 8. The toneburst wave with the center frequency of 3.5 MHzwas applied to the trial manufactured ultrasoundtransducer using a function generator and apower amplifier with a gain of 50 dB and thetransducer radiated on ultrasound pulse to mi-crobubbles. The waves scattered from microbub-bles were received with the trial manufacturedultrasound transducer used as receiver and thesecond harmonic components were extracted. Thetrial manufactured ultrasound transducers used astransmitter and used as receiver had the samestructure. The proposed ultrasound transducerwith double peak type frequency characteristicscan be used for transmission of the fundamentalwave and detection of the second harmonic com-

Fig. 6. Measurement system of received spectrum by needletype hydrophone as receiver and ultrasound transducer withdouble peak type frequency characteristics as transmitter.

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ponents with only one transducer. However, thetrial manufactured transducers used for transmis-sion and detection separately on account of theelectronic circuits.

3. Results and discussion

3.1. Properties of microbubbles

The size (diameter) distribution of microbubblesused in this study is shown in Fig. 9. This sizedistribution is measured with Coulter multisizer.The diameter was in the range of 0.7–6 �m, withthe average diameter of 1.63 �m, and the size formost bubbles of 0.87 �m and the bubble concentra-tion was 1.2×106 bubbles/ml [5].

The shell parameters Sp and Sf of the microbub-bles were estimated by the curve fitting methodbetween the simulated frequency characteristics ofattenuation constant obtained by numerical calcu-lations using Eq. (3) and the measured frequencycharacteristics, because the attenuation constant isa function of the shell parameters Sp and Sf. Themeasured frequency characteristics of attenuationconstant of microbubbles are shown in Fig. 10. Theestimated shell parameters, Sp and Sf, by the curvefitting method are given below.

Fig. 9. Measured size (diameter) distribution data for surfac-tant coated microbubbles.

Sp=3.0 N/m, Sf=0.07 �N s/m

The calculated frequency characteristics of attenu-ation constant with these estimated shell parame-ters are shown in Fig. 10.

Fig. 11 shows the sound pressure spectrumscattered from microbubbles coated with surfac-tant membrane irradiated with ultrasound of afrequency of 3.5 MHz and a sound pressure of 35kPa. The second harmonic component level at 7MHz was similar to the fundamental componentlevel at 3.5 MHz. The contrast harmonic imagingmethod using the second harmonic component toobserve vascular systems or perfusion is thus at-tained. The development of ultrasound transducerwith double peak type frequency characteristicssuitable for the contrast harmonic imaging systemis mentioned in Section 3.2.

Fig. 8. Block diagram of measurement system for detection ofharmonic component from surfactant coated microbubblesilluminated with ultrasound burst wave by the trial manufac-tured ultrasound transducer with double peak type frequencycharacteristics.

Fig. 10. Simulated and experimental frequency characteristicsof attenuation constant of surfactant coated microbubbles.

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268264

Fig. 11. Sound pressure spectrum scattered from microbubbleswith size distribution. Illuminating frequency: 3.5 MHz, illumi-nating sound pressure: 35 kPa, number of cycles in pulse: 10. Fig. 13. Calculated relationship between the thickness of sub-

vibrating plate and the peak frequency in transfer function.

3.2. Design of ultrasound transducer with doublepeak type frequency characteristics

The calculated relationship between the acous-tic impedance of subvibrating plate and the peakmagnitude of transfer function are shown in Fig.12 for the subvibrating plate with a thickness of0.15 mm and a sound speed of 6000 m/s and forthe piezoelectric ceramic vibrator with a thicknessof 0.31 mm and a sound speed of 4500 m/s. Theresonant frequency of piezoelectric vibrator wasabout 7 MHz in this case. The transfer functionsshowed the single peak type frequency character-istics in the range of acoustic impedance of subvi-brating plate less than 5.0 Mrayl. The magnitudeof transfer function increased with increase ofacoustic impedance. The function showed thedouble peak type frequency characteristics in the

range of acoustic impedance larger than 5.0Mrayl. The peak on the lower frequency sideshowed a maximum value at around 10.0 Mrayl.The peak magnitude of transfer function on thehigher frequency side decreased gradually withincrease of acoustic impedance.

The calculated results on the relationship be-tween the thickness of subvibrating plate and thepeak frequency is shown in Fig. 13 and the rela-tionship between the thickness of subvibratingplate and peak magnitude of transfer function isshown in Fig. 14. Both peaks on the lower andhigher frequency sides appeared at lower frequen-cies for thicker subvibrating plate. The peak mag-nitude of transfer function on the lower frequencyside for transmission of the fundamental wavedecreased monotonously with increase ofthe thickness of subvibrating plate. On the other

Fig. 12. Calculated relationship between the magnitude oftransfer function and the acoustic impedance of subvibratingplate.

Fig. 14. Calculated relationship between the thickness of sub-vibrating plate and the peak magnitude of transfer function.

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268 265

Table 1Acoustic properties of materials used in the trial manufactured ultrasound transducer with double peak type frequency characteris-tics

Acoustic impedance (Mrayl)Parts Sound speed (m/s)Materials Thickness (mm)

13.3 5941 0.42Subvibrating plate Glass32.0 4328PZT 0.31Piezoelectric vibrator

Ferrite rubberBacking

hand, the peak magnitude on the higher frequencyside for detection of the second harmonic compo-nent showed somewhat complex change with in-crease of thickness of subvibrating plate. Theoptimum acoustic impedance was found to beabout 10 Mrayl and the optimum thickness was0.4 mm.

A glass plate with a thickness of 0.4 mm wasused as the subvibrating plate with the propertiesthat fitted with calculated results. The glass platewas adhered on the PZT piezoelectric ceramicvibrator (Fuji Ceramics Co. Ltd Type C-6) with alow viscosity epoxy resin (Araldite AY 103, HY956). The proposed ultrasound transducers withthe PZT piezoelectric ceramic vibrator and subvi-brating plate as mentioned above were trial manu-factured. The structure of trial manufacturedtransducer is given in Table 1.

The measured frequency characteristics oftransmitting sensitivity of the trial manufacturedultrasound transducer are shown with the calcu-lated results in Fig. 15. The numerical calculationsrevealed that the peak on the lower frequency sideappears at 3.5 MHz and that on the higher fre-quency side is located at 7 MHz. However, themeasured peak frequency on the lower frequencyside was lower than the calculated peak fre-quency. The measured peak frequency on thehigher frequency side was about 7 MHz, which isabout the same as the calculated peak frequency.While the measured peak magnitude on the higherfrequency side was about 6 dB lower than thecalculated peak magnitude.

3.3. Detection of harmonic components generatedin water

The results of detected second harmonic com-ponent at different distances between the trans-

ducer and the hydrophone in measurement systemof Fig. 3 are shown in Fig. 16. The secondharmonic component level increased at long dis-tance between the transducer and the hydro-phone. This would suggest that the detectedsecond harmonic component is generated by thenonlinear effect of propagation in water and theproposed transducer can detect the second har-monic components.

The ultrasound pulse radiated from the trialmanufactured ultrasound transducer was reflectedfrom a brass cubic block with 50 mm side and thereflected ultrasound was received with the trialmanufactured ultrasound transducer in water asshown in Fig. 3. The received spectrum calculatedon the basis of the measured ultrasound waves byFFT is shown in Fig. 17. The peaks on the lowerand higher frequency sides could thus be detectedwith the ultrasound transducer as with the hydro-phone. The ultrasound pulse propagated bothways between the transducer and the brass cubicin water. The ultrasound propagation distance inthis experiment is twice that of the distance in the

Fig. 15. Measured and simulated frequency characteristics oftransmitting sensitivity of the proposed ultrasound transducerwith double peak type frequency characteristics.

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268266

Fig. 16. Frequency spectrum measured at different distancesbetween the ultrasound transducer with double peak frequencyspectrum for transmitter and needle type hydrophone forreceiver.

Fig. 18. Scattered spectra from microbubbles coated withsurfactant membrane detected with the ultrasound transducerwith double peak type frequency characteristics.

ducer and ultrasound pulse was illuminated tomicrobubbles in the sample container located at adistance of 100 mm from acoustic radiating sur-face of the ultrasound transducer shown in Fig. 5.

The spectra were scattered from the microbub-bles and detected with another trial manufacturedultrasound transducer. The scattered spectra areshown in Fig. 18. The spectrum reflected from thebrass cubic block located at the same position asthat of the microbubble sample container was alsodisplayed as reference data in Fig. 18. The levelratio of the second harmonic component (7 MHz)to the fundamental component (3.5 MHz) wasattained in this experiment. The spectrum scat-tered was confirmed to contain a high level ofsecond harmonic component over 10 dB as com-pared with the reflected spectrum. The secondharmonic component in the reflected spectrumwas caused by the nonlinear effect by propagationin water. It was confirmed that the second har-monic component contained in the waves scat-tered from the surfactant coated microbubblescan be detected by the trial manufactured ultra-sound transducer with double peak type fre-quency characteristics and the level of the secondharmonic component from surfactant coated mi-crobubbles was about 10 dB higher than that ofthe second harmonic component generated inwater.

The level ratio of the second harmonic compo-nent to the fundamental component from mi-crobubbles coated with surfactant is shown in Fig.

experiment in Figs. 3 and 16. This would be thereason why the higher second harmonic compo-nent level was detected by the trial manufacturedultrasound transducer rather than by thehydrophone.

3.4. Detection of harmonic components scatteredfrom microbubbles

The electric signal of tone burst wave with thecenter frequency of 3.5 MHz, a voltage ampli-tudeof 210 V and ten cycles of burst was appliedto one of the trial manufactured ultrasound trans-

Fig. 17. Spectrum reflected from the brass cubic block reflectorilluminated with ultrasound by the trial manufactured ultra-sound transducer with double peak type frequency characteris-tics.

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268 267

19 against the different voltages applied to thetrial manufactured ultrasound transducer. Thesecond harmonic component level increased withincrease of applied voltage in the range of 70–100V. The increasing tendency diminished at voltageshigher than 100 V. On the other hand, the secondharmonic component level in the spectrumreflected from the reflecting brass cubic blockleveled off at voltages higher than about 150 V.Furthermore, the results of measurement on therelationship between the number of cycles in ap-plied tone burst and the level ratio of secondharmonic component to the fundamental compo-nent is shown in Fig. 20. The level ratio washighest in the range of 5–10 cycles in burst.

The applied burst waves with large number ofcycles have a narrow band of frequency spectrumand can concentrate the input energy at drivenfrequency. Thus, it is easier to induce the nonlin-ear behavior of microbubbles by the applied burstwave with a larger number of cycles. A higherreceived level of the second harmonic componentwas then expected to be observed with a largenumber of cycles in applied burst waves of lessthan ten cycles. However, the lower level of thesecond harmonic component was observed with alarge number of cycles in applied burst waves ofmore than ten cycles. The reason for this phe-nomenon would be the difference between theresonant frequency of microbubbles and the fre-quency of applied burst waves. It was shown inFig. 10 that the resonant frequency of microbub-bles used in this study is 3 MHz. The frequency of

Fig. 20. Relationship between the received level ratio of secondharmonics to fundamentals and the number of cycles in driv-ing burst wave for ultrasound transducer with double peaktype frequency characteristics.

transmitted ultrasound was 3.5 MHz. This is themost popular frequency in ultrasound diagnosticequipment. The burst wave with a smaller numberof cycles showed a wider band of frequency spec-trum. Thus, the nonlinear behavior of mirobub-bles with the resonant frequency of 3 MHz can beinduced with the applied burst wave with thecenter frequency of 3.5 MHz. On the other hand,as the frequency spectrum of applied burst wavewith a large number of cycles concentrated at 3.5MHz, the component at 3 MHz decreased. Theexcitation efficiency of the nonlinear behavior ofmicrobubbles was decreased by applied burstwaves with a large number of cycles. This wouldbe a result from the received second harmoniccomponent level decreasing with applied burstwith a large number of cycles more than tencycles.

4. Conclusion

The nonlinear response of microbubbles coatedwith surfactant and exposed to the burst ultra-sound was examined by experiments and numeri-cal calculations. The ultrasound transducer withdouble peak type frequency characteristicsequipped with a glass subvibrating plate on apiezoelectric ceramic vibrator was proposed andmanufactured on trial, and the performance of thetransducers thus constructed was evaluated. Fur-thermore, microbubbles coated with surfactant

Fig. 19. Relationship between received level ratio of secondharmonics to fundamentals and applied voltage for ultrasoundtransducer with double peak type frequency characteristics.

S. Takeuchi et al. / Colloids and Surfaces B: Biointerfaces 25 (2002) 257–268268

were exposed to burst ultrasound through thetrial manufactured ultrasound transducer withdouble peak type frequency characteristics andthe harmonic waves scattered from microbubbleswere detected by the trial manufactured trans-ducer. The feasibility of this ultrasound trans-ducer for contrast harmonic imaging wasexperimentally studied. Estimation of the soundpressure spectrum scattered from microbubblescoated with surfactant and exposed to ultrasoundwith a frequency of 3.5 MHz, and a sound pres-sure of 35 kPa revealed that the level of thesecond harmonic component at 7 MHz similar tothe level of the fundamental component at 3.5MHz is generated. The relationship between thenumber of cycles in illuminated ultrasound pulseand the second harmonic component excitationefficiency showed that the second harmonic com-ponent excitation efficiency increases graduallywith increase of the number of cycles in burst ofmore than six cycles.

Considerations of the relationship between thevoltage applied to the ultrasound transducer withdouble peak type frequency characteristics andthe level ratio of the second harmonic componentto the fundamental component led to the findingthat the second harmonic component level in-creases with increase of applied voltage in therange of 70–100 V and the increasing tendencydiminishes in the range of voltage higher than 100V. The highest ratio of the second harmonic

component level to the fundamental componentlevel was found to be 5–10 cycles in applied burstand the proposed ultrasound transducer wasshown useful for the contrast harmonic imagingmethod.

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