www.elsevier.com/locate/ultras

Ultrasonics 44 (2006) e185–e188

Intravascular ultrasound tissue harmonic imaging: A simulation study

M.E. Frijlink a,*, D.E. Goertz a,b, A. Bouakaz c, A.F.W. van der Steen a,b

a Biomedical Engineering, Erasmus MC, University Medical Center Rotterdam, The Netherlandsb Interuniversity Cardiology Institute of the Netherlands, Utrecht, The Netherlands

c Universite F. Rabelais, Tours, France

Available online 30 June 2006

Abstract

Recently, the in vivo feasibility of tissue harmonic imaging (THI) with a mechanically-rotated intravascular ultrasound (IVUS) cath-eter was experimentally demonstrated. To isolate the second harmonic signal content, both pulse inversion (PI) and analog filtering wereused. In the present paper, we report the development of a simulation tool to investigate nonlinear IVUS beams and the influence ofrotation on the efficiency of PI signal processing. Nonlinear 20 MHz beams were simulated in a homogeneous tissue-mimicking medium,resulting in second harmonic pressure fields at 40 MHz. The acoustic response from tissue was simulated by summing radio-frequency(RF) pulse–echo responses from many point-scatterers. When the transducer was rotated with respect to the point-scatterers, the fun-damental frequency suppression using PI degraded rapidly with increasing inter-pulse angles. The results of this study will aid in theoptimization of harmonic IVUS imaging systems.� 2006 Elsevier B.V. All rights reserved.

Keywords: Intravascular ultrasound; Nonlinear; Tissue harmonic imaging; Simulation

1. Introduction

Intravascular ultrasound (IVUS) is capable of providingreal time cross-sectional images of coronary arteries and,therefore, it has become an important clinical tool for thedetection and evaluation of coronary artery diseases as wellas for therapy guidance and clinical research [1]. At pres-ent, clinicians generally use rotating single-element IVUScatheters with center frequencies between 30 and 40 MHz.

Tissue harmonic imaging (THI) has been shown toincrease the diagnostic value of conventional echocardiog-raphy below 10 MHz by improving the image quality. Wepreviously developed an experimental set-up to study thefeasibility and potential of THI at IVUS frequencies. Thesuppression of stent imaging artifacts was shown whenhigh frequency THI (transmit fc = 20 MHz, receivefc = 40 MHz) was applied in vitro [2]. More recently, we

0041-624X/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.ultras.2006.06.044

* Corresponding author. Present address: Thorax Center Ee23.02,Erasmus MC, PO Box 1738, 3000 DR Rotterdam, The Netherlands.Tel.: +31 10 4088031; fax: +31 10 4089445.

E-mail address: m.frijlink@erasmusmc.nl (M.E. Frijlink).

demonstrated in vivo the feasibility of THI for an IVUSsystem using a 20–40 MHz mechanically-rotated IVUScatheter [3]. In that study, tissue harmonic signals were iso-lated using a combination of analog filtering and pulse-inversion (PI).

The PI technique requires (at least) two firings of a pulseand its inverted counterpart for each acoustic line [4]. Withtissue or catheter motion, the fundamental frequency signal(i.e., transmit bandwidth signal) is not completely can-celled, and the harmonic intensity becomes smaller due tosignal misalignment. Motion artifacts of PI-based THIhave been studied by Shen and Li [5]. Their results indi-cated that the tissue harmonic signal is significantly affectedby tissue motion, and that for axial motion, the tissue har-monic intensity decreases much more rapidly than with lat-eral motion. This study was conducted under conditionsrelevant to low frequency array based scanning.

A number of different approaches have been developedto model the nonlinear propagation in the field of an ultra-sonic transducer [6]. The most common approach is tosolve the Khokhlov–Zabolotskaya–Kuznetsov (KZK)equation, which is a nonlinear parabolic equation that

e186 M.E. Frijlink et al. / Ultrasonics 44 (2006) e185–e188

accounts for the combined effects of diffraction, absorp-tion, and nonlinearity for directional sound beams [7].Comparisons of nonlinear simulation results and measure-ments show excellent agreement [6],[8]. For relatively shortpulses, as typically used in diagnostic ultrasound, the time-domain implementation of the KZK-equation is advanta-geous because many harmonic components could then betaken into account for the relatively broadband imagingpulses [7].

In this study, we simulated fundamental 20 MHz (F20),second harmonic (H40), and fundamental 40 MHz (F40)fields for an unfocused circular IVUS element using a twodimensional nonlinear parabolic KZK-equation and med-ium characteristics (attenuation, nonlinearity, scattering)in the range of those of vascular tissue and blood. Thepulse–echo responses from point-scatterers, randomly posi-tioned in three dimensions, were calculated for successiveinverted pulses as the beam was rotated. The influence ofrotation on the performance of PI was then investigated.

2. Methods

2.1. Simulation design

The simulation of the transmitted nonlinear field by anunfocused circular transducer is based on a time-domainimplementation of the KZK-equation based on Lee andHamilton’s numerical approach [9]. The two dimensionalimplementation has been written in FORTRAN and hasbeen previously evaluated [10]. The attenuation of acousticwaves propagating in a wide variety of lossy media obeys apower law dependence on frequency. The algorithmdescribed by Bouakaz et al. [10] was modified to accountfor a frequency dependent attenuation different than apower law exponent of 2 (which corresponds to the powerlaw exponent of attenuation of water).

The received signal from an individual scatterer is cal-culated using an analytically derived spatial impulseresponse for an unfocused circular transducer [11]. Inorder to be able to use this spatial impulse response incombination with propagation in a frequency dependentattenuating medium, the distance from an individualpoint-scatterer to the piston transducer is approximatedby a single value, similar to the approach described byJensen et al. [12].

For the purpose of simulating ultrasound backscatteredsignals, tissue can be represented by many point scattererspositioned randomly in three dimensions [13],[14]. Allpoint scatterers were assigned the same scattering strengthand frequency dependent backscatter was taken intoaccount. The backscatter signal from the cloud of scatter-ers is calculated by a summation of the individualresponses from each scatterer. The scatterer density wassufficient to produce Rayleigh envelope statistics.

The three-dimensional scatterer volume could be rotatedwith respect to the transmitted field to simulate catheterrotation of a mechanically scanned IVUS transducer.

2.2. Simulation parameters

The nonlinear beams were calculated for a circular,unfocused transducer with a diameter of 0.9 mm, similarto IVUS elements used in previous IVUS THI studies[3]. Due to the circular symmetry, a two-dimensionalsimulation is sufficient to calculate three-dimensionalfields. In all calculations, the excitation pulse was aGaussian enveloped sine wave with a 30% fractionalbandwidth.

The propagation medium characteristics were chosen tobe in the range of those of vascular tissue and blood. Arte-rial tissue and blood have a frequency dependent attenua-tion with power law exponents of 1.1 and 1.2, respectively,in the frequency range from 15 to 60 MHz [15],[16]. In the10–50 MHz range, this is approximated by an attenuationthat has a linear frequency dependency in the range from0.5 to 1.5 dB/cm/MHz. In this study, a frequency depen-dent attenuation value of 1.0 dB/cm/MHz was used. Thesound speed of the propagation medium was chosen tobe 1560 m/s, the mass density 1050 kg/m3 and the nonlin-ear parameter (B/A) 6.0 [17].

The backscatter signal from the scatterers is calculatedby the summation of responses from all scatterers thatare within the �20 dB beamwidth. In our case, this meansthat all scatterers within a distance of 0.5 mm from the z-axis (corresponding to the propagation axis) are taken intoaccount between z = 0.5 and z = 6.0 mm. Lockwood et al.[15] showed that the power law exponent of the frequencydependent backscatter in the artery wall ranged betweenc = 1.1 and 1.4, and that this parameter of blood rangedfrom c = 1.3 to 1.4 in the same frequency range. A fre-quency dependence of c = 1.3 has been chosen in thisstudy.

2.3. Simulations

2.3.1. Nonlinear beam simulationsTwo-dimensional beam profiles were calculated in F20

and H40 mode for a maximum fundamental excitationpressure of 2 MPa. For comparison, a F40 beam profilewas also calculated at a low excitation pressure of50 kPa.

2.3.2. Effects of rotation on pulse inversion

To study the effect of catheter rotation on the effective-ness of PI in suppressing fundamental frequency energy,two inverted 20 MHz pulses (0� and 180�) were propagatedthrough the attenuating medium. Echoes from multiplepoint-scatterers have been calculated to simulate the RFpulse–echo responses at different angles with respect tothe IVUS transducer. Fig. 1 shows the simulation set-up,showing the circular transducer and the point-scatterers.One data set consisting of 32 different realizations of a vol-ume of randomly positioned scatterers was calculated for aF20 2 MPa amplitude pulse-pair. The average cross-corre-lation value between RF-lines was calculated as a function

α

Fig. 1. Schematic simulation set-up, showing randomly distributed point-scatterers in a 3D volume with respect to a rotating transducer.

-4 -2 0 2 4 6-0.2

0

0.2

0.4

0.6

0.8

1

Cro

ss-c

orre

latio

n

Average cross-correlation between RF-lines [2-3 mm]

raw RFH40 RFF40 RF

Inter-pulse angle [degrees]

Fig. 3. Cross-correlation between raw, H40 and F40 RF-lines at adistance from 2 to 3 mm from the transducer, plotted as a function ofinter-pulse angle (in degrees).

M.E. Frijlink et al. / Ultrasonics 44 (2006) e185–e188 e187

of inter-pulse angle. This is done for both raw and filteredRF-lines (32–50 MHz, 5th order Butterworth). For com-parison, the average cross-correlation for F40 RF-lineshas also been calculated. The incremental inter-pulse anglewas 0.15�, which corresponded to the experimentallyemployed line-density of 2400 RF-lines per rotation [3].The effectiveness of PI for fundamental frequency suppres-sion was studied at a distance of 2–3 mm from the trans-ducer as a function of inter-pulse angle. The meanfundamental signal content of pulse-pairs was calculatedby summing the frequency content between 18 and 22 MHz.

3. Results

3.1. Nonlinear beam simulations

Two-dimensional beam profiles for F20, H40 and F40modes are plotted in Fig. 2. These images are normalized

Fig. 2. Two-dimensional beamprofiles in F20, H40 and F40 mode. The beamindividual images.

with respect to the maximum signal within the individualimages. The H40 beam shows less near field energy and areduction in sidelobe energy compared to both F20 andF40. The attenuation of the medium causes the F40 todecay faster than both F20 and H40.

3.2. Effects of rotation on pulse inversion

The average inter-pulse cross-correlation estimates forthe raw, H40 and F40 RF-lines is given in Fig. 3 as a func-tion of inter-pulse angle. These curves show the mean of100 cross-correlation curves for windowed RF-lines corre-sponding to backscatter from 2 to 3 mm from the trans-ducer. It can be seen that the cross-correlation peak isnarrower for H40 and narrowest for F40, which is attrib-uted to the beam width at this distance (Fig. 2). Thesecurves indicate the legitimacy of averaging neighboringRF-lines to improve the signal-to-noise ratio (SNR) forsmall inter-pulse angles. For example, the decorrelationbetween H40 RF-lines (from 2 to 3 mm) is only <0.1 withinan angle of 0.5�.

The fundamental suppression through PI at a distanceof 2–3 mm for the 2 MPa amplitude pulse-pair (0� and

profiles have been normalized with respect to the maximum signal within

0 2 4 6 8 100

5

10

15

20

25

30

Fund

amen

tal s

uppr

essi

on [

dB]

Inter-pulse angle [degrees]

Average fundamental reduction

Fig. 4. The fundamental suppression with PI as a function of inter-pulseangle as calculated for a 2 MPa pulse-pair calculated for backscatter2–3 mm from the transducer.

e188 M.E. Frijlink et al. / Ultrasonics 44 (2006) e185–e188

180�) is expressed as a function of inter-pulse angle inFig. 4. This figure shows that the fundamental suppressiondecreases rapidly with increasing inter-pulse angles, whichis linked to the reduced cross-correlation between rawF20 RF-lines for increasing inter-pulse angles (Fig. 3).Thus, a reduced line-density corresponding to an increasedinter-pulse angle, leads to a reduced fundamental suppres-sion when PI is applied. Fig. 4 indicates a fundamental sup-pression of 16 and 10 dB when PI is applied with an inter-pulse angle of 0.70� and 1.4�, respectively, corresponding toapproximately 512 and 256 RF-lines per rotation. Theseline-densities correspond to those used in current clinicalmechanically scanned IVUS systems.

4. Conclusion and discussion

Nonlinear fields at 20–40 MHz have been simulated forcircular IVUS transducers through media with frequencydependent attenuation values in the range of those of vas-cular tissue and blood. The influence of transducer rotationon the fundamental suppression of pulse inversion has beenstudied for a range of inter-pulse angles.

In the simulations with a rotating transducer, the mini-mal inter-pulse angle was chosen to be 0.15�, based on aline-density of 2400 lines per rotation. Using this line-den-sity, the commercially and clinically used rotational speedof thirty rotations per second will than result in a pulse-rep-etition-frequency (PRF) of approximately 75 kHz, which isstill lower than the maximum PRF of a rotating single-ele-ment IVUS system as limited by sound propagation speed.So in spite of a lower line-density (e.g., 256 lines per rota-tion) at 30 rotations per second of current commerciallyavailable IVUS systems, no physical limitations exist toincrease to a line-density of 2400 lines per rotation.

A degradation of fundamental suppression with PI wasobserved for increasing inter-pulse angles. This is due toincreased decorrelation between RF pulse-pairs for increas-

ing inter-pulse angles. Future simulations might gain insightin the competing effects of decorrelation and pulse averag-ing, resulting in a trade-off between SNR and resolution.

The results from this simulation study will guide theoptimization of harmonic IVUS systems with mechanicallyscanned single-element catheters. The PRF, line-densityand transducer size and geometry could be altered to opti-mize the fundamental suppression with PI. This simulationtool could also be used to investigate different pulseschemes (coded excitation) for isolating harmonic signals.Further, such simulations may also be useful in the contextof guiding the implementation and optimization of nonlin-ear contrast imaging systems.

References

[1] Y. Saijo, A.F.W. van der Steen, Vascular Ultrasound, Springer-Verlag, Tokyo, 2003.

[2] M.E. Frijlink, D.E. Goertz, A.F.W. van der Steen, Reduction of stentartifacts using high-frequency harmonic ultrasound imaging, Ultra-sound in Medicine and Biology 31 (2005) 1335.

[3] M.E. Frijlink, D.E. Goertz, L.C.A. van Damme, R. Krams, A.F.W.van der Steen, Intravascular ultrasound tissue harmonic imagingin vivo, IEEE Ultrasonics Symposium (2004) 1118.

[4] D.H. Simpson, C.T. Chin, P.N. Burns, Pulse inversion doppler: Anew method for detecting nonlinear echoes from microbubblecontrast agents, IEEE Transactions on Ultrasonics Ferroelectricsand Frequency Control 46 (1999) 372.

[5] C.C. Shen, P.C. Li, Motion artifacts of pulse inversion-based tissueharmonic imaging, IEEE Transactions on Ultrasonics Ferroelectricsand Frequency Control 49 (2002) 1203.

[6] V.F. Humphrey, Nonlinear propagation in ultrasonic fields: Measure-ments, modelling and harmonic imaging, Ultrasonics 38 (2000) 267.

[7] M.F. Hamilton, D.T. Blackstock, Nonlinear Acoustics, AcademicPress, San Diego, 1998.

[8] F.A. Duck, Nonlinear acoustics in diagnostic ultrasound, Ultrasoundin Medicine and Biology 28 (2002) 1.

[9] Y.S. Lee, M.F. Hamilton, Time-domain modeling of pulsed finite-amplitude sound beams, Journal of the Acoustical Society of America97 (1995) 906.

[10] A. Bouakaz, C.T. Lancee, N. de Jong, Harmonic ultrasonic field ofmedical phased arrays: Simulations and measurements, IEEE Trans-actions on Ultrasonics Ferroelectrics and Frequency Control 50(2003) 730.

[11] P.R. Stephanishen, Transient radiation from pistons in an infiniteplanar baffle, Journal of the Acoustical Society of America 49 (1971)1629.

[12] J.A. Jensen, D. Gandhi, W.D. O’Brien, Ultrasound fields in anattenuating medium, IEEE Ultrasonics Symposium (1993) 943.

[13] A.T. Kerr, J.W. Hunt, A method for computer simulation ofultrasound doppler color flow images-i. Theory and numericalmethod, Ultrasound in Medicine and Biology 18 (1992) 861.

[14] J.W. Hunt, A.E. Worthington, A.T. Kerr, The subtleties of ultra-sound images of an ensemble of cells: Simulation from regular andmore random distributions of scatterers, Ultrasound in Medicine andBiology 21 (1995) 329.

[15] G.R. Lockwood, L.K. Ryan, J.W. Hunt, F.S. Foster, Measurementof the ultrasonic properties of vascular tissues and blood from 35–65 mhz, Ultrasound in Medicine and Biology 17 (1991) 653.

[16] F.S. Foster, C.J. Pavlin, K.A. Harasiewicz, D.A. Christopher, D.H.Turnbull, Advances in ultrasound biomicroscopy, Ultrasound inMedicine and Biology 26 (2000) 1.

[17] F.A. Duck, Physical Properties of Tissue, Academic Press Limited,London, 1990.