Ultrasound in Med. & Biol., Vol. 33, No. 5, pp. 762–767, 2007Copyright © 2007 World Federation for Ultrasound in Medicine & Biology

Printed in the USA. All rights reserved0301-5629/07/$–see front matter

doi:10.1016/j.ultrasmedbio.2006.11.016

● Original Contribution

ULTRASONIC SPEED OF SOUND DISPERSION IMAGING

YOAV LEVY,* YEHUDA AGNON,† and HAIM AZHARI**Faculty of Biomedical Engineering and †Faculty of Civil and Environmental Engineering, Technion, IIT,

Haifa, Israel

(Received 14 August 2006; revised 5 November 2006; in final form 25 November 2006)

Abstract—The feasibility for speed of sound dispersion (SOSD) imaging was investigated here. A throughtransmission new method for measuring the SOSD was utilized. With this method a long pulse comprising of twofrequencies one being the double of the other is transmitted through the object and detected on its other side.SOSD projection images were obtained by scanning objects immersed in water using a raster mode utilizing acomputerized scanning system. Using this approach SOSD projection images were obtained for solids and fluidsas well as for a tissue mimicking breast phantom and an in vitro soft tissues phantom. The results obtained here,have clearly demonstrated the feasibility of SOSD projection imaging. SOSD may serve as a new contrast sourceand potentially may aid in breast diagnosis. (E-mail: haim@bm.technion.ac.il) © 2007 World Federation forUltrasound in Medicine & Biology.

Key Words: Medical imaging, Ultrasound, Speed of sound dispersion, Tissue characterization.

INTRODUCTION

The speed of sound dispersion (SOSD) phenomenon insoft tissues is very weak (Wells 1999), therefore, it isdifficult to detect and measure and, hence, it was ne-glected in most applications. However, several tech-niques for SOSD measurements have been suggested andimplemented for in vitro specimens. For example, SOSDwas measured in human brains by Kremkau et al. (1981),in lungs by Pedersen and Ozcan (1986) and in hemoglo-bin solutions by Carstensen and Schwan (1959). Also,Marutyam et al. (2006) have measured SOSD in lambhearts and Akashi et al. (1995) and Levy et al. (2006) inbovine hearts.

Recent studies indicated that speed of sound disper-sion (SOSD) may be used for ultrasonic tissue charac-terization. Marutyam et al. (2006) reported that theSOSD depends on the orientation of anisotropic tissue.Levy et al. (2006) have shown that there is a significantdifference in the dispersion index between differentspecimens.

In Levy et al. (2006), a method for measuring thespeed of sound dispersion using a single transmission,which utilizes a long pulse comprising of two frequen-cies, one being the double that of the other was intro-

Address correspondence to: Haim Azhari, D.Sc., Faculty of

Biomedical Engineering, Technion IIT, Haifa 32000, Israel. E-mail:haim@bm.technion.ac.il

762

duced. This method is suitable for imaging using athrough transmission mode. The objective of this studywas to investigate the feasibility of utilizing this methodfor SOSD imaging.

MATERIALS AND METHODS

TheoryConsider an examined object (e.g., woman breast)

placed between two transducers and immersed in thewater bath (Fig. 1). An ultrasonic signal which is com-prised of two frequencies f1, f2, is transmitted and travelsfrom point A to point B. Using spectral analysis, thesignal can be decomposed into its two disjoint compo-nents. The phase of each component at point A is

�A ( f, t) � �0f� 2�ft (1)

where �0f � �A ( f, t � 0) is the initial phase of thetransmitted wave.

The phase of the wave reaching point B is

�B( f, t) � �A( f, t � �t( f )) � �0f� 2�f (t � �t( f )) (2)

where �t(f) is the traveling time for an ultrasonic wave ofa specific frequency f to travel from point A to point B.

If the distance between points A and B is L andcf ( l ) is the frequency-medium-dependent phase velocityof the ultrasonic signal along the way from A to B, �t ( f )

can be expressed by

Speed of sound dispersion ● Y. LEVY et al. 763

�t ( f ) � �0

L1

cf ( l )· dl (3)

In order to compare the phases of two frequencies, it isconvenient to normalize the phase by 2�f, converting itinto a time scale,

�B ( f, t)

2�f�

�0f

2�f� �t � �

0

L1

cf ( l )· dl� (4)

The difference between the normalized phases of twofrequencies f1 and f2 will thus be equal to

�B ( f1, t )

2�f1�

�B ( f2, t )

2�f2� �

0

L � 1

cf2( l )�

1

cf1( l )� · dl

��0f1

2�f1�

�0f2

2�f2(5)

and, since �0f can be set to equal zero either by thesystem’s hardware set-up or by postprocessing, we canneglect the last two terms and obtain

�B ( f1, t)

2�f1�

�B ( f2, t )

2�f2� �

0

L � 1

cf2( l )�

1

cf1( l )� · dl. (6)

The term on the right hand side is the difference in thetime of flight from point A to point B through the imagedobject between frequency f1 and frequency f2 resulting

Signal Generator Amplifier / Filter

A/DTrigger

Transmitter

Imaged Object

Receiver

Fig. 1. Schematic depiction of the system’s measurement set-up. An object is placed in a water tank between two ultrasonictransducers. A signal is transmitted from one transducer anddetected after passing through the object by the other trans-ducer. An image is obtained by scanning the object along a set

of horizontal lines (raster mode).

from the speed of sound dispersion. This time of flight

difference is denoted by �TOF ( f1, f2). Water is consid-ered as nondispersive medium (Carstensen 1954), there-fore, the frequency-dependence of the time of flightrepresents solely the imaged object properties. Defining�TOF ( f1, f2) per unit length � at distance l from thetransmitter as

�(l, f1, f2)–1

cf2 (l )�

1

cf1 (l )(7)

the time difference between the normalized phases oftwo frequencies f1 and f2 can be written as

�B ( f1, t)

2�f1�

�B ( f2, t)

2�f2� �TOF (f1 � f2)

��0

L

�(l, f1, f2) · dl. (8)

Hence, measurement of the difference between the nor-malized phases gives a projection of the accumulative �along the track from A to B. Nevertheless, it is not trivialto obtain this measurement since the phases which areused on the left-hand side of eqn 8 are cumulative andcan exceed 2�. Thus, in practice, only the wrapped phaseof each frequency, ��B ( f,t), is measured (e.g., using theFourier transform of the recorded signal).

In order to overcome this problem, let us considera special case where the second frequency equalstwice the first frequency, i.e., f2 � 2f1. In case thatthe nondimensional parameter fulfils the condition

|2f1�0

L��l, f1, 2f1� ·dl| 0.5, it was shown by Levy

et al. (2006) that the difference in the time of flight canbe calculated from the wrapped phases

�0

L

�(l, f1, 2 f1) · dl ���B ( f1, t)

2�f1�

��B (2f1, t)

4�f1

�1

2f1· round�–

��B ( f1, t)

��

��B (2f1, t)

2� � (9)

where round[] is the operation of rounding to the nearestinteger.

In order to reconstruct a projection image I (x, y, f1)of the SOSD, the object can be scanned in a raster mode,so as to depict the relation

I (x, y, f1) � �0

L

�(x, y, z, f1, 2f1) · dz. (10)

The constraint |2f1�0

L� �l, f1, 2f1� ·dl | 0.5 is mandatory

for accurate measurement of the accumulative disper-

764 Ultrasound in Medicine and Biology Volume 33, Number 5, 2007

sion. However, for imaging purposes it is sufficient toavoid phase wrapping in the region of interest (ROI).Therefore, the constraint is on the variation of the accu-mulative dispersion in the ROI

�ROI � max��0

L

� (x, y, l, f1, 2f1) · dl�� min��

0

L

� (x, y, l, f1, 2f1) · dl�1

2f1(11)

where {x, y} � ROI.

Ultrasonic measurementsThe scanning system utilized to generate the accu-

mulative dispersion index projection of the imaged ob-ject comprised of a water tank with a specially builtcomputer controlled mechanism that can produce spatialmotion with three degrees of freedom for a pair oftransducers (Panametrics, 5 MHz, focused transducers,diameter 12.7 mm and focal length 10.7 cm) placedabout twice the focal length apart (Azhari and Stolarski1997, 1999). The system can scan a cylindrical volumedefined by the user (up to 20 cm in diameter and 15 cmin height) located at the center of the water tank. In theimaging configuration utilized here, the object wasscanned in a raster mode, yielding a rectangular projec-tion image I (x,y, f1) (see eqn 10). The scanning resolu-tion was set by the user before each scan. Typical scan-ning resolution was 0.3 mm � 1 mm along the horizontaland vertical directions, respectively.

Signals were generated by a Tabor 8026 arbitrarywaveform generator and a Panametrics 5800 pulser/receiver was used as a receiver. The estimated meanpower applied to the transmitting transducer was 0.012Watts. Considering attenuation and other loses, this im-plies that we were well within the safe radiation range

Fig. 2. (Top) A Photograph of the PVC step phantom. (Bo

of the steps is incrementally increased

(0.720 Watt/cm2 I-SPTA ). See for example: ter Haar andDuck (2000). A Gage CompuScope 12100 two-channel50-MHz 12-bit A/D converter was used digitally to storethe detected waves.

The experimental procedureA continuous wave, which was constructed by mix-

ing a pair of sinusoidal waves with frequencies f and 2f,was generated. The initial phase for both frequencies wasset to zero using the signal generator control. The trans-mitted continuous wave was actually a long but finitesinusoidal train. A long rect sampling window from thereceived signal was used for the spectral analysis. Atleast 12 s of the wave were sampled by the A/D forsignal analysis.

Using eqn 9, the corresponding time of flight dif-ference was calculated for each measurement point. Thewrapped angels, ��( f ), were calculated using Matlab’sFFT function (MATLABTM, Mathworks, Natick, MA,USA). An image depicting a projection of the accumu-lative dispersion index I (x,y,f1) was then obtained.

All experiments were done at room temperature(about 21°C).

Imaged objectsThe accumulative dispersion index projections

I (x,y,f1) were acquired for four objects: (1) a plastic stepphantom, (2) a commercial breast phantom, (3) a balloonwith three different fluids and (4) a biological phantomcomprised of two soft tissues (in vitro).

The step phantom (see Fig. 2 top) was made ofpolyvinylchloride (PVC). The step size was 2 mm andthe minimal thickness was 2 cm. The breast phantom wasan ATS Laboratories model BB-1 breast phantom. TheBB-1 mimics the geometry and acoustic properties of thehuman breast and contains target structures randomlyembedded within a tissue mimicking material. The bal-loon was filled with soybean oil, water and glycerin(purity min 98%, Frutarom Ltd., Haifa, Israel). Due to

Its corresponding SOSD projection image. The thickness

ttom) by 2 mm starting from 20 mm.

Speed of sound dispersion ● Y. LEVY et al. 765

the differences in densities, the soybean oil floated on topof the water and the glycerin sank below the water. Thetwo in vitro soft tissue specimens used here were bovineheart and turkey breast (specimens were obtained from alocal commercial slaughterhouse). The soft tissue spec-imens were stored in a refrigerator (they were not frozen)and were brought to room temperature before the exper-iment. To eliminate the influence of thickness on theresults the specimens were cut to have the same thick-ness (3 cm).

RESULTS

The projection of the accumulative dispersion indexI (x,y,f1), obtained for the PVC step phantom ( f1 � 2.5MHz) is shown in Fig. 2 (bottom). As can be noted theindividual steps are clearly visible, reflecting the in-creased time of flight difference, �TOF ( f1, f2), resultingfrom the increased thickness. Darker colors representhigher accumulative dispersion index values. The meandifference �TOF ( f1, f2) between each step and the thin-nest step were: 0.7, 1.9, 3.6, 4.4, 6.0 [ns] (see Fig. 3).Applying linear regression to the data, the typicalvalue of � for PVC was found from the slope of theregression line and its value was 6.5 � 1.1 [nanosec-onds/cm] (with 95% confidence level).

The projection of the accumulative dispersion indexI (x,y,f1) � 1.5 MHz obtained for the three fluids phan-tom is depicted in Fig. 4. As can be noted, there is a clearcontrast between the regions containing the differentfluids. Darker color indicates higher SOSD. The inter-mediate layer between the glycerin and the water stems

Fig. 3. The measured increase in �TOF ( f1, f2) (marked by anasterisk) relative to the thinnest step obtained for each step ofthe PVC phantom as a function of the increase in the step’sthickness. The solid line corresponds to the calculated regres-

sion line.

from a mixture of fluid bubbles formed when the waterwas poured atop the glycerin.

The projection of the accumulative dispersion indexI (x,y,f1 � 1 MHz) obtained for the BB1 commercialbreast phantom is depicted in Fig. 5. In this case, lowerfrequencies were used to improve the penetrationthrough the phantom. As can be observed the embedded

Fig. 4. A SOSD projection image of the phantom containingthree fluids. Note the contrast between the layers. (The inter-mediate layer between the glycerin and the water stems from amixture of fluid bubbles formed when the water was poured

atop the glycerin).

Fig. 5. A SOSD projection image obtained for the commercialbreast phantom. The embedded targets have formed regions of

discontinuity within the phantom matrix (indicated by the arrows).

766 Ultrasound in Medicine and Biology Volume 33, Number 5, 2007

targets (some of which are marked by arrows) depicthigh accumulative dispersion index values. Importantlyit should be clarified that although dispersion in water isnegligible, in this image it appears as a dark region. Thisstems from the fact that the condition of

�2f1�0

L

��l, f1, 2f1� · dl� 0.5 (see above)

was not met for the water and hence in this case a 2�phase wrapping occurred. However, the region of inter-est, i.e., the breast phantom, has complied with condition(eqn 11).

The projection image of the accumulative disper-sion index obtained for the in vitro soft tissue phantom( f1 � 2.5 MHz) is depicted in Fig. 6. As can be noted,there is a significant difference in gray levels between theregions containing the two types of tissues. Both tissuespecimens had the same thickness. Thus, the only sourceof contrast is the SOSD. As can be noted the SOSD ishigher for the turkey breast tissue.

DISCUSSION

SOSD has been suggested as an additional acousticproperty for utilization in medical applications. The mostdiscussed idea was to use SOSD for bone assessment(Wear 2000; Strelitzki and Evans 1996; Droin et al.1998). Analysis of SOSD in soft tissues has also beenconducted, (e.g., in brain by Kremkau et al. (1981), inlung by Pedersen and Ozcan (1986), in hemoglobinsolutions by Carstensen and Schwan (1959), and in hearts

Fig. 6. A SOSD projection image obtained for the in vitro tissuephantom. Both tissue specimens had the same thickness. Thus,the only source of contrast is the SOSD. As can be noted, the

SOSD is higher for the turkey breast tissue.

by Akashi et al. (1995) and by Marutyam et al. (2006).

To the best of our knowledge SOSD imaging has notbeen suggested. This may stem from two main reasons.First SOSD is a very weak phenomenon and hencedifficult to measure. And secondly previously suggestedmethods had either low SNR or required too long acqui-sition times.

The method suggested by Levy et al. (2006) offersimproved SNR and a single transmission measurementof the SOSD. This makes it particularly suitable forultrasonic SOSD projection imaging as was demon-strated by the results.

There are two challenges associated with the sug-gested method: (1) boundary artifacts and (2) phasewrapping. As can be noted (Figs. 2, 4, 5, 6), there is anartifact which occurs at boundaries separating differentregions in the imaged object. This artifact appears as astrong gradient in SOSD values. It emphasizes bound-aries and hence, may increase the visibility of smalltargets. The source of this artifact may be the frequency-dependent acoustic diffraction which occurs at suchboundaries.

As for phase wrapping, the constraint on the varia-tion of the accumulative dispersion in the ROI (eqn 11),imposes a limit on the allowed variation of the SOSDproperty in the imaged object. Violation of this constraintmay lead to a phase wrapping in certain regions withinthe image. (A problem which resembles the phase wrap-ping problem of MRI Phase contrast flow imaging).Algorithms for phase unwrapping may be needed in suchcases.

Another issue which should be accounted for inclinical situation such as in breast imaging, is that SOSDmay not be negligible along the path before a tumor to bedetected or characterized. Hence, a significant SOSD inthe ROI may not necessarily reflect the properties of thattumor. There are two suggested solutions to this prob-lem. The first is to squeeze the tissue of interest as donein conventional X-ray mammography. This will reducepossible effects of the surrounding tissue. The secondsolution is to take advantage of the integrative nature ofthe measurement (see eqn10) and generate a full orpartial Radon transform of the object by acquiring pro-jection images from various angles around the object.Then, using a back projection method (see for exampleKak and Slaney 1987), obtain a cross sectional image ofthe SOSD of the suspicious tumor.

As for the potential effect of the SOS dispersionon ultrasound beam-forming and scan conversion for adispersive medium, it should be pointed out that theSOSD is a much weaker phenomenon. Its commonvalues in soft tissues are about two orders of magni-tude smaller than the variation of SOS. Therefore, itsinfluence on beam forming and scan conversion is

negligible.

Speed of sound dispersion ● Y. LEVY et al. 767

In conclusion, the results obtained here have clearlydemonstrated the feasibility of SOSD projection imag-ing. As was shown here, SOSD images can be obtainedfor solids (Fig. 2), for fluids (Fig. 4) as well as for thetissue mimicking breast phantom (Fig. 5) and soft tissues(Fig. 6). SOSD may serve as a new contrast source andpotentially may aid in breast diagnosis.

Acknowledgments—The authors are grateful for funding provided bythe Galil Center for Telemedicine and Medical Informatics and theTechnion V.P.R. Research Funds, Eliyahu Pen Research Fund, DentCharitable Trust, Japan Technion Society and the Montreal BiomedicalFund. Finally, the authors thank Mr. Aharon Alfasi for his extremelyvaluable technical support.

REFERENCES

Akashi N, Kushibiki J, Chubachi N, Dunn F. Acoustic properties ofselected bovine tissues in the frequency range 20–200 MHz. JAcoust Soc Am 1995;98:3035–3039.

Azhari H, Stolarski S. Hybrid ultrasonic computed tomography. Com-put Biomed Res 1997;30(1):35–48.

Azhari H, Sazbon D. Volumetric imaging with ultrasonic spiral CT.Radiology 1999;212(1):270–275.

Carstensen EL, Schwan HP. Acoustic properties of hemoglobin solu-

tions. J Accoust Soc Am 1959;31:305–311.

Droin P, Berger G, Laugier P. Velocity dispersion of acoustic waves incancellous bone. IEEE Trans Ultrason Ferroelectr Freq Control1998;45:581–592.

Kak AC, Slaney M. Principles of computerized tomographic imaging.New York: IEEE Press, 1987.

Kremkau FW, Barnes RW, McGraw CP. Ultrasonic attenuation andpropagation speed in normal human brain. J Accoust Soc Am1981;70:29–38.

Levy Y, Agnon Y, Azhari H. Measurement of speed of sound disper-sion in soft tissues using a double frequency continuous wavemethod. Ultrasound Med Biol 2006;32(7):1065–1071.

Marutyan RK, Yang M, Baldwin SL, Wallace KD, Holland MR, MillerJG. The frequency dependence of ultrasonic velocity and the an-isotropy of dispersion in both freshly excised and formalin-fixedmyocardium. Ultrasound Med Biol 2006;32(4):603–610.

Pedersen PC, Ozcan HS. Ultrasound properties of lung tissue and theirmeasurements. Ultrasound Med Biol 1986;12(6):483–499.

Strelitzki R, Evans JA. On the measurements of the velocity of ultra-sound on the os calcis using short pulse. Eur J Ultrasound 1996;4:205–213.

ter Haar G, Duck FA. The safe use of ultrasound in medical diagnosis.London: British Institute of radiology, 2000.

Wear KA. Measurments of phase velocity and group velocity in humancalcaneus. Ultrasound Med Biol 2000;26:641–646.

Wells PNT. Ultrasonic imaging of the human body. Rep Prog Phys1999;62:671–722.

Zhaoa B, Basira OA, Mittal GS. Estimation of ultrasound attenuationand dispersion using short-time Fourier transform. Ultrasonics

2005;43(5):375–381.