INVESTIGATION OF NEW TECHNIQUES FOR ULTRASONIC

IMAGING

Research Thesis

In Partial Fulfilment of the

Requirements for the

Degree of Doctor of Philosophy

Yoav Levy

Submitted to the Senate of

the Technion - Israel Institute of Technology

Adar, 5767 Haifa February 2007

ACKNOWLEDGMENTS

The research thesis was done under the supervision of Dr. Haim Azhari of the Faculty of

Bio-Medical Engineering, Technion. Ass/Prof Yehuda Agnon of the faculty of Civil and

Environmental Engineering, Technion, served as an adviser.

The generous financial help of the Technion is gratefully acknowledged.

CONTENTS

ACKNOWLEDGMENTS

CONTENTS

LIST OF FIGURES

ABSTRACT 1

GLOSSARY 3

INTRODUCTION 4

ULTRASONIC IMAGING 4

Imaging Methods 4

Velocity Estimation 6

Bio-Effects 6

SPEED OF SOUND DISPERSION 7

CODED EXCITATION 8

OBJECTIVES AND OUTLINE OF THE THESIS 10

OBJECTIVE 10

THESIS OUTLINE 10

METHODS 13

PAPER A: "MEASUREMENT OF SPEED OF SOUND DISPERSION

IN SOFT TISSUES USING A DOUBLE FREQUENCY CONTINUOUS

WAVE METHOD" 13

PAPER B: "ULTRASONIC SPEED OF SOUND DISPERSION

IMAGING" 40

PAPER C: "SPEED OF SOUND DISPERSION MEASUREMENT

USING A CHIRP SIGNAL" 61

PAPER D: "VELOCITY MEASUREMENTS USING A SINGLE

TRANSMITTED LINEAR FREQUENCY MODULATED CHIRP" 85

PAPER E: "A METHOD FOR LOCAL SPECTRAL ANALYSIS

USING CODED EXCITATIONS AND ITS APPLICATION IN

VELOCITY ESTIMATION" 102

DISCUSSION 118

CONTRIBUTIONS 118

FUTURE WORK 124

CONCLUSIONS 125

REFERENCES 126

LIST OF FIGURES

Figure 1 – a sample of a long burst comprising of two

frequencies, one being the double that of the other 119

Figure 2 – A sample of a linear frequency modulated signal

(Chirp). 119

Figure 3 - The speed of sound dispersion index versus the

average frequency for the turkey breast (left) and bovine

heart (right). The error bars correspond to the 95%

confidence level range. 121

Figure 4 – A schematic illustration of the setup used for

measurement of SOSD in soft tissue using pulse-echo

mode. 123

1

ABSTRACT

Ultrasonic imaging offers a valuable non-invasive diagnostic tool. The purpose of this study

was to investigate new techniques for ultrasonic imaging in order to: (a) Introduce a new

ultrasonic imaging contrast which may contribute to tissue characterization and tumour

detection. (b) Improve the performance of current methods. The chosen strategy to achieve

both challenges was to combine novel spectral analysis methods with the transmission of

special signals.

While most imaging techniques have focused on dominant properties such as tissue

echogenity and attenuation, speed of sound dispersion (SOSD) phenomenon is very weak

and difficult to measure, and hence has not been used for imaging. In this study, three new

methods for measuring SOSD which are sensitive for the weak dispersion in soft tissues are

introduced. Using the new techniques, SOSD is utilized as a new imaging contrast source.

Spectral analysis applied to backscattered ultrasound signals is used in many applications

such as attenuation mapping, tissue characterization, temperature monitoring and mean

scatterer spacing estimation. Furthermore, it plays a major role in velocity estimation since

velocity is associated with the frequency dependant Doppler shift. Signal to noise ratio

(SNR) is a great concern in such applications. Hence, it is desirable to utilize high energy

transmitted signals. The signal energy can be augmented by increasing the intensity of the

transmitted signal. However, this approach is limited by safety aspects. Alternatively, one

can increase the transmission duration, but this approach commonly decreases the axial

resolution. A method for performing localized spectral analysis using long structured

signals was developed.

In this study, it was shown that the combination of long structured signals and appropriate

algorithms yields benefits in terms of SNR, measurement accuracy and acquisition rate.

With respect to the measurement of SOSD, this study has clearly demonstrated the

feasibility of SOSD projection imaging and that SOSD may serve as a new contrast source.

Images, based on SOSD projections, and measurements of SOSD in soft tissues in pulse-

echo mode were presented for the first time. These new imaging techniques may contribute

2

to tissue characterization, tumour detection and breast diagnosis. One of the methods

developed for SOSD measurement was also found suitable for estimation of target velocity

in single ultrasonic transmission.

3

GLOSSARY

Abbreviations

A-Mode Amplitude Mode

B-Mode Brightness Mode

CT Computed Tomography

M-Mode Motion mode

SNR Signal to Noise Ratio

SOSD Speed of sound dispersion

TOF time of flight

TFR Time frequency representation

2D Two-dimensional

3D Three-dimensional

4

C h a p t e r 1

INTRODUCTION

This chapter is an overview of research areas which are related to this study.

Ultrasonic Imaging

In ultrasonic imaging, image formation is obtained by analysing ultrasonic waves passing

through an object. In this context, ultrasound is the mechanical vibration of matter with

frequencies above 20 kHz: above audible sound. Ultrasonic imaging methods are divided

into two families, “pulse-echo” and “transmission”. The pulse–echo method depends on the

emission of a pulse of ultrasound and the reception of its echo from an imaged target. The

transmission method is based on the measurement of a transmitted pulse after passing

through an imaged object.

Imaging Methods

A variety of imaging methods are derived from the two major imaging techniques.

A-Mode

The "A" in A-mode stands for "amplitude". The amplitude of an ultrasonic pulse reflected

from tissue structures along the beam path are presented on a display. The range from

which the echoes are reflected can be calculated from the time that has elapsed between the

pulse transmission and the reception of the echoes, given the wave propagation speed. This

type of information which is obtained for the beam path is referred to as A-line.

B-Mode

B-Mode is similar to A-mode, but the amplitude of reflected sound is displayed as

brightness along a one dimensional line which corresponds to time.

The A-mode and B-mode techniques are now used infrequently in medical imaging, but

they are the basic building blocks for the more advanced modes, currently used.

5

M-Mode

The M-Mode consists of a series of B-Mode lines displayed side-by-side so that movements

of tissues along the beam path can be traced. A high repetition rate of the measurements is

the advantage of this method and therefore it is still used for cardiac imaging.

B-Scan

B-Scan is a two-dimensional real time imaging method which is used to create a cross-

sectional view of imaged organs. The 2D images are formed out of sequential A-lines

(presented using brightness mode) which are obtained while sweeping the ultrasonic beam

to cover the imaged area. This is the most used ultrasonic imaging mode. Usually, the

measurements of other modes, if used, are presented on top of the B-Scan image. The

images are acquired with a high frame rate of up to 100 frames per second.

3D and 4D imaging

Three-dimensional (3D) ultrasonic images are obtained by compounding two-dimensional

B-Scan images. In modern ultrasonic devices, the 3D images are acquired fast enough to be

presented sequentially at several images per second. The term 4D imaging stands for

displaying 3D images as function of time, the fourth dimension.

Transmission

The transmission imaging method is based on measurements of an ultrasonic pulse which

has passed through an object. In this method a projection of the imaged object is obtained.

Depending on the signal generation and analysis used, different properties of the imaged

object can serve as the source of contrast for the projection. Projections of the absorption in

the imaged object are obtained by measurement of the amplitude of the received signal.

Projections of the speed of sound in the imaged object are obtained by measuring the total

time of flight (TOF) of the transmitted signal.

Ultrasonic Computed Tomography

Cross sectional images are formed out of multiple projections acquired from different

angles around the object and by using standard CT reconstruction algorithms. Projections of

the speed of sound and projections of the absorption in the imaged object can serve as the

source of contrast for the tomographic reconstruction.

6

Velocity Estimation

The Doppler Effect is named after an Austrian physicist Johann Christian Doppler. In

ultrasonic Doppler measurements, the change in a received frequency is used to estimate a

target’s velocity. This frequency shift is due to the relative motion between the sound

source and the reflecting target.

Continuous-wave Doppler

In continuous wave Doppler, two different transducers are used: one to send and the other

to receive a continuous harmonic signal. The velocity of the target is estimated out of the

frequency difference between the sent and received signals. In this method the depth of the

moving target can not be resolved.

Pulse-echo Doppler

Pulse-echo Doppler systems were developed in order to resolve the range from which the

ultrasonic beam is reflected by the moving target (e.g. blood). A single transducer is used to

transmit several pulses into the tissue and receive their reflections (A-lines). The movement

of the blood in the tissue causes changes in the A-lines. The velocity of the blood at a

certain tissue depth is estimated by analysing the variations in the A-lines at the

corresponding time delays (relative to pulse emission). The evolution of the power density

spectrum of the detected velocities as function of time is displayed as a sonogram.

Color Doppler

Color Doppler is a technique for displaying a map of blood flow in real-time. The velocity

estimation for multiple ranges and directions results in a flow map that is presented on top

of the B-scan image. The flow direction and mean velocity are designated by color and the

image brightness corresponds to the magnitude of the flow (Behar et al. 2003).

Power Doppler

In power Doppler, the total integrated Doppler power is displayed in color. This allows

better visualization of small vessels at the sacrifice of the velocity information.

Bio-Effects

Ultrasound imaging is considered to be a hazardless imaging modality. There is no doubt

that the diagnostic ultrasonic radiation is safer than X-ray radiation and that it is safer than

the radioisotopes which are used in other imaging modalities such as SPECT and PET.

7

However, ultrasonic imaging involves the transmission of energy to the body and this

energy has two major bio-effects: it may cause thermal heating and cavitation (Sheiner et al.

2007).

The temperature of a tissue may be raised by ultrasonic radiation, especially in places where

the ultrasonic absorption is high such as bone surfaces. Doppler ultrasound is more likely to

cause tissue heating than simple imaging since it utilizes many more transmissions per

second and they are targeted towards small regions. The thermal index (TI) is an indication

of the potential tissue temperature rise for three types of tissues. TIS is an index used to

provide an estimate for soft tissue exposures. TIB is used for bones close to the beam focus.

TIC is the cranial-bone thermal index (O’Brien et al. 1999). High energy ultrasonic beams

are utilized to cause tissue heating for therapeutic purposes.

Cavitation is the formation of transient or stable bubbles. The bubbles grow and then

contract due to the ultrasonic field. They may collapse causing instantaneous bursts of very

high temperatures and pressures, which are potentially harmful. The existence of gas in the

tissue being imaged increases the probability for cavitation. Therefore the danger of

cavitation is relatively higher in tissues that contain gas bodies, such as tissues of the lung

or intestine and tissues with artificial micro-bubbles (a contrast agent).

There are other bio-effects that should be considered when discussing ultrasonic radiation.

(a) In the presence of liquids, the ultrasonic beam may cause acoustic streaming which

potentially can cause shearing near solid objects and that may lead to thrombosis. (b)

Ultrasonic radiation force may cause electrical changes in cell membranes (Nyborg 2002).

Speed of Sound Dispersion

Speed of sound dispersion (SOSD) refers to the phenomenon of the change of speed of

sound with frequency. SOSD is very weak in soft tissues and was considered negligible in

medical imaging (Wells 1999). Hence, the measurement of the SOSD is considered more

difficult than the measurement of other acoustical properties such as attenuation (He 1999).

It has been suggested by O'Donnell et al. (1981) that the SOSD in an unbounded medium is

connected to the attenuation by the "Kramers-Kronig" relationship. They also derived

useful approximations for this relation.

8

The measurement of speed of sound dispersion in nonbiological substances was done by

several researchers. Wolfgang and Yih-Hsing (1978) measured the dispersion in dispersive

solids. Chin et al. (1990) and He (1999) measured the dispersion in highly-attenuating

specimens in order to verify the Kramers-Kronig relationship for acoustic waves. Lang et

al. (2000) measured the dispersion in nanocrystalline materials.

Few investigators have studied the speed of sound dispersion in biological tissues. Kremkau

et al. (1981) measured the speed of sound dispersion in normal brain tissue. Wear (2000),

Strelitzki and Evans (1996) and Droin et al (1998) measured the dispersion in bones.

Pedersen and Ozcan (1986) measured the dispersion in lung tissues. Carstensen and

Schwan (1959) measured acoustic properties of hemoglobin solutions including dispersion.

Recently, Marutyan et al (2006) have studied the SOSD in myocardial tissue.

Coded Excitation

The signal to noise ratio (SNR) is a great concern in ultrasonic applications. Hence, it is

desirable to utilize high energy transmitted signals. The signal energy can be augmented by

increasing the intensity of the transmitted signal. However, this approach is limited by

safety aspects. Alternatively, one can increase the transmission duration since in most of the

medical imaging systems the average power delivered to the imaged tissue is significantly

lower than the maximum allowed radiation level (M. O‘Donnell 1992), but this approach

commonly decreases the axial resolution.

An approach for utilizing long signals without sacrificing the axial resolution is the

implementation of coded excitation (Misaridis and Jensen 2005, Behar 2004). With this

approach, a long coded signal such as a chirp is used to transmit high energy while

preserving low intensity constraints. Using coded signals, the spatial resolution can be

recovered with an appropriate compression algorithm, such as matched filter techniques

(Pollakowski and Ermert 1991). The concept of using coded excitation was borrowed from

other modalities (e.g. radar, Soumekh 1999).

Frequency modulated excitation codes have been considered for ultrasonic imaging as well

as binary codes, such as Golay sequences. The Golay sequences are used in pairs for

sidelobes cancellation (Bae et al. 2002). In a thorough study, Misaridis and Jensen (2005a,

9

2005b and 2005c) conclude that frequency modulated signals have the best performance in

ultrasonic imaging. However, other codes are used in some imaging systems.

10

C h a p t e r 2

OBJECTIVES AND OUTLINE OF THE THESIS

This chapter states the objectives of the research and sketches its outline.

Objective

Ultrasonic imaging offers a valuable non-invasive diagnostic tool. The purpose of this study

was to investigate new techniques for ultrasonic imaging in order to: (a) Introduce a new

ultrasonic imaging contrast which may contribute to tissue characterization and tumour

detection. (b) Improve the performance of current methods. The chosen strategy to achieve

both challenges was to combine novel signal analysis methods with the transmission of

special coded signals.

Thesis outline

This thesis is comprised of five papers (A-E), three of them were accepted for publication

and the two others have been submitted.

Paper A: "Measurement of Speed of Sound Dispersion in Soft Tissues Using a Double

Frequency Continuous Wave Method"

While most ultrasonic imaging techniques have focused on dominant properties such as

tissue echogenity, speed of sound and attenuation. The speed of sound dispersion (SOSD)

phenomenon is very weak and difficult to measure, and hence has not been used for

imaging. In this paper, a novel method for measuring the speed of sound dispersion is

introduced. The method combines a short pulse transmission followed by a long burst

comprising of two frequencies, one being the double that of the other. In the paper, the

method is validated by measurement of SOSD in plastic samples. Then the applicability of

the method for usage in soft tissues is tested by measurements of SOSD in in-vitro soft

tissues samples. The significance of the difference in the speed of sound dispersion index

11

between the studied materials is checked to confirm the potential of SOSD to be used as a

new index for soft tissue characterization by ultrasound.

Paper B: "Ultrasonic Speed of Sound Dispersion Imaging"

In paper B, the feasibility for speed of sound dispersion (SOSD) imaging was investigated.

Using a through transmission mode, the method which was introduced in paper A for

SOSD measurement, was utilized. SOSD projection images which were obtained by

scanning objects immersed in water using a raster mode utilizing a computerized scanning

system are presented. Using this approach SOSD projection images were obtained for

solids and fluids as well as for a tissue mimicking breast phantom and an in-vitro soft

tissues phantom. The results obtained in the paper, have clearly demonstrated the feasibility

of SOSD projection imaging.

Paper C: "Speed of Sound Dispersion Measurement Using a Chirp Signal"

In the study covered in paper C, two new methods for speed of sound dispersion

measurement were developed. The main advantage of these methods is the ability to

measure SOSD in the pulse-echo mode in soft tissues. These methods are based on the

transmission of a linear frequency modulated “chirp” pulse. The first method, entitled as the

“signals bank method" is based on assessment of similarity between the measured signal

and a synthesized bank of signals. The second method, titled the "cross correlation method"

is computationally faster and is based on the calculation of the phase of the peak of the

complex cross correlation function. The performance of the methods in terms of robustness

and computational effort are compared in the paper. To the best of our knowledge, SOSD

measurements in the pulse-echo mode in soft tissues are published for the first time in this

paper.

Paper D: "Velocity Measurements Using a Single Transmitted Linear Frequency

Modulated Chirp"

12

In paper D, a new method for velocity estimation using a single linear frequency modulated

chirp transmission is presented and implemented for ultrasonic measurements. The method

is based on the calculation of the complex cross correlation function between the

transmitted and reflected signals. The velocity is then calculated from the phase of the peak

of the envelop of this cross correlation function. In this paper, the suggested method was

verified using computer simulations and experimental measurements in an ultrasonic

system.

Paper E: "A Method for Local Spectral Analysis Using Coded Excitations and its

Application in Velocity Estimation"

In paper E, a method for performing localized spectral analysis is suggested. The method is

based on transmitting a long frequency modulated signal. The frequency dependent

information of the detected backscattered waves is obtained by using a time frequency

transform such as the short time Fourier transform (STFT). The spatial resolution is

retrieved by the rearrangement of the frequency-time relationship of the signal.

In this paper, a simulation program was used to confirm the ability of this method to serve

as a tool for velocity estimation. The simulated echoes reflected from a moving target after

the transmission of a long chirp signal were analyzed. The performance of the suggested

method was compared to a conventional method for velocity estimation.

13

C h a p t e r 3

METHODS

Paper A: "Measurement of Speed of Sound Dispersion in Soft Tissues Using a Double

Frequency Continuous Wave Method"

Abstract

A method for measuring the speed of sound dispersion is introduced. The method

combines a short pulse transmission followed by a long burst comprising of two

frequencies, one being the double that of the other. The method allows the determination of

the speed of sound dispersion using a single transmission. To validate the method, the

dispersion was first measured in plastic samples and then in in-vitro soft tissues samples.

The results obtained for perspex samples are in excellent agreement with values reported in

the literature. The dispersion index in soft tissues ranged for a bovine heart from 0.63 ±

0.24 (m/sMHz) at 1.5 MHz to 0.27 ± 0.05 (m/sMHz) at 4.5 MHz and for a turkey breast

from 1.3 ± 0.28 (m/sMHz) at 1.75 MHz to 0.73 ± 0.1 (m/sMHz) at 3.8 MHz. The

14

significant difference in the speed of sound dispersion index between the studied materials

indicates that dispersion may be used as a new index for soft tissue characterization by

ultrasound.

Keywords: Ultrasound, Speed of sound, Dispersion, Tissue characterization.

15

Introduction

Tissue characterization by ultrasonic measurements may offer a valuable noninvasive

diagnostic tool. Numerous studies have investigated the typical acoustic properties of

normal and abnormal tissues. While most studies of soft tissue properties have focused on

dominant properties such as speed of sound (e.g., Manoharan (1988)) and attenuation (e.g.,

Bhatia and Singh (2001)), less attention has been given to dispersion. Presumably, this

stems from the fact that the speed of sound dispersion phenomenon is very weak and could

be considered to be negligible in most applications.

Measurement of speed of sound dispersion in nonbiological substances was done by

several researchers. Wolfgang and Yih-Hsing (1978) measured the dispersion in dispersive

solids. Chin et al. (1990) and He (1999) measured the dispersion in highly-attenuating

specimens in order to verify the Kramers-Kronig relationship for acoustic waves. Lang et

al. (2000) measured the dispersion in nanocrystalline materials.

Few investigators have studied the speed of sound dispersion in biological tissues.

Kremka et al. (1981) measured the speed of sound dispersion in normal brain. Wear (2000),

Strelitzki and Evans (1996) and Droin et al (1998) measured the dispersion in bones.

Pedersen and Ozcan (1986) measured the dispersion in lung tissues. Carstensen and

Schwan (1959) had measured acoustic properties of hemoglobin solutions.

In most of the above-mentioned studies, the dispersion was calculated by investigating the

variation of the phase as a function of the acoustic wave frequency. Usually, a short

broadband ultrasonic pulse was sent through the object and the phase of each frequency was

extracted using FFT. One limitation of this technique is its relatively low SNR as compared

with continuous wave (CW) measurements. This may induce inaccuracies in phase

16

measurements for each individual frequency. Another challenge in calculation of the

dispersion from a broadband pulse is the determination of the pulse's time of arrival (Zhao

2005). This is a problematic task, since the pulse shape is distorted in dispersive and

attenuating media. This problem was investigated thoroughly by Wear (2001). He (1999)

handled this issue by implementing a trial and error procedure for preparation of the

recorded signal prior to the spectral analysis. Others have used phase unwrapping

procedures (Strelitzki and Evans (1996), Droin (1998), Wear (2000)).

Measurements of speed of sound dispersion using continuous waves were done by Ting

and Sachse (1978) and Pedersen and Ozcan (1986). With their implemented techniques,

many sequential transmissions of continuous waves with increasing frequencies are

required. The technique implemented by Ting and Sachse (1978) requires repeated

measurements of several frequency transmissions through specimens with variable

thicknesses. Pedersen and Ozcan (1986) measured the phase of consecutive frequencies

from nearly-DC to the maximal studied frequency (800 kHz), in order to obtain the

cumulative phase. Both techniques are time consuming.

In the present study, we introduce a method which utilizes a long pulse comprising of two

frequencies, one being the double that of the other. Using this method, we were able to

measure the weak phenomenon of the speed of sound dispersion in soft tissue specimens.

Methods and Materials

Theory

Consider a specimen of an examined material placed between two transducers and

immersed in the water bath (Fig. 1). An ultrasonic harmonic wave with a specific frequency

f is transmitted and travels from point A to point B. The phase of the signal at point A is

17

0, 2fA f t ft (1)

where 0 , 0f A f t is the initial phase of the transmitted wave.

The phase of the wave reaching point B is

0, , ( ) 2 ( )fB Af t f t t f f t t f (2)

where ( )t f is the traveling time for an ultrasonic wave of specific frequency f to travel

from point A to point B.

If the distance between points A and B is L and fc l is the frequency-medium-

dependent phase velocity of the ultrasonic signal along the way from A to B , ( )t f can be

expressed by

0

1( )

L

f

t f dlc l

. (3)

In a simple configuration, where the medium comprises only water and the examined

specimen, the above integral can be replaced by

,

( ) s s

f s w

L L Lt f

c c

(4)

where sL is the depth of the specimen, wC is the sound velocity in water (water is

considered as nondispersive medium Carstensen (1954)) and ,f sc is the frequency-

dependent sound velocity of the specimen.

Replacing ( )t f in Eqn 2 yields

18

0

,

, 2f

s sB

f s w

L L Lf t f t

c c

. (5)

In order to compare the phases of two frequencies, it is convenient to normalize the phase

by 2 f , converting it into a time scale,

0

,

,

2 2

fB s s

f s w

f t L L Lt

f f c c

. (6)

If the specimen is dispersive, this term will vary with the frequency. The difference

between the normalized phases of two frequencies 1f and 2f will thus equal

1 2

1 2

0 01 2

1 2 , , 1 2

, ,

2 2 2 2

f fB B s s

f s f s

f t f t L L

f f c c f f

(7)

and, since 0 f can be set to be zero either by the system setup or by manipulating the data

in postprocessing, we can neglect the last two terms and obtain

2 1

1 2

1 2 , ,

, ,

2 2

B B s s

f s f s

f t f t L L

f f c c

. (8)

The term on the right hand side is the difference in the time of flight ( )TOF through the

specimen resulting from the speed of sound dispersion,

19

2 1, ,

s ss

f s f s

L LTOF L

c c . (9)

From this equation the, frequency-dependent speed of sound difference for the two

frequencies for a specific specimen, i.e., 2 1, ,f s f sc c , can be determined by

1 2 2 1, , , ,

s

f s f s f s f s

s

TOF Lc c c c

L

. (10)

The group velocity of the sound in the specimen, ,g sc , is related to the phase velocity by

(Strelitzki and Evans 1996)

,

,,

,

1

f s

g sf s

f s

cc

dcf

c df

. (11)

In low-dispersive media, ,f sdc

dfis small and , ,f s g sc c ; therefore, the approximation

2 1

2

, , ,f s f s g sc c c is valid and we get the final form of the variation in the speed of sound,

1 2

2

, , ,

s

f s f s g s

s

TOF Lc c c

L

. (12)

Naturally, there is a linear relation between sTOF L and the specimen depth sL . Thus,

in order to overcome noise and measurement errors, the variation in the speed of sound can

be calculated from the slope of the curve that describes sTOF L as function of sL This

20

can be done by repeating each experiment with a given frequency pair 1f and

2f several

times using different specimen depths.

The problem stems from the fact that the phases which are used on the left-hand side of

Eqn 8 are cumulative. However, in practice, only the wrapped phase of each frequency,

' ,B f t , is measured (e.g., using the Fourier transform of the recorded signal). Thus, the

left-hand side of Eqn 8 needs to be rewritten as

1 2 1 1 2 2

1 2 1 2

, , ' , 2 ' , 2

2 2 2 2

B B B Bf t f t f t n f t n

f f f f

(13)

where 1n and 2n are unknown integers.

In order to overcome this problem, let us consider a special case where the second

frequency equals twice the first frequency, i.e., 2 12f f . In this case, the difference in the

time of flight can be calculated from the wrapped phases,

1 1 1 2 1 1 1 2

1 1 1 1 1

' , 2 ' 2 , 2 ' , ' 2 , 2

2 4 2 4 2

B B B Bf t n f t n f t f t n n

f f f f f

. (14)

Thus, in this configuration, the cumulative phases are not needed any more for

calculating sTOF L : we just have to find the integer 1 22m n n . After rearrangement

and substituting into Eqn 8, we obtain,

21

1 1

1

' , ' 2 ,2

2

B B

s

f t f tm f TOF L

. (15)

If the dispersion is very low (as is the case in many materials), then sTOF L is very

small as well. In the case that the nondimensional parameter fulfils the condition

12 0.5sf TOF L , the integer m can be simply found by

1 1' , ' 2 ,

2

B Bf t f tm round

(16)

where round[] is the operation of rounding to the nearest integer. Therefore, sTOF L

can be determined from

1 1

1 1 1

1 1 1 1

1 1 1

' , ' 2 ,

2 4 2

' , ' 2 , ' , ' 2 ,1.

2 4 2 2

B B

s

B B B B

f t f t mTOF L

f f f

f t f t f t f tround

f f f

(17)

By substituting this equation into Eqn 10, the value of (2 1, ,f s f sc c ) can be determined.

Finally, by using this value, a dispersion index is defined as

2 1

1 2

2 1

( , )f fc cc

f ff f f

. (18)

Ultrasonic Measurements

The scanning system utilized to measure the plastic specimens is comprised of a water-bath

with a specially-built computer-controlled mechanism that can produce spatial motion with

22

three degrees of freedom for a pair of transducers (Panametrics, 5 MHz, focused

transducers, diameter 12.7 mm and focal length 10.7cm) placed about twice the focal length

apart (Azhari and Stolarski (1997), Azhari and sazbon (1999)). The system can scan a

cylindrical volume defined by the user (up to 20 cm in diameter and 10 cm in height)

located at the center of the water bath.

Signals were generated by a Tabor 8026 arbitrary wave-form generator and a Panametrics

5800 pulser/receiver was used as a receiver. A Gage CompuScope 12100 two-channel 50-

MHz 12-bit A/D converter was used digitally to store the detected waves.

The experimental procedure for the plastic specimens started by acquiring an ultrasonic

projection depicting the TOF of the step phantom, using a short ultrasonic pulse. This

projection was used for calculating the group velocity ,g sc of the sound in the specimen.

Afterwards, a continuous wave, which was built by mixing a pair of sinusoidal waves with

frequencies f and 2f, was generated. The initial phase for both frequencies was set to zero

using the signal generator. The two steps can be combined into a single measurement, as

shown in Fig 2. The transmitted continuous wave was actually a long but finite sinusoidal

train with a defined front. A rect sampling window was taken from the front end of this

train and its length was set to be shorter than the time needed for the first reverberation to

occur. This was done in order to avoid measurement artifacts stemming from the formation

of standing waves in the specimens. At least 12 µs of the wave were sampled by the A/D

for signal analysis.

Using Eqn 17, the corresponding TOF was calculated for each step in the phantom. A

plot depicting sTOF L as a function of sL was then obtained by combining all the

results. Using the least-squares method, a straight line was fit to this set of data. Then the

velocity difference between ,s fc and ,2s fc was found from the slope of the fitted line. It

23

should be clarified that the line-fitting stage is not a necessity for the suggested method, but

was implemented in order to augment the accuracy of our calculation. (The values could be

readily extracted from a single measurement, as explained in the previous section, eqn 12.)

The above procedure was repeated several times using waves composed of different pairs

of frequency mixtures ranging from {1 MHz and 2 MHz} to {3 MHz and 6 MHz}. Finally,

combining all the obtained results, the dispersion index 1 2( , )f f defined in Eqn 18 was

plotted versus the average frequency used, i.e., 2 1( ) / 2f f .

A slightly different set-up was implemented for the soft tissue specimens. Instead of

scanning different tissue samples with various thicknesses, the same sample was placed

within a plastic cylinder (10 cm in length and 4 cm in diameter) positioned between the

transducers pair so that its axis was aligned with the line of sight connecting the two

transducers. After completing one set of measurements, as described above, the tissue

sample was slightly pushed out of the cylinder and a small slice was cut and removed

(similar to cutting a salami, see also scissors icon in Fig.1). Then, the above procedure was

repeated and a new set of measurements was obtained. This was done to ensure that the

only parameter changed between measurements was the tissue thickness, assuming that the

acoustic properties were constant throughout the sample.

In addition, to ensure that the plastic cylinder did not affect the measurements, a

comparative study was done in water, with and without the cylinder. The signals were

compared and no changes were observed.

All the above experiments were done at room temperature (about 21oC).

24

Specimens

In this research, the dispersion was first studied in two plastic materials and then in two

soft tissues (in-vitro). The plastics were polyvinylchloride (PVC) and

polymethylmethacrylate (perspex). They were studied in order to validate the method, to

establish some standard reference and to allow comparison with results published by others.

The soft tissues used here were bovine heart and turkey breast. The soft tissue specimens

had been refrigerated until the experiment.

In order to increase the accuracy and reliability, several measurements of each specimen

with varying thicknesses were done. Several thicknesses of the plastic specimens were

obtained by building a “step-phantom” with parallel faces, varying in distances from 2 cm

to 3 cm from each other. Small slices were chopped from the soft tissue specimens during

the experiment, in order to measure several widths of each soft tissue specimen. The

thicknesses of the plastic specimens were measured with a caliper (accuracy ±0.1 mm). The

thicknesses of the tissue specimens were calculated using two steps. First, the speed of

sound in the tissue was estimated. Then, by the measuring the TOF, the thickness was

determined (estimated accuracy ±1 mm).

Results

Plastic Specimens

The calculated dispersion index 1 2( , )f f versus 2 1( ) / 2f f obtained for the PVC

specimen is plotted in Fig 3. The average values for each pair of frequencies studied are

25

depicted along with their corresponding 95% confidence level range (vertical bars). As can

be noted, the dispersion index is positive throughout the studied range of frequencies but

monotonically decreases from 9.7 ± 2.5 (m/sMHz) at 1.5 MHz to 2.9 ± 0.5 (m/sMHz) at

4.5 MHz. Also, as can be noted, the relative scatter of the data tends to decrease as the

frequency is increased.

The dispersion index 1 2( , )f f versus 2 1( ) / 2f f for the perspex specimen is presented

in Fig 4. As can be observed, the dispersion index values are smaller compared with those

obtained for the PVC. Also, one may note again that the dispersion index is higher for the

lower frequency range and that it decreases as the frequency increases. The abrupt increase

in 1 2( , )f f from 1.5 MHz to 1.875 MHz may be attributed to measurement errors (note

the large 95% confidence range). The dispersion index decreases in this case from 6.5 ± 4

(m/sMHz) at 1.5 MHz to 1.5 ± 0.5 (m/sMHz) at 4.5 MHz.

Soft Tissues

A demonstrative data set obtained for the turkey breast specimen, depicting sTOF L

as a function of sL for the frequency pair {2.25 MHz and 4.5 MHz}, is shown in Fig. 5.

The linear relation is clearly noted. The negative sTOF L values stem from the fact that

the speed of sound increases with the frequency for the range studied here. As can be noted,

sTOF L in this case ranges from about 10 ns to 60 ns. The speed of sound dispersion

index for the turkey breast is presented in Fig. 6. Again, the trend for a decrease in

1 2( , )f f as the frequency increases is noted. The dispersion index decreases in this case

from 1.3 ± 0.28 (m/sMHz) at 1.75 MHz to 0.73 ± 0.1 (m/sMHz) at 3.8 MHz. These values

are significantly smaller than those obtained for the plastic specimens.

26

The speed of sound dispersion index values obtained for the bovine heart are presented in

Fig. 7. As can be noted, in this case, the dispersion indices are generally smaller than those

obtained for the turkey breast. The tendency for the dispersion index to decrease with the

frequency can be noted. However, although the dispersion index values in the frequency

range studied were reduced by 50%, the rate of decrease is more moderate than for the

turkey breast. The dispersion index decreases, in this case, from 0.63 ± 0.24 (m/sMHz) at

1.5 MHz to 0.27 ± 0.05 (m/sMHz) at 4.5 MHz.

Discussion

A novel method for measuring the speed of sound dispersion has been introduced and its

application in soft tissue specimens has bean demonstrated. It combines a short (broad-

band) pulse transmission followed by a long burst comprising of two frequencies, one being

double the other. The method allows the determination of the dispersion using a single

transmission. Although we have used here data obtained from several tissue thicknesses, it

should be pointed out that this is not a necessity for the suggested method, but was done in

order to improve the accuracy of our calculations. Also, the method does not require

absolute phase evaluation or any phase unwrapping procedure.

Studying our findings in the plastic specimens reveals that our dispersion measurements

in perspex are in excellent agreement with He's (1999) results. We have measured 7 ± 4

(m/sMHz) at 1.5 MHz and 2 ± 0.4 (m/sMHz) at 3.8 MHz. According to He’s (1999)

measurements (which were obtained using a short pulse method), the speed of sound

dispersion at 1.25 MHz is around 7 (m/sMHz) and it is around 2.5 (m/sMHz) at 3.5 MHz.

This provides a validation to the reliability of our suggested method.

27

Carstensen and Schwan (1959, Fig 6) had measured acoustic properties of hemoglobin

solutions and found that the speed of sound dispersion in beef hemoglobin

(30 g Hb/100 ml , 250C) at 1 MHz is around 0.7 (m/sMHz) and it is around 0.25

(m/sMHz) at 4 MHz. Kremkau et al. (1981) measured the speed of sound dispersion in

normal brain to be 1.2 (m/sMHz) and 1 (m/sMHz) for fresh and fixed tissue, respectively.

Our results are in the same order of magnitude.

Positive dispersion (i.e., the speed of sound increases with the frequency) was found for

all the studied specimens. The dispersion index, on the other hand, decreases as a function

of the frequency in all the studied materials. This behavior agrees with the results reported

by Chin et al. (1990) for polyurethane and He (1999) for perspex and Carstensen and

Schwan (1959, Fig 6) for hemoglobin solutions. Droin et al. (1998) and Wear (2000)

reported similar trends for polycarbonate specimens.

Naturally, the structure of bones differs substantially from that of soft tissues.

Nevertheless, it is worth noting that, comparing the results obtained for the soft tissue

specimens in this study with those reported for bones, reveals opposite trends. In bones,

negative dispersion was reported by Wear (2000), Strelitzki and Evans (1996) and Droin et

al (1998).

Another observation obtained in this study is the consistent decrease in the dispersion

index scatter with the increase in frequency. This is indicated by the smaller size of the 95%

confidence range in Figs. 3,4,6 and 7 for the higher frequencies. This may be attributed to

the lower ultrasonic diffraction occurring at high frequencies. Due to the diffraction

phenomenon, which is more dominant for the lower frequency waves, the acoustic paths

28

may be slightly different for different frequency waves and that may consequently change

the TOF .

In conclusion, a novel method for measuring the speed of sound dispersion has been

introduced. With this method, dispersion in soft tissues was measured. The differences in

the dispersion index between the studied materials were found to be significant. This

indicates that dispersion may be used as a new index for soft tissue characterization by

ultrasound if a through transmission imaging technique (e.g., ultrasonic breast CT) is

utilized to map its variations in a studied object.

29

Acknowledgments

The authors are grateful for funding provided by the Galil Center For Telemedicine And

Medical Informatics and by the Technion V.P.R. Research funds, Eliyahu Pen Research

fund, Dent Charitable Trust, Japan Technion Society and the Montréal Biomedical Fund.

Finally we thank Mr. Aharon Alfasi for his extremely valuable technical support.

30

References

Azhari H, Stolarski S. Hybrid ultrasonic computed tomography. Comput Biomed Res. 1997

Feb;30(1):35-48.

Azhari H, Sazbon D. Volumetric imaging with ultrasonic spiral CT. Radiology

1999;212(1):270-275.

Bhatia KG, Singh VR. Ultrasonic characteristics of leiomyoma uteri in vitro. Ultrasound

Med Biol. 2001;27:983-987.

Carstensen EL. Measurement of Dispersion of Velocity of Sound in Liquids. J. Accoust.

Soc. Am 1954;26:858-861.

Carstensen EL, Schwan HP. Acoustic Properties of Hemoglobin Solutions. J Accoust Soc

Am 1959;31:305-311

Chin C, Lahham M, Martin BG. Experimental Verification of the Kramers-Kronig

Relationship for Acoustic Waves IEEE Trans Ultrason Ferroelectr Freq Control

1990;37:286-294.

Droin P, Berger G, Laugier P. Velocity Dispersion of Acoustic Waves in Cancellous Bone.

IEEE Trans Ultrason Ferroelectr Freq Control 1998;45:581-592.

He P. Experimental Verification of Models for Determining Dispersion from Attenuation.

IEEE Trans Ultrason Ferroelectr Freq Control 1999;46:706-714.

Kremkau FW, Barnes RW, McGraw CP. Ultrasonic attenuation and propagation speed in

normal human brain. J Accoust Soc Am 1981;70:29-38.

Lang MJ, Duarte-Dominguez M, Arnold W. Extension of frequency spectrum methods for

phase velocity measurements in ultrasonic resting. Rev Sci Instrum 2000;71:3470-3473.

31

Manoharan A, Chen CF, Wilson LS, Griffiths KA, Robinson DE. Ultrasonic

characterization of splenic tissue in myelofibrosis: further evidence for reversal of fibrosis

with chemotherapy. European-journal-of-haematology 1988;40:149-154.

Pedersen PC, Ozcan HS. Ultrasound properties of lung tissue and their measurements.

Ultrasound Med Biol. 1986 Jun;12(6):483-99.

Wolfgang S, Yih-Hsing P. On the determination of phase and group velocities of dispersive

waves in solids J. Appl. Phys. 1978;49(8):4320-4327.

Strelitzki R, Evans JA. On the measurements of the velocity of ultrasound on the os calcis

using short pulse. European Journal of Ultrasound 1996;4:205-213.

Ting CS. Sachse W. Measurement of ultrasonic dispersion by phase comparison of

continuous harmonic wave. J Acoust Soc Am 1978;64(3):852-857.

Wear KA. Measurments of phase velocity and group velocity in human calcaneus.

Ultrasound Med Biol 2000;26:641-646.

Wear KA. A numeric method to predict the effect of frequency-dependent attenuation and

dispersion on speed of sound estimates in cavcellous bone. J Acoust Soc Am

2001;109(3):1213-1218.

Zhaoa B, Basira OA, Mittal GS, Estimation of ultrasound attenuation and dispersion using

short time Fourier transform, Ultrasonics 2005;43(5);375-381.

32

List of Figures captions.

Fig. 1. A Schematic depiction of the experimental system used here. A specimen of an

examined material was placed in water between two transducers. An ultrasonic wave was

transmitted through the specimen from A to B, detected and digitized. The specimen was

sliced (symbolized by the scissors icon) between different measurements to vary its

thickness (see text).

Fig. 2. Schematic depiction of the transmitted waves needed for the suggested method. A

short pulse transmission which is used for measuring the group velocity Cg is followed by a

long burst comprising of two frequencies, one being the double of the other.

Fig. 3. The speed of sound dispersion index 1 2( , )f f versus 2 1( ) / 2f f for the PVC

specimen. The error bars correspond to the 95% confidence level range.

Fig. 4. The speed of sound dispersion index 1 2( , )f f versus 2 1( ) / 2f f for the perspex

specimen. The error bars correspond to the 95% confidence level range.

Fig. 5. A demonstrative data set obtained for the turkey breast specimen, depicting

sTOF L as a function of sL for the frequency pair {2.25 MHz and 4.5 MHz}.

Fig. 6. The speed of sound dispersion index 1 2( , )f f versus 2 1( ) / 2f f for the turkey

breast. The error bars correspond to the 95% confidence level range.

Fig. 7. The speed of sound dispersion index 1 2( , )f f versus 2 1( ) / 2f f for the bovine

heart. The error bars correspond to the 95% confidence level range.

33

Fig. 1

34

Fig. 2.

35

Fig. 3.

36

Fig. 4.

37

Fig. 5.

38

Fig. 6.

39

Fig. 7.

40

Paper B: "Ultrasonic Speed of Sound Dispersion Imaging"

Abstract

The feasibility for speed of sound dispersion (SOSD) imaging was investigated here. A

through transmission new method for measuring the SOSD was utilized. With this method

a long pulse comprising of two frequencies 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 a computerized scanning

system. Using this approach SOSD projection images were obtained for solids and fluids as

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 source and potentially may aid in breast

diagnosis.

Keywords: Medical imaging, Ultrasound, Speed of sound Dispersion, Tissue

characterization.

41

Introduction

The speed of sound dispersion (SOSD) phenomenon in soft tissues is very weak (Wells

1999), therefore, it is difficult to detect and measure and hence it was neglected in most

applications. However, several techniques for SOSD measurements have been suggested

and implemented for in-vitro specimens. For example, SOSD was measured in human

brains by Kremkau et al. (1981), in lungs by Pedersen and Ozcan (1986), in hemoglobin

solutions by Carstensen and Schwan (1959). Also, Marutyam et al. (2006) have measured

SOSD in lamb hearts, and Akashi et al. 1997 and Levy et al. (2006) in bovine hearts.

Recent studies indicated that speed of sound dispersion (SOSD) may be used for

ultrasonic tissue characterization. Marutyam et al. (2006) reported that the SOSD depends

on the orientation of anisotropic tissue. Levy et al. (2006) have shown that there is a

significant difference in the dispersion index between different specimens.

In Levy et al. (2006) a method for measuring the speed of sound dispersion using a single

transmission which utilizes a long pulse comprising of two frequencies, one being the

double that of the other was introduced. This method is suitable for imaging using a through

transmission mode. The objective of this study was to investigate the feasibility of utilizing

this method for SOSD imaging.

Methods and Materials

Theory

Consider an examined object (e.g. woman breast) placed between two transducers and

immersed in the water bath (Fig. 1). An ultrasonic signal which is comprised of two

42

frequencies f1, f2 is transmitted and travels from point A to point B. Using spectral analysis,

the signal can be decomposed into its two disjoint components. The phase of each

component at point A is

0, 2fA f t ft (1)

where 0 , 0f A f t is the initial phase of the transmitted wave.

The phase of the wave reaching point B is

0, , ( ) 2 ( )fB Af t f t t f f t t f (2)

where ( )t f is the traveling time for an ultrasonic wave of a specific frequency f to

travel from point A to point B.

If the distance between points A and B is L and fc l is the frequency-medium-

dependent phase velocity of the ultrasonic signal along the way from A to B , ( )t f can be

expressed by

0

1( )

L

f

t f dlc l

(3)

In order to compare the phases of two frequencies, it is convenient to normalize the phase

by 2 f , converting it into a time scale,

0

0

, 1

2 2

f

L

B

f

f tt dl

f f c l

. (4)

43

The difference between the normalized phases of two frequencies 1f and

2f will thus be

equal to

1 2

2 1

0 01 2

1 2 1 20

, , 1 1

2 2 2 2

f f

L

B B

f f

f t f tdl

f f c l c l f f

(5)

and, since 0 f can be set to equal zero either by the system's hardware setup or by post

processing, we can neglect the last two terms and obtain

2 1

1 2

1 2 0

, , 1 1

2 2

L

B B

f f

f t f tdl

f f c l c l

. (6)

The term on the right hand side is the difference in the time of flight from point A to point

B through the imaged object between frequency f1 and frequency f2 resulting from the speed

of sound dispersion. This time of flight difference is denoted by1 2

TOF f f ( , ) . Water is

considered as nondispersive medium (Carstensen 1954), therefore, the frequency-

dependence of the time of flight represents solely the imaged object properties. Defining

1 2TOF f f ( , ) per unit length at distance l from the transmitter as

2 1

1 2

1 1( , , )

f f

l f fc l c l

(7)

44

the time difference between the normalized phases of two frequencies 1f and

2f can be

written as

1 2

1 2 1 2

1 2 0

, ,( , ) ( , , )

2 2

L

B Bf t f tTOF f f l f f dl

f f

. (8)

Hence, measurement of the difference between the normalized phases gives a projection of

the accumulative along the track from A to B. Nevertheless, it is not trivial to obtain this

measurement since the phases which are used on the left-hand side of Eqn (8) are

cumulative and can exceed 2 . Thus, in practice, only the wrapped phase of each

frequency, ' ,B f t , is measured (e.g. using the Fourier transform of the recorded signal).

In order to overcome this problem, let us consider a special case where the second

frequency equals twice the first frequency, i.e., 2 12f f . In case that the nondimensional

parameter fulfils the condition 1 1 1

0

2 ( , ,2 ) 0.5

L

f l f f dl , it was shown by Levy et al.

(2006) that the difference in the time of flight can be calculated from the wrapped phases

1 1 1 1

1 1

1 1 10

' , ' 2 , ' , ' 2 ,1( , ,2 )

2 4 2 2

L

B B B Bf t f t f t f tl f f dl round

f f f

(9)

where round[] is the operation of rounding to the nearest integer.

In order to reconstruct a projection image 1

I x y f( , , ) of the SOSD, the object can be

scanned in a raster mode, so as to depict the relation

45

1 1 1

0

( , , ) ( , , , , 2 )

L

I x y f x y z f f dz . (10)

The constraint 1 1 1

0

2 ( , ,2 ) 0.5

L

f l f f dl is mandatory for accurate measurement of the

accumulative dispersion. However, for imaging proposes it is sufficient to avoid phase

wrapping in the region of interest (ROI). Therefore, the constraint is on the variation of the

accumulative dispersion in the ROI

1 1 1 1

10 0

1max ( , , , ,2 ) min ( , , , , 2 )

2

L L

ROI x y l f f dl x y l f f dlf

(11)

where { , }x y ROI .

Ultrasonic Measurements

The scanning system utilized to generate the accumulative dispersion index projection of

the imaged object comprised of a water tank with a specially built computer controlled

mechanism that can produce spatial motion with three degrees of freedom for a pair of

transducers (Panametrics, 5 MHz, focused transducers, diameter 12.7 mm and focal length

10.7cm) placed about twice the focal length apart (Azhari and Stolarski (1997), Azhari and

sazbon (1999)). The system can scan a cylindrical volume defined by the user (up to 20cm

in diameter and 15cm in height) located at the center of the water tank. In the imaging

configuration utilized here the object was scanned in a raster mode, yielding a rectangular

projection image 1

I x y f( , , ) (see eqn.(10)). The scanning resolution was set by the user

before each scan. Typical scanning resolution was 0.3mm X 1mm along the horizontal and

vertical directions respectively.

46

Signals were generated by a Tabor 8026 arbitrary wave-form generator and a Panametrics

5800 pulser/receiver was used as a receiver. A Gage CompuScope 12100 two-channel 50-

MHz 12-bit A/D converter was used digitally to store the detected waves.

The experimental procedure

A continuous wave, which was constructed by mixing a pair of sinusoidal waves with

frequencies f and 2f, was generated. The initial phase for both frequencies was set to zero

using the signal generator control. The transmitted continuous wave was actually a long but

finite sinusoidal train. A long rect sampling window from the received signal was used for

the spectral analysis. At least 12 µs of the wave were sampled by the A/D for signal

analysis.

Using Eqn (9), the corresponding time of flight difference was calculated for each

measurement point. An image depicting a projection of the accumulative dispersion index

1I x y f( , , ) was then obtained.

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

Imaged Objects

The accumulative dispersion index projections 1

I x y f( , , ) were acquired for four objects:

(i) a plastic step phantom, (ii) a commercial breast phantom, (iii) a balloon with three

different fluids and (iv) a biological phantom comprised of two soft tissues (in-vitro).

47

The step phantom (see Fig.2 top) was made of polyvinylchloride (PVC). The step size was

2 mm and the minimal thickness was 2 cm. The breast phantom was an ATS Laboratories

Model BB-1 breast phantom. The BB-1 mimics the geometry and acoustic properties of the

human breast and contains target structures randomly embedded within a tissue mimicking

material. The balloon was filled with soybean oil, water and glycerin (Purity min 98%, by

Frutarom LTD.). Due to the differences in densities, the soybean oil floated on top of the

water and the glycerin sank below the water. The two in-vitro soft tissue specimens used

here were bovine heart and turkey breast (specimens were obtained from a local

commercial slaughterhouse). The soft tissue specimens were stored in a refrigerator (they

were not frozen) and were brought to room temperature before the experiment. To eliminate

the influence of thickness on the results the specimens were cut to have the same thickness

(3 cm).

Results

The projection of the accumulative dispersion index 1

I x y f( , , ) , obtained for the PVC

step phantom (f1 = 2.5 MHz) is shown in Fig 2 (bottom). As can be noted the individual

steps are clearly visible, reflecting the increased time of flight difference,1 2

TOF f f ( , ) ,

resulting from the increased thickness. Darker colors represent higher accumulative

dispersion index values. The accumulative SOSD mean difference between each step and

the thinnest step were: 0.7, 1.9, 3.6, 4.4, 6.0 [nanosecond] (see Fig 3). Applying linear

regression to the data, the typical value of for PVC was found from the slope of the

regression line and its value was 6.51.1 [nanoseconds/cm] (with 95% confidence level).

48

The projection of the accumulative dispersion index 1

1 5I x y f MHz( , , . ) obtained for the

three fluids phantom is depicted in Fig 4. As can be noted, there is a clear contrast between

the regions containing the different fluids. Darker color indicates higher SOSD. The

intermediate layer between the Glycerin and the water stems from a mixture of fluid

bubbles formed when the water was poured atop the Glycerin.

The projection of the accumulative dispersion index 1= 1 MHzI x y f( , , ) obtained for the

BB1 commercial breast phantom is depicted in Fig 5. In this case, lower frequencies were

used in order to improve the penetration trough the phantom. As can be observed the

embedded targets (some of which are marked by arrows) depict high accumulative

dispersion index values. Importantly it should be clarified that although dispersion in water

is negligible, in this image it appears as a dark region. This stems from the fact that the

condition of 1 1 1

0

2 ( , ,2 ) 0.5

L

f l f f dl (see above) was not met for the water and hence in

this case a 2 phase wrapping occurred. However, the region of interest, i.e. the breast

phantom, has complied with condition (11).

The projection image of the accumulative dispersion 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 the regions containing the two types of tissues. 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.

Discussion

SOSD has been suggested as an additional acoustic property for utilization in medical

applications. The most discussed idea was to use SOSD for bone assessment (Wear (2000),

49

Strelitzki and Evans (1996), Droin et al (1998)). Analysis of SOSD in soft tissues has also

been conducted, (e.g. in brain by Kremkau et al. (1981), in lung by Pedersen and Ozcan

(1986), in hemoglobin solutions by Carstensen and Schwan (1959), and in hearts by Akashi

et al. 1997 and by Marutyam et al. (2006)). To the best of our knowledge SOSD imaging

has not been suggested. This may stem from two main reasons. First SOSD is a very weak

phenomenon and hence difficult to measure. And secondly previously suggested methods

had either low SNR or required too long acquisition times.

The method suggested by Levy et al. (2006), offers improved SNR and a single

transmission measurement of the SOSD. This makes it particularly suitable for ultrasonic

SOSD projection imaging as was demonstrated by the results.

There are two challenges associated with the suggested method: (a) boundary artifacts and

(b) phase wrapping. As can be noted (Figs.2,4,5,6), there is an artifact which occurs at

boundaries separating different regions in the imaged object. This artifact appears as a

strong gradient in SOSD values. It emphasizes boundaries and hence, may increase the

visibility of small targets. The source of this artifact may be the frequency-dependent

acoustic diffraction which occurs at such boundaries.

As for phase wrapping, the constraint on the variation of the accumulative dispersion in

the ROI (Eq.(11)), imposes a limit on the allowed variation of the SOSD property in the

imaged object. Violation of this constraint may lead to a phase wrapping in certain regions

within the image. (A problem which resembles the phase wrapping problem of MRI Phase

contrast flow imaging). Algorithms for phase unwrapping may be needed in such cases.

In conclusion, the results obtained here, have clearly demonstrated the feasibility of

SOSD projection imaging. As was shown here, SOSD images can be obtained for solids

(Fig.2), for fluids (Fig.4) as well as for the tissue mimicking breast phantom (Fig.5) and soft

50

tissues (Fig.6). SOSD may serve as a new contrast source and potentially may aid in breast

diagnosis.

Acknowledgments

The authors are grateful for funding provided by the Technion V.P.R. Research funds,

Eliyahu Pen Research fund, Dent Charitable Trust, Japan Technion Society and the

Montréal Biomedical Fund. Finally we thank Mr. Aharon Alfasi for his extremely valuable

technical support.

51

References

Akashi N, Kushibiki J, Chubachi N, Dunn F. Acoustic properties of selected bovine tissues

in the frequency range 20–200 MHz. J Acoust Soc Am 1995;98:3035–3039.

Azhari H, Stolarski S. Hybrid ultrasonic computed tomography. Comput Biomed Res. 1997

Feb;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 Solutions. J Accoust Soc

Am 1959;31:305-311

Droin P, Berger G, Laugier P. Velocity Dispersion of Acoustic Waves in Cancellous Bone.

IEEE Trans Ultrason Ferroelectr Freq Control 1998;45:581-592.

Kremkau FW, Barnes RW, McGraw CP. Ultrasonic attenuation and propagation speed in

normal human brain. J Accoust Soc Am 1981;70:29-38.

Levy Y, Agnon Y and Azhari H. Measurement of Speed of Sound Dispersion in Soft

Tissues Using a Double Frequency Continuous Wave Method UMB 2006;32(7):1065-

1071.

Marutyan RK, Yang M, Baldwin SL, Wallace KD, Holland MR, And Miller JG. The

Frequency Dependence of Ultrasonic Velocity And The Anisotropy Of Dispersion In Both

Freshly Excised And Formalin-Fixed Myocardium. Ultrasound Med Biol. 2006; 32(4):603–

610.

Pedersen PC, Ozcan HS. Ultrasound properties of lung tissue and their measurements.

Ultrasound Med Biol. 1986 Jun;12(6):483-99.

52

Strelitzki R, Evans JA. On the measurements of the velocity of ultrasound on the os calcis

using short pulse. European Journal of Ultrasound 1996;4:205-213.

Wear KA. Measurments of phase velocity and group velocity in human calcaneus.

Ultrasound Med Biol 2000;26:641-646.

Wells P N T, Ultrasonic imaging of the human body, Rep. Prog. Phys. 1999;62:671-722.

Zhaoa B, Basira OA, Mittal GS, Estimation of ultrasound attenuation and dispersion using

short time Fourier transform, Ultrasonics 2005;43(5);375-381.

53

Figure captions.

Figure 1: Schematic depiction of the system's measurement setup. An object is placed in a

water tank between two ultrasonic transducers. A signal is transmitted from one transducer

and detected after passing through the object by the other transducer. An image is obtained

by scanning the object along a set of horizontal lines (raster mode).

Figure 2: (Top) a Photo of the PVC step phantom. (Bottom) its corresponding SOSD

projection image. The thickness of the steps is incrementally increased by 2 mm starting

from 20 mm.

Figure 3: The measured increase in the accumulative SOSD (marked by *) relative to the

thinnest step obtained for each step of the PVC phantom as a function of the increase in the

step's thickness. The solid line corresponds to the calculated regression line.

Figure 4: A SOSD projection image of the phantom containing three fluids. Note the

contrast between the layers. (The intermediate layer between the Glycerin and the water

stems from a mixture of fluid bubbles formed when the water was poured atop the

Glycerin).

Figure 5: A SOSD projection image obtained for the commercial breast phantom. The

embedded targets have formed regions of discontinuity within the phantom matrix

(indicated by the arrows).

54

Figure 6: A SOSD projection image obtained for the in-vitro tissue phantom. 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.

55

Fig. 1

B

Signal Generator Amplifier / Filter

A/D Trigger

Transmitter

Imaged

Object

A

Receiver

56

Fig 2.

Photo of the Steps Phantom

SOSD Projection image

Photo of the Steps Phantom

SOSD Projection image

57

Fig. 3.

58

Fig. 4.

Soybean

oil

Water

Glycerin

Soybean

oil

Water

Glycerin

59

Fig. 5.

60

Fig. 6.

Bovine

heart

Turkey

breast

61

Paper C: "Speed of Sound Dispersion Measurement Using a Chirp Signal"

SPEED OF SOUND DISPERSION

MEASUREMENT USING A CHIRP SIGNAL

Yoav Levy1, Yehuda Agnon

2 and Haim Azhari

1

1Faculty of Biomedical Engineering

And

2Faculty of Civil and Environmental Engineering

Technion, IIT, Haifa, Israel, 32000

62

Abstract

In this study, two new methods for speed of sound dispersion measurement were

developed. These methods are based on transmission of a linear frequency modulated

“chirp” pulse. The first method, entitled as the "signals bank method" is based on

assessment of similarity between the measured signal and a synthesized bank of signals.

This method is robust and performs well even at high frequencies where the signal is more

attenuated. However, it requires a relatively long computation time (several seconds on a

PC). The second method, titled the: "cross correlation method" is computationally faster

and is based on calculation of the phase of the peak of the complex cross correlation

function. Therefore it is valid only for narrowband measurements and it may be biased by

frequency dependent attenuation.

To the best of our knowledge, using these methods, speed of sound dispersion was

measured in the pulse-echo mode in soft tissues for the first time. Both methods are suitable

for projection imaging as well.

Keywords: ultrasound, speed of sound dispersion, chirp, pulse-echo, soft tissue.

63

Introduction

Quantitative ultrasound (QUS) is a method for pathologies diagnostic which was suggested

many years ago (Greenleaf 1986). There are several acoustic properties which are used for

tissue characterization such as speed of sound (Manoharan 1988), sound attenuation (Bhatia

and Singh 2001), average ultrasonic scatterer size (Mamou 2006) and other. However, more

contrast sources are needed in order to improve the reliability of the QUS diagnostic results.

Speed of sound dispersion (SOSD) may serve as a new source for ultrasonic contrast.

Methods for measurement of SOSD based on the analysis of broadband pulses were applied

to study solids and bones (He 1999, Strelitzki and Evans 1996, Droin 1998 and Wear

2000). However, SOSD phenomenon is very weak in soft tissues (Wells 1999) and hence is

difficult to measure. Few investigators have studied the speed of sound dispersion in

biological soft specimens. Kremka et al. (1981) measured the speed of sound dispersion in

normal brain, Pedersen and Ozcan (1986) measured the dispersion in lung tissues.

Carstensen and Schwan (1959) had measured acoustic properties of hemoglobin solutions

and Marutyan et al (2006) have studied it in myocardial tissue. All these methods are either

relatively slow or require high SNR. In more recent studies it was shown that the SOSD

may be rapidly measured in soft tissues (Levy et al 2006) and may be used for medical

imaging (Levy et al 2007).

All the above mentioned methods have utilized through transmission waves. However, this

limits their potential application in ultrasonic imaging and tissue characterization. A pulse-

echo based technique is more desirable since it offers much better accessibility to many

organs in the body. In this study two new methods for speed of sound dispersion

64

measurements using a pulse-echo as well as through transmission technique and a chirp

signal are introduced. The methods were tested in both through and pulse-echo modes.

Methods and Materials

Theory

Consider an examined homogeneous object placed between two transducers and

immersed in the water bath. An ultrasonic linearly modulated signal (chirp) is transmitted

from point A, travels through the object and recorded at point B. Alternatively, a single

transducer is used and the echo reflected from its back face is recorded. The signal is

distorted by a frequency dependent dispersion of the phase velocity in the object. This

phase velocity dispersion depends on the object's material. In this section two alternative

methods for measuring the dispersion of the phase velocity are derived. The first method is

based on finding the maximal similarity of the measured signal and a synthesized signal

taken from a pre-calculated bank of synthetic signals. The second method utilizes an

analysis of the cross correlation function between the measured signal and a reference

signal.

The Synthetic Signals Bank Method

The first method is based on a model which describes the distortion of a signal by a

dispersive medium. Wear (2001) described the distorted signal y t recorded at point B, by

a convolution of the undistorted reference signal, x t , and the impulse response of the

object h t

65

(1) *yt xt ht

The reference signal is the signal obtained for a wave which travels from point A to Point B

through the water (assumed to be non-dispersive (Carstensen 1954)) or the echo reflected

from a reference surface in the absence of the object. The Fourier transform of h t may be

modeled by,

(2) 22 fd i ftfHf Te e

where f is the frequency, T is the transmission coefficient at the water-object borders, is

an attenuation coefficient, d is the thickness of the object and t(f) is the time delay of a

given frequency relative to the reference signal. t(f) is given by (see Wear 2001):

(3) 1 1

s w

tf dcf c

where wc is the speed of sound in water and sc f is the phase velocity in the object. The

time delay t(f) can be divided into two components: (a) 0t and (b) dt f where

(4) 0

0s w

d dt

c f c

and

(5) 0

d

s s

d dt f

c f c f

.

Where 0sc f corresponds to a frequency independent component of the phase

velocity. Hence, the term 0t describes the frequency independent time of flight difference

66

between the signal traveling through the object and the reference signal. This term causes a

“pure” time shift of the signal and preserves the signal's shape (i.e. no distortion). The

second term dt f is a small perturbation of the first term which takes into account the

dispersion of the phase velocity in the medium. This term induces distortion in the signal’s

shape when traveling through the object. Therefore, for modeling the dispersion induced

distortion in the signal’s shape, the “pure” signal’s time shift may be ignored as well as the

intensity scaling caused by the transmission coefficient, 2T . Consequently, the shape

distortion transfer function dH f may be modeled by

(6) 2 dfd i ft f

dHf e e

While dt f is not known, the attenuation coefficient, f , can be calculated by

comparing the spectra of the distorted signal to the reference spectrum and the object's

thickness, d, is measurable.

Consider a narrowband linear frequency modulated chirp signal. For this signal the phase

velocity as a function of the frequency may be approximated by a linear function (Wear

2000)

(7) s s c s cc f c f b f f

where fc is the center frequency of the transmitted signal and sb is a slope of the phase

velocity function. In the narrow band case, the attenuation coefficient part f d

e

in the

distortion transfer function, dH f , can be assumed constant and hence can be ignored.

Combining eqn 5 and eqn 6 together with the approximation given by eqn 7, yields (see

Appendix),

67

(8)

2

22

0

s

s

b di f

c f

dH f e

Using this model, a bank of synthesized signals, corresponding to a range of optional phase

velocity dispersion slope values sb , may be generated by applying the impulse response

function to the reference signal (eqn 8 and eqn 1). The basic phase velocity 0sc f , can

be approximated by the signal's group velocity which can be measured using a standard

method (e.g. see Wear 2000, eqn. 3). By correlating the distorted signal with the signals in

that bank, the synthesized signal which has the “maximal likelihood” to the measured signal

can be found. Thus, the corresponding phase velocity dispersion slope value sb , for the

object can be determined. This slope is used for characterizing the material.

The Cross Correlation Phase Method

In this section, an alternative method for measuring the dispersion coefficient, sb , using the

cross-correlation function between the reference and the chirp signals which has traveled

through the object is derived.

The term phase-encoded-chirp was introduced by Ha (1996), to denote a chirp which has a

constant phase shift relative to a reference chirp. Ha calculated the approximation to the

cross correlation function between the encoded chirp and the reference chirp to be

proportional to:

(9) ( ) sinc( )cos 2 cR t BW t f t

where BW is the chirps' bandwidth, fc is the chirps' central frequency and is the encoding

phase. The approximation of the cross correlation function is comprised of a sinc envelop

and a carrier frequency fc. According to Ha, in case of a cross correlation between a

68

reference chirp and a phase encoded chirp, the phase of the carrier frequency at the peak of

the sinc envelop (t=0) is equal to the phase between the chirps.

An inspection of eqn. 6, shows that the shape distortion transfer function dH f adds a

different phase 2 f t fd

to every frequency component of the signal. Since the effect

of dH f is frequency dependent, the distorted signal is not exactly an "encoded signal"

according to Ha's definition. However, Ha's approximation for the cross correlation

function can be used by finding an averaged phase shift angle

(10) 2average df t f

where f is the averaged frequency in the signals and dt f is the average time

delay of the components in the signal. For a linear frequency modulated chirp the average

frequency is simply the central frequency

(11) cf f

Using eqn 5 and the narrowband approximation (eqn 7) and the relation

0s c sd b f c f yields

(12)

2 20 0 0

s s cd

s s s s

d b f d b fd dt f

c f c f c f c f

Therefore, the dispersion coefficient bs, can be calculated using equations 10,11 and 12

(13)

2

2

0

2

average s

s

c

c fb

f d

Eqn 13 is sufficient for dispersion coefficient measurements in a homogeneous specimen.

However, for medical imaging it is important to study the relation between the phase of the

peak of the cross correlation function and the dispersion in a general object which may be

69

heterogeneous with an unknown thickness. In the more general case, (ignoring the

attenuation) the distortion transfer function is location dependant and can be expressed as,

(14)

0

2 ,

L

di f t f x

dH f e

where L denotes the distance from the transmitter at point A to the receiver at point B or the

pulse-echo path along the x direction, and ,dt f x is the frequency dependent time delay

at that location is

(15) 1 1

,, 0,

d

s s

t f x dxc f x c f x

where ,sc f x is the phase velocity of frequency f at point x. In a narrowband signal, the

variation of the phase velocity is fairly small compared to the phase velocity and the

following approximation holds,

(16)

2 2

0, ,,

0, 0,

s s s

d

s s

c f x c f x b x ft f x dx dx

c f x c f x

Hence, dH f becomes

(17)

2

2

0

20,

L

s

s

b xi f dx

c f x

dH f e

2

0,

s

s

b x

c f x is a time delay per unit length per unit frequency and is referred herein as

the: “normalized slope” of the phase velocity dispersion. The cumulative normalized slope

70

,

2

0 0,

L

s

s

b xdx

c f x

, in eqn 17 is a projection of the normalized slope of the phase velocity

dispersion along the path from point A to point B through the object or along the traveling

distance of the pulse-echo wave. For a homogeneous object, the cumulative normalized

slope in eqn. 17 is reduced to

(18)

2

020, 0

L

s

s

b db x sdxc f x c f

s

where d is the object's width (as in eqn 8).

The cumulative normalized slope is linearly related to the phase of the peak of the cross

correlation function between the reference and distorted chirps.

(19)

2

2

0

20,

L

s

average c

s

b xf dx

c f x

Using this equation the integrative value (which is actually a projection) of the “normalized

slope” of the phase velocity dispersion is obtained.

Experimental Measurements

The experimental system

The scanning system, utilized to scan a step phantom, is comprised of a water tank with a

specially built computer controlled mechanism that can produce spatial motion with three

degrees of freedom for a pair of transducers (Panametrics, 5 MHz, focused transducers,

diameter 12.7 mm and focal length 10.7cm) placed about twice the focal length apart

(Azhari and Stolarski (1997), Azhari and Sazbon (1999)). In the phase velocity dispersion

slope measurements for a plastic specimen, the transducers were static and the examined

object was placed between them. In the imaging configuration utilized here the object was

71

scanned horizontally. The scanning resolution was set to 0.3mm along the horizontal

direction. Measurements in soft tissue were done in an external water bath with an

unfocused transducer (Panametrics, 5 MHz, diameter 6.3[mm]) placed at a 45 [mm]

distance from a reflecting bronze block.

Signals were generated by a Tabor 8026 arbitrary wave-form generator and a Panametrics

5800 pulser/receiver was used as a receiver. A Gage CompuScope 12100 (two-channel 50-

MHz or one-channel 100-MHz) 12-bit A/D converter was used to digitally store the

detected waves. A specially built high voltage analog switch was used to isolate the receiver

from the transmission signal in the pulse-echo measurements.

The Studied Specimens

Two specimens were used in this study (i) a plastic step phantom, (ii) a soft tissue (in-

vitro) phantom.

The step phantom (see Fig.1 (a)) was made of polyvinylchloride (PVC). The step size was

2 mm and the minimal thickness was 2 cm. The soft tissue specimens used here was turkey

breast (specimen was obtained from a local commercial slaughterhouse). The soft tissue

specimen was stored in a refrigerator (it was not frozen) and was brought to room

temperature before the experiment. The specimen’s thickness was 45 [mm].

The experimental procedure

Phase velocity cumulative dispersion slope measurement in through transmission:

72

The aim of this part of the experiment was to show that (as predicted by eqns 17,18,19)

the cumulative dispersion slope in the "signals bank" method and the measured angle in

the "cross correlation" method are linearly related to the imaged object width.

A 12s long chirp signal having a 1 MHz bandwidth and a central frequency of

2.5[ ]cf MHz was programmed in the wave generator. Initially, a reference signal of

transmission from one transducer to another in water was recorded. Using this signal, a

distorted signals bank was created. The distorted-signals bank was synthesized using eqns

17,18 for a set of optional cumulative dispersion slope values in the range

50 [nano sec]

20

b ds

c fs

. The velocity 0sc f was approximated using the method

described by Wear (2000) for group velocity measurement.

In the "imaging configuration" used to scan a polyvinylchloride (PCV), the step phantom

was placed in the water between the two transducers. The signals, sent from one transducer

to another through the phantom were recorded. The recorded signals were analyzed in both

(a) the "signals bank" and (b) the "cross correlation" methods.

For method (a), the recorded signal was correlated with the pre-calculated signals in the

bank of synthesized signals to find the most-likely signal in the bank. The signals were

interpolated using the FFT method (interpft function in Matlab, MathWorks Inc., Natick,

MA) prior the correlation.

Using method (b), the recorded signals were correlated with the reference signal, and the

corresponding angle for every step was calculated from the phases of the cross correlation

functions at their envelopes' peaks. Each phase is the phase of HR t at its maximal

magnitude, where HR t is the analytical signal ˆHR t R t iR t , and R̂ t is the

73

Hilbert transform of the cross-correlation function between the transmitted and reference

chirp waves.

For both methods the results for each step were plotted against the step width. The results

were also normalized by their corresponding step width and plotted in a different graph for

validation.

Phase velocity dispersion slope measurement in the pulse-echo mode:

The aim of this part in the experiment was to use both methods for measurement of phase

velocity dispersion slope as a function of the frequency for plastic and soft tissue specimens

in the pulse-echo mode.

In the measurement of the dispersion slope using the pulse-echo mode a single transducer

was used for transmission and reception of the signals. The transmitted signals were chirp

signals, 1 MHz bandwidth, 12s long and varying central frequency cf . A phase

inversion was applied to the echo received from the PVC phantom prior to correlation

calculation. The turkey breast specimen was placed between the transducer and a reflecting

bronze cube. The ultrasonic beam was perpendicular to the tissue fibers direction. The

signals bank was synthesized using eqn 8 for a set of optional values for the dispersion

slope in the ranges 20[ /( )]sb m s MHz and 2[ /( )]sb m s MHz for the PVC and

turkey breast phantoms respectively. The recorded signals were analyzed in both (a) the

"signals bank" and (b) the "cross correlation" methods.

For method (a) The recorded signal for each sample and for each central velocity cf , was

correlated with the signals in the bank of synthesized signals to find the most-likely signal

74

in the bank. The signals were interpolated using the FFT method (interpft function in

Matlab) prior the correlation.

For method (b) the recorded signals were correlated with the reference signals. The phase

velocity dispersion slope of the corresponding samples at frequency cf was calculated using

eqn 13.

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

Results

In Fig.1, the results obtained using the measurements of the angle of the peak of the cross

correlation function and the cumulative normalized dispersion slope of the steps of the

PVC step phantom are presented ( 2.5[ ]cf MHz ). Fig.1(a) presents a simple B-Scan image

of the phantom. Fig.1(b) presents the values of the angle of the peak of the cross correlation

function for each step. The error bars present the standard deviation of the measurements

along the steps. Fig.1(c) presents the values of the normalized angle of the peak of the

cross correlation function for each step. The error bars present the standard deviation of the

measurements along the steps. The results for all the steps fell in the range of 0.37±0.01

[rad/cm]. Fig.1(d) shows the cumulative normalized dispersion slope for each step. The

error bars present the standard deviation of the measurements along the steps. In Fig.1(e)

those values are normalized by the steps’ widths. The error bars present the standard

deviation of the measurements along the steps. All values fell in the range of

8.2 0.5[nano sec/cm] .

75

The calculated phase velocity dispersion slope versus cf obtained for the PVC specimen in

the pulse echo mode for the two analysis methods are plotted in Fig 2. The average values

for each central frequency studied are depicted along with their standard deviation values

(error bars). As can be noted, the slope is positive throughout the studied range of

frequencies but decreases monotonically. The values which were calculated using the

signals bank method (Fig2 top) decrease from 5.3 ± 0.9 [m/(sMHz)] at 2 MHz to 2.4 ± 0.4

[m/(sMHz)] at 4.5 MHz. The values which were calculated using the cross correlation

method (Fig2 bottom) decrease from 6.3 ± 1.1 [m/(sMHz)] at 2 MHz to 2.9 ± 0.7

[m/(sMHz)] at 3.75 MHz. As can be noted the results obtained using the cross-correlation

method for frequencies of 4MHz and higher were too scattered and unreliable.

The calculated phase velocity dispersion slope versus cf obtained for the turkey breast in

the pulse echo mode for the two analysis methods are plotted in Fig 3. The average values

for each central frequency studied are depicted along with their standard deviation values

(error bars). As can be noted, the slope is positive throughout the studied range of

frequencies but decreases monotonically. The values which were calculated using the

signals bank method (Fig3 top) decrease from 0.76 ± 0.05 [m/(sMHz)] at 2 MHz to 0.23 ±

0.02 [m/(sMHz)] at 5.5 MHz. The values which were calculated using the cross correlation

method (Fig3 bottom) decrease from 0.64 ± 0.5 [m/(sMHz)] at 2 MHz to 0.25 ± 0.04

[m/(sMHz)] at 5.5 MHz.

76

Discussion

In this study, two new methods for speed of sound dispersion measurement were

developed. To the best of our knowledge, using these methods, speed of sound dispersion

was measured in the pulse-echo mode in soft tissues for the first time.

In the first part of the experiment, it was shown that values of projection measurements in

both methods are linearly related with the width of the measured object and therefore both

methods are suitable for projection imaging.

In the second part of the experiment, the feasibility of performing measurements in pulse-

echo mode was confirmed. Although the results obtained here for the PVC specimen are

similar to those obtained using a different method (Levy et al. 2006), the results obtained

here for the turkey breast specimen are smaller than those reported there. This stems from

the fact that in this study the ultrasonic beam was perpendicular to the tissue fibers whereas

in the other study it was done along with fibers orientation. This finding is consistent with

the phenomenon reported for the myocardium by Marutyan et al. (2006). They have

reported that the speed sound and SOSD change substantially with the orientation of the

myofibers. Their findings indicate that SOSD along the myofibers is more than twice the

SOSD perpendicular to the myofibers.

Although both methods presented here are based on transmission of the same signal, they

are very different. The signals bank method is a robust method which performs better in

low SNR cases (see Fig.2). This method can be used with any signal shape and with any

sound velocity model. It can be shown that in the narrowband approximation and for a chirp

signal, this method is similar to wavelet analysis of a scaled mother wavelet, where the

mother wavelet is the reference signal (Similar to Bilgen 1999). Using more complicated

sound velocity model may offer the ability for conducting measurements in a wideband.

77

Ignoring the attenuation does not degrade the reliability of the results of this method, yet, in

this method, the attenuation response of the measured object may be incorporated in the

overall transfer response function using eqn 6. On the other hand, the computational effort

during the data analysis in this method is large (required several seconds of computation on

a PC per transmitted signal). The cross correlation method is an elegant fast (about two

orders of magnitude shorter computation time) measurement technique based on

approximations and averaging. Therefore it is valid only for narrowband measurements and

it may be biased by frequency dependent attenuation.

Acknowledgments

We are grateful for funding provided by the Galil Center For Telemedicine and Medical

Informatics and by the Technion V.P.R. Research Funds, Eliyahu Pen Research Fund, Dent

Charitable Trust, Japan Technion Society and the Montréal Biomedical Fund.

Finally, we thank Mr. Aharon Alfasi for his extremely valuable technical support.

APPENDIX

Using eqn 5

(A.1)

0

0 0

s s

d

s s s s

c f c fd dt f d

c f c f c f c f

.

and the narrowband approximation (eqn 7)

78

(A.2)

0 0

s c s c s s c sd

s s s s

c f b f c f b f f b ft f d d

c f c f c f c f

.

Assuming weak dispersion (i.e. 0s sd b f c f ), dt f can be approximated by

(A.3)

20

sd

s

b ft f d

c f

.

79

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Azhari H, Sazbon D. Volumetric imaging with ultrasonic spiral CT. Radiology

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Bilgen M, Wavelet Transform-Based Strain Estimator for Elastography. IEEE transactions

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Droin P, Berger G, Laugier P. Velocity Dispersion of Acoustic Waves in Cancellous Bone.

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Ha STT, Zhou H, Sheriff RE and McDonald JA, Fourier transform approximations for

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He P. Experimental Verification of Models for Determining Dispersion from Attenuation.

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Levy Y, Agnon Y and Azhari H. Measurement of Speed of Sound Dispersion in Soft

Tissues Using a Double Frequency Continuous Wave Method UMB 2006;32(7):1065-

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Mamou J, Oelze ML, O Brien WD , Zachary JF. Perspective on Biomedical Quantitative

Ultrasound Imaging. IEEE SIGNAL PROCESSING MAGAZINE 2006;May:112-116

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Manoharan A, Chen CF, Wilson LS, Griffiths KA, Robinson DE. Ultrasonic

characterization of splenic tissue in myelofibrosis: further evidence for reversal of fibrosis

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Marutyan RK, Yang M, Baldwin SL, Wallace KD, Holland MR, And Miller JG. The

Frequency Dependence of Ultrasonic Velocity And The Anisotropy Of Dispersion In Both

Freshly Excised And Formalin-Fixed Myocardium. Ultrasound Med Biol. 2006; 32(4):603–

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Strelitzki R, Evans JA. On the measurements of the velocity of ultrasound on the os calcis

using short pulse. European Journal of Ultrasound 1996;4:205-213.

Wear KA. Measurments of phase velocity and group velocity in human calcaneus.

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81

Figure captions.

Figure 1: (a) A B-scan image of the scanned stepped PVC phantom. (b) The angle obtained

by the cross-correlation method for each step. (c) The angles shown in (b) normalized by

the step thickness. (d) The cumulative normalized dispersion slope obtained for each step of

the phantom. (e) The values of (d) normalized to the thickness of each step.

Figure 2: (Top) The dispersion slope values as a function of frequency obtained by the

pulse-echo mode and the “signals bank” method in PVC. (Bottom) The dispersion slope

values as a function of frequency obtained by the pulse-echo mode and the “cross-

correlation” method.

Figure 3: (Top) The dispersion slope values as a function of frequency obtained by the

pulse-echo mode and the “signals bank” method in a turkey breast specimen. (Bottom) The

dispersion slope values as a function of frequency obtained by the pulse-echo mode and the

“cross-correlation” method.

82

83

84

85

Paper D: "Velocity Measurements Using a Single Transmitted Linear Frequency

Modulated Chirp"

Abstract

Velocity measurement is a challenge for a variety of remote sensing systems such as

ultrasonic and radar scanners. However, current Doppler-based techniques require a

comparatively long data acquisition time. It has been suggested to use coded signals, such

as linear frequency modulated signals (chirp), for ultrasonic velocity estimation by

extracting the needed information from a set of several sequential coded pulses. In this

study a method for velocity estimation using a single linear frequency modulated chirp

transmission is presented and implemented for ultrasonic measurements. The complex cross

correlation function between the transmitted and reflected signals is initially calculated. The

velocity is then calculated from the phase of the peak of the envelop of this cross

correlation function. The suggested method was verified using computer simulations and

experimental measurements in an ultrasonic system. Applying linear regression to the data

has yielded very good correlation (R=0.989). With the suggested technique higher frame

rates of velocity mapping can be potentially achieved relative to current techniques. Also,

the same data can be utilized for both velocity mapping and image reconstruction.

Key Words: Velocity measurement, Coded excitation, Linear frequency modulated chirp.

86

Introduction

Measurement of velocity is a challenge for a variety of remote sensing systems such as

ultrasonic and radar scanners. Commonly, the Doppler frequency shift caused by a moving

reflector is measured and converted into velocity estimation. This method is well

established and has been implemented using many techniques. However, current Doppler-

based techniques require either the transmission of a long continuous wave, which

sacrifices axial resolution, or the acquisition of echoes from several pulses to generate a

velocity map of each region in the image. Therefore, both methods require a comparatively

long data acquisition time, typically on the order of the period of the Doppler frequency

shift.

Coded excitation methodology (Misaridis and Jensen 2005) is used in ultrasonic imaging

systems to improve signal to noise ratio (SNR). In this methodology, a long coded signal is

used to transmit high energy while preserving low intensity constraints. While typically a

long pulse duration leads to poor spatial resolution, using coded excitations the high spatial

resolution can be recovered using an appropriate signal processing algorithm (e.g., matched

filter (Misaridis and Jensen 2005)). It has been suggested to use coded signals, such as

linear frequency modulated signals (chirp), for ultrasonic velocity estimation by extracting

the needed information from a set of several sequential coded pulses (Wilhjelm and

Pedersen 1993).

In this study we present a method for velocity estimation using a single coded pulse

transmission.

87

Theory

A chirp from f0 to f1 whose length is Tm can be represented by the following formula

(Jensen1996, eqn 9.20)

2

0 0sin 2 ;0 me t f t S t t T (1)

where f0 is the start frequency, f1 is the end frequency and S0 is the sweep rate of the signal

( 1 00

m

f fS

T

).

The instantaneous frequency of the signal is (Wilhjelm and Pedersen 1993)

0 0f t f S t . (2)

The time of appearance of each frequency t f is

0

0

f ft f

S

. (3)

Other properties of the chirp signal are

1 0f f f (4)

1 0

2m

f ff

(5)

where f is the frequency bandwidth of the chirp and fm is the center instantaneous

frequency.

A received signal sr t from a moving reflector with a velocity v along the beam axis can

be represented by (Jensen 1996, eqn 9.21)

'sr t a e t t

c v

c v

(6)

where a is a reflection coefficient (a frequency independent reflection is assumed), c is the

acoustic velocity in the medium and t' is a time shift that is related to the path from the

transducer to the moving target. The signal's intensity is not important in the following

discussion, therefore, we set a = 1.

When c >> 2v

88

21

21 1

c v v

c v c

v

c

(7)

The instantaneous frequency '( )f t of the reflected signal in its corresponding coordinates

(setting t = 0 for the signal front end) is given by

0 0

0 0

1 1

2

0 0

' ' '

'

'where

'

0 mT

f t f S t

f f

f f

S S

t

(8)

Consider an ultrasonic chirp signal which was reflected from a moving target. During the

reflection, the instantaneous frequency of each point of the transmitted chirp is changed,

according to the Doppler frequency shift, from f to f. On the other hand, the phase of each

point is preserved. Therefore, the phase of the point in the received signal whose

instantaneous frequency is f is equal to the phase of the point in the transmitted signal

whose instantaneous frequency is f/. The phase gap between the phase of the point whose

instantaneous frequency is f in the transmitted signal and the point in the received signal

which has the same instantaneous frequency ( f ) is equal to the phase gap between

the points for which the instantaneous frequencies are f and f/ in the transmitted signal

(within the range where the transmitted and received bands overlap). The phase gap

f can be calculated by the expression:

2

t f

ft

f f t dt

. (9)

For cases in which the parameter α is approximately unity (α ≈ 1), the frequency can be

taken as constant over the integration range:

f t f . (10)

Therefore, using the approximation in eqn 10 and using eqn 3, the integral in eqn 9 can be

solved:

89

0

2

0

2

2

11 2

ff f t f t

ff

fS

fS

(11)

Substituting eqn 7 into eqn 11, the phase gap between corresponding points in the chirps

for a specific instantaneous frequency f is given by the expression

2

0

22

vf f

S c

. (12)

Under typical physiological blood flow conditions the changes in f0 and S0 as a result of

the reflection from the moving blood (calculated in eqn 8) are too small for a reliable

Doppler velocity estimation using a single pulse transmission (Wilhjelm and Pedersen

1993). However as shown below, the cross correlation function of the transmitted and

received chirp signals in the time domain is sensitive to the resulting changes in the start

frequency and the sweep rate, and hence can be utilized for velocity estimation using a

single transmission.

Consider the chirp e t , which was defined in eqn 1. This chirp can be turned into a phase

encoded chirp ,e t (Ha et al 1993), where is the encoded phase

2

0 0, sin 2e t f t S t . (13)

The corresponding approximated cross correlation between ,0e t and ,e t is given by

Ha et al (1991):

sinc cos 2 mR f f . (14)

The cross correlation function R( ) is comprised of an envelop (the sinc function) and a

carrier frequency equal to the center instantaneous frequency fm. The phase of the carrier

frequency at the peak of the cross correlation envelop ( = 0) is .

Two additional approximations should be done in order to use Ha’s approximation as a

cross correlation function between a transmitted chirp pulse and its corresponding reflected

chirp signal:

a. Use the original spectrum for determination of f and fm.

90

b. Approximate the phase gap between the chirps (which is a function of the phase) by

the phase gap between corresponding points in the transmitted and reflected chirps

having the center instantaneous frequency fm.

Those approximations are valid as long as 1 ( 2c v ).

Substituting eqn 12 into eqn 14, an approximation for the cross correlation function

between a transmitted chirp pulse and its corresponding reflected chirp signal is

2

0

2sinc cos 2 2m m

vR f f f

S c

(15)

One can note that the cross correlation function envelope peaks at 0 and

2

0

22 m

vf

S c

will be the peak’s phase. Let us define the phase at the peak of the cross

correlation envelop as the: "Optimal-Correlation Phase" (OCP). This phase is measured by

taking the phase of HR at its maximal absolute value where HR is the analytical

signal ˆHR R iR where R̂ is the Hilbert transform of the cross correlation

function between the transmitted and reflected chirp waves. In case of a stationary reflector

the OCP is zero since there is no frequency shift, i.e. 0v .

Using eqn 15, the velocity of the moving reflector along the beam can be determined from

the OCP, OCP , by the expression

0

24

OCP

m

S cv

f

. (16)

Simulation Methods

A numerical computer simulation was written in order to verify that the approximations that

were made during the theoretical derivation of eqn 16 are acceptable. During these

simulations transmitted chirps in varying lengths were correlated with a synthetic set of

echoes which represent reflections from targets with varying velocities. The velocity of the

moving reflector along the beam is determined from the OCP by eqn. 16 for each

combination of chirp length and reflector velocity. The transmitted signals were simulated

using eqn. 1 and the echoes were calculated according to eqn. 8. The synthetic signals were

multiplied by a hamming window to emulate a realistic situation in which the transducers

impulse response modulates the signal. Parabolic interpolation was used to determine the

accurate speak of the correlation function. Finally, a map depicting the relative error in

91

velocity estimation, as a function of target velocity and chirp length was generated from

these simulation results.

In addition, the effect of noise on velocity estimation was evaluated. SNR was varied from -

20db to +20db by adding white Gaussian noise to the simulated data. At each SNR level

100 simulations were conducted. The estimated velocity was normalized to the accurate

value and its mean and standard deviation (SD) were calculated as a function of SNR.

Experimental Methods

A transducer (Panametrics, 5 MHz, diameter of 6.3 mm) was placed in a water-bath in front

of a computer-controlled moving target. The target was a stainless steel cube which could

be moved at velocities of up to several cm/sec, defined by the user (these values served as a

“gold-standard”). Chirp signals were generated by a Tabor 8026, arbitrary wave form

generator, and a Panametrics 5800 pulser/receiver was used as a receiver. A Gage

CompuScope 12100, one-channel 100-MHz mode, 12-bit A/D converter was used to

digitally store the detected waves. A schematic depiction of the experimental system used

here is shown in Fig. 1.

The reflection from a static target was initially recorded and served as a reference signal

which represents the transmitted signal. The target was then moved at constant velocities

ranging from -50 mm/s to 50 mm/s and incremented by 10 mm/s. At each velocity several

reflections of chirp signals were recorded. Each recorded signal was correlated with the

reference signal and the velocity (calculated from the OCP, eqn 16) was plotted vs. the

target velocity.

Results

Simulations

The relative error map which was generated by the numerical computer simulations is

depicted in Fig. 2. The map presents the normalized error of the velocity estimation for a

moving target reflector which velocity ranged from 0.1 [m/s] to 1 [m/s]. The chirp had a

92

frequency sweep from 3 MHz to 5 MHz and its length ranged from 10 s to 40 s. The

velocity estimation error obtained by these simulations was less than 10%. As can be noted,

the accuracy improves for a longer chirp signals. The correlation function (eqn 15) for the

stationary target is depicted in Fig.3a, for comparison the correlation function obtained

from a moving target (1 m/s) is depicted in Fig.3b. As can be observed, the correlation

function for the moving target is asymmetric and distorted relative to the stationary case.

The simulated effect of noise on the velocity estimation (chirp frequency ranged from 3

MHz to 5 MHz, its length was 40 s and target velocity was 0.25 [m/s]) was also evaluated

by varying the SNR from -20db to +20db. The results are depicted in Fig.4. The error bars

depict the mean and SD of the estimated velocity normalized to the accurate value. As can

be noted the mean velocity estimates are fairly stable throughout the SNR range.

Measurements

Using an ultrasonic transmitted chirp signal 40 s in length and a frequency sweep ranging

from 3 MHz to 5 MHz, the velocity of the moving metal target was evaluated

experimentally as explained above.

The results obtained from the set of measurements are depicted in Fig.5. In this figure the

estimated velocity (calculated from the OCP, eqn 16) is plotted versus the target's velocity

set by the controller. The error bars represent the standard deviation for each measured

value. Applying linear regression to the data has yielded the regression line of:

arg 0.8478 -0.0005 [m/s]Measured t etV V , (R=0.989), where MeasuredV represents the values

obtained by the suggested method, and argt etV is the velocity set be the motion control

system.

93

Discussion

In this study a method for velocity estimation is introduced. The main advantage of the

technique is its ability to obtain the velocity estimation using a single pulse (chirp)

transmission. With this technique the same chirp signal can potentially be utilized for both

imaging and velocity estimation. This would enable the velocity map to be generated at the

same frame rate as the standard ultrasonic image which can also be reconstructed from the

same data set.

Another advantage offered by the suggested method is an adjustable dynamic range. The

dynamic range of the estimation can be determined from eqn 16 by substituting instead

of .

0max 24 m

S cv

f . (17)

For comparison, in the common Doppler shift method the maximal detectible velocity maxv

is determined by (Jensen JA 1996, eqn 6.45),

max

04

PRFc fv

f

(18)

where PRFf , is the pulse repetition frequency and 0f is the central transmitted frequency.

This imposes limitation on the common method from two aspects: First, PRFf is limited by

the distance to the target. Secondly, decreasing 0f is commonly associated with a decrease

in the axial resolution. With the suggested technique, on the other hand, the maximal

detectable velocity can be adjusted by either changing 0S (the sweep rate) and/or mf (the

center instantaneous frequency). This offers the operator more freedom in setting the

measurement system.

It should be noted though, that the mathematical derivation outlined above was done for a

case in which the phase of the reflected signal is not inverted. This is not the case for an

ultrasonic reflection from a target for which the acoustic impedance is lower than the

medium’s acoustic impedance. In the later case, the signal is reflected with a phase shift

of and therefore the corresponding average phase gap between the transmitted and

94

reflected chirps becomes: . For a system which contains targets with a variety of

impedances (higher and lower than the medium), the dynamic range is further limited to an

absolute phase change of no more than 2

. Hence, the chirp's parameters should be set to,

0max 28 m

S cv

f . (19)

Studying the regression line obtained in the experimental part, it can be noted that the slope

differs from unity, i.e.: arg 0.8478Measured t etV V . This may stem from the following

reasons: (i) The central instantaneous frequency fm actually represents the combined effect

of all the frequencies in the transmitted band. Hence, the changes in fm caused by the

moving target are not identical to the changes which a single frequency would experience

due to the Doppler effect. (ii) The actual transmitted signal is not an ideal LFM chirp, but

is distorted by the impulse response of each element in the transmission system. (iii) The

lower frequencies are dominant in the received signal (due to the frequency dependency of

the attenuation) and therefore the OCP tends to be smaller than expected. Nevertheless, this

problem can be simply overcome by using a calibration process.

In conclusion, the suggested method can be used to estimate the velocity of a moving target

using a single transmitted linear frequency modulated chirp. This may potentially yield high

frame rate of velocity estimations. The method was verified using computer simulations

and experimental measurements with an ultrasonic system.

95

References

Ha STT, Sheriff RE, and Gardner GHF. Instantaneous frequency, spectral centroid, and

even wavelets, Geophys. Res. Lett., 1991;18: 1389-1392.

Jensen JA. Estimation of Blood Velocities Using Ultrasound. Cambridge University press

1996.

Misaridis T, Jensen JA. Use of Modulated Excitation Signals in Medical Ultrasound. Part I:

Basic Concepts and Expected Benefits. IEEE Trans Ultrason Ferroelec Freq Contr

2005;52:177-191.

Wilhjelm JE and Pedersen PC. Target velocity estimation with FM and PW echo ranging

Doppler systems – Part I: Signal analysis. IEEE Trans Ultrason Ferroelec Freq Contr

1993;40:366–372.

96

Captions list

Fig 1: A schematic depiction of the ultrasonic experimental set-up used in this study.

Fig 2: A map depicting the relative error in velocity estimation of a moving target obtained

by the computer simulations. The velocities ranged from 0.1 m/s to 1 m/s. The chirp

frequency ranged from 3 MHz to 5 MHz and its length ranged from 10 s to 40 s. As can

be noted the error is smaller for longer chirp signal lengths.

Fig 3: (a) The correlation function derived for the stationary target (chirp frequency ranged

from 3 MHz to 5 MHz and its length was 40 s). (b) The correlation function derived for a

moving target (same chirp, velocity=1 m/s). As can be noted the correlation function for the

moving target is asymmetric and distorted relative to the stationary case.

Fig 4: Simulated effect of noise on the velocity estimation. SNR was varied from -20db to

+20db. The error bars depict the mean and SD of the estimated velocity relative to the

accurate value. As can be noted the mean velocity estimates are fairly stable throughout the

SNR range.

Fig 5: Measured velocity (using the OCP, eqn 16) vs. the target velocity set by the motion

control system. The error bars represent one standard deviation. The solid line represents

the regression line obtained for this data.

97

Fig 1

Signal Generator

Receiver

A/D

Trigger

Signal

Velocity

Control

Data

Signal Generator

Receiver

A/D

Trigger

Signal

Velocity

Control

Data

98

Fig. 2

99

Fig 3

100

Fig.4

101

Fig 5

102

Paper E: "A Method for Local Spectral Analysis Using Coded Excitations and its

Application in Velocity Estimation"

A METHOD FOR LOCAL SPECTRAL

ANALYSIS USING CODED EXCITATIONS

AND

ITS APPLICATION IN VELOCITY

ESTIMATION

Yoav Levy1, Yehuda Agnon

2 and Haim Azhari

1

1Faculty of Biomedical Engineering

And

2Faculty of Civil and Environmental Engineering

Technion, IIT, Haifa, Israel, 32000

February 13, 2007

Correspondence:

Haim Azhari D.Sc.

Faculty of Biomedical Engineering,

Technion IIT,

Haifa 32000,

Israel.

Tel. 972-4-8294130,

Fax. 972-4-8294599,

E-mail: haim@bm.technion.ac.il

103

Abstract

A method for performing localized spectral analysis is suggested. The method is based on

transmitting a long frequency modulated signal. The frequency dependent information of

the detected backscattered waves is obtained by using time frequency transform such as

short time Fourier transform (STFT). The spatial resolution is retrieved by rearrangement of

the frequency-time relationship of the signal.

A simulation program was used to confirm the ability of this method to serve as a tool for

velocity estimation. The simulated echoes reflected from a moving target after transmission

of a long chirp signal were analyzed. The performance of the suggested method were

compared to a conventional method for velocity estimation under different SNR values

(range:-30db:+10db). The velocity estimation using the suggested method was superior to

estimates obtained by using the “conventional” method in poor SNR scenarios (SNR<0).

Although some reduction in axial resolution may occur when using the suggested method

the method performs well in poor SNR scenarios (mean square errors <0.1 for SNR >-

20db).

The suggested method can potentially be useful in spectral based applications such as:

velocity estimation, tissue classification, attenuation mapping and temperature monitoring.

The suggested method can be particularly useful in noisy measurements.

Keywords: spectral analysis, frequency modulated signals, chirp, ultrasound, Doppler,

STFT

104

Introduction

Spectral analysis applied to backscattered ultrasound signals is used in many applications

such as attenuation mapping [1], tissue characterization [2], temperature monitoring [3] and

mean scatterer spacing estimation [4]. Furthermore, it plays a major role in velocity

estimation since velocity is associated with the frequency dependant Doppler shift.

Signal to noise ratio (SNR) is a great concern in such applications. Hence, it is desirable to

utilize high energy transmitted signals. The signal energy can be augmented by increasing

the intensity of the transmitted signal. However, this approach is limited by safety aspects.

Alternatively, one can increase the transmission duration, but this approach commonly

decreases the axial resolution.

An approach for utilizing long signals without sacrificing the axial resolution is the

implementation of Coded Excitation [5]. With this approach, a long coded signal such as

chirp is used to transmit high energy while preserving low intensity constraints. Using

coded signals, the spatial resolution can be recovered with an appropriate compression

algorithm, e.g., matched filter [6]. However, this scheme of spatial resolution retrieval is

not appropriate for spectral analysis based applications since most of the spectral

information embedded in the signal is lost in the compression process.

In this study we present a new method for utilizing long frequency modulated signals in

spectral analysis based applications.

Theory

In many spectral-analysis based ultrasonic applications, an A-Line signal is analyzed using

its time-frequency representation (TFR). TFR is a representation of the frequency

(amplitude and phase) contents within a sliding temporal window versus time. One way for

generating such representation is using short-time Fourier transform (STFT). After

transformation, the received signal in a time-frequency representation is designated by

tS f,t where t and f are the time and frequency variables of that transform respectively.

We shall assume herein that f represents only frequencies which are within the band of the

105

transmitted signal. As in most applications in which one is interested in localizing the

components of the received signal, a time to space transformation is needed. For short

transmitted pulses the range can be approximated by / 2x t c , where c is the average

speed of sound in the medium, x is the range within the medium from which echoes are

reflected and t is the time from the signal transmission. Hence, the following frequency

distance representation can be written, 2

x t

t cS f,x = S f,

However, this approximation is not useful when using a long signal in the transmission

(usually for SNR improvement). This stems from the fact that a large overlap between

echoes can be generated. Consequently, the spectral analysis of the signal which is

commonly based on sampling a temporal window W (i.e. time t: t+W), is not informative,

since it comprises echoes from a plurality of spatially separated reflectors.

The axial resolution lower boundary axialR is defined as the width of the medium from

which reflections may contribute to xS f,x for a specific location x. Consider a spectrum

xS f,x which is calculated using a TFR, by applying a W seconds long sliding analysis

window. Assuming that the transmitted signal is mT seconds long, the echo reflected from

the closest scatterer within the window and stemming from the “tail” of this signal will be

detected at time

(1) 0

1

2m

Xt T

c

Where 0

X corresponds to the location of that closest reflector. The time at which the echo

reflected from the farthest reflector within the window is simply,

(2) 2 1t t W

Thus, the distance between the closet and the farthest reflectors is given by

(3)

2 02 2

m

axial

T +W ccR = t X

106

As can be noted from Equation 3 the resolution axialR is limited by the signal length mT .

Consequently, as stated above, there is a contradiction between the need for better SNR

(which can be improved by taking longer mT ) and spatial resolution (which can be

improved by taking shorter mT ). This dilemma can be resolved by using specially built

signals for transmission.

Consider a frequency modulated signal with a predefined mapping from frequency to time,

i.e. there is a unique correspondence ff t , where ft is the transmission time for

frequency f . The axial resolution for each frequency component, axialR f , can be

calculated as follows: The farthest scatterer that can contribute a signal with frequency f to

xS f,x is located at

(4)

22

ft t +WX f = c

The closest scatterer that can contribute a signal with frequency f to xS f,x is placed at

(5) 12

ft tX f = c

therefore

(6) 2 12

axial

W cR f = X f X f

As can be noted, the resolution as a function of frequency does not depend on the length of

the transmitted signal mT . Hence, in order to reach an axial resolution which is independent

of the transmission length for xS f,x , the following transform can be utilized:

(7) 2

f

x t

t tS f,x = S f, c

In conclusion, by reordering the TFR of echoes obtained from a long transmitted signal, the

spatial resolution of the measurements can be preserved.

Methods

107

To validate the ability of the suggested technique to improve SNR while preserving the

spatial resolution, a comparative simulation of the usage of a short harmonic signal vs. the

usage of a long frequency modulated signal in a spectral analysis based application was

done. The application that was selected for comparison was velocity estimation of moving

reflectors which simulates blood flow in a tissue.

Spectral analysis

A linear frequency modulated signal, i.e. chirp, was used as a long signal to be compared

with the short conventional harmonic signal. Consider a transmitted chirp who's frequency

sweeps linearly from 0f to f and it is mT [seconds] long. For this signal:

(8) 0

0

f

f ft =

S

where

(9) 1 00

m

f fS =

T

A short time Fourier transform (STFT) of the sum of the reflections generates the

matrices tS f,t . Using equations 7,8,9 tS f,t can be transformed into a useful form

(10) 0

0

x t

f fS f,x = S f,t

S

while preserving the spatial resolution regardless of the length of the transmitted chirp.

Simulation

In this study we have generated a simulation of ultrasonic velocity estimation of a

synthesized phantom comprising of randomly positioned reflectors. A small region of the

phantom was shifted as a function of time to simulate blood flow (see Fig.1).

Velocity estimation was calculated for sequential (marked 0:i) simulated RF A-lines using

the method presented by Jensen [7, chapter 7.2] using autocorrelation of an analytic

demodulated signal cfmr i where i is the line number.

108

The RF A-lines, generated by the harmonic signal, where demodulated by the transmission

frequency, 0f , and turned into time-dependent complex analytical signal ,cfmr i t using the

Hilbert transform. Those signals were turned into depth-dependent signals using the relation

/ 2x c t . The velocity estimation for depth x was done using (similar to [7])

(11) 2

*

00

1, , 1

4 1

cNprf

cfm cfm

ic

c fv x r x i r x i

f N

where v x is the reflectors’ velocity along the beam direction, c is the sound velocity in

the medium, prff is the frequency of the pulses transmission, cN is the number of analyzed

RF A-lines and

Imagarctan

Real

ZZ

Z

is the argument of the complex number Z. The

values obtained for v x were smoothed using a median filter. These values served as a

reference and are referred herein as the “conventional” method.

The following algorithm was applied for velocity estimation using the chirp signal:

a The simulation program synthesized radio-frequency (RF) A-lines which simulated

the reflected echoes from the phantom as a function of time.

b The spectrum matrix ixS f,x was obtained for each RF A-line i as described in the

previous section (Spectral analysis).

c The spectrum matrix ixS f,x contains the frequency dependent phase information.

Hence, the velocity estimation for depth x by frequency f was done using the

following estimation

(12) 1

2*

0

1,

4 1

c

i i

Nprf

x x

ic

c fu x f S f,x S f,x

f N

d The final velocity for depth x, v x , was obtained by averaging the velocities

calculated for each frequency ,u x f .

e The values obtained for v x were smoothed using a median filter.

109

The simulation was performed several times and a varying level of white Gaussian noise

was added to the RF A-lines in each simulation stage. SNR values were calculated relative

to signals obtained using the “conventional” method. The simulation parameters are listed

in Table 1.

Results

To demonstrate the stages of the suggested method, for generating xS f,x are depicted in

Fig. 2. A simulated target comprising of two reflectors positioned 10 mm apart was used

(Fig.2a). The corresponding RF A-line obtained by transmitting the chirp signal which

parameters are listed in Table 1, is shown in Fig.2b. The TFR, tS f,t for that A-line is

shown in Fig.2c. The xS f,x function obtained using eqn 10 is depicted in Fig.2d. As can

be observed the full spectrum obtained from each reflector now corresponds to its spatial

location.

Next, a comparison between the simulation results obtained for the two methods, i.e. the

“conventional” and the suggested method, for several noise levels are presented in Fig.3.

SNR values ranged from -30db to +10db. The velocities vectors, v x , normalized to the

actual (gold standard) flow velocity which were calculated using the chirp based velocity

estimation and the conventional velocity estimation are plotted (in solid line) on the left

hand side and the right hand side correspondingly. The expected values are plotted using

dashed line. As can be noted, the axial resolution of the conventional method is slightly

better than the axial resolution obtained for the new method. However, the velocity

estimation obtained by the new method is superior to that of the conventional method for

low SNR values. This is further emphasized in Fig.4, where the mean square error of the

normalized velocity as function of the SNR for both methods is shown.

Discussion

A method for using long frequency modulated transmitted signals in spectral analysis based

applications without sacrificing the spatial resolution was developed. The frequency

dependent information of the measurement is rearranged using the frequency-time

110

relationship of the transmitted signal. Hence, the long transmission time does not degrade

significantly the resolution (see Fig.2).

A simulation program was used to confirm the ability of the new method to serve as a tool

for velocity estimation. As was demonstrated by the results (Figs. 3 & 4), velocity

estimation using the suggested method is superior to estimates obtained using the

“conventional” method in poor SNR scenarios. Although using the suggested method some

reduction in axial resolution may occur, however, the suggested method can be useful in

noisy measurements.

In a recent study Levy and Azhari [8] have shown that it is possible to estimate target

velocity using a single transmission of a chirp signal by cross correlating the signal which

was reflected from the target with the transmitted chirp. However, since that method is

based on averaging of phases, it is not suitable for cases where the target is not spatially

isolated (several wavelengths) from other reflectors and for cases where the target is

comprised of several reflectors. On the other hand, the new suggested method works well

even when the target comprises of many adjacent reflectors. (As indicated in Table 1 an

average of 10 reflectors per wavelength was used here).

In this paper, the signal used for transmission was a chirp signal. However, other long

frequency modulated transmitted signals with more complicated frequency to time of

transmission mapping may be used provided that there is a unique correspondence ff t .

In conclusion, a new method for local spectral analysis using long frequency modulated

signals is suggested. The new method performs well in poor SNR scenarios. The suggested

method can potentially be useful in other spectral based applications such as: tissue

classification, attenuation mapping, temperature monitoring etc.

111

References

[1] Graham Treece, Richard Prager, and Andrew Gee. " Ultrasound Attenuation

Measurement in the Presence of Scatterer Variation for Reduction of Shadowing and

Enhancement"ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 52,

no. 12, 2346-2360 december 2005

[2] Karen A. Topp, James F. Zachary, William D. O Brien, Jr. "Quantifying B-Mode

Images of In Vivo Rat Mammary Tumors by the Frequency Dependence of Backscatter". J

Ultrasound Med 20:605-612, 2001.

[3] Bigelow, T.A., and O Brien, W.D., Jr. "Estimating the Thermal Dose From

Backscattered RF Echoes" Proceedings of the 4th International Symposium on Therapeutic

Ultrasound, pp 151-153, 2004.

[4] Wagner C. A. Pereira, S. Lori Bridal, Member, IEEE, Alain Coron, and Pascal Laugier.

"Singular Spectrum Analysis Applied to Backscattered Ultrasound Signals from In Vitro

Human Cancellous Bone Specimens", ieee transactions on ultrasonics, ferroelectrics, and

frequency control, vol. 51, no. 3, 302-312 march 2004

[5] Misaridis T, Jensen JA. Use of Modulated Excitation Signals in Medical Ultrasound.

Part I: Basic Concepts and Expected Benefits. IEEE Trans Ultrason Ferroelec Freq Contr

2005;52:177-191.

[6] Martin Pollakowski and Helmut Ermert, “Chirp Signal Matching and Signal Power

Optimization in Pulse-Echo Mode Ultrasonic Nondestructive Testing”. ieee transactions on

ultrasonics, ferroelectrics, and frequency control. vol. 41, no. 5, September 1991

[7] Jensen JA. Estimation of Blood Velocities Using Ultrasound. Cambridge University

press 1996.

[8] Yoav Levy and Haim Azhari. Velocity measurements using a single transmitted linear

frequency-modulated chirp. Ultrasound in Med. & Biol., Vol. xx, No. x, pp. xxx, 2007

(accepted for publication, but wasn't printed yet.)

112

Figures captions:

Fig 1: Schematic illustration of the simulated environment.

Fig 2: (a) A simulated target comprising of two reflectors positioned 10 mm apart. (b) The

corresponding RF A-line obtained by transmitting the chirp signal. (c) tS f,t for the A-

line presented in (b). (d) The xS f,x function obtained for the A-line in (b).

Fig 3: A comparison between the simulation results obtained for the suggested method (left

column) and the “conventional” method (right column). The SNR values ranged from

+10db (top) to -30db (bottom).

Fig 4: The mean square error of the estimated normalized velocity, using the conventional

method (Δ) and the suggested method (*). As can be noted the suggested method provides

better velocity estimation than the conventional method for SNR<0.

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Table 1: Simulation Parameters

Phantom parameters:

Measured depth 35 mm

Vessel diameter 5 mm

Vessel position 15-20 mm

Number of Reflectors 10 reflectors per wavelength (for 4MHz)

Reflectors Velocity 0.5 m/s

Sound velocity 1540 m/s

General parameters:

fprf 10 kHz

RF lines for estimation 8

Sampling rate 100 MHz

SNR Values No noise, 0, -10, -20, -30 [DB]

v x smoothing window size 0.77 mm

Chirp velocity estimation:

Central frequency 4 MHz

Signal length Tm = 20 microseconds

Signal Bandwidth 4 MHz

Spectrogram segment size W=512 samples

Spectrogram FFT length 2048

Spectrogram windowing method Hamming

Conventional velocity estimation:

Central frequency 4 MHz

Sine periods 12

114

Figure 1

v

Wave

Generator

Receiver A/D

Trigger

Estimator

Simulated region

115

Figure 2

116

Figure 3

117

Figure 4

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C h a p t e r 4

DISCUSSION

Contributions

The major contributions of this research to the field of ultrasonic imaging is the

introduction of a new contrast for ultrasonic medical imaging, the SOSD, and by

developing approaches for spectral analysis of long signals which do not sacrifice the axial

resolution of the measurement. The results obtained by this research show that the

objectives of introducing a new ultrasonic imaging contrast and improving performance of

current methods have been met. A unified method, combining novel spectral analysis

methods with special long signals transmissions, was used to achieve those goals.

With respect to the measurement of SOSD, this study has clearly demonstrated the

feasibility of SOSD projection imaging and that SOSD may serve as a new contrast source.

Images, based on SOSD projections, and measurements of SOSD in soft tissues in pulse-

echo mode were presented for the first time. These new imaging techniques may contribute

to tissue characterization, tumour detection and breast diagnosis.

SOSD has been suggested as an additional acoustic property for utilization in medical

applications such as bone assessment (Wear (2000), Strelitzki and Evans (1996), Droin et al

(1998)). A few studies have also measured SOSD in soft tissues. However, to the best of

our knowledge SOSD imaging has not been suggested. This may stem from two main

reasons. First, SOSD is a very weak phenomenon and hence difficult to measure. Secondly,

previously suggested measurement methods had either low SNR or required very long

acquisition times. Previous methods for SOSD measurement were based on either sending a

single short broad-band pulse or sending many continuous waves. In the pulse based

techniques, usually, a short broadband ultrasonic pulse is sent through the object and the

phase of each frequency is extracted using FFT. The main limitation of this technique is its

relatively low SNR as compared with continuous wave measurements. This may induce

inaccuracies in phase measurements for each individual frequency. Measurements of speed

119

of sound dispersion using continuous waves were done in several ways. However, in those

techniques, many sequential transmissions of continuous waves with increasing frequencies

are required. For medical imaging, a fast method with a high SNR is needed. In order to

combine the high SNR of continuous waves with a measurement by single transmission as

in pulses based methods, we developed "imaging oriented" methods based on the

transmission of long bursts comprised of structured frequencies content.

Two signal types were used in those studies, a long burst comprising of two frequencies,

one being the double that of the other and a linear frequency modulated signal (Chirp). A

sample of the first signal is shown in Figure 1, and a sample of the second type is shown in

Figure 2.

Figure 1 – A sample of a long burst comprising of two

frequencies, one being the double that of the other.

Figure 2 – A sample of a linear frequency modulated signal

(Chirp).

120

The frequencies range in which the studies were conducted was from 1MHz to 6MHz. In

lower frequencies the diffraction of the acoustic beams was more dominant than the

velocity dispersion (see paper A, Fig 4.). Frequencies above this range were absorbed in the

measured specimens and the received signals analysis was problematic (see paper c, Fig 2

bottom).

In the first method, a long burst consisting of two frequencies was used for the

measurement of the SOSD. In the case of a dispersive imaged object (i.e. an object in which

the velocity of the sound is frequency dependent), there is a difference in the time of flight

(TOF) of the two frequencies through the object. In the measurement, this TOF difference

is expressed as a phase shift. Hypothetically, by measuring a travelling signal in a water

bath with and without a dispersive object in the signal’s path (see paper A, Fig. 1 for a

schematic depiction of the experimental system), the SOSD of that imaged object could be

measured from the relative phase shift between the two frequencies due to dispersion.

However, in practice, putting the imaged object in the signal's path causes a change in the

global time of flight of the signal and that is expressed in the measurement window as a

remarkable change in the phases of both frequencies. The relatively tiny phase difference

caused by the dispersion cannot be distinguished from the dominant phase shift caused by

the change in the global TOF. The method introduced in paper A, addresses this problem by

selecting a specific frequency combination for the transmitted long burst. An algorithm was

developed for the extraction of the relative phase shift in the measured signal, caused by the

dispersive object, for the case of a burst comprising of two frequencies, one being double

the other. The results obtained using this method for SOSD in soft tissues were verified by

cutting the specimens and demonstrating the linear relation between the specimen length

and the TOF difference (see paper A, Fig. 5. for a demonstrative data set).

The second contribution of paper A is evident in Figure 3 (same as paper A, Figs 6,7),

which displays the speed of sound dispersion index versus the average frequency for the

turkey breast (left) and bovine heart (right). It can be noted that the SOSD is significantly

different for those different tissues (t value of 6.92 at 3MHz). Hence, these results support

the hypothesis that SOSD may be used for soft tissues classification. This hypothesis is also

supported with respect to the issue of muscle fiber orientation. The results obtained in paper

C for the turkey breast specimen are smaller than those reported in paper A. This stems

from the fact that in the study presented in paper C, the ultrasonic beam was perpendicular

121

to the tissue fibers whereas in the other study it was performed along the fibers’ orientation.

This finding is consistent with the phenomenon reported for the myocardium by Marutyan

et al. (2006). They found that the speed sound and SOSD changes substantially with the

orientation of the myofibers. Their findings indicate that SOSD along the myofibers is

more than twice the SOSD perpendicular to the myofibers.

Figure 3 - The speed of sound dispersion index versus the average

frequency for the turkey breast (left) and bovine heart (right). The

error bars correspond to the 95% confidence level range.

The method suggested in paper A, offers improved SNR and a single transmission

measurement of the SOSD. This makes it particularly suitable for ultrasonic SOSD

projection imaging as was demonstrated in paper B. The results obtained in paper B have

clearly demonstrated the feasibility of SOSD projection imaging. As was shown there,

SOSD images can be obtained for solids (Paper B, Fig.2), for fluids (Paper B, Fig.4) as well

as for the tissue mimicking breast phantom (Paper B, Fig.5) and soft tissues (Paper B,

Fig.6).

As can be noted in paper B, Figs.2,4,5,6, there is an artifact which occurs at boundaries

separating different regions in the imaged object. This artifact appears as a strong gradient

in SOSD values. It emphasizes boundaries and hence, may increase the visibility of small

targets. The source of this artifact may be the frequency-dependent acoustic diffraction

which occurs at such boundaries. However, since tissues borders in the human body are less

definite, this artifact is expected to be less significant in “in-vivo” measurements.

Turkey Breast Bovine Heart

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The SNR improvement in the suggested measurement method was obtained by increasing

the transmission duration, but this approach decreases the axial resolution and therefore this

method is more appropriate for projection imaging. However, this limits the potential

application of SOSD in ultrasonic imaging and tissue characterization. A pulse-echo based

technique is more desirable since it offers much better accessibility to many organs in the

body. In the study, presented in paper C, two new methods are introduced for SOSD

measurements using a chirp signal. The methods were tested in both through and pulse-

echo modes. Although both methods presented in that paper are based on the transmission

of the same type of signal, they are very different. The signals bank method is an

established technique which was adapted for SOSD measurements. This method is similar

to wavelet analysis of a scaled mother wavelet, where the mother wavelet is the reference

signal (Similar to Bilgen 1999). It is a robust method which performs better in low SNR

cases (see paper C Fig.2). This method can be used with any signal shape and with any

sound velocity model. Using more complicated sound velocity model may offer the ability

for conducting measurements in a wideband. Ignoring the attenuation does not degrade the

reliability of the results of this method, yet, in this method, the attenuation response of the

measured object may be incorporated. On the other hand, the computational effort during

the data analysis in this method is large (requiring several seconds of computation per

transmitted signal on a PC). The cross correlation method is an elegant and fast (about two

orders of magnitude shorter computation time) measurement technique based on

approximations and averaging. Therefore it is valid only for narrowband measurements and

it may be biased by frequency dependent attenuation. Figure 4 shows a schematic

illustration of the setup used for pulse-echo measurement in soft tissue. The same setup can

be used for example in breast imaging.

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Figure 4 – A schematic illustration of the setup used for

measurement of SOSD in soft tissue using pulse-echo mode.

Assuming a linear dispersion model in a dispersive medium, it can be shown that a chirp is

rescaled while passing through the medium. It is well known that a chirp which is reflected

from moving target is rescaled as well (Jensen 1999). We concluded that the cross

correlation method, which was derived in paper C, for dispersion analysis should be

applicable for velocity estimation as well. Paper D describes the derivation of the relation

between the estimated velocity and the phase in the peak of the cross correlation function.

The remarkable achievement in this research is the development of a method for velocity

estimation in ultrasound, using a single transmission. The conventional velocity estimation

using a pulsed wave is based on measurements of a shift in the phase of a single frequency

caused by movement of the target between the reflections. Therefore, the conventional

method needs at least two transmissions for velocity estimation. The new method was

tested experimentally (paper D, Fig 1 shows the experimental set up and Fig 5 shows the

experimental results).

The method presented in paper D for velocity estimation using the cross correlation

function is based on the averaging of phases. The application of this method is problematic

for cases where the target is not spatially isolated by several wavelengths from other

reflectors and for cases where the target is comprised of several reflectors. It seems that

averaging, using a cross correlation, is not the optimal approach for utilizing long structured

signals for spectral analysis. However, since SNR is a great concern in spectral analysis

based applications and since the intensity of the transmitted signal is limited by safety

Signal

Generator

Receiver

A/D

Trigger

Signal

Data

124

aspects, it is desirable to find a way to utilize coded excitations in such applications without

losing the spectral information during the compression of the coded signal. A method for

using long frequency modulated transmitted signals in spectral analysis based applications

without sacrificing the spatial resolution is presented in Paper E. The frequency dependent

information of the measurement is rearranged using a frequency-time relationship of the

transmitted signal. Hence, the long transmission time does not significantly degrade the

resolution (see paper E, Fig.2).

A unique algorithm for velocity estimation using Fourier analysis of reflections from

broadband pulse was used in a simulation program to confirm the utility of the new method

for velocity estimation. As was demonstrated by the simulation results (Paper E, Figs. 3, 4),

velocity estimation using the suggested method is superior to estimates obtained using the

“conventional” method in poor SNR scenarios. Although using the suggested method some

reduction in axial resolution may occur, the suggested method can be useful in noisy

measurements. The suggested method can potentially be useful in other spectral based

applications such as: tissue classification, attenuation mapping, temperature monitoring etc.

Future work

In this study, the feasibility of speed of sound dispersion imaging was demonstrated. The

next step in the development of this application should take place in a clinical laboratory.

The new algorithms should be tuned for specific medical applications such as breast

imaging and the clinical value of the results should be evaluated by the end users, the

medical doctors.

The algorithm for velocity estimation using Fourier analysis of reflections from broadband

pulses should be examined experimentally. For simplicity, the basic velocity estimation

algorithm was tested is this study, however other velocity applications such as velocity

distribution mapping may potentially be obtained as well.

The new method for using long frequency modulated transmitted signals in spectral

analysis based applications may have a variety of other applications such as attenuation

mapping, temperature monitoring, and tissue characterization.

125

Conclusions

In this study, it was shown that using long structured signals for ultrasonic imaging together

with appropriate algorithms may yield benefits in terms of SNR, measurement accuracy and

acquisition rate. Especially, the following achievements were accomplished:

Three methods for the measurement of SOSD in soft tissues were developed.

SOSD was measured in soft tissues using both transmission and pulse-echo modes

and was found to be significantly different in different tissues.

The feasibility of SOSD to serve, using the developed methods, as a new contrast

for ultrasonic imaging was demonstrated.

A method for velocity estimation using a single ultrasonic transmission was

developed and experimentally validated.

A method for the spectral analysis of backscattered reflection from long structured

signals was developed.

It was shown in a simulation that the combination of a unique algorithm for velocity

estimation using a transmission of broadband signal and the method for spectral

analysis of backscattered reflection from long structured signals was superior to

estimates obtained by using the “conventional” method in poor SNR scenarios.

126

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