Modelling the Behaviour of Microbubble Contrast

Agents for Diagnostic Ultrasound

Chien Ting Chin

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Graduate Department of Medicd Biophysics University of Toronto

@ Copyright Chien Ting Chin 2001

Nationai Liimy I f F l ,canada Bibliothèque nationale du Canada

Acquisitions and Acquisitions et Bibiiographic SeMces servicm bibliographiques

The author has granted a non- exclusive licence dowing the National Lïb~ary of Canada to reproduce, loan, distn'bute or sell copies of this thesis in microform, paper or electronic formats.

The author retahs omership of the copyright in this thesis. Neither the thesis nor substantial extracts fiom it may be p d e d or otherwise reproduced without the author's permission.

L'auteur a accordé une licence non exchisive permettant a la Bibliothèqye nationale du Canada de reproduire, prêter, distn'buer ou vendre des copies de cette thèse sous la fome de micmfiche/fihn, de reproduction sur papier ou sur format électronique.

L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de ceHe4 ne doivent être imprimés ou autrement reproduits sans son autorisation.

Modelling the Behaviour of Microbubble Cont rast

Agents for Diagnostic Ult rasound

Chien Ting Chin

Doctor of Philosophy, 2001

Department of Medical Biophysics

University of Toronto

Abstract

Encapsulated microbubble contrast agents that can be injected intravenously constitute one

of the most important developments in recent years in ultrasound imaging. These microbub-

bles oscillate nonlinearly in dtrasound fields and produce nonlinear echoes which can be

detected by novel imaging methods. The performance of these novel methods depends

strongly on the characteristics of nonlinear scattering by the bubbles. Currently a sys

tematic approach to optimizing them does not exist. This is due in part to the lack of a

theoretical rnodel for predicting the acoustic response of microbubble contrast agents. This

thesis presents some developments made to address this deficiency.

A theory for the nonlinear motion of a single bubble formed the basis of this study.

The modei was extended to account for the multipiicity of bubble size and the heterogeneity

of the dtrasound field. Experiments were designed and performed to quantitatively test

the rnodel. The resuits generdy confirmed the validity of the model, while some quantita-

tive discrepancies led to the hypothesis that the s h d plays an important role in nonlinear

scattering, which was aIso confirmed by experiment.

Contents

Abstract

Dedicat ion

List of Figures

Chapter 1 Introduction 1

1.1 Contrast Agents in Medicd Imaging . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Physics of Microbubble Contrast Agents . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Acoustic Impedance and Scattering . . . . . . . . . . . . . . . . . . . 6

1.2.2 Oscillation of Bubbles . . . . . . . . . . . . . . . . . . . . . 8

1.2.3 Basic Behaviour of Rayleigh's Mode1 . . . . . . . . . . . . . . . . . . 11

. . . . . . . . . . . 1.2.4 More Sophisticated Models of Bubble Osc~ations 14

. . . . . . . . . . . . . . . . . . . . 1.3 Other Behaviour of Bubbles and Cavities 17

3 Dissolution of Microbubbles . . . . . . . . . . . . . . . . . . . . . . . 17

1.3.2 CavitationPhysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.3.3 Sonolirminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Nonlinear Imaging 25

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Linearity 25

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Harmonic Imaging 27

. . . . . . . . . 1.4.3 Noniineax Propagation and Tissue Hannonic Imaging 27

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Thesis Outline 31

Chapter 2 A Population Mode1 of Contrast Microbubbles 33

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction 34

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Theory 37

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Single bubbIe 37

. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Secondary scattering 42

. . . . . . . . . . . . . . . . . . . 2.2.3 Echoes from suspensions of bubbles 44

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Resdts and Discussion 45

. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Single bubble mode1 45

. . . . . . . . . . . . . . . . . . . . 2.3.2 Prediction of population response 31

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Conclusions 54

Chapter 3 Experimentd Verificat ion 57

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction 58

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Method 60

3.3 R d ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Discussion .. Ti

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Conclusions 73

vi

Chapter 4 Effects of Shell Disruption 75

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction 76

4.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Results 82

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Discussion 83

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Conclusions 89

Chapter 5 Applications and Future Prospects 90

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction 90

. . . . . . . . . . . . . . . . . . . 5.2 Recent Developments in Contrast Imaging 91

. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Intermittent haging 91

. . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Pulse Inversion Detection 92

. . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Power Modulation Imaging 96

. . . . . . . . . . . . . . . . . . . . . . . . 5.3 Applications of the Bubble Mode1 99

. . . . . . . . . . . . . . . . . . . . . 5.4 Nonlinear Scattering at High Frequency 106

Chapter 6 Conclusions 110

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Summary 110

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Limitations 111

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 FutureDîrections 112

. . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Single Bubble Mode1 112

. . . . . . . . . . . . . . . . . 6.3.2 Evoiution of the Bubble Sizes In Vivo 114

Bibliography

List of Figures

1.1 The appearunce of contrast agents Wat increase backscatter, attenuation, or

speed of sound in the tissue. Notice that, in the image for inmeased speed of

sound, the bottom of the region containing the contrast agent is distorted along

. . . . . . . . . . . . . . . . . . . . . . . . . . . . with the connectiue tissue. 4

1.2 An idetzlized bubble system. A sphere filled with o gas zs sumounded by a

boundless region of liquid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Resonant hepencies of bubbles from 1 to 10 Pm, calculated from Mnnaert 's

Jomulu (1.1 3) und Shima 's formula (1.14). . . . . . . . . . . . . . . . . . . 13

1.4 The scatterkg cross-section of an isolated Rayleigh bubble oscillator to 5 MHz

ultrasound. Notice thot ut higher t r a m i t t e d amplitudes, the resonant bu6 ble

szze for a fized frequency is shified d o m signzficantly. . . . . . . . . . . . . . 14

1.5 Scattered echo spectra from a 0.95 pm radius exposed to 5 MHz ultmound.

Each spectrum is normalized to the transmitted amplitude. A s the tmnsmitted

amplitude is increased, the second and higher harmonic components are in-

creased; at the highest t ~ a m i t t e d amplitude, the echo spectrum becomes very

broad and the harmonic peaks are no longer distinct. . . . . . . . . . . . . . 15

1.6 The shrinkage of bubble as a result of gas dzssoivtion and dzffùsion. Each

curve represents the euolution of a bubble piaced in water znitially saturated

uniformly with air ut 1 atm. As the bubble shrinks, the e&cf of surface tension

increases and the shrinkage rate accelerates. The Cumes corresponds to bubbles

yith initial diameters of (from the bottom) 2, 3, 4 , .. ., 10 pm. . . . . . . . 20

1.7 Operation of hannonic imaging. . . . . . . . . . . . . . . . . . . . . . . . . 28

1.8 Nonlinear distortion of a large amplitude sound vave an water due to convec-

tion (middle panel) and nonlznear bulk modulus (right panel). The distortion

is built up ouer distance (2) trauelled. . . . . . . . . . . . . . . . . . . . . . 30

1.9 Calcdated transverse beam profiles on the focal plane showing 2 MEIt fun-

damental (solzd), 4 MHz fundamental (dots), and 4 MHz second harmonies

from the 2 MEIt beam (dushes). Al1 curves vere normalized. Reproduced from

Christopher (1997). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1 Each bubble in the sample volume contributes a different wauefonn to the final

. . . . . . . . . . . signal depending on zts siie and locot incident amplitude. 45

2.2 Measured transmitted pulse used for simulation. . . . . . . . . . . . . . . . . 47

Four types of calculated response to the two-ycle wave, in tenns of radius

change (lef) and radiuted pressure (right) at 40 mm. (a), (b) and (c) Re-

sponses of 1.2 Pm, 6.0 pm and 3.0 pm diameter bubbles to 5 kPa peak-to-peak

incident amplitude. (d) Response of the 3.0 pm bubble to 100 kPa incident

amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Calculateci findumental (top) and second hamonic (bottom) cross-sections ( in

rn2) of single bubbles to Pin (t) . The grey level represents lineorly the cross-

sectional areas. The tick m a r k dong the top and right edges of the figures

. . . . . . . . . . . . mark the exact mdài and amplitudes of each calculation.

(a) Measured sàze distribution of bub ble ensemble. (b) Meusured transducer

. . . . . . . . . . . . beam profile B(a) uped in calculation of agent response.

Nonnalàzed Fourier spectra of the simulated buk agent echoes. The spectra

were nonnalàzed by dàvàding by the square of the incident amplitude. The grey

levet represents dB sctale. Notice spectral broadenzng of the honnonic peaks at

hzgh incident amplitudes. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fundamental (top) and second harmonic (bottom) responses of simulated agent

os a function of incident focal amplitudes at three frequencies. The error bars

indicote standard evor of 32 simulated ensembles. . . . . . . . . . . . . . . .

. . . . . . . . . Experimental setup for the nonlinear scattering meusurement.

F i u m i t t e d four-cycle (left) and one-cycle (right) w a v e f o m and the corne-

spondincl fTemenm mectrurn fbottorn) used in both simulation and emerinrent.

Site distribution of bvbbles used in calculation and the the beam profles of the

tmnsducers used in eqerirnent. . . . . . . . . . . . . . . . . . . . . . . . . . 64

Power spectra of simulated zesponses from the four-cycle (top) and one-cycle

(bottom) pulses. The numbers represen t incident peak- to-peak focal amplitude. 65

Power spedza of scattered signal from the four-cycle (top) and one-c ycle (bot-

tom) pulses. Numbers represent incident penk-to-peak amplitude. . . . . . . . 67

Stmulated and measured scattenng c o e m e n t s vs. ancident amplitude in re-

sponse to the four-cycle pulpe. (top) Fundamental ( f o ) and second hannonic

(2 fo); (bottom) spectral bruadening (1.5 fo). Error bars in the simulated resuits

indicate standard error using 32 ensembles. . . . . . . . . . . . . . . . . . . . 69

Simvlated and measured scattering cueficients vs. incident amplitude in re-

sponse to the one-cycle pulse. (top) findamental (/O) and second hannonic

(2 fo); (bottom) spectral broadening (1.5 f , ) . Error bars in the simulated results

indicate standard e m r uskng 32 ensembles. . . . . . . . . . . . . . . . . . . 70

Optison echoes from exposvre to 2.0 MHz pulses ut a puise repetition frequency

of 2 Mz and peak-to-peak amplitude of 3.6 MPo. The first, third and twentieth

echoes demowtmte bubble shell disruption. The bubbles had not been exposed

to u l tmound pnor to the first pulse. Significantly elevated fundamental and

h a m o n i c scattenng are obserued ofter initial exposuze, but by the twentieth

. . . . . . . . . . . . . . . . . . echo, the bvbbles have virtualty d i sappead 72

. . . . . . . . Experimental setup for the nonlinear scattering measu~ement.. 79

4.2 The puking sepuence used in the shell effects rneasurement. . . . . . . . . . . 81

The l s t , I l th , 21st, 31st and 41d echoes from one of the measured data set

for the regular Definity (PFC) and the special Definity (fi). Each trace was

10 p in length. P R . = 2 M z , p, = 1.8 MPa. The PFC echoes (voltage)

were scaled by a factor of 4.46 since the spen'al N2 Defin* v a s a weaker agent. 83

Lifetimes (deJined as tirne for the RMS amplitude of the echoes to drop to half

the mozi'mvrn level) us. incident amplitude for h o agents with different gas

types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Pairs of echoes from Sonauist @nt different jîrst pulse amplitudes (p,). The

delay between the fist und second echoes is 15 p. Each trace was 5 ps in

length and was nomalired by the corresponding (fkst or second) inczdent am-

plitudes. Notice that at the hzghest p,, 60th the first und second echoes were

elevated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . First pulse scattering coeficients for the four contrast agents

. . . . . . . . Second pdse scattering coeficients for the four contrat agents

m e n a high axial resolution is desireà, generolly a v ide bandwidth is used.

However, the abzlity of hamonàc àmaging to discriminate between fundamental

. . . . . . . . and harmonzc frequencàes is limited by overlapping bandwidths.

Pulse Inversion Detection. A pair of incident pulses with opposite szgns are

tmnsmitted. The echoes are summed together, the fundamental cornponent is

cancelled out and the men hannonie components are preserued. The echoes

were culculated for a 1.9 pm diameter fiee bubble. Incident peak-to-peak am-

plitudes were 300 kPa and 150 kPa. . . . . . . . . . . . . . . . . . . . . . . .

5.3 Power Modulation Imaging. A pair of incident pulses with different amplitudes

are tmnsmitted. A wezghted difference of the echoes is used to cancel the

lineur component. Ail harmonic cornponents are preserved. The echoes were

culculated for a 1.9 pm diameter free bubble. Incident peak-to-peak amplitude

was300kPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.4 Pulse Inversion Detection (PD) and Power Modulation Imaging (PMI) em-

ploy the limited bandwidth of the transducer di#erently. The dashed line repre-

sent the frequency response of a hypothetical transducer with 100% banduridth.

PID benefits M m a higher nonlznear response, while PMI benefits frorn the

full exploitation of the trunsducer bandwidth. . . . . . . . . . . . . . . . . . 100

5.5 Scattered woveforms of a 1.9 pm bubble in response to a 5 MHz incident pulse

(FWHM pulse duration = 1.2 cycles). Each wavefonn is nonnalized by the

incident pressure. Sixteen di 'eren t incident pressures (peak- to-peak) spanning

1 to 1000 W a were simulated. . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.6 Result of P D (top) and PMI (bottom). The Y-& values correspond to the

amplitude of the first (stronger) pulse. Each wavefonn is nonnalized by the

incident pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.7 h p e n c y spectra of single puise echoes (top), and the results of the PID

(middle) and PMI (bottom) rnethods. The nurnbers next to the Cumes indicate

the peuk-to-peak incident amplitudes. . . . . . . . . . . . . . . . . . . . . . . 104

5.8 Assumed fïequency response of the hnsducers for the cornparison of PID us.

PMImethods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.9 Relatiueperfonnance of PID and PMIusing thef7equency responses infigure

5.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.10 Szmulated bubble echo spectra for: 0.65 pm bubbles in 20 MHz ultmsovnd

pulses ut 200 kPa (black) and 4.0 prn bubbles in 2 MHz ultrasovnd pulses at

50 kPa (red). The echo power from the smaller bubbles was h r e ~ e d by a

factor of 6.3 to account for the higher number density. . . . . . . . . . . . . 107

5.11 Averuged poww spectra of 1000 echoes for Definity (solid) and graphite pow-

der (dashed). The result frorn graphite powder demonstrate second and third

hannonics (40 and 60 MHz) due to nonlinear propagation; the additional 2329-

nals at these peaks, as well as spectral broadening, are due to the nonlinear

scatterhg by the contrast bubbles. . . . . . . . . . . . . . . . . . . . . . . . . 108

Chapter 1

Introduction

1.1 Contrast Agents in Medical Imaging

Medical imaging systems produce images of the human body by probing it with radiation

such as X-rays, electromagnetic waves and sound waves. Diagnostic information can be

deduced because these radiations interact Mth the body tissue and encode information

about some physical or chernical properties of the tissue. Image contrast results hom the

consequent relative ciifference in the detected mgnd amplitudes from different regions of

target tissue. Each imaging modality relies on a different contrast mechanism. X-ray imaging

reiies on Mnations in atomic number and electron density. Magnetic resonance imaging relies

on variations in hydrogen atom density and interaction with large molecules. Ultrasound

irnaging relies on microscopie k a t i o n in density, bulk modulus and mechanicd relaxation.

WhiIe these methods have proved tremendously usefid, theh abiiity to detect and localize

some disease-related structural changes in tissue, partinilady on a fine scale, is often Limited.

This is due to the fact that these diseases do not produce conspicuous changes in the relevant

physical and chernical properties. In many applications, foreign materids can be introduced

b i d e the body to create or enhance the vaxiations in the relevant physical or chernicd

properties. These materids are called contrast agents.

For X-ray imaging, the most common contrast agents are barium and iodine. Bariurn

sulphate "milk" is ingested by the patient, and by virtue of its high electron density (54 per

ion, compared to 18 per calcium ion), opacifies the lumen of the digestive tract. Iohexol is

a compound containing iodine, and is usually used at a concentration of 180-300 mg/ml.

Dosage of 5 to 100 ml can be injected via a catheter to enhance digital subtraction angiog-

raphy or computed tomography of the cerebral arteries, the coronary arteries and peripheral

vessels. Intravenous contrast agents allow computed tomography (CT) images to display

vascular information, otherwise absent hom unenhanced images. Nonvascular applications

include imaging of the bile duct and the fallopian tubes.

The most common of the rnagnetic resonance imaging contrast agents is Gadolinium-

DTPA (Gd-DTPA). The uncharged Gd atom is paramagnetic and creates a local inhomo-

geneity in the static rnagnetic field (Bo). This local inhomogeneity enhances the relaxation of

rnagnetic moments in the hydrogen nuclei. Both Tl and T2 relaxation times are shortened

by the presence of the Gd atoms, but the Tl shortenhg is more pronounced and can be

more reliably measured. Thus the signal from tissues perfbsed with the Gd-DTPA molecules

are enhanced in Tl-weighted Maging. Gd-DTPA is a s m d molecule and can diffuse freely

out of blood vessels and enter the interstitinm quickly. The useful irnaging tirne window

for vascular imaging is limited to about 1-5 minutes, and in most cases no more than 20

minutes. It is interesting to note that timing is so cntical in MRI that a study was initi-

ated to investigate the feasibility of using an ultrasound contrast agent to determine optimal

bolus timing for contrast enhanced MR angiography (Prince et al. 1999). More recently,

blood pool contrast agents consisting ofvery large molecules (up to 94 000 Da) with multiple

Gd ions have become avaliable (&OR and de Roos 1999). By limiting the diffusion of the

agent through the endothelid membrane, these agents can recirculate in the vascular system

dlowing imaging for a longer period of time. UseM enhancement couid be seen for up to

120 minutes after contrast injection.

Nuclear imaging depends on radiophmaceuticals as a source of ionizing radiation.

Radiophannaceuticals have the advantage that many elements exist in radioactive isotope

foms which are either found naturally or can be made by methods such as neutron bom-

bardment. Detecton of ionizing radiation are tremendously sensitive, only a small number of

radioactive atoms is needed in order to produce a useful image. It is possible to manufacture

radiophaxmaceuticals which are chemically identical to physiological molecules. These ra-

diopharmaceuticals accumulate in the tissue where the desired physiological function occurs

and produce a spatial map of some metabolic hinction in the body. For euample, Thalium-

201 is a potassium analogue which is taken up by myocytes that axe actively contractîng.

Therefore, nuclear imaging qualifies uniquely to be c d e d functional imaging.

Ultrasound contrast agents have become clinicdy relevant in the last few y e m . The

mechanisms of ultrasound contrast agents may involve modifying the backscatter, attenua-

tion or speed of sound in the tissue (Ophir and Parker 1989). Figure 1.1 illustrates concep

tuaily the images that remit kom these three types of agents. Of these, the modification of

CHAPTER 1. INTRODUCTION

n U itrasound Probe

Tissue Bearhg Contrast Agent - . c Connective

Tissue

Figure 1.1: The appeumnce of contra& agents that inmase bockscatter, attenuatzon, or speed

of sound in the tissue. Notice that, in the image for rnc-ed speed of sound, the bottom of

the region wntainzng the contrBst agent is distorted along uith the connective tissue.

backscatter is the most important, since, in this case, changes in the image coincides with

the location of the agent. Agents with difFerent attenuation or speed of sound modify the

appearance of tissues behind the agent-bearing region. This thesis will focus on agents that

modify the backscatter, in particular, agents that produce nonlinear backscatter.

Most ultrasound contrast agents are based on gas bubbles, which are very effective

scatterers of ultrasound. Gramiak and Shah (1968) were the fkt to exploit contrast created

by bubbles. They created free air bubbles by injecting saline via a catheter into the aortic

arch. However, catheterization is an invasive procedure and direct injection of gas bubbles

risks emboiism of sensitive organs such a s the brain, kidneys and lungs. A clinicaily useful

agent should be intravenously injectable and must be small enough to pass through the

capillaxies of the lungs and spianchnic beds. However, micron-size free bubbles are inherently

unstable and tend to dissolve within seconds. Therefore, imaging of gas bubbles has not been

feasible except by the direct injection into the imaged regions using a catheter. In recent

years, technologies have been developed to stabilize the microbubbles. There are two main

approaches, the k t is the encapsdation of the bubbles by a shel1 which limits the transport

of gas across the gas-liquid interface. The second is the substitution of the air wi t h a high

mo1ecda.r weight gas which has a low solubility and difisiviv. Such technologies dlow

microbubbles to survive in the body for severd minutes or longer. The first encapsulated

agents, such as EchovistTM (Schering AG, Berlui), were too large to pass through the capilary

bed in the lungs. These agents must be injected intra-arteridy in order for the left heart to

be imaged. Newer agents, which began with the air-aibumin Albunex (MLlallinckrodt Medicd

Inc., St. Louis, MI) (Feinstein et id. 1990), are d c i e n t l y small and stable to appear in

CHAPTER 1. INTRODUCTION 6

the systemic circulation following intravenous injection. These new agents are suspensions

of microbubbIes containhg a range of diameters from below 1 pm to about 5 Pm. Invariably

a srnd number of bubbles of 10 pm or even larger are also present, however, both the

volume fraction and number fraction of these large bubbles are typically less than 1%. The

bubbles rnay contain air, a perfluorocarbon (PFC) gas or a mix of the two. The bubbles of

most agents are encapsulated by a sheil composed of surfactant, polper , or lipid. There are

currently over twenty agents in various stage of development and trials, several of which have

received approval for clinical use in Europe, the US and Canada. Next, we shall consider

the phyiscs of ultrasound contrast agents.

1.2 Physics of Microbubble Contrast Agents

1.2.1 Acoustic Impedance and Scattering

Diagnostic ultrasound is non-invasive, inexpensive and widely available and employs no ion-

izing radiation. The basic approach is based on radar-like pulse-echo rnethods. A transducer

is used to convert electrical pulses to ultrasound and vice versa. Pulses of ultrasound are

directed into the body and allowed to interact with the body structures. A fraction of the

dtrasound energy is scattered back towards the transducer which converts it back into an

electrical signal. These backscatter signais (echoes) contain information about the acous-

tic properties (scattering, attenuation and speed of sound) of the body structures. The

most commonly desired properties of an dtrasound contrast agent are high backscatter, lom

attenuation and identical speed of sound to biological tissues.

CHAPTER 1. INTRODUCTZON 7

Scattering occurs when sound is transmitted through a region with varying acoustic

impedance. Acoustic impedance of a materid is given by

where p is the density and c is the speed of sound. In iiquids and solids, speed of sound is

given by

where ,LI = pdpldp is the bulk modulus of the medium. The speed of sound of a gas is given

by -

where p is the pressure and 7 = %/c, is the ratio of the coefficients of specific heat at

constant pressure and constant volume, respectively. At the boundary between the different

media, dtrasound is partially reflected. Refiected energy is related to impedance by

where Zi and Z2 are the acoustic impedances of two different media. Water has an impedance

of 1.5 x 106 Pa-m/s. Contrast materials should be made of material with a significantly

higher or lower impedance. Good candidates are gases (2 = 330 Pa-m/s) and inorganic

solids (such as steel with Z = 23 x 106 Pa-m/s). Of the two, a gas is both a stronger

scatterer and a more easily metabolized materid. Ekperimental work has &O shown that

contrast agents consisting of gas-filled microbubbles are more effective (Ophir and Parker

1989). Therefore, aùnost all the ultrasound contrast agents in use or in developmeni are

based on gas microbubbles.

1.2.2 Oscillation of Bubbles

Due to the large dserence in bulk moduli between water and gas, bubbles are in fact

oscillators. The heavy and nearly incompressible liquid functions as the m a s , and the light

and highly compressible gas functions as the spnng in the classic mass-and-spring mode1 of

oscillators. Consider the simple system in figure 1.2 in which a sphere Nled with a gas is

surrounded by a boundless region of liquid. Assuming the liquid to be incompressible and

Figure 1.2: An idealized bubble system. A sphere jilled vith a gas as surrounded by a boundless

irrotational, the velocity at any point in the Liquid is purely radial and is related to the

CHAPm' 1. n\rTRODUC!TTON

instantanmus velocity of the bubble radius R:

Throughout this thesis, a dot above a variable indicates totd t h e derivative, 2 = dx/dt .

Assuming the mas of the gas to be insipificant compared to the iiquid, the kinetic energy

of the liquid can be calcdated as

K.E. = lm u24rr2dr = 2p7rff' R2, 2 R

where u is the velocity of the liquid at a distance r from the centre of the bubble. The

potential energy of the gas is aven by

where pg is the pressure inside the bubble and Ro the equilibrium bubble radius. .Assuming

the expansion and compression of the gas to be adiabatic, pg is given by

where pso, &, it$ and 7 are the eqniübrium intemal pressure, bubble radius, bubble volume

and ratio of specific heat capacities respectively.

The equation of motion of the bubble boundary c m be obtained by stipulating the

C W T E R 1. INTRODUCTION

time-derivative of the total energy (K.E. + P.E.) to be zero, the result is

Equation (1.9) was derived by Rayleigh (1917), supposedly, to study the creaking noise

produced by a kettle of water just before boihg (Flynn (1964) noted that Lord Rayleigh

was dso commissioned by the Royal Navy to study propellor damage caused by bubbles).

While Rayleigh originally on?y considered a cavity collapsing without e-xtemal forces, it is

easy to allow for the bubble to be driven by an applied pressure wave p,, giving

By numerically integrating equations (1.10) one can calculate R(t) in response to an incident

pressure wave pin. Since particle velocity at any point in the liquid is given by equation

(1.5), the radiated pressure c m also be determined. Rom the radiated pressure, a scattering

cross-section, defmed as total radiated power divided by incident intensity, can be calculated.

While many of the assumptions used make equation (1.10) invaiid for quantitative prediction,

Rayleigh's mode1 nonetheless dernonstrates many behaviours that are characteristic of the

acoustic response of contrast bubbles.

1.2.3 Basic Behaviour of Rayleigh's Model

By drawing analogy to the kinetic energy of a mass moving at a Gxed velocity, K.E. = mv2/2,

an effective mass can be defined fiom equations (1.6),

Similarly, by a binomial expansion of pg, an effective spring constant can be defined from

(1 -7):

IF,,, = 6flVgoR, (1.12)

using the potential energy stored in a spring: P.E. = k(hx)* . From the m a s and spnng

constant the resonant frequencies is given by:

Therefore, the natwal resonant hequency of a bubble oscillator is simply inversely propor-

tional to its size. Entering the appropriate values for an air bubble in water, one obtains

the resonant frequency of a 2 pm diameter bubble of 3 MHz. Fortuitously for ultrasound

imaging, the resonant fiequencies of bubbles s m d enough to pass through the capillary bed

(< 5 pm) f d within the fkequency range of diagnostic dtrasound (> 1.5 MHz), making

microbubbles particdarly efticient as scatterers of dtrasound.

Equation (1.13) was fmt derived by Minnaert (1933) and does not account for sudace

tension and damping effects. More sophisticated formulas for the resonant fkequency of s m d

C W m R 1. INTRODUCTION 12

bubbles exist and were reviewed by Shima (1970). Equation (17) and (18) of Shima (1970)'

which account for compresçibility, surface tension and viscosity for linear oscillation, are

reproduced here:

B is a constant involved in the Tait equation of state for water, and has the ernpirical value

01 3000 atm. Figure 1.3 presents the resonant frequecy calculated from Minnaertk (1.13)

and Shima's (1.14) equations. One notices t hat Minnaert 's formula begins to underesti-

mate resonant kequency by a signincant factor for bubbles smaller than 3 Pm. Minnaert's

fonnula (equation 1.13), because of its simplicity and accuracy for larger bubbles, is very

commonly quoted. It is important to remember its use should not be extended beyond

order-of-magnitude estimations for megahertz applications.

To illustrate some linear and nonluiear behaviour of Rayleigh's equation, the response

of individual bubbles to 5 M H z ultrasound is next considered. Equation 1.10 was integrated

using the third order Ronge-Kutta method. The response, as measured by the acoustic

energy scattered by the bubble, is plotted against bubble radius in figure 1.4. The power of

the bubble o s d a t o r is underscored by noting that a resonant bubble has a scattering cross-

section of approximately 25 pz, whereas a single isolated red blood cell has a scattering

0.2 I I 4 t L

0.2 0.5 1 2 5 10 20 Bubbb Diameter (pn)

Figure 1.3: Resonant /requencies of bubbles from I to 10 Pm, colcukated /rom Minnaert 's

formula (1.13) and Shima's formula (1.14).

cross-section of only 6 x 10-6 pn2, (see page 132 of Mo and Cobbold (1992)) which is about

four million times weaker. At a low transmit amplitude (1 kPa peak-to-peak), the response

is strongest from a bubble of 0.95 pm radius, in agreement with the prediction by Shima.

Hapever, at a higher transmit amplitude, the nonlinearity of the bubble motion cornes into

play and the scattering peak becomes more complicated. Most notably, the resonant bubble

size is shifted down to about 0.55 Pm.

The most important feature of the nonlinear scattered signal is the harmonic content.

Figure 1.5 shows the spectra of a 0.95 pu radius bubble in response tu 5 MHz uitrasound. At

the lowest transmitted ampütude (1 kPa) , the bubble motion was nearly perfectly linear and

ody a very minimal amount of harmonic scattering is produced. At a higher transmitted

amplitude (50 kPa), the motion is weakty nodinea. and 2nd and higher harmonic compo-

O 0.5 1 1.5 2 2-5 3 3.5 4 Bubble radius (pm)

Figure 1.4: The scattering cross-section of an àsolated Rayleigh bubble oscillator to 5 MHz

ultmsound Notice that at hzgher transmitted amplitudes, the resonant bub ble szze for a fixed

frequency is shified down szgnaficBntly.

nents are evident. At the highest transmitted amplitude (1 MPa), the motion is strongly

nonlinear and scattered waves have very broad bandwidth. Harmonic peaks, in fact even

the huidamental peak, are no longer clearly distinct from each other.

1.2.4 More Sophisticated Models of Bubble OsciIIations

Since Rayleigh studied the idealized case of a spherical void freely collapsing in a liquid in

1917, rnany authors have contributed various extensions to Rayleigh's equation to account

for various red world effects. These include the gas (typicdy air) pressure, the vapour

pressure (of the liquid), surface tension, viscosity, compressibüity of the üquid, mas transfer

(dissolution and effervescence of the gas), thermal t r d e r and gravity. Mathematicdy, a

Figure 1.5: Scattered echo spectra from a 0.95 pm radius ezposed to 5 MHz ultrasound.

Each spectrum is nomalized to the tmmitted amplitude. A s the tmnsmitted amplitude is

znmased, the second and hzgher hamonic components ore increased; at the hzghest t m m i t -

ted amplitude, the echo spectnnn becomes uery broad and the hamonic peaks are no longer

distinct.

mode1 of spherical bubble oscillations can be understood as a basic differential equation that

describes the flow of the liquid outside of the bubble, and a set of boundôry conditions and

correction terms. Considered this way, the most important component is the compressibility

of the liquid. The basic differential equation is essentially an equation for the dynamics of

the liquid. When the liquid is incompressible, the differential equation is given by equation

(1.10). When a linear compressibility is assumeci, Several authors (Herring 1941; Keller and

Miksis 1980; Trilling 1952) derived a more cornplex equation accounting for a compressible

liquid which supports ünear acoustic mves to propagate at a constant finite speed. Cur-

CHAPTER 1. INTRODUCTION 16

rently, the most sophisticated form of the basic equation was derived by Gilmore (Akuüchev

et al. 1968; Hidrling and Plesset 1964; Gilmore 1952), who took into account nonhear prop

agation caused by the convective component of the Navier-Stokes equation and the nonlinear

compressibili@ of wat er.

Vokurka (1986) made a cornparison of Rayleigh's, Hemng's and Gilmore's equa-

tion by numerical computation. -4s expected, when the oscillation amplitude increases,

Rayleigh's and Herring's models become l e s accurate. Vokurka measured the amplitude by

A = and he found that, compared to Gilmore's equation, Rayleigh's equation was

satisfactory for A < 2 and Herring's equation was satisfactory for A < 4.5. However, the

choice of the basic equation does not always follow simply from the oscillation amplitude.

In the theoretical study of sonoluminescence, Keller's or Trilling's formulations (which are

equilivdent to Hemng's) are often prefened despite its inaccuracy (Gaitan et al. 1992; Ka-

math et al. 1993). This is because the processes in the gas phase are far more important

in sonoluminescence than the precise dynamics in the iiquid (see section 1.3.3). Therefore,

Keller's, or even Rayleigh's, equation is used for its simplicity and clarity.

To see why the Gilmore mode1 is often avoided when possible, it is useful to consider

its mathematical form. Gilmore's equation relates the local speed of sound C and enthalpy

H (in the liquid) at the bubble w d :

where C and H are determhed by the instantaneous pressure at the bubble wall (the Tait

C W T E R 1. INTRODUCTION

equation) ,

cm, p, and p, are the (constant) speed of sound, pressure and density of the undisturbed

Iiquid. B and n are constants in the Tait equation which have the ernpirical values of 3000

atm and 7, respectively, for water. Finally, P is the pressure at the bubble wall. In cases

when P is simply equal to p, given by equation (1.8), equation (1.15) can be easily solved

numerically. However, when more mechanisms are included in P, the solving of equation

(1.15) becomes much more complicated. In some cases, such as in sonoluminescence, P itself

is determined by a differential equation that describes the mechanisms inside the gas bubble.

The internai differential equation is then coupled to the extemal differentiai equation through

the variables R and P, making the problem very costly to solve computationally.

1.3 Other Behaviour of Bubbles and Cavities

1.3.1 Dissolution of Microbubbles

Henry's law dictates that, at a fixed temperature and pressure, a gas in contact mith a

liquid will be dissolved in the liquid untii a eqilibrium concentration is reached. If the

concentration of the dissolved gas is below the equilibrium concentration, more gas wiil

be dissoIved, conversely, if the disolved gas concentration is too high (a condition called

CKAPTER 1. INTRODUCTION 18

oversaturation), the gas will evaporate out of solution to form bubbles. A common example

is beer or softdrinks which are bottled with carbon dioxide under pressure. Inside the

presninzed container, the equilibrium is rnaintained and the amount of gas dissoIved is

determined by the temperature and pressure. When the condition is disturbed, e.g., by a

rise of the temperature or more commonly by a drop in the pressure when the bottle is

opened, the equilibrium concentration is decreased, and bubbles form and grow on the side

of the glas. Another example of oversaturation is found in deep sea diving. Every 10 meters

of depth adds about one atmosphere of pressure to the diver's body. At depths of 50 m or

more, significant amount of nitrogen and oxygen can be dissolved over time into the blood

plasma. Therefore, if a diver who has been exposed to a high pressure for a penod of time

ascends too quickly to the d a c e , an oversaturation of gas develops and bubbles are formed

in the blood stream and the synovial fluid. The most obvious symptom is joint pain, which

causes the sufferers to walk slightly stooped or bent over (NOAA 1990). For this reason,

such a condition is commonly known as the "bends"; it is also called the decompression

sickness. If a large number of macroscopic bubbles are forrned, a mgnicm number of blood

vessels can be emboiized, causing damage to the brain, kidneys and lungs - even death can

be a consequence.

Typicdy, water or aqueous liquid exposed to the atmosphere (blood is partially ex-

posed to the atmosphere in the Iungs) are saturated wïth dissolved air. The concentrations

of dissdved gases are determined by the room temperature and pressure. A bubble placed

in such a liquid is inherently unstable. Surface tension exerts an additional pressure in the

CHAPTER 1. INTRODUCTION

gas phase. The additional pressure is given by

where (T is the surface tension and R is the radius of the bubble. Therefore, the gas in a 1

pm air bubble in water expenences a 72.5 kPa overpresmire, which amounts to about 70%

of the ambient pressure. The pressure difference between the gas phase and the liquid phase

causes an inequilibrium and the gas will be gradudy dissolved. As the gas is dissolved, the

radius of the bubble shrinks, causing the pressure difference to continue to increase according

to equation (1.17). Therefore, an air bubble in a liquid saturated with air (relative to the

room pressure) will g a d u d y dissolve at an accelerating pace.

As the gas dissolves, a concentration gradient n e u the bubble boundary is established.

The rate of dissolution is ümited by the localIy accumulated concentration in the surrounding

liquid. In the absence of flow, difision is the mechanism by which the dissoived gas molecules

are transported outward kom the bubble boundary. Epstein and Plesset (1950) and Neppiras

(1980) derived an equation br the evolution of the radius of a bubble placed in a liquid

ini t idy containing a uniform concentration of dissolved gas:

where D is the diffusivity constant Cs is the equilibrium concentration, Cm is the initial con-

centration, p, is the densi@ of the gas ( approda ted to be constant) and p , is the ambient

pressure. Equation (1.18) cm also be used to predict bubble growth under oversaturation.

Solving equation (1.18) for free air bubbles under an ambient pressure of 1.0 atm yields

lifetimes of 10 ms to 6 s for bubbles of 1 to 10 pm diameters (see figure 1.6).

"O 0.2 0.4 0.6 0.8 1 1.2 Time Isec'l

Figure 1.6: The shrinkuge of bubble as a result of gus dissolution and diffusion. Each curue

represents the euolution of a bubble placed in water ànitially saturated uniformly with air at

1 atm. As the bubble shrinks, the effect of surface tension increuses and the shrinkage mte

accelemtes. The curves corresponds to 6ubbIes with initial diameters of (/mm the bottom) 2,

3, 4, ..., 10 Pm.

Experirnentally measured lifetirnes tend to be &able and somewhat longer than

that shown in figure 1.6. It is believed that irnpurity in the experimental system acts as

a surfactant which coats the bubble and reduces the gas dissolution (Neppiras 1980). On

the other hand, liquid 0ow relative to the bubble (caused by, for example, Boatation of the

bubble) c m sipniIicant1y accelerate the dissolution process. This is due to the fact that

dissoIution is ümited by the concentration gradient 6eId in the iiquid and any convection is

bound to help to equilibrate the concentration gradient.

1.3.2 Cavitation Physics

Cavitation is a Ioose t e m used to describe the formation, dynamics and effects of a cavity or

small bubble caused by mechanicd stress or sound waves (Knapp et al. 1970). When a solid

object is moving in a Liquid, the pressure drops according to the Bernoulli equation (or more

precisely the Navier-Stokes equation). At a moderate speed, this pressure &op can exeed

the ambient pressure. The Bernoulli equation can provide an order of magnitude estimate

of the speed needed to create a negative pressure:

For water at atmospheric pressure (about 101 kPa), this is merely 14.2 m/sec. A negative

pressure can be substained in a Liquid or solid until it reaches the tensile strength of the

material. The tensile strength of pure water is over 250 atrnospheres, but the presence of a

tiny amount of impunty, especidy dissolved gas, reduces the tende strength dramaticdy.

As a result, mechanical stress caused by common processes such as a turning propeller is

sufncient to rip apart the water and create cavities (Plesset 1949). The collapse of these

cavities can be quite violent and can cause severe pitting of matend even as hard as steel.

ExpIosives are used to create an underwater cavity tens of rneters large which then coiiapse

catastrophically (Cole 1948). In fact, depth charges damage submarines not by the shock

fiom the explosion but by the great destructive force unleashed during the collapse of the

caviw.

Ultrasound, iike mechanical stress, can also create cavitation. Acoustic cavitation has

been observed since the 1930s (Marinesco and Tri1Iat 1933) and a wide variety of phenornena

have been attributed to it (Neppiras 1980). A Ml dLscussion of acoustic cavitation is beyond

the scope of this introduction, but several effects axe of interest here. Stable cavitation is

the stable oscillation of one bubble or more commonly a cloud of bubbles in a sound field.

In contrast, transient cavitation is often obsevered in which the bubble or bubbles collapse

violently, causing erosion, emission of light, chernical and biological effects. Theoretical inves-

tigations of transient and stable cavitation formed the basis of much of what is known today

about the dynamics of bubble interaction with ultrasound. These include the development

of al1 the theories described in sections 1.2.2 and 1.2.4.

Transient cavitation is dso of interest because of the bioeffects that can be a result.

Rupture of cells in vitro and degradation of DNA molecules have been known since the

1950s (Flynn 1964). The pressure necessary to create cavitation, the cavitation threshold,

is known to be significantly higher in vivo than in untreated tap water (the t ~ e reason of

this is not yet clear, but it is generdy beiieved that the higher viscoscity of bodily Buid and

the lower concentration of dissolved gas combine to reduce the occurrence of cavitation).

Nonetheless, macroscopic lesions can be created with intense ultrasound and the safety of

diagnostic ultrasound, especially in the area of obstetrics, is of concem. To that end, FDA

enforces a maximum allowable output level on ail diagnostic scanners. The output level is

meanued with the Mechanical Index ( M I ) which is based on the potential for cavitation

CHAPTER 1. INTRODUCTION

inception. MI is d e h e d by

where p- is the spatial-peak-temporal-peak negative pressure measured in MPa and f is

the transmitted frequency measured in MHz ( Iv lZ is quoted without units). The maximum

allowable output for most applications is set at M I = 1.9. It is important to note that the

peak negative pressure p- is "derated", meanhg that the values measured in a water tank

were adjusted for expected attenuation by human tissue h m the transducer face to the focus

before being used in the cdculation of MI. Notice that at higher freqencies, the potential for

cavitation is lower and hence a higher pressure amplitude is allowed. The M I has become a

common measure of output pressure for cornparison between different frequencies. different

scanning modes and different manufacturers.

Since the onset of cavitation is very sensitive to the presence of microcavities knom a s

'huclei" , microbubble contrast agents were expected to enhance cavitation activties. Indeed,

Miller and Thomas (1996) and Dalecki et al. (1997) found that Mbunex in combination with

exposure to ultrasound can cause hemolysis (lysing of red blood cells) both in vitro and in

vivo. Skyba et al. (1998) showed contrast microbubbles can induce microvessel ruptures when

exposed to diagnostic uitrasound. These results naturally raise the question of bioeffects of

exposing tissue carrying contrast agent to strong dtrasound. However, it should be noted

that these experiments were performed in small animais in exposure conditions that are not

typicdy the case in humans. The in vivo pressure these animals were exposed to were

B&cantly higher than that allowed by the MI-regdations. At present, it is diEcdt to

extrapolate these animal results to clinical conditions in humans. However, signiticant side-

effects can be d e d out due to the large body of evidence that even mild side-effects are

rare (Nanda and Carstensen 1997). At the same t h e , Skyba et al. (1998) suggested that

these bioeffects have potential therapeutic applications. More reseaxch is needed to detect

these bioeffects in human and to determine the feasibility of e-xploiting them in therapeutic

interventions.

1.3.3 Sonoluminescence

One of the most spectacular effect of cavitation is sonoluminescence, the emission of light

from ultrasonically driven gas bubbles. Origindly observed in 1933 by Maxinesco and Trillat,

sonoluminescence presented a challenging puzzle to reserachers searching for a mechanism.

A wide vaxiety of models were proposed, including triboluminescence (light emission by

fiction), microdischarge and mechanochemical effects (Gaitan et al. l992). Systematic ex-

periments in a controlled environment were not available until the discovery in 1989 that a

single bubble (instead of a cloud) c m be driven to emit light bright enough to be seen by

the human eyes. Subsequently, rnany rernarkable characteristics of single bubble sonolumi-

nescence (SBSL) were observed. Typically a bubble of about 5 pm or larger is driven by

a 20 kHz sound field, and a flash of Lght is emitted in each acoustic cycle, that is, a flash

is emitted every 50 p. Surprisingly, the duration of the flash is extremely short compared

to the acoustic cycle, in fact, until recently the exact duration of SBSL emissions was not

h o m because none of the d i n g optical detectors had dficiently fast response. More

recently, the duration was determined to be about 50 picoseconds. Each emitted Lght flash

CXAPTER 1. INTRODUCTION 25

has a spectnim simiIar to that emitted by a body of very hot gas. Very recently, it was

declared (Apfel 1999) that a complete explanation of SBSL was obtained (Hilgenfeldt et al.

1999). In this model, violent collapses during the compression phase of each acoustic cycle

cause the gas to be repeatedy heated up to 20,000-30,000 K and compressed to 5,000-

7,000 atmopheres. During these repeated compressions, an interesting phenornenon occurs

which has the diatomic molecules (N2 and Oz) diffusing out into the liquid, leaving only

monoatomic noble gas (typicdy argon) in the gas bubble (Matula and Crum 1998). This

body of compressed, hot, noble gas is responsible for the emission of the light observed.

It is noted that the explanation by Hilgenfeldt et al. (1999) was based on a Rayleigh-

Plesset equation similar to equation 1.10 or to the equation by Trilling, which is the basis

of this thesis. The process is said to be dominated by the generation of shockwaves in the

gas phase and the gas diffusion process so that the nonlinear cornpressibilty introduced by

Giimore is not important in this consideration.

1.4 Nonlinear Imaging

1.4.1 Linearity

Linearity is understood in the context of a system which produces an output in response to

an input. Mathematicaily, we write

H is called the transfer function of the system. A system is defhed as l inex if it follows

this intuitive principle: the output from the sum of two inputs is the same as the surn of the

outputs from the individual inputs. This is represented mathematically by

where a and b are constants. In the context of ultrasound imaging, the concept of transfer

hnction is used to analyze many processes, such as transduction (conversion between electri-

c d and acoustic signais), acoustic propagation, acoustic attenuation and image processing.

Not a l l of these processes are linear, in pazticular, scattering of ultrasound by a bubble, as

described by equation (1.10), constitutes a nonlinear systern. In this case, the transfer h c -

tion H (which cannot be written in an explicit f om) does not obey the liiearity equation

(1 -22).

1.4.2 Harmonic Imaging

The second harmonic component of the microbubble echoes (see figure 1.5) offers a special

signature allowing them to be separated from tissue signais. The first nonlinear contrast

imaging method used clinicdy was harmonic irnaging (Burns et al. 1996). The operation

of harmonic imaging is depicted in figure 1.7. Like conventional imaging, ultrasound pulses

are transmitted into the human body. During reception, a simple high-pas filter removes

the fundamental component from the RF echoes, leaving mostly the signal scattered from

the contrast agent. This filtered signal is used to generate the harmonic image. In combi-

nation with the Doppler method, which detects changes in the echoes due to movement or

disappearance of the targets, hamonic imaging was demonstrated to be capable of detecting

blood flow at the microvascular level. Imaging of blood Bow in tissue perfused by 40 pm

vessels was demomtrated by Burns et al. (1994).

1.4.3 Nonlinear Propagation and Tissue Harmonic Imaging

Acoustic propagation in water, and by extension soft tissues, is not linear. While this fact has

been known both theoretically and experimentally for decades, its significance to ultrasonic

imaging was not realized until recently. This is due to the combination of two factors:

(1) eariier transducers and scanners did not have sufficient bandwidt h and sensitivity to

detect the nonlinear signal; and (2) most workers had not been searching for the nonlinear

signal because it was not expected that the harmonic signal cotdd have any applications.

This changed when severd groups noticed that harmonic imaging designed for contrast

applications not only produced a background image before the injection of the agent, but

CHAPTiE:R 1. INTRODUCTION

Transducer

Tissue

Contrast Agent

Image Formation --3- or

Doppler Demodulation

3 MHz ultmound 6 MHz ultrasound

Figure 1.7: Operation of harmonic imaging.

that the background image was of higher quality than conventional imaging.

The cornplete theoretical description of nonlinear propagation is very cornplex. But

some intuitive understanding can be achieved with a sixnplified approach. Two factors con-

tribute to the nonlinear propagation of sound waves in water. The fhst is the fact that sound

is a longidutinal wave of "wavefionts" of molecuiar displacement. Since the displacernent is

in the same direction as the wave propagation, a wavefiont is advmced or retarded depend-

ing on the amplitude and direction of particle (molecular) displacement. The phase velocity

CHAPTER 1. LNTRODUCTION

is the velocity at which a wavefiont is travelling:

where q is the speed of sound for infmitesimdy small amplitude sound waves and u is the

particle velocity. This is called the convective component of the noniinear distortion of the

propagated wave. ltanslated into pressure, this means the high pressure crest of the wave

will travel faster and "pile up" on top of the slowly propagating low pressure trough. The

middle panel of figure 1.8 illustrates this phenornenon. The second contribution to nonlinear

distortion is the nonlinear compressibility of water (also cailed the material nonlinearity).

The phase velocity, taking into account both convection and material nodinearity, is

where A and B are the coeEcients of the linear and quadratic tems in the Taylor expansion

of the equation of state of the medium. The ratio BIA is a material constant and is relatively

independent over the fiequency range 1-10 MHz. For water, Bl.4 = 5.2; for soft tissues, the

value is higher, ranging fiom 6.5 (liver) to 11 (fatty tissue).

A M y generalized nonlinear wave equation is as yet unsolved by analytical means.

Numerical eomputations are typicaüy Limited to certain specinc cases. For many situations,

the paracial (near the beam a*) field for the forward propagation of a focussed beam with

or without attenuation is simdated. A number of approaches, each invokving different sim-

plifications and approximations, are a d a b l e . These include the h i t e Merence method,

CHAPTER 1. INTRODUCTION

I Convection +

Figure 1.8: Nonlinear distortion of a large amplitude sound wave in water due to convection

(mzddle panel) and nonlinear bulk modvlvs (right panel). The distortion zs bu& up ouer

dis tance (2) travelled.

the pseudospectral method, and the KZK algorithm (for a more detailed discussion, see

Hamilton and Blackstock (1997) and Wojcik et al. (1998)). As an example, the nonlinear

beam was cdcdated using the NLP method, a variation of the KZK method (Christopher

1997). Figure 1.9 depicts the b e m profile of the second harmonic component from a 2 MHz

Gaussian focussed beam as weU as the bdamenta i bearns for both 2 MHz and 4 MHz.

The width of the main lobe of the harmonic beam is narrower than the 2 MHz fundamentd

beam but wider than the 4 MHz fundamental beam. The harmonic beam has significantly

Iower sidelobes than both fundamental bearns. Both these qualities afTord harmonie imagîng

improved lateral resolution over conventional imaging. Wojcik et al. (1998) fùrther cal-

cuiated the nonlinear beam after aberration caused by a realistic mode1 of abdominal wall

sections, and dernonstrated that not oniy does the improved lateral resolution ca ry over

to an attenuating and aberrating situation, but that haxmonic beams &O d e r less from

CHAPTER 1. INTRODUCTION 31

the image quality degrading effects of phase aberration. It has now been demonstrated that

hazmonic imaging without contrast agent, c d e d tissue harmonic imaging, provides some

compensation for the image degradation caused by gas pockets and fat and connective tissue

layers (Burns et al. 2000; Sranquart et al. 1999).

O 0.1 0.2 0.9 0.4 0.5 0.6 0.7 0.8 0.9 1 RADIAL DISTANCE (cm)

Figure 1.9: Calculated transverse beam profiles on the focal plane showing 2 MHz fundamental

(solid), 4 MHz fundamental (dots), and 4 MHz second hanrionics Rom the 2 MHz beum

(dadies). All curues were nonnalized. Reproduced from Chnstopher (1997).

1.5 Thesis Outline

The goal of this thesis is to develop a theoretical model for the acoustic response of mi-

crobubble contrast agents in the context of dtrasound imaging applications.

In Chapter 2, a theoretic mode1 is developed which incorporates bubbles of various

sizes placed in a heterogenous ultrasound field. This population ensemble model was created

to addreçs the most important deficiencies of the single bubble model, which begins with the

observation that single bubbie models respond to only narrow ranges of frequencies while

experimentdy, contrast agents have a very broadband response.

In Chapter 3, an experiment was designed to test quantitatively the preàicting power

of the population ensemble model. The results of this experiment demonstrated the general

validity of the model, however, some quantitative discrepancies were identified.

In Chapter 4, possible explanations of the discrepancies were considered and shell

effects were identified as a probable source of the error. An experiment was designed to test

the hypothesis that damping by the shell and acoustic disruption of the shell can be the

cause of the observed dXerence between theory and euperiment. The results demonstrated

that such is indeed the case, and the shell effect was discovered to be surpcisingly important

in single scattering.

In Chapter 5, recent developments in nonlinear contrast imaging are recounted. Some

of these developments raise questions that can be answered with the help of the microbubble

scattering model. Applications of the model in these contexts are presented.

A swnmary of the thesis and future directions for the scattering model c m be found

in Chapter 6.

Chapter 2

A Population Mode1 of Contrast

Microbubbles

Although the behaviour of a bubble in an acoustic field has been studied ertensively, few

theoretical treatments to date have been applied to simulate the acoustic response of a real

population of variabiy sized microbubbles in a finite width sound beam. In this paper,

we present a modined Triilhg equation for single bubble dynamics which has been solved

numerically for different conditions. Radiated waveforms fiom a large number of such bubbles

are combined, reflecting thek size distribution and Location and the shape of a red acoustic

beam. The resulting time-domain pressure waveforms can be compared with those obtained

IThis chapter was based on the pape.: Chin CT, Burns PN. Predicting the acoustic re- sponse of a microbnbble popdation for contra& b g k g in medical ultrasound. Ultrasotand Med Bi01 2000;26:1289-1296.

CHAPTER 2. A POPULATION MODEL OF CONTMST MICROBUBBLES 34

experimentally. The dependence of second h m o n i c radiation on incident focal amplitude at

different fiequencies is presented. This mode1 is particularly suited to the study of interaction

between a medical ultrasound beam and microbubble contrast agents in aqueous media.

2.1 Introduction

Microbubble suspensions for use a s contrast agents in medical ultrasound imaging are cur-

rently undergoing àgnificant development. When these bubbles are e-xposed to moderately

strong (> 100 kPa) ultrasound waves, they exhibit nonlineu radial oscillation and produce

echoes containing second and higher harmonies of the incident wave. The second harmonic

emissions can be used to distinguish blood from tissue echoes and form the basis of such new

methods as harmonic (Burns et al. 1996) and pulse inversion imaging (Hope Simpson et al.

1999).

Most of the research so far has been focused on empirical measurements of various

parameters of contrast agents in vitro and an vivo. Few theoretical studies have been aimed

at simulating actuai imaging conditions. The earliest studies were aimed at understanding

coIIapse of a bubble due to turbulent flows and undemater explosions (Rayleigh 1917; Plesset

1949). In such studies, the cavity collapses freely without ex temdy applied sound waves.

Another class of studies focuses on the steady state response of a bubble to (nearly) contin-

uous incident sound waves. For these, the cornplete differential equation can be lùieaized

by using the s m d amplitude approximation. Using suitable ünearization, the amplitude

and phase of the fundamental and second harmonie component can be calculated (Leighton

1997; Miller 1981). A third class of studies investigated the dynamics of a bubble in the

field generated by a üthotripter (Church 1989). In this situation, resonant oscilIation is in-

significant and gas diffusion into the bubble is the most important process. In this paper,

we present a theory for predicting acoustic response of a bubble population for diagnostic

contrast imaging.

Mathematicdy, a model of spherical bubble oscillations can be understood as a basic

differential equation that describes the BOW of the üquid outside of the bubble, and a set

of boundary conditions and correction terms that describe the gas pressure, surface tension,

liquid viscosity and damping mechanisms. The basic diaerential equation has three cornmon

forms. Rayleigh (1917) originally derived an equation to calculate the collapse of a spherical

cavity in an incompressible liquid. Subsequent authors (Hemng 1941; Keller and Miksis

1980; Trilling 1952) allowed a compressible liquid which mpports linear acoustic waves to

propagate at a finite constant speed. Currently, the most sophisticated form of the basic

equation was derived by Gilmore (Akuiichev et al. 1968; Hickling and Plesset 1964; Gilmore

1952), who took into account nonlinear propagation caused by the convective component of

the Navier-S t okes equat ion and the noniinear compressibility of water .

The Rayleigh formulation, with some important modifications by Plesset (l949),

Devin (1959) and EIler (1970), is the most well known and has the advantage of being

intuitive. This form is most commonly used in studies in bubble emboii (Eatock and Nishi

1985) and contrast agents (de Jong et al. 1994). It has been demonstrated that, when the

speed of the bubble boundary reaches a significant fraction of the speed of sound in wa-

ter, Herring's and Gilmore's formulations are significmtly more accurate than the Rayleigh

CHAPTER 2. A POPULATION MODEL OF CONTRAST ~ ~ O B U B B L E S 36

model (Vokurka 1986). An acoustic or radiative damping term was used as a modification

to linearized versions of the Rayleigh model (Devin 1959); however, such terms explicitly in-

clude the fiequency of bubble motion and are inappropriate for nonsinusoidd or broadband

motions-

There are three key components to the proposed model. Firstly, the dynamics of the

radial motion of a bubble were simulated by integrating numerically an equation similar to

one used by Trilling (1952). The Rayleigh formulation has been most widely used to model

single bubble responses for medical ultrasound contrast agents, usually with continuous wave

excitation (de Jong et al. 1994). Bubble response (such as resonant frequency and scattering

cross-sect ion) t O short pulse incident wave can deviate significant ly from cont inuous wave

response; thus, it is important to use the same incident wave in both theory and experiment.

By using a mode1 which treats the liquid phase more realistically and by considering short

pulse excitation, we improve the theoretical framework for the calculation of a single bubble

response.

Secondly, as red agents contain bubbles with a range of radii, simulation at any single

bubble size cannot be accurate, especidy over a range of Frequencies. Our model contains

an ensemble of unencapsulated bubbles with a size distribution based on that of an actual

contrast agent, OptisonTM (Mallinckrodt Inc, St . Louis, USA).

Finally, coherent interference of the scattered signal kom multiple s m d targets causes

amplitude fluctuations in the detected echo. This process is, in principle, the same as that

which produces the tissue speckle which characterizes parenchpal textures in medical ultra-

sound images. However, as the bubble response depends nonlinearly on incident amplitude,

the speckle formation process becomes nonlinear aho. In particular, the amount of hannonic

emitted may be iduenced by the beam shape. In our model, a bubble located away from

the beam center contributes a pulse with a different waveform to that fiom one located at

the center, due to the clifference in local incident pressure amplitude.

2.2 Theory

2.2.1 Single bubble

Triiling's (1952) original derivation of the single bubble theory has been modified for two

reasons: (1) m g ' s problem was that of a bubble collapsing in a othenvise undisturbed

liquid, while we are studying a stable bubble in a sound field; (2) the original equations

were cast into an approximate form for a stegwise method appropriate for the limited

computation resources of the time. We have rederived the equations into a more direct form

and removed some approximations no longer necessary in the age of high-speed computers.

Since the bubble radius R is mal1 compared to the wavelength, the incident propa-

gating wave can be described by a spatidy-uniform pressure, p, (t). The system is assumed

to be isotropie and irrotational, allowing a velocity potentid # to be defined as u = &5/&.

Trilling's assumption was that acoustic wave propagation is linear, implying the equation of

da te to be dp = clp/& This is accurate to the order of ulc. Surface tension and viscosity of

the liquid are included. Mass t r a d e r across the bubble boundary is assumed to be insignif-

icant over the time duration of interest, which is typically l e s than 10 p. The polytropic

assumption, which states that the interna1 gas pressure is given by p~ ( & / R ) ~ ~ , where pgo

CEIAPTER 2. A POPULATION MODEL OF CONTRAST MICROBUBBLES 38

is the equiiibrium gas pressure, l& the equiiibrium radius, and K a polytropic constant, is

used.

The theory begins with the conservation of momentum for the üquid phase:

Integrating from a point r to w, assuming 4 = O and u = O at r = w produces:

To obtain the desired result, one needs to rearrange equation (2.2) to relate the state at the

boundary R with the incident pressure at infinity. Intermediate terms involving 4, u and p

are to be expressed in terms of velocity of the bubble boundary U (= k) and the pressure

just outside the bubble boundary P(t ) (= p(R(t), t ) ) .

To eliminate a+/ût, we recail the ünear wave equation for outgoing sphencal waves:

where p and c are the iiquid density and speed of sound, respectively. Dserentiating both

equations (2.2) and (2.3) with respect to t, and rearranging, we have:

CHAPTER 2. A POPULATION MODEL OF CONTRAST MZ%ROBUBBLES 39

We seek to evaluate equation (2.4) at r = R. To eliminate &/%IR and a p / û t l R v we

can use four h e a r equations to solve for four quantities (dîl/atlRt ûplâtl,, &/&I and

&/&IR). Three of these equations are equation (2.1) and the expressions for dU/dt and

dR/dt in t e m s of partial derivatives of u and p with respect to t and r. The last equation

arises kom conservation of mas:

in which the terms involving p are replaced by p through the equation of state. Substituting

the results into equation (2.4), and using the equation of state to evaluate the integral J d p l p ,

we obtain h d y the equation for the motion of the bubble boundary:

It is noted that equation (2.6) can be simpued somewhat by a few approximations. The

term is typicdIy mal1 compared to unity, and the logarithmic term on the right hand

side of equation (2.6) can also be simpüfied. In the iimits P < pot? and p, < p o 2 ,

CHAPTEIR 2. A POPULATION MODEL OF CONTRAST MICROBOBBLES

Therefore, equation (2.6) becomes

Equation (2.7) is equilivalent to (2.6) to the order of U2/c? (and as long as the minimum

bubble radius is greater than 10% of the initial radius), and it is the form published by

Trilling (1952) and Vokurka (1986).

The pressure at the bubble boundary P is given by

where p is the viscosity of water and a is the surface tension. The form for viscous damping

was derived by Pontsky (1951) which, unlike the linearized darnping term introduced by

Devin (1959), is suitable for nonsinusoida1 motion. There are two approaches to account for

thermal damping. Devin (1959) and Eller (1970) derived a Iineaxized darnping term by as-

suming a s m d sinusoidal oscillation. Their damping term includes explicitly the frequency

of the bubble motion and can not be converted ~ ~ O U ~ O U S ~ Y into a form for wideband m e

tions. To account for nonperiodic motions of excited bubbles, Prosperetti (1991) developed

a therrnd behaviour mode1 in which the gas component is assumed to have a unifonn pres-

sure but the gas temperature varies spatially. The result is a partial differential equation For

the gas temperature as a function of t h e and radius. The partial differentiai equation is

conpled with equation (2.6) and can increase the computation load by orders of magnitude.

Chapman and PIesset (19?1), using a linearized approach, estimated that thermal damping

CHMTER 2. A POPULAïTON MODEL OF CONTRAST lMICROBUBBLES 41

for a 2-pn air bubble in water represents about 25% of total damping and is about equal

to half the viscous damping. However, their calcdation also showed that viscous damping

and thermal damping have very different dependence on the bubble size, making it unadvis-

able to model thermal damping a s an additional viscous tem, a rather tempting notion at

hst sight. Unfortunately between the Iineaxized approach and the hl1 approach there has

not been a verified method to model the thermal damping that can be justifiably applied

to a wideband rnildly-nonlinear model. In this thesis, the effect of thermal damping is not

included.

Now equations (2.6) and (2.8) can be solved numericdly to give the time-course of the

bubble radius R(t). The velocity potential $ (r, t) throughout the liquid cm be calculated

from equation (2.2) as

Equation (2.9) satisfies the wave equation (2.3) by Wtue of being of the form f (t - r /c ) / r .

The pressure can then be calculated from equation (2.2):

PS' SY - for r » X

r

where f ' (x ) = df (z)/dx. Equations (2.6), (2.9) and (2.10) differ somewhat from Trilling's

(1952), suice he considered oniy the case p, = O and approximated the logarithmic terms

C W T E R 2. A POPULATION MODEIX OF CONTRAST MICROBUBBLES

to the form (P - p,)/p&

2.2.2 Secondary scattering

Before the response of a population of bubbles c m be calculated, it must be ascertained that

one bubble's scattered ultrasound wave does not interfere with the scattering process of its

neighbours, in another word, secondary scattering is insignificant. The ratio of pcimary to

secondary scattering is equal to the ratio of the incident intensity to the p n m q scattering.

This secondary scattering ratio is therefore given by o,/r2, where os is the (primary) scat-

tering cross-section and r is the distance between neighbouring bubbles. ResuIts from single

bubble calculatioos show that the maximum scattering cross-section at 1-10 MHz is of the

order of 10-Iom2. The distance between neighbouring bubbles is calculated next.

In analogy to molecules in an ideal gas, it is assumed that the bubble density is

sufnciently low that bubbles rarely corne into contact and that each bubble exerts no force

on each other. The position of each bubble is then cornpletely independent of each other.

The probability that x bubbles are Found within a volume V is then @en by the Poisson

distribution:

where N is the average number of bubbles per unit volume. For any given bubble, the

probability density function of the distance to its nearest neighbour r is written as f (r),

çuch that f (r)dr is the probability that the nearest neighbour is at a distance between r and

CHAPTER 2. A POPULATION MODEL OF CONTRAST hIICROBUBBLES 43

r + dr. To calculate f (T ) , consider a coordinate system with its ongin at the position of an

arbitrary bubble. Since the presence of this bubble at the (fixed) origin does not influence

the positions of al1 the other bubbles, it can be removed from our consideration without loss

of generality. Cleady then, f (r)dr is equal to the probability that there are no bubbIes inside

the sphere with radius r and that there is a single bubble inside the spherical shell between

T and r + dr. Therefore,

.In 3 where V = and dV = 4*rzdr. Expanding e-NdV as a series and then dropping al1 terms

of (dl / )2 and higher orders from equation (2.12), one obtains

- ~ , J N f ( r ) = 4 ? r r 2 ~ e 3

-4 distance unit r, can be dehed as Jr: = 1/N, equation (2.13) then becomes

Note that r, is not the mean distance between a bubble and its nearest neighbour, integrating

J r f (r)dr, one obtains the mean distance between a bubble and its nearest neighbour to be

0 . 8 9 3 0 ~ ~ = 0.5540~-' '~.

Using Optison as an example, the maximum in vivo concentration is about 0.196,

this gives N = 5 x 10~ml-'. Therefore, on average, the secondary scattering ratio is 2%.

CHilPTER 2. A POPULATION MODEL OF CONTRAST MTCROBUBBLES 44

Note that this value is sigxdicantly over-estimated since the value of N for all bubble sizes

was used. In reaüty, only a small fraction ( les than 1%) of bubbles have os = 10-~Orn?

Asniming 1% of the bubbles are resonant (os = 10-Lom2), the average secondary scattering

ratio drops to 0.4%. It is also interesthg to consider the probability of significant secondary

scattering. If a secondsry scattering ratio of 10% is defined as significant, two bubbles has

to be less than 31 pm apaxt. The probability that a resonant bubble fin& another resonant

bubble within 31 pm is calculated from equation (2.14) to be 1.1%. With these results, one

can calculate, with confidence, the scattering from a bubble population by sumrning linearly

the scattered wave from each individu4 bubbles.

2.2.3 Echoes from suspensions of bubbles

We now mode1 a randorn suspension of N bubtles exhibiting the motion described above.

The i-th bubble has random radius RE and radial and axial positions and zi as shown in

figure 2.1. The axial length of the sampled volume need only be as long as the duration of

the longest bubble echo in order for the echo properly to be calculated. The single bubble

echo is estimated conservatively to be at most four times as long as the incident pulse. For

typical imaging pulses of l e s than eight cycles, it follows bubbles more than 32 wavelengths

apart do not contribute interferhg echoes; therefore, the sample volume is short cornpared *

to the focal depth of typical imaging beams, dowing us to approximate the beam to be

Wilfom in the auid direction. .4ssuming the minimum f-number (focal lengthlaperture) of

an imaging beam to be 3, which gives a -6 dB depth-of-focus of 63 wavelengths, the enor in

assnming an & d y d o m beam is l e s than 7.5% or 0.7 dB.

Radiated Bubbles 2"' Harmonic

Radiated a Fundamental

To Receive \ Sarnple Volume

Transducer

Figure 2.1: Each bubble in the sample volume contributes a diflerent wavefonn to the final

signal depending on its size and local incident amplitude.

The incident pressure wavefom for the i-th bub ble is given by p, (t) = A. B (ai) Pin(t)

where ilo is the peak-to-peak focal pressure amplitude, B(a) is the normalized beam profile

and Pi,,(t) is the normalized pressure wavefonn. The radiated pressure wavefonns calculated

f m equation (2.10) were scaled by B(%) and time-shifted according to and summed to

give a the-domain echo from the bubble ensemble.

2.3 Results and Discussion

2.3.1 Single bubble mode1

The single bubbIe mode1 was numerically solved with a third order Runge-Kutta method for

a range of bubble radii l& fiom 1 to 15 pm and a range of peak amplitudes A. between 1

kPa and 1 MPa for each normalized incident wavefonn P*(t). Air bubbles in water were

CHAPTER 2. A POPULATION MODEL OF CONTRAST MICROBUBBLES 46

considered, using parameted listed in table 2.1. The transmitted waveform used was based

on that recorded with a hydrophone frorn a focused disk transducer. The transducer was

excited with a 2.9 MHz, two-cycle pulse fiom an arbitrary waveform generator. The reason

this pulse was chosen was that it is M a r to pulses used in clinical scanners and identical

to pulses used in ongoing benchtop contrast agent experirnents. Figure 2.2 shows t b

and fiequency- domain plots of Ph(t). In reality, when the peak amplitude approaches 1

MPa, nonlinear propagation generates a second hamnonic field, which, in a mildly nonlinear

nearly lossless medium such a s water, c m reach -15 dB relative to the fundamental field.

This second hannonic field contributes to the nonlinear components in the signal scattereci

by the bubbles. However, the relative contribution of the propagation h m o n i c s in the

scattered signal is not immediately predictable. Both the magnitude and the phase angle of

the harmonic component in the transmitted field have a signincant effect on the scattered

harmonic (Urnemura et al. 1996). Furthemore, due to the uncertainty of the in vivo

nonlinear parameter and attenuation, the magnitude of the haxmonic field is unpredictable

even when the fundamentai field is to some extent estimable. Therefore, it is a t this point

TabIe 2.1: Paranzefers vsed in the numerical calculatzon.

Value 988 kg-m-3

0.0725 N-m-' 0.0009 Pa sec 101325 Pa

Parameter Water density

Surface tension Water viscosity

Ambient pressure Polytropic constant

S ~ e e d of sound in water

*The equilibrium gas pressure p~ is not a fixed parameter and is instead determined from the ambient pressne po, eqrrilibrium r a b & and d a c e tension a.

Variable P O

P PO K;

c 1.33 1481 msec-'

CHAPTER 2. A POPULATION MODEL OF CONTMST RUCROBUBBLES

1 2 3 4 5 O 3 6 9 Time (p) Frequency (MHz)

Figure 2.2: Measured transmitted pulse vsed for simulation.

more instructive to study the bubble population response to undistorted incident waves.

Since the presently proposed method is a time-domain method, the effects of nonlinearly

propagated incident waves can easily be studied.

Figure 2.3 illustrates four typical responses in radius change and radiated pressure.

In figure 2.3a, a srnail bubble (2% = 1.2 pm) which has a resonant frequency (5.3 MHz)

much higher than that of the incident pulse radiates only weakly (0.1 Pa when driven by

5.0 'Pa). Similady, a large bubble (2& = 6pm) with a low resonant frequency (1.1 MHz)

radiates at a simila amplitude but with reverse phase (figure 2.3b). A 3.0 pm bubble (2.8

M H z ) , on the other hand, radiates 10 times more strongly (figure 2.3~). However, when the

incident ampütude is increased to 100 kPa, the motion becomes nonlinear and signincaat

distortion appears in the echo (figure 2.3d).

For each incident pulse Pk(t), severd hundred responses For Merent bubble sizes and

CHAPTER 2. A POPULATION MODEL OF CONTRAST MICROBUBBLES 48

O 2 4 6 Time us)

O 2 4 6 Time @)

Figure 2.3: Four types of c u h l a t e d response to the two-cycle wave, in t e m of radius change

(ieft) and radtated pressure (right) at 40 mm. (a), (b) and (c) Responses of 1.2 Pm, 6.0 pm

and 3.0 pm diameter bubbles to 5 kPa peak-to-peak incident amplitude. (d) Response of the

3.0 pm bubble to 100 kPa inczdent amplitude.

incident amplitudes were generated. To reduce calculation time without sacnficing accuracy,

irregular samphg of bubble sizes was used. The large quantity of data can be visuaüzed

quickly by distilling some quantities of interest fiom the wavefoms and displayhg them as

maps. For h m o n i c irnaging, these quantities are the fundamental and second harmonic

cross-sections. Cross-section is defined as the total radiated power within a frequency band

divided by the incident intensity. Figure 2.4 shows maps of these cross-sections. One sees

that the fundamental cross-section shows a strong resonance at about 3.0 prn diameter and

the response is essentially independent of incident amplitude up to about 100 kPa. Above

100 kPa, nonlinear effects set in to broaden the response, reduce the resonant size and reduce

the peak crosssection. The reduction of fundamental crosssection is due to a transfer of

energy to higher hamionin. Thus, in the second h m o n i c cross-section, one can see a

gradual increase towards a maximum at about 500 kPa frorn the same resonant bubbles.

Near 1 MPa, so much energy is transferred to the higher harmonies that even the second

harmonic cross-section is reduced.

These maps produce useful insight into the interaction between bubble nonlinearity

and beam shape. For safety reasons, regdatory agencies require the spatial peak pressure

of each scanner to be measured and reported in tems of MI. However, most of the bubbles

in the imaged volume are insonated at amplitudes lower than that implied by the displayed

MI. The fiaction of bubbles exposed to merent incident amplitudes is a function of the

beam profle. Therefore, a spatial average of incident amplitude would be a more sensible

measwement than MI when contrast performance between different machines or different

imaging modes is compared.

C W T E R 2. A POPULATION MODEL OF CONTRAST MlCROBUBBLES

2 4 6 8 Bubble radios Ro (pm)

O 2 4 6 8 Bubble radius R, (un)

Figure 2.4: Caleulat ed fundamental (top) and second harmonzc (hottom) cross-sections (in

ma) of single bubbles to Pi,,@). The grey leuel represents lznearly the cross-sectional areas.

The tick marks dong the top and nght edges of the figures mark the exact radiz and amplitudes

of euch calculation.

CHAPTER 2. A POPULATION MODEL OF CONTRAST MICROBUBBLES 51

Another consequence is the effective sidelobe suppression that harmonie irnaging offen

under certain conditions. For example, if the amplitude is 300 kPa at the focus and 60 kPa at

the highest sidelobe, then figure 2.4 suggests that the bubbles in the sidelobe will contribute a

Eractionally smaller amount of energy to the h m o n i c signal than to the Fundamental signal.

Similady, bubbles at the rim of the main lobe contribute l e s to the total harmonic signal.

Thus, h m o n i c imaging &ers less from sidelobe artifacts and has sharper laterd resolution.

These effects help to explain why harmonie imaging produces high quality images despite

its lower axial resolution compared to conventional imaging. The mechanism is related to

the image quality improvement seen in tissue harmonic imaging which relies on nonlinear

propagation of ultrasound pulses (Christopher 1997; Ward et al. 1997) (see also section

1.4.3).

2.3.2 Prediction of population response

The distribution of bubble radii, &, in our ensemble is based on that of OptisonTL1 (Skyba

et al. 1996) and is plotted in figure 2.5a. Due to the Limitations of optical sizing equipment

using visible Iight (wavelength = 0.4-0.6 pm), measmement of bubbles smaller t han 1.0 pm

is not available. -4 total of about 1400 simulated bubbles were used in a sample volume

of 10 mm radius (a) and 7.5 mm thickness (z ) , corresponding to a concentration of 1 pl/l.

T m - t w o independent randorn ensembles were used to estimate the standard error of the

caldated values. The beam profile B(a), recorded eom hydrophone measurements, is

plotted in figure 2.5b. Time-domain echoes were calculated at a range of incident focal

peak-to-peak amplitudes Ao. To understand further the dependence on frequency, the whole

CHAPTER 2. A POPULATION MODEL OF CONTRAST MICROBUBBLES 52

calculation (starting from single bubbles) was repeated for two additional incident waveforms

at about 1.4 and 5.8 MHz. These waveforms were generated by cornpressing and dilating in

time the transmitted puise in figure 2.2.

1

O 10 20 -10 O 10 Bubble Diameter (2RJ (pm) Axial Distance (a) (mm)

Figure 2.5: (a) Measured szze distribution of bubble ensemble. (6) Measvred transdvcer beam

profile B(a) used in calculation of agent response.

Second and higher harmonies were found in the the-domain echoes, as reveded by

Fourier andysis. The normalized spectra for 2.9 MHz incident frequency at different incident

amplitudes are plotted as a map in figure 2.6. The spectra were normalized by dividing by

the square of the incident amplitude. Up to the sixth harmonie can be seen. One can observe

that the h m o n i c peaks were broadened at higher incident amplitude, to the extent that

at 1 blPa (a typicd diagnostic imaging peak pressure) the spectnun is ahos t completely

smeared out, leaving the fundamental peak b a d y distinguishable from the harmonies.

O 3 6 9 12 15 18 Frequency (MHz)

Figure 2.6: Nonndized Fourier spectra of the simulated bulk agent echoes. The spectra were

nonnalized by dividing by the square of the incident amplitude. The grey level represents dB

scale. Notice spectral bmadening of the harmonzc peaks at high inczdent amplitudes.

The powers at the position of the receiving transducer at fundamental and second

haxmonic frequencies were calculated and plotted in figure 2.7. The power radiated drops

by almoût a factor of 100 between 1.4 and 5.8 MHz. This fiequency dependence for buk

contrast agent has been demonstrated by experiment (de Jong and Hoff 1993). The negative

freqnency dependence can be explained thus: whüe there are many more s m d bubbles (0.5

- 2.0 p) in rnost agents, the scattering cross-section at resonance of the individual bubbles

demeases more quickly with decreasing bubble size (and inmeasing frequency), so that the

CHAPTER 2. A POPULATION MODEL, OF CONTRAST MICROBUBBLES 54

combined effect is a negative dependence. In the fundamentai band, the power received is

approximately proportional to the square of the incident amplitude. The power exponent

was measured to be 2.1 izO.15 for A. < 100 kPa, and gradudy decreases to l .7f 0.3 between

100 kPa and 1 MPa. In the harmonic band, the maximum power exponent for 2.9 MHz and

5.8 MHz is about 3.75 & 0.15 and decreases to about 2.8 10 .3 at incident amplitudes above

100 kPa. But at 1.4 MHz, the maximum siope reached only about 3.0 at 200 kPa. At both

fundamental and second harmonie, responses at all frequencies show a saturation effect above

100-200 kPa. While these results were calculated for a focused disk transducer, qualitatively

similar results can be expected for other common transducer geornetries, including arrays.

Presently, the accuracy of the model is limited by the lack of a thermal model and a shell

model. Thermal damping is expected to reduce the total scattered amplitude and degree

of nonlinearity. The shell can be expected to increase damping and increase the resonant

fiequency. The accuracy of the model is also limited by an uncertainty in some physical

parameters such as shell thickness, material properties, in vivo size distribution and local

incident amplitude.

2.4 Conclusions

We have developed a new model of contrast agent response to a real ultrasound beam.

Individual free bubble responses to pulsed incident waves were calculated numerically from a

differential equation çimiIar to 'Ililluig's (1952). Maps of bubble response properties, such as

fundamental and harmonic scattering cross-sections, can provide insïght into the interaction

CHAPTER 2. A POPULATION MODEL OF CONTRAST MICROBUBBLES

1.4 MHz * . . . . . 2-9 MHz 5.8 MHz

+ I * 1

Incident Peak-ta-Peak Amplitude A, (Pa)

1 0' 10' 106 Incident Peak-*Peak Amplitude A, (Pa)

Figure 2 . 7 Fundamental (top) and second hannonzc (bottom) responses of szmuZated agent as

a fvnction of zncident focal amplitudes ut three Fequencies. The error bars zndicate standad

m o r of 32 simulateci ensembles.

A POPULATION MODEL OF CONTRAST MICROBUBBLES

between bubble size and incident ampIitudes, which in tuni provide a possible exphnation

of reduced sidelobe ghosts and Mproved lateral resolution of h m o n i c imaging. A large

number of single bubble responses were combined to produce radio fkequency tirne-domain

echoes that redisticdy reflect the distribution of bubble sizes and the non-uniformity of the

incident and receive beams. This makes the single bubble theory experimentdy verifiable

as a method for predicting bdk agent acoustic response in Mtro and in vivo. In particular,

the model predicts a smearing of the fundamental and harmonic responses at high incident

pressures. As hannonics Erom tissue echoes due to nonlinear propagation do not show the

same effect, this may have important consequences for strategies to separate tissue and

bubble echoes. An experiment designed to test the quantitative accuracy of this model is

presented in the next chapter.

Chapter 3

Experimental Verification

Abstract l

A t heoreticd contrast agent model, extending existing single bubble models to a population

of simulated bubbles, was previously reported to produce time-domain scattered signals of

a form comparable to those obtained from a diagnostic imaging systern. In this paper,

experiments were camied out to test this model quantitatively. A diluted suspension of

contrast agent microbubbles Bowing in a chamber was exposed to 5 MHz pulsed ultrasound

of various bandwidths. Scattered signais were detected at 90° by a broadband transducer.

The experirnent a1 results generdy c o n h our model for predict ing scatt ered signds, but

the measured second hamtonic scattering is up to 10 dB lower than the theoretical prediction.

It was also observed that scattering is hcreased at hi& transmitted amplitude (> 1.5 MPa).

'This chapter is based on the manuscript: Chin CT and Burns PN. Experimental ver& cation of an ensemble model for scattering by a population of contrast agent microbubbles. Uitrasound Med Bi01 (submitted) .

Sheli disruption is believed to be a possible cause for both effects, and it is proposed that

the sheU behaviour is significsnt in determinhg the acoustic reponse of contrast agents.

Introduction

Microbubble suspensions for use as contrast agents in medical ultrasound imaging are cur-

rently undergoing signifiant development . Most of the successful contrast imaging met hods

exploit the phenornenon of nonlinesr scattering of ultrasound by the microbubbles. However,

quantitative understanding of nonlinear scattering is still poor.

The most successful quantitative measurements of ultrasonic characteristics of con-

trast agents have been performed using continuous waves (CW) at low (often unspecified)

transmitted amplitudes. Bleeker et al. (1990) established that, at low concentration, at-

tenuation and backscatter are approxirnately linearly related to the number of Albunex

microspheres. de Joug et al. (1992, 1993) measured the attenuation and scattered power of

Albunex over a frequency range of 1-10 MHz and found them to agree well with a linear

model based on visco-elastic particles. Hoff and Sontum (1998) reported at tenuat ion spectra

of the contrast agent NClOOlOO to agree with a similar model. Marsh et al. (1988) found

excellent agreement between measured t r e o n and backscatter spectra and prediction

fiom a h e m model.

A number of studies have been directed at quantitative measurements of the second

harmonic scattering of contrast agents. de Jong (1994) measured the second harmonic corn-

ponent generated when ten-cycle bursts propagate through a sample of diIuted Mbunex at

low (25 kPa and 50 kPa) tranmitted ampiitude. Uhlendorf and Hoffman (1994) reported

that the relative second harmonic output of SHU563A (Sonavist), in response to 35-cycle

bursts, increased by more than 30 dB when the incident amplitude was increased Erom 25

kPa to 400 kPa. Using 10-cycle bwsts, Krishna and Newhouse (1997) reported a quadratic

dependence of second harmonic scattering of Albunex on transmitted amplitude; a more

complicated dependence was found Eor FS069 (Optison). SUnilarly, using a CW Doppler

technique, Chang (1996) found that, for incident amplitudes below 80 kPa, Mbunex and

Optison produced a second harmonic amplitude in approximate proportion to the second

power of the transmitted amplitude. The quadratic dependence, used by many of the authors

cited, was derived originally by Miller (1981), who used a power series expansion technique

on the Rayleigh-Plesset model. When only the first nonlinear term was retained, a quadratic

dependence was the r e d t . Such a technique was intended for weakly nonlinear oscillation

and becomes invalid when the amplitude of the radial motion reaches a significant Fraction

of the initial radius. We now know that in diagnostic ultrasound contrast imaging, radid

excursions of five times the radius is possible (Dayton et al. 1999).

To help understand the nonlinear scattering of contrast agents, a theoretical mode1

was developed to predict the acoustic response of a population of microbubbles to pulsed

ultrasound such as that used in diagnostic imaging as described in Chapter 2. It was proposed

that to account for the basic nonlinear behaviour of contrast agents, it is necessary to consider

a randody distributed ensemble of bubbles with a range of bubble sizes. Cdculatioos using

this model have demonstrated a signiscant difference to the power series approximation

(Hope Simpson et al. 1999).

One specific prediction made by the model is the spectral broadening of radio fie-

quency (RF) echoes at high transmitted amplitudes, which codd potentidy be used to

address a problem with harmonic contrast imaging. Hmonics produced by nonlinear

propagation in solid tissue compete with harmonies produced by nonlinear scattering by

microbubbles and limit the performance of second harmonic imaging. Since nonlinear prop-

agation does not produce spectral broadening, techniques that exploit the scattered signal

a t 1.5 times the transmitted frequency could be used to distinguish between solid tissue and

blood Bow signals. To test the validity of the rnodel, h e a r and nonlinear scattering of pulsed

ultrasound kom diluted Definity (Dupont Pharmaceuticals, Wilmington, DE) was measured

and compared to the results of numerical simulation.

3.2 Method

IdealIy, with a multi-step model, one would like to verifjr evperirnentally each of the indi-

vidud steps. However, experimentd verification of the single bubble rnodel is difficult. The

microbubbles themselves are fragile and often axe destroyed before they can be selected and

manipulated into the sensitive volume of an experimentd system. Consequently when sig-

nais are detected fiom a single bubble, there is significant uncertainty in both the size and

position of the detected bubble. Thus, its value as a cnticd quantitative test of the accuracy

of the single bubble model is limited. Therefore, the complete population mode1 was tested

by measnring the scattering properties of population of bubbles at a cünical concentration.

Definity diluted to 0.075% was use&

The experimental setup, as shown in figure 3.1, employed separate transmit and re-

ceive tramducers at right angles to each other. This design has the important advantage

over the single transducer pulse-echo experiment in that the nodinear circuit elernents such

as diode-based expanders and Iimitea are eliminated.

Contrast Agent

Waveform 1 l b Generator -.-J 250 MHz .*.: I \

6.5 MHz Transducer

Signal Amp.

40MHz8bits 1-165MHr 0-20 d 8 Digitizing C' Bp Filter Attenuator

Oscilloscope

Figue 3.1: Eqerïmental setup for the nonlznear scattering memurement.

A Sony/Tektronix (Beaverton, OR) AWG2020 250 MHz arbitrary waveform genera-

tor was programmed to produce Gaussian enveloped pulses centred at 5.0 MHz with two

different bandwidths (figure 3.2), which were then amplined by an ENI (Rochester, NY)

240L 50 dB power amplifier. A Matec (Northborough, MA) 5.0 MHz transducer (aperture

f/2, focal Length = 19 mm) was used to produce ultrasound pulses that propagate into a flow

ceII which has mylar membranes as acoustic windows. The distance between the transmit-

ting transducer and the sample m1ume was kept short to reduce propagation nonhearity.

The scattered ultrasound was detected by a Blatek (CoUege Park, PA) 6.5 MHz transducer

(aperture f/4, focal length = 38 mm) at 90°. The signal was attenuated with a Te-

(Indianapolis, IN) variable attenuator (necessary at high transmitted amplitudes) and then

amplified by a Miteq (Hauppauge, NY) 50 dB signal amplifier. The amplified signal was

then fiitered with a custom 1-16.5 MHz bandpass filter to remove noise and digitized at 40

MHz with &bit resolution using a LeCroy (Chestnut Ridge, NY) 7200 digital oscilloscope.

The transmitted pulses used in the calculation were meanired with a calibrated hydrophone

(Sonic Technologies, Hatboro, PA). The bubble size distribution and beam shapes of both

transmit and receive transducers were obtained fiom experimental measurements and are

displayed in figure 3.3. The size distribution of Optison was used here. Definity may have

more sub-micron bubbles than Optison, but over the narrow range of frequencies used in this

study (conespondhg to 1.6-1.9 pm), the number density is very similar between Defintiy

and Optison. Due to the limitations of optical sizing equipment using visible light (wave-

length = 0.4-0.6 pm), measurement of bubbles srnaller than 0.5 Pm (radius) is not available.

The power spectra of the calculated ensemble response (using equations 2.6 and 2.8) are

plotted in figure 3.4.

This setup effectively eüminated interference lrom direct acoustic coupling or solid

structure reflection, dowing measurements at transmit pressures below 70 Wa. The second

harmonic component of the transmitted beam due to nonlinear propagation in water was

measured with the Sonic Technologies hydrophone. At the matcimm transmitted amplitude

of 3.8 MPa, the second h m o n i c component was 22 dB below the hindamental. However,

during the experiment, a portion (7 mm) of the beam path (19 mm in total) was within the

sample ceiI. Since the diluted agent has a higher nonlinear parameter, the actual propagation

harmonic rnay be higher.

O 5 10 15 Freq. (MHz)

O 5 10 15 Freq. ( M H z )

Figure 3.2: ICfansmitted four- y c f e (Ieft) and one-cycle (right) w a v e f o m and the correspond-

h g frequency spectrurn (bottom) wed in both simulation and ezperiment.

Since bubble echoes are known to decay in a manner that depends on ultrasound

amplitude (Burns et al. 1994), it was decided that data would only be collected from bubbles

that were never exposed. This was accompüshed by employing a very low pulse repetition

kequency (Pm) of 8 Hz and by Bowing the diluted Defhity through the Bow cell. Flow

velocity in the fiow cell was measured separately to ensure complete refreshrnent of contrast

bubbles between pulses. To prevent agitation and flow-induced bubbles from contamioating

O 5 10 15 20 -2 -1 O 1 2 Diameter t wrn) Distance (mm)

Figure 3.3: Size distribution of bubbles w e d in calculation and the the beam profiles of the

t~unsducers used in experiment.

the measurement, pumps were not used, instead, the flow was gravity-fed. A magnetic

stirrer was used to reduce the effects of floatation of the bubbles, but the stirrer was set to

the minimum speed. Agent exposed to ultrasound was not reused For data collection. Since

many contrast agents start to decay after preparation or dilution as a result of Koatation

and passive dissolution, all measurernents were made within 20 minutes of dilution.

Two kinds of noise data were collected. The random noise fiom the receiver and

associated electronics was collected without transmitted ultrasound. Random noise cannot

be subtracted directly kom the contrast agent signak, instead the noise power vins subtracted

from the power spectra. AU the combinations of attenuation and oscilIoscope gain settings

were tested. The signais due to electromagnetic interference £rom the transmitter and scatter

Frequency (MHz)

O 2 4 6 8 10 12 14 16 Frequency (MHz)

Figure 3.4: Pozuer spectm of simulated responses jbm the four-cycle (top) and one-cycle

(bottorn) pulses. The numbers repîesent incident peak-to-peak focal amplitude.

C . T E R 3. FXPE-NTAL VERIFTCATION 66

from solid structures (such a s the flow cell) was coilected with the transmitter t m e d on

but without contrast agent. Ekctromagnetic and acoustic interference is correlated and,

therefore, the signds from 1000 puises were averaged to e h i n a t e fandom noise. -AU the

transmitted amplitudes (70 kPa to 3.8 MPa) were tested. At each incident peak-to-peak

focal amplitude Pa, scattered echoes from 99 pulsing events were recorded and the mean

power spectnim was then calculated and corrected for the transducer frequency response and

noise. The suit able interference signal (according to transmit ted amplitude) was subtracted

from each of the 99 echoes. The Fourier power spectra were then calculated from each echoes

and then averaged. Finally the suitable noise power spectrttm (according to attenuator and

oscilloscope settings), which is itself generated from 99 traces, was subtracted from this

averaged power spectnun. The variance of the corrected power spectnim was also calaulateci

using the variance of the raw spectra and of the noise spectra.

cond harmonic

3.3 Results

The results are plotted in figure 3.5. It is de ar that se scattering near 10 MHz

is conspicuous and increases more rapidly than fundamental scattering. Spectral broadening

is also obsenred, especially around 3 and 7.5 MHz. Scattering coefficients were calculated

as the total energy detected within a fiequency band divided by the peak incident intensity.

Notice that, if a power law dependence is asnuned between second harmonic component P2/

and the incident amplitude PA, that is, P2f a c, then the scattering coefficient qf d l be

. . -

S . .

Frequency (MHz)

Figure 3.5: Power spectra of scattered signal from the four-cycle (top) and one-cycle (bottom)

pulses. Numbers represent inczdent peak-to-peak amplitude.

CHAPTER 3. EXPERlMENTAL VEmICAnON

related to Pa by

Scattering coefficients for the hindamental(0.75 fo-1 .% JO), second h m o n i c (1.75 f0-2.25 fO)

and spectral broadening (1.25 fo-1.75 fo) frequency bands for the four-cycle and one-cycle

waveforms are plotted against PA in figure 3.6 and 3.7, respectively. Simulation results are

also plotted in the same graphs, the error bars in the simulation data represent standard

error of the mean from thirty-two random subensembles.

Measured fundamental scattering was constant for PA < 500 kPa, as predicted. -4bove

0.5 MPa, the theory predicts a 3 dB depression of the fundamental scattering coefficient as

the bubbles convert absorbed energy into second and higher harmonies (Chin and Burns

2000). The measurements seem to be consistent with this prediction. For PA > 1.3 MPa,

there was a significant increase in fundamental scattering, which cannot be explained by the

present rnodel.

A quantitative discrepancy exists between simulation and measurement for the sec-

ond harmonic scattexkg. The simulation predicted that for PA < 200 kPa, second harmonic

scattering coefficient is proportional to Pfi7, whïie at higher transmit amplitudes, second

h m o n i c scattering saturates at about 8 dB below fundamental scattering. Experimental

measurements reveded an increasing power dependence. For the four-cycle pulse, the power

law coefncient below 500 kPa (the dope on the log-log plot) was approximately 0.5, and

gradudy Ïncreased to 1.2 for Pa > 1 MPa. For the one-cycle puise, the power depen-

Peak-to-peak Focal Amplitude (kPa)

i 5 f Theory 1 5 /: Ex pr.

50 100 200 500 IO00 2000 5000 Peak-to-peak Focal Amplitude (kPa)

Figure 3.6: Simvlated and measured scattering coeficients vs. incident amplitude in response

to the four-cycle pulse- (top) Fundamental (fo) and second harmonie (2 f*); (bottom) spectml

broadenzng (1.5 fo). Error bars in the simulated results indicate standard e m r using 32

ensembles.

5

0

3 - k*

8 p o c

.œ L a3 CI -1s U

V1

-20

2

Figure 3.7: Simvlated and measured scattering coeficients vs. znc2dent amplitude in response

to the one-cycle pulse. (top) Fundumental ( fo l and second harmonic (2 fo); (bottom) spectml

broadening 11.5 fo). E m r bars in the simulated results indàcate standard emor uszng 32

ensembles.

O I B I 6 6

. . . . . . .

. . . . . .

. . . . . . : . . . . . . : . . . . . . . . . E

50 100 200 500 lm 2000 5000 Peak-to-peak Focd Amplitude @Pa)

. I I r

............... . . . . . . . . . . . . . . ......:...... : : * . S . i 3%:

.II

5 Y

-20 U rA

-25

............. . . . . . . . - . . . . . . - : . :. . . . . . . . . . . . . . . .

. . ............ 1 . . . . . . . . . . . . . . . ,. . . . . . . . . . . . . . . . . - 1 S/ Theory . * 1 s t Expcr.

.

- 5 - . . - . . - . . . . . . - . . . - * . * . . . . *

.. . . . . . *S.?

. . . . . . . . . - . . . . : . . . . . . . . . . . . ErI . . . . . . . . . . . . .

2 : A ...... .:. . . . . . ; . . y . . . . . . . . . . : m.. . . . . .

r 3° - f Theory W . . . . . .:. . .d. . . . . . . . . . .:. . .A ... + PExpcr.

-30 t t * I'

50 100 200 500 Loo0 2000 5000 Peak-to-peak Focal Amplitude (Wa)

j" . & & A t * Ik * m I

- - 2, Thcory A 2 l p x p n .

dence increased from approximately 0.4 to 0.5. The occurrence of this increase coincided

with the increase in fundamental scattering. The difference between the simulation and the

experiment on the level of second harmonic scat tehg is as large as 10 dB.

Finally, as seen in figure 3.6 and 3.7 the quantitative clifference between simulation and

experiment with respect to spectral broadening is signiscant. While the simulation predicted

a very sharp increase in 1.5 fo scattering, a relatively high level of spectral broadening was

meanired ewn at PA < 500 kPa.

3.4 Discussion

Previously published studies of nonlinear scattering of contrast agents were limited in several

aspects. Most of them were conducted using continuous wave or nearly-CW bursts. Also,

a number were limited in the range of transmitted amplitude, sometimes below the lomest

output of chical scanners. In this paper, a quantitative measurement of nonlinear scattering

€rom Definity is reported. The bandwidths of the transmitted pulses were comparable to

those used in clinical irnagers. The transmitted amplitudes (MI = 0.04-1.7) ais0 cover the

range of power used in practice.

The agreement between theory and measurement was found to be generally good.

However, three specific discrepancies were identzed: (1) scattering coefficients, both funda-

mental and harmonic, increase rather than saturate for PA > 500 kPa, (2) measured second

harmonie scattering is up to 10 dB lower than theoretical prediction, (3) for the four-cycle

pulse, spectral broadening at PA < 500 kPa is signincantly underestimated by the theory.

1 Echo #I 1

1 Echo #3 1

1 - . 3

Echo #20 0.5 -

n

L 3 O

-0.5

-1 1 1 1 L

O 2 4 6 8 10 Time @s)

Figure 3.8: Optison echoes horn exposure to 2.0 MHz pulses at a pulse repetition frequency

of 2 kHz and peak-to-peak amplitude of 3.6 MPa. The first, third and twentieth echoes

demonstrate bubble shell dllsmption. The bubbles hod not been exposed to ultrasound prior

to the fi~st pulse. Sipificantly elevated fundamer-tal and hamonic scattering are obserued

aftw initial exposure, but by the twentieth echo, the bubbles have virtuaily disappeared.

The first two of these could possibly be explained by the presence of a motion-dampening

shell that is disnipted at high PA. The sheIl serves to stabilize the bubble but dampens

the motion of the bubble and reduces nonlinear scattering. There have been several reports

that contrast bubble echoes decay over millisecond timescdes under multi-pulse ultrasound

exposure (Burns et al. 1994; Dayton et al. 1999; Takeuchi 1998). The present study demon-

strates that scattering is increased during the few microseconds when the k t ultrasound

pulse strikes the bubbles. We hypothesize that this is a consequence of shell disruption. A

brief experiment demonstrates this. Pulsed ultrasound at a center Erequency of 2.0 MHz

and a peak-to-peak pressure of 3.6 MPa was transmited into a solution of Optison. Figure

3.8 shows the Brst, third and twentieth echoes from previously unexposed Optison bubbles.

The third echo, only 1 msec after the k t , produced significantly elevated fundamental and

harmonic scattering. The echoes then diminished in magnitude and effectively disappeared

within twenty pulses. It is speculated that shell dismption allows the bubbles to oscillate

more freely for the duration of a few pulses before gas dissolution reduces the bubbles to an

insignincant size. S pect r d broadening and subharmonic emission has been associat ed wi t h

cavitation events (Leighton 1997; Miller et al. 1984). Dimption of a sub-population of the

microbubbles may therefore be the source of the spectral broadening seen at low amplitudes.

3.5 Conclusions

Linear and nonünear scattering coefficients by a contrast agent were measured and cornpared

to a mode1 simulating a popdation of microbubbles. Some quantitative discrepancies were

noted, which may be explained by the presence of the bubble shell. It is suggested that

the sheU has multiple important roles in the behaviour of contrast agents. Both the basic

mechanical properties of the sheli and the effects on acoustic scattering are not yet fully

elucidat ed.

Chapter 4

Effects of Shell Disruption

Abstract l

This study is designed to investigate the effect of the shell on single-pulse scattering by a

population of contrast rnicrobubbles. Scattering was rneasured shortly (15 ps) after exposure

to a previous ultrasound pulse with variable intensity. The short time delay limits the in-

fluence of gas diffusion. The results suggest that single-pulse scattering is dependent on the

dimption properties of the bubble shell. In a previous paper, we attempted to ver* exper-

imentdy a mode1 for ultrasound scattering by a population ensemble of microbubbles. The

compsrison reveded some quantitative discrepancies between mode1 predictions and experi-

mental results. We proposed that the dimptible shell used to encapsulate the microbubbles

is responsible for the discrepancies. The results of this study c o h the significance of the

LThis chapter is based on a manascript: Chin CT and Burns PN. Investigation of the Effects of Microbubble SheU Disrtrption on Population Scattering and Implications for ModeIling Contrast Agent Behaviour. IEZE 'Ems UItrason Ferrodec Ekeq Contr (submitted).

shell properties.

4.1 Introduction

A number of factors Iimit the usefulness of mathematical theories for predicting the acoustic

response of microbubble contrast agents. Some of the difficulties relate to the multiplicity of

bubble sizes in a red population of bubbles and the heterogeneity of real incident ultrasound

fields. To account for these factors, a theoretical model for predicting the time-domain

acoustic response fkom a bubble population was created (Chapter 2). To test the model,

we measured the nonlinear scattering coefficients of the contrast agent Definity (DuPont

Phaxmaceuticals Co., Boston, MA) (Chin and Burns 1998). Gaussian-enveloped four-cycle

ultrasound pulses centred at 5.0 MHz were transmitted into diluted agent ff owing in a cell.

The scattered mgnals were detected with a broadband transducer located at 90 degrees to

the incident beam. The results generaily agreed with the model predictions, but several

discrepancies between t heoretical prediction and experimental results were apparent. First ,

measured second hazmonic scattering was up to 10 dB lower than the theoretical prediction;

second, scattering coefncients, both fundamentai and harmonie, increased rather than remain

Bat for incident acoustic pressures p > 500 kPa; hally, spectral broadening at p > 500 kPa

was significantly underestimated by the theory.

Several possible causes of the disnepancies couid be considered: themai dampening,

mass transfer and acoustic disniption. Thermal dampening is known to reduce bubble os-

cillation amplitude and therefore nonlinearitgr, however, as the incident amplitude and the

radial amplitude of the bubble increases, the effect of thermal dampening is &O increased

(Prosperetti 1991). Therefore, thermal dampening would not be expected to cause an in-

crease in fundamental and harmonic scattering at high incident amplitudes. Secondly, mass

transfer could occur by rectified cifision, a relatively well-understood process. Since the

difision rate is different during the expanded phase (when gas evaporates into the bubble)

compared to the contracted phase (when gas dissolves into the liquid), gas fiows preferren-

tially into the bubble owr a complete cycle of bubble oscillation (Leighton 1997). However,

rectified diffusion is generally believed to be a slow process that involves at least hundreds of

microseconds (Church 1989). Therefore, we focus on acoustic disruption as a possible source

of the observed behaviour.

Two factors are believed to be important in bubble disniption, the gas behaviour and

shell behaviour. When the shell of a bubble is disrupted, it is believed that its ability to

Mpede gas dissolution is compromised. The content of the bubble is allowed to dissolve into

the surroundhg liquid at an increased rate. The dissolution rate is limited by the diffusivity

constant and the solubility of the gas molecules (although some remnants of the shell may

reduce the actual dissolution rate below the free bubble level). Consequently, the lifetime of

the contrast bubbles after initial disruption is mainly determined by the gas type.

We performed two experiments, the £irst to meanue the effect of the gas type, the

second the effect of the shell. In the fkst experiment, the decay of the scattering power

was measured for an agent containhg nitrogen and an o t h e h identical agent containhg

peduoropropane. In the second experiment, the effect of a previous exposure to ultrasound

was rneasured by insonation with two pulses separated by a very short penod of time. To

isolate the effects due to gas type, the measurements were made before dissolution of the gas

could cause a measurable effect on scattering.

4.2 Method

The experimental setup is outlined in figure 4.1. A Sony/Tektronix AWG2020 (Beaverton,

OR) arbitrary waveform generator produced Gaussian enveloped pulses which were then

amplified by an ENI 240L 50 dB power amplifier (Rochester, M). Separate transmit and

receive transducers were used to eliminate the needs for nonhear circuit components. The

transmit and receive beams cross at right angle at the centre of a flow ce11 which has mylar

membranes as acoustic windows. The distance between the transmitting transducer and the

sample volume was kept short to reduce propagation nonlinearity. The scattered ultrasound

was detected by a receiving transducer at 90'. The signal was attenuated with a variable

attenuator by up to 12 dB and then amplified with a custom designed switched mgnd

amplifier. This amplifier can be switched electronicaily between gains of 35 and 53 dB.

The amplifier has a dynarnic range of 65 dB and at most -54 dB of harmonic nonlinearity.

The arnplined signal was then Giltered with a custorn 1-16.5 MHz bandpass filter to remove

noise and digitized at 50 MHz with 12-bits resolution with a Gage PDA 8012A (Montreai,

Canada) A/D converter installed in a personal cornputer. This setup effectively ehinated

interference from direct acoustic couphg or solid structure reflection, dowing measurements

at transmit pressures below 40 kPa.

In the first experiment, the agents were exposed to dtraçound pulses at a pulse

CHAPTER 4, EFFECTS OF SEIELL DISRUPï7ON

54/34 dB

Figure 4.1: Ezperimental setup for the nonlinear scattering rneasurement.

repetition frequency (PRF) of 2 kHz. A pair of Picker (Highland Heights, OH) 3.5 MHz

transducers were used as the transmitter and receiver. The ultrasonic pulse used had a

centre fiequency of 2.2 MHz and the Ml-width-half-maximum pulse length was equal to

2.9 periods. The diluted agents were allowed to flow for 20 seconds in order to cornpletely

refiesh the bubbles. The flow was then stopped and the suspension allowed to settle for

30 seconds before ultrasound pulses were transmitted. The echo data were collected for

2 seconds, and the process was repeated ten tirnes. The agents tested were Definity and

a special experimental formulation of Defini@ in which the perfiuoropropane was replaced

with nitrogen.

The second experiment focussed on the effects of the shell. Inference of the significance

of shell was made fiom measurements on several different agents. These agents cover a range

of gas types and sheU properties. Four contrast agents were available for this study: Levovist,

Sonavist (Schering Ag, Berlin), Definiw (DuPont Pharmaceuticals Co., Boston, MA) and

Optison (Mnllinckrodt Inc., St. Louis, MI). Table 4.1 lists their constitution and properties.

Table 4.1: The constitution and pmperties of the contrast agents used in the shell effect experinrent.

..

The agents, flowing continuously, were exposed to two ultrasound pulses (5.0 MHz,

FWHM = 3.7 periods) separated by 15 p. The first pulse had variable amplitude (p,) and

the second pulse had a h e d arnpütude (pb) , as shown in figure 4.2. The first pulse rneasured

the amplitude dependence of the acoustic response of the bubbles. The second pulse detected

any changes to the scattering properties caused by the exposure to the first pulse. A Matec

(Northborough, MA) 5.0 MHz transducer (aperture f/2, focal length = 19 mm) was used

as the transmitter and a Blatek (College Park, PA) 6.5 MHz transducer (aperture f/4, focal

length = 38 mm) was used as the detector. The switched amplifier was designed to allow

both the first and second echoes, which had power clifference of up to 24 dB, to be digitized

with hi& fidelity. The pulse pairs were repeated at a PRF of 40 Hz. Flow velocity through

the sampled volume was rneasured independently to c o b suf6cient refreshment of the

bubbles between pulse pairs. The diluted contrast suspension was ftowed through the celI at

a d ic ien t ly fast rate that the sensitive volume of the transducers was refieshed with bubble

as each pulse pair amves, while the delay was short enough to effectively freeze the bubble

displacement.

For each agent and for each first pulse amplitude (p,), two hundred echo pairs were

Levovist Sonavist Defini@ O~t ison 1.

Gas type air air

C3Fs

Shell solubiüty/diffusivity

high high iow

me palmitic acid

p o l p e r p hospholipid

,, CIIFSH~

cornpliance high low high

. low 11 albumin . medium

First Pulse Second Pulse 40-2000 kPa 240 kPa

Figure 4.2: The pulszng sequence used in the shell e h t s meusurement.

recorded. Ail measurements were performed in l e s than 30 minutes after preparation or

dilution, this ensured that the agent properties had not changed significantly by passive

processes. Data were dso collected without scatterers in the Bow ce11 so that extraneous

power due to noise and interference could be subtracted during analysis. The recorded

data were andyzed o f i e using Matlab (The MathWorks Inc, Natick, MA). The power

spectra were calcdated, and the noise power spectra were subtracted. The spectra were then

corrected for the receiver fiequency response, and the power spectrum due to interference

is subtracted as the last step. The fundamental (fo), second h m o n i c ( 2 f o ) and spectral

broadening (1.5 fo) scattering coefficients were measured fkom these spectra using a width of

0.5 fo eaeh.

From the fmt experiment, each rneasurement consisted of 4000 consecutive echoes from the

stationary agent. For each agent and at each incident amplitude, typically ten to twelve

(minimum seven) independent measurements were made. An =ample of five of the k t

forty-one echoes are plotted for one measurernent at 1.8 MPa (peak-to-peak) for each agent

in figure 4.3. The special Definity (Nz) was a weaker agent, therefore, the echoes for the

regular Definity (PFC) were scded by a factor for display. Noise power was subtracted from

the echo power. The time it took EtbfS echo amplitudes to drop to half the maximum level

was measured a s the Iifetime. The means of these lifetimes were plotted against incident

peak-to-peak amplitude in figure 4.4.

For the second experiment, fundamentai (fo), second h m o n i c (2 fO) and spectral

broadening (1.5 fO) scattering were measured from both echoes. An example of three echo

pairs for Sonavist are plotted in figure 4.5. The first two of these pairs, having been exposed

to amplitudes of 262 kPa or lower, showed good correlation between the first and second

echoes of the pair and dernonstrated comparable scattering coefficients. In the 1 s t pair, with

an exposure of 3034 kPa, scattering fkom both the first and second echoes were elevated.

These meanirernents fields on (p,,pFe) which are the scattering coefficients at nth harmonic

(n fo) as b c t i o n s of incident pressure amplitude p, and amplitude of previous (if nonzero)

puise p,,. Thus, the first echo yielded q (p,, O), 02 (pw , O) and ais (p,, O) and the second

echo yidded ol (pb, pu), 02 (pb, pw) and 01-5 (pb, p,) where pw was varied from 33 kPa to 3034

kPa and ph was held constant a t 260 kPa. The results are plotted in figures 4.6 and 4.7.

C ' T E R 4. EFFECTS OF SHELL DISRUpcITON

PFC (v / 4.46)

Figure 4.3: The Ist, Ilth, 21st, 31st and 41st echoes from one of the measured data set for the regular Definity (PFC) and the specàal Definity (IVz). Each trace was 10 ps in length. PRF = 2 Mit, pp = 1.8 MPa. The PFC echoes (voltage) were scaled by a factor of 4.46 since the special N2 DefiBity tuas a weaker agent.

4.4 Discussion

Several authors have reported on aspects of acoustic disruption. Uhlendorf and Hoffmann

(1994) mesnired nonlinear scattering fiom the agent Sonavist usine; long (35 cycles) bursts

of 5 MHz ultrasound. It was suggested that the transient nonlinear response, called "Acous-

tically Stimulated Acoustic Emissionn , is a result of the mpture of the bubble shell. Morgan

et al. (1998) showed opticdy that a single ultrasound pulse can be sufncient to initiate the

cornplete dissolution of contrast bubbles. Chomas et al. (1998) made optical and acoustic

measurement on microbubbles under medium to high ampiitude (0.8-2.6 MPa) ultrasound

for an experimentd agent with a Lipid shell and high rnolecular weight gas core. Dayton

O 1 2 3 4 5 Incident Amplitude (MPa)

Figure 4.4: Lifetimes (defined os tzme for the RMS amplitude of the echoes to drop to half the mmimum level) us. incident amplitude for tmo agents &th different gas types.

et al. (1999) made detailed optical measurement on two agents with different shell materials

and noted that the difference in acoustic response to a train of ultrasound pulses might be

related to the differences in shell materials. Frinking et al. (1999) demonstrated that the

agent Quantison can release fiee gas bubbles after exposure to a high amplitude burst (1.6

MPa, 10-cycle at 0.5 or 1.0 MHz). When probed 0.6 ms after the high amplitude burst, the

fiee gas bubbles produced 15-20 dB more fundamental scattering and 10 dB more relative

harmonic scatt ering compared to intact Quantison part icies.

In this study, two experiments were performed to iderit* the effects of dtrasound ex-

posure to contrast agents- In the fkst experiment, the agents are exposed to multiple pulses

transmitted at a PRE' of 2 kHz. As the incident amplitude increased, the echo decay time

CiNtlPTER 4. EFFECTS OF SHE:LL DISRUPTION

First Echo Second Echo

Figure 4.5: Pairs of echoes frorn Sonavist fiom diferent first pulse amplitudes ( p J . The delay between the Jirst and second echoes is 15 ps. Each trace was 5 ps in length and uas nomalited Qy the correspondzng (frst or second) incident amplitudes. Notice that at the hzghest p,,,, 60th the fist and second echoes were elevated.

decreased from about 1000 msec to a minimum of 2.6 msec. The special Definity contain-

ing nitrogen disappears about two to ten tirnes faster than the regular Definity containhg

peduoropropane. This established that gas type has a strong effect on the decay of bubble

echoes and that gas dissolution over the microsecond timescale is negligible.

The second experiment was designed to detect changes on the microsecond timescde

caused by a single dtrasound pulse. From figure 4.6, Definity (DMP-1 E), Optison (FSO69)

and Levovist (SHU508a) aU demonstrated fundamental scattering remained essentially con-

stant, with a s m d (about 2 dB) decrease at high amplitudes (p, > 500 kPa), in agreement

Figure 4.6: F W pvkre scattering coefieients for the four contrast agents

?

Second Pulse fo So08vist f Opison '

Ddinity trvov Mt

1

Frrst Puise lecidtnt AniDliaxdt &Fa)

Figure 4.7: Second p d e smttMg coefiieents for the four eontsast agents

with the theory Nonlinear scattering (a2 and ois) for a.il agents increased with increasing p,.

Figure 4.7 shows that the second pulse scattering of both Dennity and Optison was relatively

unaEected by the amplitude of the first pulse. Finaily, Sonavist (SHU563a) demonstrated

drûmatic increases of both linear and nonlinear scattering for incident amplitudes above 500

kPa. Figure 4.7 shows the dependence of h e m and nonünear scattering on ultrasound ex-

posure history. Sonavist demonstrated significant increases in the second pulse scattering;

in particular 01.5 was boosted by more than two orders of magnitude.

hpart fiom the dependence on the incident amplitude p,, acoustic scattering is

demonstrated to be dependent on contrast agent and disruption by strong ultrasound pulses.

First pulse nonlinear scattering is the lowest in undisrupted Sonavist, ranging Erom unde-

tectable to about 50 dB below fundamental scattering level; it is intermediate in Levovist,

Optison and Definity, ranging &om 60 to 20 dB below fundamental scattering level; and

the highest in disrupted Sonavist, ranging from 50 to 8 dB below fundamental scattering

level. Increases in scattering coefficients from the second echo were observed from Sonavist

at incident amplitudes higher than 400 kPa. This corresponds to the ciramatic increases in

first pulse scattering and is consistent with a steep threshold of disruption of the agent's stiff

po1per shell. Spectral broadening (oId) was consistently detected in agents with a flexible

shell. In Sonavist, spectral broadening is detected only during and after acoustic disruption.

The results support the hypotheses that (1) nonlinear (2fo and 1.5 fo) scattering is

related to sheU flexibility; (2) increased single-pulse scattering at hi& incident amplitudes

is associated with acoustic disntption of the bubble shelI; and (3) spectral broadening is

asociated with shelI disniption and is observed at low incident amplitudes fiom agents with

CHAPTER 4. EFFECTS OF SHELL DISRUPTION

a flexible shell.

4.5 Conclusions

Previously, ultrasound contrast agents were broadly classified as either diffusible (air-based)

or non-difhisible (PFGbased) agents. Diffusible agents decay quiddy when evposed to a

series of ultrasound pulses over millisecond timescales, and non-dfisible agents can sur-

vive upto thousands of milliseconds. By isolating the effects of shell type lrom gas type,

the present work demonstrates that shell properties have a strong iduence in the acoustic

response of contrast microbubbles over microsecond timescales, indicating that the shell, as

well as the gas, is an important determinant of bubble behaviour in an acoustic field.

Chapter 5

Applications and Future Prospects

5.1 Introduction

During the course of my research, some developrnents of contrast irnaging methods changed

our perspective on the importance of stable hannonic scattering by microbubbles. Section

5.2.1 describes the development of intermittent imaging, which provides superior sensitivity

at the expense of imaging frarne rate since the bubbles are disrupted by the imaging pulses.

Intermittent imaging produced the first perfusion images of the myocardium, which was

considered the HoIy Graii during the introduction of encapsulated agents. For a period

of t h e , imaging methods that were sufnciently sensitive were d l disruptive, and it mas

thought that the role of a nondisiuptive bubble scattering mode1 wodd be diminished. More

recently, highiy sensitive nonlinear imaging met hods were developed. These met hods, w hich

are reviewed in sections 5.2.2 and 5.2.3, have d c i e n t sensitivity to image blood Bow in the

myocardium and other demanding situations using low h1I puises which are non-destructive

CHAPTER 5. APPLICATIONS AND FUTURE PROSPECTS 91

or mildly-destructive. As a result of these developments, the interest in a nondismptive

model is revived. A number of questions relating to the basic mechanisms of these rnethods

remain unanswered. The bubble model presented in Chapter 2 was used to investigate some

of these questions in section 5.3.

h o t h e r area of future development is the application of contrast microbubbles in

high fiequency ultrasound. Section 5.4 presents preliminary theoretical and experimental

results of noniinear scattering by a contrast agent.

5.2 Recent Developments in Contrast Imaging

5.2.1 Intermittent Imaging

The combination of harmonic filtering (which detects the second harmonic scattering) and

Doppler mode (which detects motion of the scatteren) was demonstrated to be sufficient

to detect blood flow in vessels as small as 44 pm in a kidney (Burns et ai. 1994), which is

relatively stationary and well pemised. However, irnaging of myocardial blood Bow presents

a greater challenge. The v a s d a r space accounts for ordy 10-15% of the volume of the

myocardium, limiting the number of microbubbles that contribute signal intensity. The

motion of the myocardium itself is much greater than the motion of the blood relative to

the tissue, rendering the Doppler technique useless in blood fiow detection. A significant

advancement was made possible by Uhlendorf and Hoffmann (1994) when they reported

disruption of microbubble echoes within a few milliseconcis. The fast decay or decorrelation of

the contrast echoes appears indistingnishable fkom that fiom scatterers moving very quickiy

(XU..PTER 5. APPLEA'MONS AN. FUTURE PROSPECTS 92

through the imaged volume. As a result, pseudo-Doppler signals can be detected. Such an

observation led to the development of a highly sensitive contrast imaging strategy enploying

strong (MI > 1.0) dtrasound and hannonic Doppler detection. Since the method relies

on the dismption of the contrast echoes, continuous redtime imaging is not possible. .!fier

each frame of image is obtauied, transmission of ultrasound must be suspended to allow Eresh

microbubbles to enter the imaged volume. In the myocardium, N1 recovery of the contrast

signals in the hedthy myocardium takes 4 to 8 seconds (Linka et al. 1998). As a result,

€rame rates as low as 0.1 Hz are used. Such a technique was called intermittent imaging

or interval-delay imaging. Imaging of myocardial blood flow was reported by Porter et al.

(1995, 1996). In the liver, the evolution of signal intensity frorn intenml-delay irnaging was

correlated to vascular volume and was demonstrated to improve characterization of lesions

(Wilson et d. 2000).

5.2.2 Pulse Inversion Detection

There is a tradeoff between axial resolution and achievable contrast in harmonic imaging (see

section 1.4.2). This is because axial resolution is fundamentdy related to the bandwidth

of the transmitted pulse. A fher resolution requires the use of a wider bandwidth which is

detrimental to discrimination between the fundamental and hannonic echoes based on the

frequency (figure 5.1). Pulse inversion detection (PD) (Hope Simpson et al. 1999) was

invented to address this problem.

Pulse inversion exploits the fact that nonlinear scattering violates the hearity prin-

C W T . 5. APPLICATlOn'S AND FUTURE PROSPECTS

Figure 5.1: When a high axial resolution is desired, generolly a wide bandvidth is used.

However, the abilzty of homonie imaging to discriminate between findamental and harmonic

f+equencies is h i t e d by ouerlapping banduidth.

ciple, equation (1.22). Specificdy,

Therefore, the pulse inversion strategy c d h for two pulses with opposite signs (pin and -pin)

to be transmitted instead of one. When each pair of echoes (pcchol and pedio2) are collected,

they are summed together h t o a single echo signal and images were constmcted using the

sum signds. For Iinear scatterers, the sum signal is zero. For nonlinear scatterers such as

microbubble contrast agents, the sum signal is nonzero (figure 5.2).

A conceptual tool used by severd authors (Hope Simpson et al. 1999; Jiang et al.

1938) eonsists of a simplified model for the harmonic scattering by microbubbles. In this

model, harmonies are produced by assuming that the scattered pressure follows a polynomial

CHAPTER 5. APPLICATIONS AND FUTURE PROSPECTS

Figure 5.2: Pulse Inversion Deteetion. A pair of incident pulses &th opposzte signs are

h 10

cJ a M *a

P- -IO

tmnsmitted. The echoes are summed together, the fvndurnental component is cancelled out

Pa,, + P&2

oJIb 1

li*

7

und the even hamonic components are preserved. The echoes were calculated for a 1.9 prn

diametw fkee bub ble. Incident peak-to-peak amplitudes were 300 kPa and 150 kPa.

O 1 2 3 Time (CLS)

CEfWPTER 5. APPLICATTONS AND FUTURE PROSPECTS

relation to the instantaneous pressure of the incident wave:

where al, al etc. are constants. The rationale for equation (5.2) is that, for continuous wave

excitation,

Pin = p-4 COS (ut) ,

then each even power term P;! will produce even harmonies of orders 0,2,4, ,272; and

*"+' Will produce odd hmonics of orders 1,3,5, - , Zn + 1: each odd power term pin

4 a4 + 7 + p, - + *) cos ( 2 4 + p q + - .) cos ( h t ) 2 ( 3 a 3

+ + .) cos (4'dt) +

If only al and a* are nonzero, then equation (5.4) predicts that second harmonic amplitude

to be proportional to the second power of the incident pressure amplitude, the same as

predicted by the weakly nonlinear approximation used by Milier (1981).

While a visual inspection of any scattered waveforms, such a s the second row of figure

5.2 would suggest that the polynomial mode1 is very iimited in accuracy, it has proven to be

useful in the early conceptual development of multi-pulse non-destmctive detection methods,

CHAPTER 5- APPLTCAïTONS AND FUTURE PROSPECTS

such as pulse inversion. Applying equation (5.4) to PD, one obtahs

so that the linear scattering term, p ~ a l cos(2wt), dong with ali the odd harmonic terms,

me cancelled out and aU the even harmonic tems are preserved. Therefore, by using two

pulses, PID d o w s discrimination of the linear component of the echo without the use of a

filter which limits axial resolution. The method was extended to allow more than two pulses

to be used, thus adding motion discrimination to two-puise pulse inversion.

Recently, multi-pulse PID has achieved sufficient sensitivity so that constrast bubbles

can be detected without using high transmitted pressures which destroy the bubbles. Sub-

sequently, redtime imaging of myocardial blood fiow in human patients was demonstrated

(Tiemann et al. 1999). The ability to image at a frame rate of 15 Hz or higher is a major

improvement over intermittent imaging.

5.2.3 Power Modulation Imaging

Another method closely related to pulse inversion is based on the Following violation of the

hearity equation:

Power modulation irnaging (PMI) operates by transmitting two pulses of different amplitudes

(pin and pin/2) and then u h g a weighted difference - 2pcend) of the two echoes to

(3UPTER 5. MPLlCATPfONS tU\JD FUTURE PROSPECTS 97

cancel the linear signal (Jiang et al. 1998). Figure 5.3 illustrates the operation of PMI using

the same bubble as figure 5.2.

Using the polynomial mode1 again, the resultant signal is given by

- + *) cos ( 3 4 + + - cos ( k t ) + - - . (5.7) + ( P i 2 '" 64 1

While the Linear scattering tem, p ~ a l cos(2wt), is cancelled out, nonlinear t e m s of both

odd and even orders are preserved.

Considering only the linear and quadradic t e m s (al and a*) and using a signal-

t+noise ratio approach, Jiang et al. (1998) argued that PID should be superior to PMI.

Since then, however, both methods have been implemented on commercial scanners and

clhicai experience has shown both methods to be cornpetitive as realtime rnodalities for

rnyocardial perfusion imaging. The explanation of power modulation's success starts with the

recognition that a3 # O and a non1inea.r scattering component is preserved at the fundamental

frequency: s p i a 3 COS (ut), see equation (5.7). Therefore, PMI was configured to operate at

the centre of the transducer bandwidth (Brock-Fisher et al. 2000). By foregoing the second

hannonic echoes, both the transmitted waveform and the received echoes are placed within

the same frequency band. This has the important advantage that the fidi bandwidth of the

transducer is used for both the transmission and reception processes. In contrast, PID must

be configured so that the centre frequency of the transmitted waveform is placed somewhere

in the lower half of the transducer bandwidth, resulting in the second harmonic echoes

CHAPTER 5. APPrTCATPT"NS AND FUTURE PROSPECTS

- -

O 1 2 3 Time (CLs)

Figure 5.3: Pover Modulation Imaging. A pair of incident pulses urith different amplitudes

are tmnsmitted. A weighted diference of the echoes is used to cancel the linear component.

AI1 honnonic components are p~eserued- The echoes were colculated for a 1.9 prn diameter

j k e bubble. Incident peak-to-peak amplitude was 300 kh.

C W T E R 5. APPLICATlONS AND FUTURE PROSPECTS 99

appearing within the upper half of the transducer bandwidth (figure 5.4). However, the

better exploitation of the transducer bandwidth may corne at the cost of reduced bubbles

response. It c m be expected the third order nonlineazity which gives rise to the detected

signal in the PMI scheme is lower than the second harmonic component which is detected

by PD. However, the relative merits of the two methods are currently unknown, since the

polynomial bubble mode1 (equation 5.2) is not supported quantitatively by any theoretical

or experimental evidence.

5.3 Applications of the Bubble Mode1

.4t present, the relative strength and weakness of pulse inversion imaging and power modula-

tion imaging are not f d y understood. .4s Far as a clinician is concemed, these two methods

must be compared as fuUy implemented imaging modes on cornmencal scanners in a clinical

setting. However, actud implementation on a machine involves many factors that make it

dificuit to identify the factors that determine the performance of each method. Further-

more, commercial and Iegal concerns often ümit opportunities to test experimentaily these

methods in a comparable rnanner. One key question is: given that contrast agents Molate

ünearity in both the sense of ttsign" (equation 5.1) and the sense of "proportionality" (equa-

tion 5.6), which type of nonlinearity is stronger? When this question is ansnrered, the other

effects, such as nonlinear propagation, kequency-dependent attenuation, frequency response

of the transducer, electronic noise, etc, can be added so that each method can be rigourously

optîmized and compared.

CHAPTER 5. APPLICATIONS AND FUTURE PROSPECTS

O 1 2 3 4 5 6 Frequency (MKz)

O 1 2 3 4 5 6 Frequency (MHz)

Figure 5.4: Pukre Inversion Detection (PID) and Power Modulation Imaging (PMI) employ

the limited bandwidth of the transducer differently. The dashed line represent the fiepency

response of a hypothetical transducer with 100% bandwidth. PID bene@ from a higher

nonlinear response, while PMI benefits from the full exploitation of the transducer bandwidth.

The purpose here îs to demonstrate the application of the scattering model in the

optimizatîon of low-intensity nonlinear imaging methods. It is instructive to consider an

individual bubble of the resonant size. In this discussion, several factors are not included.

Where a quantitive analysis is desired, a number of factors can be readily added: the distri-

bution of bubble sizes, attennation and nonIinear propagation in the tissue, and, especidy,

beam dïfbaction pattern. Figure 5.5 shows the scattered waveforms of a 1.9 Fm bubble

CHAPTER 5. APPLICATIONS IWD FUTURE PROSPECTS 101

in response to a 5 MHz ultrasound puIse with positive phase. As the incident pressure is

increased, the scattered waveforms become distorted, producing harrnonic components (see

also figure 2.3). Figure 5.6 shows the corresponding results using the PID and PMI schemes.

Figure 5.5: Scattered waveforms of a 1.9 pm bubble in response to a 5 MHz incident pulse

(FWHM pulse duration = 1.2 cycles). Euch wavefonn is nomalzzed by the incident pressure.

Sizteen different incident pmssures (peak-to-peak) spannàng 1 to 1000 kPa were simulated.

Figure 5.6 shows that, like harmonic irnaging, both Pm and PMI produce increasing

response with respect to incident pressure. The frequency spectra of some of these waveforms

are plotted in figure 5.7. Once again, as incident amplitude is increased, second and third

harmonic cornponents appear, and ha l ly the bubble produces spectrally broadened signais,

which is the result of the unevedy spaced sharp pressure pesks seen in the Iast few c w e s of

CHAPTER 5. APDDICATTONS AlVD FUTURE PROSPECTS

Figure 5.6: Result of PID (top) and PMI (bottom). The Y-& values comspond to the

amplitude of the first (stronger) pulse. Each wauefonn is normatized by the incident pressure.

CHAPTER 5. APPLKAïTONS AND FUTURE PROSPECTS 103

figure 5.5. P D (middle panel), as expected, preserves the second harmonic component while

surpressing the linear signal at fo. However, a s m d amount of fundamental scattering (about

-18 dB fiom the 2 fo component) is observed for 10 kPa and 100 kPa incident amplitudes. This

is the resutt o fa nonlinear component of the fundamental scattering that is dependent on the

phase of the incident pulse. This nonlinear component is not predicted by the polynomical

model. PMI (bottom panel) demonstrates a lower performance at both fo and 2f0 at the

lowest amplitudes (10 kPa or less). At 100 kPa, a significant amount of scattering at JO

appears, which corresponds to the "third order nonlinearity" predicted by the polynomial

model.

An amplitude of 100 kPa corresponds to M l = 0.045, which is a relevant amplitude

for realtime perfusion imaging. At thîs amplitude, PID produces significant amount of

2 f0 signds and PMI produces dmost equal amounts of fo and 2fo signals. However, an

inspection of figure 5.7 reveals that quantitative merits of these methods will also depend

on the bandwidth of the transducer. In an attempt at a ''fair" cornparison, diEerent centre

frequencies transducers have been assumed for each methods (figure 5.8). For PID, a centre

frequency of 1.5 fo was used, and for PMI, a centre fiequency of fo was used, in both cases, a

fractional bandwidth of 50% was used. Using these assumed transducer fiequency responses,

the performance of P D and PMI can be quantitatively compared in figure 5.9. For incident

amplitudes below 300 kPa, PID outperforms PMI, however, 300 kPa ( M I = 0.13) is still a

useM amplitude for redtime perfusion imaging. Thedore, the bubble scattering model is

able to explain the comparable performance between P D and PMI.

CKAPTER 5. APPLICA2TONS AND FUTURE PROSPECTS

- 1 Power Modulation 1

"- O 0.5 1 1.5 2 2.5 3 3.5 4

Frequency I fo

Figure 5.7: &quency spedra of single pulse echoes (top), and the results of the PID (mid-

dle) and PMI (bottom) methoh. The numbers next to the m e s indzcate the peak-to-peak

incident amplitudes.

CHAPTER 5. APPLICATTONS AND FUTURE PROSPECTS

Transmitted amplitude (kPa)

Figure 5.8: Assumed jkquency response of the transducers for the cornparison of PID vs.

PMI methods.

Figure 5.9: Relative performance of PID and PMI using the frequency responses in figure

C W T E R 5. MPUCATIONS AND FUTURE PROSPECTS

5.4 Nonlinear Scattering at High Frequency

High freqency (2û-200 MHz) ultrasound h a . been applied to detect (Christopher et al. 1997)

and map (Goertz et al. 2000) blood Bow in individual vessels as small as 10 Pm. Contrast

agents c m potentialiy improve the sensitivity of these methods by enhancing the blood flow

signal relative to the surrounding tissue and noise. Using equation (1.14) and figure 1.3,

one can predict the size of bubbles that resonate at these high frequencies, for example, the

resonant diameter a t 20 MHz is 0.65 Pm. FVhile bubbles smaller than 1.0 prn can not be

sized accurately, their presence can be optically obsewed. Therefore: theoretical simulations

and acoustic experiments were performed at this frequency.

For the sake of sirnplicity, a consideration of single bubble response to 2.0 MHz and

20 MHz ultrasound pulses are compared. Generally scattering cross-section decreases a p

proximately with the bubble size, therefore it is expected that scattering foc high frequency

is weaker. However, the number density of mall bubbles is expected to be higher. Since

quantitative size distribution below 1.0 pm is not available, only an order of magnitude can

be roughly estimated by extrapolation. The size distribution of Definity follows an exponen-

tial relation from 1.0 to 15 Pm. Extrapolating this relation down to 0.65 Pm, one obtains

a number density ratio of 6.3 between 0.65 pm and 4.0 pm (the resonant size for 2.0 MHz)

bubbles. Even with the advantage of higher bubble density, the s m d bubbles are stiU Iess

efficient a t h e a r and nonlinear scattering than the 4.0 pm bubbles. However, when higher

incident amplitudes are used, comparable responses can be obtained fiom the higher fre-

quency. Figure 5.10 shows that echo responses with comparable harmonic components can

CHAPTER 5. APPL.ICA?TTnhfS AND FUTURE PROSPECTS

50 20MHz 200kPa 2 MHz 50 kPa

8 40 w

3 330 3

8 < 20

10

O

Figure 5.10: Simuloted bubble echo spectm for: 0.65 pm bubbles in 20 MHz ultrasound

pulses at 200 kPa (black) and 4.0 pm bubbles in 2 MHz ultmsound pulses ut 50 kPa (red).

The echo power/rom We smaller bubbles was increased by a factor of 6.3 to account for the

higher number density.

be obtained, albeit different acoustic conditions are required.

Nonlinear scattering at 20 MHz was measured from Definity (Dupont Phaxmaceuticals

Co., Boston, MA) in collaboration with Sarah Wong and David Goertz. A scaied-down

version of the expenmental setup shown in figure 3.1 was used. The transmitting and

receiving transducers were custom made for high resoIution mouse imaging in Dr. Stuart

Foster's laboratory. The transmitter has a peak freqency response a t 19 MHz and the receiver

has a peak frequency response at 40 MHz; both transducers have fractional bandwidths of

about 100%. Since s i p a l to noise ratio was a s i g n i b t limitation at these frequencies, the

bandwidth of the transmitted pulses wsç set be to narrower than the pulses used in Chapters

CHAPTER 5. APPLICATTONS AND FUTURE PROSPECTS 108

2,3 and 4; the fd-width-haif-maximum pulse lengt h was 5 periods (at 20 MHz). Figure 5.11

shows the averaged echo spectra fkom Definity and suspended graphite powder. The plotted

power spectra were corrected for the frequency responses of the receiving transducer and

electronics. The transmitted pressure was approlcimately 2.6 MPa, which was significantly

higher than the amplitude used in the calculation (figure 5.10). At this high amplitude,

nonlinear propagation produces a significmt arnount of harmonics, as demonstrated by the

result fkom graphite powder. Nonetheless, the nonlineax scattering is dernonstrated by a

second harmonic component that is 8.5 dB higher than the graphite powder. Even more

conspicuously, significant amount of spectral broadening was detected around 0.5, 1.5 ad 2.5

O 10 20 30 40 50 60 70 Frequency (MHz)

Figure 5.11: Averaged power spectm of 1000 echoes for Definity (solid) and gmphzte powder

(dashed). The result from graphite powder demonstrate second and thzrd harmonics (40

and 60 MHz) due to nonlineur propagation; the additional sipals at these peuh, as vell as

spectral bmodening, are due to the nonlinear scattering by the contrust bubbles.

C W m 5. APPEA'MONS ANCI FUTURE PROSPECTS 109

fo. These signds are likely associated with agent destruction as the incident amplitude was

very high. This result represents one of the fht harmoaic measurements hom ultrasound

contrast agents at such a high incident fiequency. W e the low signal-to-noise ratio is stül

a iimiting factor for imaging applications, the possibility of detecting nonlinear scattering

from contrast bubble does open the oppotunity for applications at a very fine scale.

Chapter 6

Conclusions

In this thesis, efforts to develop a purely mechanistic model for the prediction of nonlinear

scattering by microbubble contrast agents were presented. A number of models for the radial

motion of a single bubble were reviewed. A model was developed from Trilling's equation

with a number of minor modifications for applications to ultrasound contrast agents. This

single bubble model was extended to a population model employing a multiplicity of bubbles

with a realistic size distribution placed in a realistic heterogenous sound field. The inclusion

of a range of bubble diameters d o m the model to respond to a broad range of fiequency,

unlike the single bubble model. The heterogeneity of the sound field addresses the limitation

of using MI, which reflects the pressure amplitude ofonly one point in the field, for nonlinear

imaging applications.

A quantitative test of the model's prediction of nonlinear scattering was carried out.

The experiment was one of the first quantitative measurements of the h e a r (JO) and non-

h e a r (2 fo and 1.5 fo) scattering by a contrast agent to diagnostic ultrasound pulses. Exper-

imental data were collected from previously unexposed bubbles in order to avoid disruption

effects by strong incident ultasound pulses. The results confirm the generd validity of the

model, but some quantitative discrepancies were observed.

Consideration of these discrepancies and the limitations of the rnodel led to the hy-

pothesis that shell effects may play an important role in single pulse scattering. A second

ultrasound pulse was used to probe the hypothesized effects due to sheil disruption. Effects

due to the gas dissolution were isolated by using a very short time delay in the two pulse

experiment. The results demonstrated the significance of shell disruption in single pulse

scat tering.

6.2 Limitations

Severd factors still limit the potentid of the microbubble population scat tering model. Some

of these are the same ones that limit the clinical applications of other ultrasound techniques

such as tissue characterization. These generdy involve lack of accurate knowedge of attenu-

ation and aberration of the incident ultrasound beam by tissue layers. The most important

consequence of this is the uncertainty of the in vivo incident ultrasound amplitude. Another

problem is the lack of knowledge of sheU properties and bubble size distribution in vivo.

A more accurate description of acoustic disruption, bot h by t heoretical and experimental

means, is also greatly needed. These problems are actively being addressed by many workers

CHAPTER 6. CONCLUSIONS 112

in the field. One can envision that, with some answers that wiU no doubt appear in the near

future, the present theory can be extended to form a complete description of ultrasound

contrast imaging.

While the current model cannot account for the shell disruption effect, the value of

the model is in fact demonstrated by the identification and measurernent of the shell effects.

By making quantitative predictions based on known or hypothesized rnechanisms, one of the

most important values of a model is to draw attention to experimental observations that

are unexpected or incompatible with the hypothesized mechanisms. It is beüeved that the

population scattering model, which in the hture may include modifications to account for

disruption and other effects, will continue to contribute new interesting questions in the field

of contrast imaging.

6.3 Future Directions

6.3.1 Single Bubble Mode1

In chapter 4, it was established that a dimptible shell is the most important cornponent

currently missing hom the single bubble model. A nurnber of approaches have been used

in attempting to account for the shelI. The simplest approach assumes that the shell is

made of a homogeneous elastic solid that obeys Hooke's law. Assuming the radial motion to

be small (in the linear regime), the shift to the resonant frequency (see equation 1.13) was

obtained (de Jong et ai. 1992). de Jong also introduced a shelI friction factor analogous to

the viscous loss. By fitting theoretical result to experiment measurement of attenuation and

linear scatter a t 10w amplitudes, a method introduced by Medwin (ICI??), de Jong and Hoff

(1993) obtained numericd values for the stiffness and loss parameters of the shell for the

agent Aibunex. A theoretically simpler approach was taken by Hoff (Hoff 1996; Hoff et al.

1996) who replaced the two phases (gas and shell) of the bubble with a single phase with an

effective buk rnodulus. The real and imaginary parts of Hoff's effective bulk rnodulus are

related to the shell stiffness and loss parameters, respectively. Both de Jong (1994) and Hoff

(1999) went on to include shell parameters obtained by these linear methods in nonlinear

scattering caiculations using the Rayleigh mode1 (equation 1.10). Building on the heuristic

approach of de Jong, Church (1995) developed a Rayleigh-like equation that incorporatecl a

continuous layer of incompressible, solid elastic matenal as the shell. Using Miller's (1981)

weakly nodinea. approximation, Church then derived explicit fomulae for fundamental

and second h m o n i c scattering cross sections that are dependent on shell parameters. So

Far, there doesn't seem to be my theoretical or heuristic models that account For acoustic

disniption in the literature. A theoretical description of shell disniption may need to take into

account that the shells on many agents are oniy a few molecules thick. This rnay present a

substantial challenge since the mechanics of molecular films is still an active area of reseach.

Granick (1999) noted that "when the thickness of a üquid film becomes comparable to

molecdar dimensions, classicd intuition based on continuum properties no longer applies."

This means that existing shell models based on the mechanics of solids or liquids may be

M c i e n t for the description of ultrasound contrast agents.

C W T E R 6. CONCLUSIONS

6.3.2 Evolution of the Bubble Sizes In Vivo

M e r injection into the bIood stream, the microbubbles undergo a number of changes that

affect theu performance as contrast agents. There are two processes by which the microbub-

bles are cleared fkom the blood stream. Microvarcular networks (especially in the lungs)

passively iîlter the larger bubbles. In addition, depending on the chemistry of the shell ma-

terid, the immune system may remove the microbubbles from the circulating blood. Since

typically the agent is injected into a peripheral vein and scanning is performed on the sys-

temic side of the circulation systern, the fùst microbubbles to appear in the image have

passed through the pulmonary system once. Within a minute, d i the bubbles will have

made multiple passages through the lungs. With each passage, some of the larger bubbles

are filtered by the capiUaRes. Unfortunately, the size distribution of microbubbles in vivo

cannot yet be measured reliably, therefore, the effects of lung filtration axe not yet quaatified.

However, the size distribution of lung capillaxies is known and a simple numerical method

for r n o d w g the size distribution of microbubbles after the lung passage has been proposed

(Bouakaz et al. 1998). Kupffer ceUs in the Iiver sinusoids actively scavenge and phagocy-

tose the microbubbles of several agents. Within a few hours of injection, the microbubbles

are collected in the liver parenchyrna. These bubbles can still scatter ultrasound efficiently.

Since Kupffer cells are present only in normal liver parenchyrna, the absence of contrast

has been suggested as an indication of liver tumours (Forsberg et al. 1995). At present, it

is not known how phagacytosis of rnicrobubbles depends on size, sheU materials and other

properties.

Since the nodinear scattering of contrast agent is dependent on the bubbie sizes,

CXU..PTER 6. C O ~ U S I O N S 115

the lack of quantitative information of an vivo size distribution limits, to some extent, the

appücation of the population mode1 to chicai imaging. Experimental methods to detennine

the evolution of the size distribution after the injection need to be developed.

6.4 Final Remarks

The field of microbubble contrast agents has corne of age, with rapid progress still aising

in the basic physics, detection met hods and clinical applications. The study of fundamental

mechanisms of nonlinear oscillation has not yet produced a tum-key solution to design and

optimize agent detection methods. Instead, the theoretical mode1 provided useful insights

and contributed to the posing of scientSc questions and the interpretations of experimental

results. A theoretical understanding of the basic acoustic behaviour of contrast agents is

expected to play an expanding role in dtrasound contrast Maging.

Bibliography

Akulichev VA, Boguslavskii W, Ioffe -41, NaugolTnykh KA. Radiation of Bnite-amplit ude

spherical waves. Sov Phys Acoust 1968;13:281-285.

Apfel R. And there was light! Nature 1999;398:378-379.

Bleeker HJ, Shung KK, Barnhart JL. Ultrasonic characterization of Albunex, a new con-

trast agent. J Acoust Soc Am 1990;87:1792-1797.

Bouakaz A, de Jong N, Cachard C, Jouini K. On the effect of lung filtering and car-

diac pressure on the standard properties of ultrasound contrast agent. Ultrasonics

1998;36:703-708.

Brock-Fisher GA, Poland MD, Rafter PG, Mooney MG. Experimental observations of

the sensitivity and frequency response of the power modulation techaique for contrast

imaging. 5th Heart Centre European Symposium on Ultrasound Contrast Imaging

2000;5:56.

Burns PN, Hope Simpson D, Averkiou MA. Nonlinear imaging. Ultrasound Med Bi01

2000;25:S19-S22.

Burns PN, Powers JE, Hope Simpson D, Braina A, Kolin A, Chin CT, Uhlendorf V. Har-

monic power mode Doppler using rnicrobubble contrast agents: an improved method

for smaU vesse1 flow imaging. Proc IEEE Ultrasonic Symposium 1994;1547-50.

Burns PN, Powers JE, Hope Simpson D, Uhlendod V, Fritzsch T. Harmonic imaging:

principles and preliminary results. Angiology 1996;47:S63-S74.

Chang PH, Shung KK, Levene HB. Quantitative measurements of second har-monic

Doppler using ultrasound contrast agents. Ultrasound Med Biol l996;22:12OH 214.

Chapman RB, Plesset MS. Thermal effects in the free oscillation of gas bubbles. J Basic

Eng 1971;93:373-376.

Chin CT, Burns PN. Experimental verification of ensemble mode1 for scattering by

microbubble population in a contrast agent. Proc IEEE Ultrasonic Symposium

1998;1827-1830.

Chin CT, Burns PN. Predicting the acoustic response of a rnicrobubble population for

contrast imaging in medical ultrasound. Ultrasound Med Bi01 2OOO;26: 1289-1296.

Chornas JE, Sikes RA, Ferrara KW. Correlation andysis of received echoes from contrast

agents in-vitro and in-vivo. Proc IEEE Ultrasonic Symposium 1998; 1803-1806.

Christopher DA, Starkoski BG, Burns PN, Foster FS. High-hequency pulsed Doppler

uItrasound systern for detecting and mapping blood flow in the microciculation. Ultra-

sound Med Bi01 1997;23:997-1015.

Christopher T. Finite amplitude distortion-based inhomogenenous pulse echo ultrasonic

imaging. JEEE Tram Ultrason Ferroelec Freq Contr 199'7;44:125-139.

Church CC. A theoretical study of cavitation generated by an extracorporeal shock wave

lithotripter. J Acoust Soc Am 1989;86:215-227.

Church CC. The effects of an elastic soüd surface layer on the radial pulsations of gas

bubbles. J Acoust Soc Am 1995;9?1510-1521.

Cole RH. Undemater explosions. Princeton, NJ: Princeton University Press, 1948.

Dalecki D, Raeman CH, Child SZ, Cox C, Francis CW, Meltzer RS, Carstensen EL. Hemol-

ysis in vivo from exposure t O puised ultrasound. Ultrasound bled Bi01 1997;23:307-313.

Dayton PA, Morgan KE, Klibanov AL, Brandenburger GH, Ferrara KPV. Optical and

acousticd obsenmtions of the effects of ultrasound on contrast agents. IEEE Tram

Ultrason Ferroelec Freq Contr 1999;46:220-232.

de Jong N, Cornet R, Lancee CT. Higher haxmonics of vibrating gas Mled microspheres.

part one: simulations. Ultrasonin 1994;32:447-453.

de Jong N, Hoff L. Ultrasound scattering properties of Albunex microspheres. Ultrasonics

1993;31:175-181.

de Jong N, Hoff L, Skotland T, Born N. Absorption and scatter of encapsulated gas

Wed rnicrospheres: theoretical considerations and some measurements. Ultrasonics

1992;30:95-103.

Devin Jr C. Survey of thermal, radiation, and viscous damping of pdsating air bubbles

in water. J Acoust Soc Am i959;31:1654-1667.

Eatock BC, Nishi RY. Numerical studies of the spectrum of low-intensity ultrasound

scattered by bubbles. J Acoust Soc Am 1985;77:1692-1701.

EUer AI. Damping constants of pulsating bubbles. J Acoust Soc Am 1970;47:1469-70.

Epstein PS, Plesset MS. On the stability of gas bubbles in liquid-gas solutions. J Chem

Phys l95O;lB: 1505-9.

Feinstein SB, Cheirif J, Ten Cate FJ, Silverman PR, Heidenreich PA, Dick C, Desir

RM, Armstrong WF, Quinones MA, Shah PM. Safety and efficacy of a new transpul-

monary ultrasound contrast agent: initial muhicenter ciinicd results. J .Am Coli Car-

diol 1990;16:316-324.

Flynn HG. Physin of acoustic cavitation in liquids. Physical acoustics: principles and

methods 1964;1:57-172.

Forsberg F, Liu JB, Merton DA, Rawool NM, Goldberg BB. Parenchpal enhancement

and turnor visualization using a new sonographic contrast agent. J Ultrasound Med

1995;14:949-957.

Frinking PJA, de Jong N, Cespedes EI. Scattering properties of encapsulated gas bubbles

at high ultrasound pressures. J Acoust Soc Am N99; l05:523-533.

Gaitan DF, C m LA, Church CC, Roy RA. Sonoluminescence and bubble dynamics for

a single, stable, cavitation bubble. J Acoust Soc Am 1992;91:31663183.

Gilmore FR. The growth or collapse of a spherical bubble in a viscous compressible üq-

uid. Technical Report No. 26-4, Hydrodynamics Lab, California Institute Technology,

Pasadena, CA, USA, 1952.

Goertz DE, Christopher DA, Yu JL, Kerbel RS, Burns PN, Foster FS. High-freguency

color Bow imaging of the microcicdation. Ultrasound Med Bi01 2000;26:63-71.

Gramiak R, Shah PM. Echocardiography of the aortic root. Invest Radiol1968;3:356-366.

Granick S. SoR matter in a tight spot. Phys Today 1999;52:2&31.

Hamilton MF, Blackstock DT. Nonlinear acoustics. San Diego: Acadernic Press, 1997.

Hening C. Theory of the pulsations of the gas bubble produced by an underwater explo-

sion. Technical Report No. 236, Office of Scientific Research and Developrnent, USA,

1941.

Hickling R, Plesset MS. Collapse and rebound of a spherical bubble in water. Physics of

Fluids 1964;7:7-14.

Hilgenfeldt S, Grosçmann S, Lohse D. A simple explanatioo of light emission in sonolumi-

nescence. Nature 1999;398:402-405.

Hoff L. Acoustic properties of ultrasonic contrast agents. Ultrasonics 1996;34:591-393.

Hoff L, Johansen TF. Nonlinear scatter from sonazoid. Proc IEEE Ultrasonic Symposium

1999;2:1681-1684.

Hoff L, Sontum PC. Acoustic characterisation of Nycomed's NClOOlOO contrast agent.

Proc IEEE Ultrasonic Symposium 1998;179%1802.

Hoff L, Sontum PC, Hoff B. Acoustic properties of shell-encapsulated, gas-filled ultrasonic

contrast agents. h o c IEEE Ultrasonic Symposium 1996;2:144l-1444.

Hope Simpson D, Chin CT, Burns PN. Pulse inversion Doppler: a new method for detect-

ing nonlinex echoes from mirrobubble contrast agents. IEEE Trans Ultrason Ferroelec

Freq Contr l999;46:372-382.

Jiang P, Mao 2, Lazenby JC. A new tissue h m o n i c imaging scheme with better funda-

mental frequency cancellation and higher signal-to-noise ratio. Proc IEEE Ultrasonic

Symposium 1998;1589-1594.

Kamath V, Prosperetti A, EgoNopoulos FN. A theoreticai study of sonoluminescence. J

Acoust Soc Am 1993;94:248-260.

Keller JB, Miksis M. Bubble oscillations of large amplitude. J Acoust Soc Am 1980;68:62&

633.

Knapp RT, Daily JW, Hammitt FG. Cavitation. McGraw-Hill, New York 1970;chap 4.

Krishna PD, Newhouse VL. Second harmonic characteristics of the ultrasound contrast

agents Albunex and FS069. Ultrasound Med Bi01 1997;23:453-459.

Kroft LJM, de Roos A. Blood pool contrast agents for cardiovascular MR imaging. J Magn

Reson Imaging 1999;10:395-403.

Leighton TM. Acoustic Bubble. New York: hcademic Press, 1997.

Linka AZ, Sklenar J, Wei Ky Jayaweera .AR., Skyba DM, Kaul S. Assessrnent of transmu-

rai distribution of myocardial perfusion wit h contrast echocardiography. Circulation

1998;98:1912-1920.

kfaxhesco N, Trillat JJ. Action des ultrasons sur les plaques photographiques. C R Acad

Sci 1933;196:85&860.

Marsh JN, Hughes MS, Brandenburger GH, Levene H, Miller JG. Frequency and con-

centration dependence of the backscatter coefficient of the uftrasound contrast agent

albunex. J Acoust Soc Am 1988;104:1654-1666.

BIBLrOGWHY 122

Matula TJ, C m LA. Evidence for gas exchange in single-bubble sonoluminescence. Phys

Rev Lett 1998;80:865-868.

Medwin H. Counting bubbles acousticaIIy: a review. Ultrasonics 1977; l5:?-13.

Miller DL. Ultrasonic detection of resonant cavitation bubbles in a flow tube by their

second-harmonic emissions. Ultrasonics 1981; l9:21?-224.

MilIer DL, Thomas WI. Contrast-agent gas bodies enhance hemolysis induced by

lithotripter shock waves and high-intensity focused ultrasound in whole blood. U1-

trasound Med Bi01 1996;22:1089-1095.

Miller DL, Williams AR, Gross DR. Chamctenation of cavitation in a flow-through ex-

posure chamber by means of a resonant bubble detector. Ultrasonics 1984;22:224-230.

Minnaert M. On musical air-bubbles and the sounds of nuinhg water. Phi1 Mag 1933;S7

V16:235-248.

Mo LYL, Cobbold RSC 1992;Theoretical rnodels of ultrasonic scat tering in blood. In K. K.

Shung and G. A. Thieme (Eds.), UZtrasonic scattering in biologzcal tissues, pp. 125-170.

CRC Press.

Morgan KE, Dayton PA, Kruse DE, Klibanov AL, Brandenburger GH, Ferraxa U V .

Changes in the echoes bom dtrasonic contrast agents with imaging parameters. IEEE

Trans Ultrason Ferroelec Freq Contr 1998;45:1537-1548.

Nanda NC, Carstemen EL. Echo-enhanhg agents: safetyi Advances in Echo Imaging

using Contrast Enhancement 1997;2.

Neppïras EA. Acoustic cavitation. Phys Rep 1980;61:15%251.

NOAA. Diving Manual. USA, Dept. of Commerce: National Oceanic and Atmospheric

Anminstration, 1990.

Ophir J, Parker KJ. Contrast agents in diagnostic ultrasound. Ultrasound Med Bi01

1989; l5:319-333.

Plesset MS. The dynamics of cavitation bubbles. J Appl Mech 1949;16:277-282.

Poritsky H. The collapse or growth of a spherical bubble or cavity in a viscous fluid. Proc

First US Nat Congres on Appl Phys 1951;1:813-821.

Porter TR, Xie F. Visually discernable myocardid echocardiographic contrast after intra-

venous injection of sonicated dextrose aibumin rnicrobubbles containhg high molecdar

weight, l e s soluble gaese. J Am Coll Cardiol 1995;25:509-515.

Porter TR, Xie F, Kncsfeld D, Ambruster RW. Improved myocardid contrast with sec-

ond h m o n i c transient ultrasound response imaging in humans using intravenous

perfluorocarban-exposed sonicated dextrose albumin. J Am Coll Cardiol l996;2?: 1497-

1501.

Prince MR, Anzai Y, Neimatallah M, Dong Q, Rubin JM. MFtA contrast bolus timing

with ultrasound bubbles. J Magn Reson Imaging 1999;10:389-394.

Prosperetti A. Thermal behaviour of oscillating gas bubbles. J Fluid Mech 1991;223:587-

616.

Rayleigh JW. On the pressure developed in a liquid during the collapse of a spherical

cavity. Phil Mag 1917;S6:94-98.

Shima A. The natural fkequency of a bubble oscillating in a viscous compressible liquid.

J Basic Eng 1970;92:555-62.

Slcyba DM, Camarano G, Goodman NC, Price RJ, Skalak TC, Kaul S. Hemodynamic

characteristics, myocardial kinetics and microvascular rheology of FS069, a second-

generation echocardiographic contrast agent capable of producing myocardial opacifi-

cation fiom a venous injection. J Am Coll Cardiol L996;28:1292-1300.

Skyba DM, Price RJ, Linka AZ, Skalak TC, Kaul S. Direct in vivo visualization of in-

travascular destruction of microbubbles by ultrasound and its local effects on tissue.

Circulation 1998;98:290-293.

Takeuchi Y. Pulsed stroboscopie visualizer to synchronously monitor the microballon un-

der insordication. Proc IEEE Ultrasonic Symposium 1998; 1645-16.19.

Tiemann K, Lohmeier S, Kuntz S, Koster J, Pohl C, Burns PN, Porter SR, Nanda NC,

Luderitz B, Becher H. Real-time contrast echo assessrnent of myocardial pemision at

low ernission power. Echocardiography 1999; I6:'i'99-809.

Tranquart F, Grenier N, Eder V, Pourcelot L. Clinicd use of ultrasound tissue harmonic

irnaging - evduation of image qudity compared with conventional sooography. Ultra-

sound Med Bi01 1999;25:889-894.

Trilling L. Collapse and rebond of a gas bubble. J Appl Phys 1952;23:14-17.

UhIendod V, Hoffmann C. Nonfinear aconstical response of coated microbubbles in diag-

nostic ultrasound. Proc. IEEE Ultrasonic Symposium 1994;1559-1562.

Urnemura S, Kawabata K, Sasaki K. Enhancement of sonodynamic tissue damage produc-

tion by second-harmonic superimposition: theoretical analysis of its mechanism. IEEE

sans Ultrason Ferroelec Freq Contr 1996;43:1054-1062.

Vokurka K. Cornparison of Rayleigh's, Herring's and Gilmore's models for gas bubbles.

Acustica 1986;59:214-219.

Ward B, Baker AC, Humphrey VF. Nonlinear propagation applied to the improvement of

resolution in diagnostic medical ultrasound. J Acoust Soc Am 1997; lOl:143-154.

Wilson SR, Burns PNy Muradali D, Wilson JA, Lai X. Harmonic hepatic us with mi-

crobubble contrast agent: Initial experience showing improved characterization of he-

mangioma, hepatoceilular carcinoma, and met astasis. Radiology 2000;215:153-16 1.

Wojcik Gy Modd J, Ayter S, Carcione L. .4 study of second hannonic generation by

focused medical transducer pulses. Proc IEEE Ultrasonic Symposium 1998;1583-1588.