Acoustic characterization of monodisperse lipid-coatedmicrobubbles: Relationship between size and shell viscoelasticproperties

Miguel A. Parrales,a) Juan M. Fernandez, and Miguel Perez-SaboridAerospace Engineering and Fluid Mechanics Department, University of Seville,Camino de los Descubrimientos s/n, 41092 Sevilla, Spain

Jonathan A. Kopechek and Tyrone M. PorterMechanical Engineering Department, Boston University, 110 Cummington Street, Boston,Massachusetts 02215

(Received 24 October 2013; revised 9 May 2014; accepted 7 July 2014)

The acoustic attenuation spectrum of lipid-coated microbubble suspensions was measured in order

to characterize the linear acoustic behavior of ultrasound contrast agents. For that purpose, micro-

bubbles samples were generated with a very narrow size distribution by using microfluidics techni-

ques. A performance as good as optical characterization techniques of single microbubbles was

achieved using this method. Compared to polydispersions (i.e., contrast agents used clinically),

monodisperse contrast agents have a narrower attenuation spectrum, which presents a maximum

peak at a frequency value corresponding to the average single bubble resonance frequency. The

low polydispersity index of the samples made the estimation of the lipid viscoelastic properties

more accurate since, as previously reported, the shell linear parameters may change with the equi-

librium bubble radius. The results showed the great advantage of dealing with monodisperse popu-

lations rather than polydisperse populations for the acoustic characterization of ultrasound contrast

agents. VC 2014 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4890643]

PACS number(s): 43.35.Bf, 43.35.Yb, 43.80.Qf, 43.20.Fn [TGL] Pages: 1077–1084

I. INTRODUCTION

Ultrasound contrast agents are gas-filled microbubbles,

which are injected into the blood pool in order to increase

the blood echogenicity for ultrasound imaging applica-

tions.1–3 These contrast agents also have a great potential

use for drug and gene delivery for treating different dis-

eases.4–6 Due to their compressibility, the microbubbles per-

form volumetric oscillations, giving rise to a strong resonant

echo when driven by an ultrasound field with a specific fre-

quency. Consequently, they scatter more energy than rigid

particles of the same size, or even larger liquid-filled par-

ticles (red blood cells, for instance).7–9 Traditional methods

for contrast microbubbles generation (agitation, sonication)

produce very polydisperse suspensions, whose acoustic

response is difficult to optimize. Effectively, the size of each

microbubble plays a crucial role since resonance is only

reached when it precisely matches the operating frequency

of the ultrasound equipment. Nevertheless, these production

techniques are widely used in clinical applications due to the

simplicity and the high production ratio.10

Contrast microbubbles for medical applications are

commonly coated by phospholipid shells to prevent a rapid

dissolution of the gas core.5 This kind of shell also alters the

frequency response of the microbubble to acoustic excita-

tion. The stiffness of the shell leads to an increase in the

microbubble resonance frequency while the shell viscosity

increases attenuation, due to the phospholipid viscous

dissipation during the oscillatory motion of the coated bub-

ble.11,12 The performance of lipid-coated microbubbles as

ultrasound contrast agents strongly depends on the shell

viscoelastic behavior; consequently, considerable effort has

been invested in estimating these properties. Estimates of the

viscoelastic properties are based on two different techniques:

acoustic attenuation measurements of microbubbles suspen-

sions13,14 and optical measurements of the oscillatory motion

of single microbubbles.15,16 While optical methods are more

accurate and sophisticated, they need a considerable invest-

ment in instruments such as ultra-high-speed cameras or

lasers. In contrast, acoustic methods use basic ultrasonic

equipment and are able to provide a direct measurement of

the more relevant physical quantities.

It is important to note that the measured attenuation

spectrum is influenced heavily by the microbubble size dis-

tribution. In fact, it has been shown that larger microbubbles

tend to be the primary source of attenuation in polydisper-

sions, thus complicating the analysis of the measurements

and the estimation of the shell properties.17,18 An inability to

control the microbubble size distribution accurately can

result in inaccurate estimates of the shell viscoelastic param-

eters (elasticity and viscosity). Therefore, in order to get a

novel generation of monodisperse contrast agents, it is essen-

tial to achieve both ultrasound echo optimization in medical

applications as well as the simple and accurate determination

of the lipid-shell mechanical behavior with acoustic charac-

terization methods. To address these needs, researchers

began using microfluidic devices to produce monodisperse

lipid-coated microbubbles.19,20 Unlike polydisperse micro-

bubble suspensions, monodispersions allow one to measure

a)Author to whom correspondence should be addressed. Electronic mail:

mparrales@us.es

J. Acoust. Soc. Am. 136 (3), September 2014 VC 2014 Acoustical Society of America 10770001-4966/2014/136(3)/1077/8/$30.00

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attenuation as a function of mean microbubble diameter and

to more accurately estimate the shell viscoelastic

properties.21

In this article, we present an experimental procedure to

estimate the viscoelastic properties of lipid-coated microbub-

bles. The theoretical background for these estimations is

based on the linearized Rayleigh–Plesset equation modified

with the Marmottant model11 to account for the shell rheol-

ogy. Consequently, in order to assure accurate measurements,

we generated monodisperse samples of microbubbles and

acquired the acoustic attenuation for different equilibrium ra-

dius, thus avoiding the difficulties when using polydisperse

contrast agents. We found that the linear viscoelastic parame-

ters vary with the equilibrium radius, which is effectively

observed in single coated bubble characterization with optical

methods15 and light scattering.16 These results finally provide

us with confirmation of the accuracy and reliability of our ex-

perimental method, which may stimulate great interest for

broadening further investigations in the field of the rheology

of membranes.

II. THEORY

An isolated gas-filled microbubble with radius Ro at

rest, is immersed in an infinite liquid medium, with density

q1 and viscosity lL, under a hydrostatic pressure p1. An

acoustic perturbation pa with a characteristic wavelength

k� Ro, will make the bubble oscillate radially and symmet-

rically. The equations of motion describing the radial oscilla-

tions of a coated microbubble, and the acoustic scattering

and absorption properties of both a single bubble and a

microbubble suspension, is described in this section. We

applied the incompressible fluid motion equations over the

oscillating bubble, and balanced the inertial forces of the

moving boundary with the pressure difference in the sur-

rounding liquid medium, leading to the well-known

Rayleigh–Plesset equation,9,22

RR::

þ 3

2_R

2 ¼ 1

q1pL � pa � p1ð Þ; (1)

where pL stands for the liquid pressure just outside the bubble.

This term can be related with the gas pressure inside the bub-

ble pg by setting the normal stress balance across the bound-

ary, pL ¼ pg � 2r=R� 4lE_R=R, where pg ¼ pg0ðR=RoÞ�3j

,

where pg0 is the gas pressure at rest and r is the surface ten-

sion. In this last expression, a polytropic gas behavior, with a

coefficient j, has been assumed, and the total losses

have been modeled by using a linear effective viscosity

lE ¼ ðlL þ lac þ lthÞ, which takes into account the three

main damping mechanisms during the oscillations: viscous

dissipation, acoustic reradiation, and heat transfer.23–25

Thex acoustic and thermal viscosities have been defined as

lac ¼ q1x2oR3

o=4c1 and lth ¼ �pg0ImU=4xo, respectively,

where xo is the characteristic oscillation frequency and c1 is

the sound speed in the liquid. We found that both the poly-

tropic coefficient, defined as j ¼ ReU=3, and the thermal vis-

cosity were related to a complex function U, which can be

written as25

U ¼ 3c

1� 3 c� 1ð ÞiPe

ffiffiffiffiffiffiffiiPep

cotffiffiffiffiffiffiffiiPep

� 1� � ; (2)

where c is the adiabatic coefficient and Pe ¼ xoR2o=Dg is the

Peclet number, with Dg the gas thermal diffusivity.

The effects of the coating on the microbubble dynamics

can be modeled according to Marmottant et al.11 formula-

tion. Assuming that the shell is represented by a thin lipid

monolayer with viscoelastic properties, the pressure differ-

ence across the bubble wall can now be written as

pL ¼ pg � 2rðRÞ=R� 4lE_R=Rþ 4js

_R=R2; (3)

where js is the shell surface viscosity and rðRÞ represents the

radius-dependent surface tension coefficient, which can

be linearized by rðRÞ ’ 2vðR=Ro � 1Þ in the elastic

regime, where v is the shell elastic modulus.11,12 The

Rayleigh–Plesset equation can be linearized assuming small

oscillations around the equilibrium radius, Ro. Therefore, con-

sidering R ’ Roð1þ XÞ with jXj � 1, the linear microbubble

radial dynamics equation yields24,25

X::

þ 2d _X þ x2nX ¼ � pa

q1R2o

; (4)

where d ¼ ð2lE=q1R2o þ 2js=q1R3

oÞ is the damping factor

and xn is the bubble natural frequency, defined by

x2n ¼

3jp1q1R2

o

þ 4vq1R3

o

: (5)

The differential equation for the radial dynamics shows that

the coated microbubble behaves as a damped harmonic os-

cillator, which reaches the maximum amplitude response

when driven at xn. If we compare Eq. (4) with the equation

of motion for a free microbubble, we observe that the lipid

coating adds an additional viscous damping term.

Additionally, lipid-coated microbubbles have a higher natu-

ral frequency due to the stiffness of the lipid shell.12

The oscillating bubble behaves as a monopolar acoustic

source and reradiates acoustic energy from the excitation

pulse.9 The radiated acoustic pressure at a distance rfrom the linearly oscillating bubble can be written as

ps ¼ q1R3oX::

ðsÞ=r, where s ¼ ðt� r=c1Þ is the retarded

time. Assuming time-harmonic acoustic excitations and oscil-

lations of the form X ¼ X̂ expð�ixotÞ, we can finally write

p̂s ¼p̂aRo

xn=xoð Þ2 � 1� iC

eikr

r¼ p̂afs

eikr

r; (6)

where k ¼ xo=c1 is the wavenumber, fs is the omnidirec-

tional scattering function, and C ¼ 2d=xo stands for the total

damping dimensionless coefficient. Therefore, in relation

with the oscillatory response, the sound scattered by the bub-

ble reaches a relative maximum at the natural frequency.9,13

The ratio of the total acoustic power scattered to the

external acoustic intensity is given by the scattering cross

section

1078 J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014 Parrales et al.: Viscoelastic properties of coated bubbles

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rs ¼ð

Xjfsj2dX ¼ 4pjfsj2; (7)

where dX is a solid angle element. This parameter measures

the efficiency of the microbubble as a sound scatterer.9 The

absorption cross section ra is defined as the ratio of the

absorbed acoustic power (due to viscous and thermal losses) to

the incident intensity,13 and it is given by ra ¼ ðC=Cac � 1Þrs,

where Cac ¼ 4lac=q1xoR2o. Finally, the total acoustic power

removed by the bubble is obtained by using the extinction cross

section, defined as

re ¼ rs þ ra ¼ ðC=CacÞrs: (8)

This last parameter is related to the attenuation properties of

a bubbly medium as we will show.13

Let us now assume a dilute microbubble homogeneous

suspension at a relatively low concentration n (bubbles per

cubic meter), so that multiple scattering can be ignored. The

size distribution of the bubble population is given by the

probability density function f ðRoÞ. The reduction in the

acoustic intensity over a distance dz through the suspension

is given by dIðzÞ ¼ �aIðzÞdz, where a is the attenuation

coefficient.13 By linear superposition, the attenuation coeffi-

cient is written in terms of the extinction cross section as

a ¼ð1

0

nref ðRoÞdRo: (9)

Note that, if the microbubble suspension were monodisperse,

this parameter would be just a ¼ nre. In this case, the maxi-

mum value of the attenuation is reached at the natural fre-

quency of the bubbles xn. Experimentally, the attenuation

coefficient of each sample is obtained by comparison with a

reference acoustic intensity measurement Iref associated to a

bubble-free medium.14,21,26 More details about the experi-

mental characterization and attenuation measurements are

given in Sec. III.

III. EXPERIMENTS

A. Monodisperse microbubble generation

The production of monodisperse contrast microbubbles

can be achieved by using microfluidics techniques. In our case,

we have manufactured two different polydimethylsiloxane-

(PDMS-) based microdevices via soft-lithography methods.

The microchannel geometry of each microdevice was designed

to operate them under two different microbubble generation

regimes, flow-focusing27–29 and co-flow.30 Once all the micro-

channels were fabricated in the PDMS device, it was then oxy-

gen plasma treated and bonded to a glass slide. An inverted

microscope was used to monitor microbubble production

(Fig. 1).

For microbubble production via flow-focusing, microflui-

dic devices were fabricated based upon the design published

by Hettiarachchi et al.19 To generate contrast microbubbles, a

lipid solution and octafluoropropane were pushed through their

respective microchannels. The lipid solution consisted of a

mixture of dipalmitoylphosphatidylcholine, dipalmitoylphos-

phatidic acid, and N–(carbonyl-methoxypolyethyleneglycol

2000)–1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine in a

81:8:10 molar ratio. The flow rate (�0:3 ml/h) of the lipid

solution was controlled with a syringe pump (KDS100,

Fisher Scientific), while the octafluoropropane gas flow was

controlled with a pressure regulator (�1:4 bar). By maintain-

ing the liquid flow rate and gas pressure constant, we pro-

duced microbubble suspensions with a very narrow size

distribution.21 For microbubble production via co-flow,

microfluidic devices were fabricated based upon the design

published by Castro-Hernandez et al.30 In this case, we used

the same lipid solution and air instead of octafluoropropane.

The gas and liquid flow rates were controlled via two inde-

pendent pressure regulators, so that the resulting operating

pressures were between 2.30 and 2.50 bar. Compared with

the flow-focusing devices, co-flow devices required a higher

gas pressure for microbubble production but had a signifi-

cantly higher rate of production (see Fig. 2). In order to col-

lect the resulting coated microbubbles for size measurements

and acoustic characterization, a pipette tip was inserted into

the outlet hole of the microdevice. The resulting suspension

was then removed from the tip successively by a syringe with

a hypodermic needle. An inverted Nikon microscope was

used both to monitor the microbubble production and capture

micrographs of the suspension. The size distribution of each

batch was finally measured using a Coulter counter (Z2,

Beckman Coulter, Inc.) or laser diffraction (LA-950, Horiba

Scientific). In order to compare the experimental acoustic

FIG. 1. (Color online) Microfluidic ex-

perimental setup for generating mono-

disperse lipid-coated microbubbles.

J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014 Parrales et al.: Viscoelastic properties of coated bubbles 1079

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characterization with the theoretical prediction for the

attenuation in a contrast microbubble suspension, the meas-

ured size distribution was fitted by a Weibull density function

(Fig. 3),

f Roð Þ ¼lK�Ro

lRo= �Ro

� �K�1exp � lRo= �Ro

� �Kh i

; (10)

where �Ro is the microbubble mean radius and l is a shape

parameter defined by l ¼ ½ðK � 1Þ=K�1=K.

We controlled the mean size of contrast microbubbles

precisely by adjusting the gas pressure and liquid flow rate.

Moreover, the periodic and stable generation of lipid-coated

microbubbles with these two microfluidic devices avoids the

non-uniform distribution of lipids covering the bubbles, as

reported in previous studies using agents generated via agita-

tion/sonication.31,32

B. Acoustic characterization

The experimental setup for measuring frequency-

dependent attenuation for suspended monodisperse lipid-

coated microbubbles is shown in Fig. 4. Monodispersions

were dispensed into a sample holder made of polymethylme-

thacrylate plastic. The sample holder had acoustic windows

consisting of a 4 mm depth chamber, which were covered by

two Mylar (polyethylene terephthalate plastic) sheets of

12 lm thickness each. The sample holder was submerged in a

tank of deionized water and positioned just in front of a stain-

less steel reflector, which was located at the transducer focal

region. Attenuation measurements were made with a

2.25 MHz transducer (Panametrics, USA) and a 1 MHz trans-

ducer (Met-flow, Switzerland), operating independent of each

other. The 2.25 MHz transducer was excited by a pulser/

receiver (5072PR, Panametrics, USA), emitting an acoustic

pulse that traveled through the sample chamber, reflected off

the steel surface, and returned to the transducer active surface.

The received reflections were amplified by the pulser/receiver

and digitized with a digital oscilloscope (Wavesurfer 64XS,

LeCroy, USA) before being saved on a desktop computer for

frequency analysis using MATLAB software (The MathWorks,

Inc., MA, USA).21,26 The 1 MHz transducer was excited by a

one-cycle square wave (65% duty cycle) generated by an arbi-

trary waveform generator (3390, Keithley Instruments). In

this case, we removed the steel reflector and placed a needle

hydrophone (100-100-1, M€uller) behind the sample holder in

order to receive the transmitted acoustic signal after propagat-

ing through the microbubble suspension. The signal was

amplified (MVA-10, M€uller), digitalized, and saved on the

desktop computer for analysis.

As a preliminary stage, the transducer reference signal

needed to be acquired and saved. The reference acoustic

transmission spectrum Iref , measured using a free-bubble

sample, is shown in the Fig. 5 for the 1 MHz transducer.

FIG. 2. Generation of contrast micro-

bubbles. (a) Flow-focusing microde-

vice (�103 lbubbles/s). (b) Co-flow

microdevice (�105 lbubbles/s). (c)

Micrograph of a monodisperse sample

with a mean bubble size of approxi-

mately 12 lm.

FIG. 3. (Color online) Microbubble size distribution measured with a

Coulter counter, fitted by a Weibull distribution with K ¼ 6:8 and �Ro

’ 2:85 lm.

FIG. 4. (Color online) Acoustic experimental setup for measuring the acous-

tic attenuation of contrast microbubble suspensions.

1080 J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014 Parrales et al.: Viscoelastic properties of coated bubbles

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Effectively, we observe that the maximum intensity gain

was reached at the transducer center frequency. When a con-

trast microbubble sample was used instead, the measured

transmission Isample changed due to the frequency dependent

properties of bubble scattering and absorption. As we can

check in Fig. 5, a remarkable narrow transmission band-gap

appears in consequence. Thus, by using dI ¼ �aIðzÞdz, we

finally write the attenuation coefficient of each sample as

a ¼ 1

lln

Iref

Isample

� �; (11)

where l is the total path traveled by the acoustic wave

through the suspension.

IV. RESULTS AND DISCUSSION

Using the flow-focusing microfluidic device, we have

generated different batches of narrowly distributed lipid-

coated microbubbles, with a mean diameter of 5:960:2 lm,

as shown in Fig. 3. In Fig. 6, we show the attenuation

coefficient measurements for the monodisperse suspension

while excited by the 2.25 MHz transducer. The attenuation

spectrum had a maximum peak for a frequency value corre-

sponding to the average single bubble natural frequency,

Eq. (5). The measured spectrum was remarkably narrow

around the resonance peak, due to the quasi-monodisperse

size distribution. In contrast, when a polydisperse sample

(generated by agitation techniques and using the same gas

and lipid solution) was used instead, as shown in Fig. 7, the

measured attenuation had a much broader spectrum. These

results were in good agreement with previously published

measurements.18,21

As observed, the frequency-dependent attenuation meas-

ured for monodispersions was proportional to the microbubble

concentration n. This scaling is only valid for low concentra-

tion suspensions where multiple scattering between the bub-

bles can be neglected.14 In the concentration range used for

our study, we used the single scattering theoretical approach

(Sec. II) to get the total acoustic energy removed from the

propagating wave by the microbubbles: the attenuation coeffi-

cient within the sample is proportional to the sum of the

extinction cross section for all the bubbles. As we have

shown, the extinction depends on the microbubble radius, ex-

citation frequency, and, finally, on the viscoelastic properties

of the lipid shell, i.e., reðRo; xo; v; jsÞ. It is very difficult to

measure the shell elasticity and viscosity directly; alterna-

tively, these properties are estimated by fitting the attenuation

measurements using a single scattering approach.6–8,13,33

Knowing the size distribution of our monodisperse samples,

we successfully fitted the attenuation theoretical curves to the

measured attenuation spectra by setting the shell elastic mod-

ulus to v ¼ 0:28 N/m and the shell surface viscosity to js

¼ 3� 10�8 kg/s, as shown in Fig. 6. These values were in a

very good agreement with those obtained by previous experi-

mental studies for lipid-coated microbubbles,15,16,34,35 thus

showing the consistency and reliability of the method that we

propose. As expected, for the polydisperse samples, the diffi-

culty in identifying both the main resonance frequency peak

FIG. 5. Acoustic transmission power spectrum for the reference signal, and

the measured one for the microbubble monodisperse sample.

FIG. 6. (Color online) Attenuation coefficient in a monodisperse sample at

different concentrations n (�103 microbubbles/ml). �: n ¼ 1:4, �: n ¼ 3:5,

�: n ¼ 5:3, and þ: n ¼ 6:5. Solid lines represent the theoretical fitted

curves. The resulting phospholipid shell parameters were: elastic modulus

v ¼ 0:28 N/m and surface viscosity js ¼ 3� 10�8 kg/s. The inset corre-

sponds to a micrograph of the monodisperse coated microbubble

suspension.

FIG. 7. Attenuation coefficient in a polydisperse sample at different concen-

trations n (�105 microbubbles/ml). �: n ¼ 1:2, �: n ¼ 2:2, �: n ¼ 3:1, and

þ: n ¼ 4:5. The inset corresponds to a micrograph of the polydisperse

coated microbubble suspension.

J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014 Parrales et al.: Viscoelastic properties of coated bubbles 1081

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and the bandwidth associated with damping mechanisms

(Fig. 7) lead to a very high uncertainty range for the shell

parameters.21 In contrast, great accuracy can be achieved

when dealing with monodisperse samples.

It has been hypothesized recently that the viscoelasticity

of the lipid shell may not be linear, which may be reflected

by a dependence of the shell viscoelastic properties on the

microbubble size.36 To test this hypothesis with our experi-

mental method, we measured the acoustic attenuation of

monodisperse samples with different mean radius, generated

via the co-flow configuration.30 For that purpose, we excited

the samples with the 1 MHz transducer and acquired the

transmitted signal directly using the needle hydrophone. The

fitted results for the different suspensions are shown in

Fig. 8. As observed, the main resonance peak identified in

the attenuation spectrum was inversely related with micro-

bubble size. The viscoelastic properties estimated for each

sample as a function of microbubble radius are reported in

Table I. We observe in Fig. 9 that the elastic modulus and

the surface viscosity increase linearly as the equilibrium size

of the coated microbubble becomes bigger. This result is

consistent with the experimental trend found in previous

studies via optical characterization.15,16,36 These measure-

ments also confirmed that the lipid-shell behaves

non-linearly except when the bubbles oscillate with small

amplitudes. Effectively, for �Ro ¼ 4 lm, an oscillation ampli-

tude of jXj � 1% only implies Dv=vo � 0:2% and Djs=jso

� 0:1%. Our observations emphasize the need to develop

new constitutive relations to take into account this non-

linear behavior. Moreover, the non-linear correction for the

shell viscoelastic model explains theoretically the compres-sion-only behavior observed when lipid-coated microbub-

bles oscillate with large amplitudes.11,36

FIG. 8. (Color online) Attenuation coefficient for different monodisperse samples with increasing values of the mean microbubble radius. (a) �Ro ¼ 3:7 lm,

(b) �Ro ¼ 4:8 lm, (c) �Ro ¼ 5:5 lm, (d) �Ro ¼ 6:3 lm.

TABLE I. Results obtained for the acoustic characterization and lipid-shell

properties estimations using monodisperse contrast agents.

�Ro (lm) fn (MHz) v (N/m) js (�10�8 kg/s)

2.9 1.37 0.28 3.0

3.7 1.14 0.35 3.6

4.8 0.84 0.50 4.2

5.5 0.78 0.76 5.4

6.3 0.70 0.85 6.0

1082 J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014 Parrales et al.: Viscoelastic properties of coated bubbles

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V. CONCLUSIONS

In this study, we have measured the attenuation in

monodisperse microbubble suspensions over a frequency

range that includes the resonance frequency of the bubbles.

The results reported in this experimental work show the

great advantage of using monodisperse lipid-coated micro-

bubbles rather than polydisperse ones for the acoustic char-

acterization of ultrasound contrast agents. We show that the

acoustic attenuation for lipid-coated monodisperse samples

is characterized by a very narrowband spectrum around the

natural frequency of the bubbles. Furthermore, the attenua-

tion measurements of such a suspension provide an accurate

estimation of the lipid-shell viscoelastic parameters by fitting

the theoretical model to the experimental curves.

First methods for obtaining the shell properties were based

on acoustic attenuation measurements of polydisperse sam-

ples,7,13,14 which are characterized by a very simple instrumen-

tation. More recently, the coating parameters have usually

been estimated from optical characterization of single bub-

bles,15,16,35,36 which avoid the uncertainty related to polydis-

persity. Here, we take advantage of previous methods by

combining the simplicity of acoustic attenuation measurements

and the accuracy of working with monodisperse suspensions.

The values obtained for the elasticity and the viscosity

of the shell were in good agreement with the reported values

in the literature.15,16,36 This confirms the reliability of the

present experimental methodology, which is able to get as

much accuracy as the optical characterization techniques.

The dependence that we observe for the viscoelastic proper-

ties with the equilibrium radius of the bubbles emphasize

that the coating shell behaves non-linearly for moderated

oscillations. This result may lead to the development of new

constitutive laws for lipid-membrane rheology.

ACKNOWLEDGMENTS

M.A.P. acknowledges the NanoMedAl group at Boston

University for the 4 months hosting, and Francisco del

Campo and Lucia Martin-Banderas (Dpto. Farmacia y

Tecnologia Farmaceutica) at University of Seville for the

experimental support. Also, he wishes to thanks D. Lohse

from the Physics of Fluids group at University of Twente for

the training on ultrasound contrast agent experimental

techniques. This work was funded by the Ministry of

Economy of Spain through the project No. DPI2011-28356-

C03-01 and funded by the National Science Foundation

(CBET 1134420).

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FIG. 9. (Color online) Viscoelastic parameters experimental estimation in

function of the mean equilibrium microbubble radius from different mono-

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� 0:28 N/m. (b) Surface viscosity linear regression: js ¼ 9� 10�3 �Ro

þ 2:7� 10�9 kg/s.

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