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193
IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 57, . 1, JANUARY 2010
Abstract—Ultrasound contrast agents (UCA) populations
are typically polydisperse and contain microbubbles with radii
over a given range. Although the behavior of microbubbles of
certain sizes might be masked by the behavior of others, the
acoustic characterization of UCA is typically made on full pop-
ulations. In this paper, we have combined acoustic and optical
methods to investigate the response of isolated lipid-shelled
microbubbles to low-pressure (49 and 62 kPa peak negative
pressure) ultrasound tone bursts. These bursts induced slow
deflation of the microbubbles. The experimental setup included
a microscope connected to a fast camera acquiring one frame
per pulse transmitted by a single-element transducer. The be-
havior of each bubble was measured at multiple frequencies, by
cyclically changing the transmission frequency over the range
of 2 to 4 MHz during subsequent pulse repetition intervals.
The bubble echoes were captured by a second transducer and
coherently recorded.
More than 50 individual microbubbles were observed. Mi-
crobubbles with radii larger than 3 μm did not experience any
size reduction. Smaller bubbles slowly deflated, generally until
the radius reached a value around 1.4 μm, independent of
the initial microbubble size. The detected pressure amplitude
backscattered at 2.5 cm distance was very low, decreasing from
about 5 Pa down to 1 Pa at 2 MHz as the bubbles deflated.
The resonant radius was evaluated from the echo amplitude
normalized with respect to the geometrical cross section. At
2-MHz excitation, deflating microbubbles showed highest nor-
malized echo when the radius was 2.2 μm while at higher exci-
tation frequencies, the resonant radius was lower. The relative
phase shift of the echo during the deflation process was also
measured. It was found to exceed π/2 in all cases. A heuristic
procedure based on the analysis of multiple bubbles of a same
population was used to estimate the undamped natural fre-
quency. It was found that a microbubble of 1.7 μm has an un-
damped natural frequency of 2 MHz. The difference between
this size and the resonant radius is discussed as indicative of
significant damping.
I. I
A characterization of coated microbubbles is
important to optimize their use as ultrasound con-
trast agents (UCA) in clinical applications. Microbubbles
are efficient ultrasound (US) scatterers due to the high
compressibility of the internal gas. It is generally assumed
that their scattering cross section is significantly increased
by resonance. The extent of such an increase and the reso-
nance frequency are strongly related to the physical prop-
erties of the microbubbles and, in particular, of their shell
[1]. Hence, efficient insonation of a UCA population can
only be achieved once the UCA behavior in US fields is
suitably characterized.
The most popular methods for UCA characterization
are based on optical and/or acoustic observations. A typi-
cal model-based approach consists of measuring the acous-
tic attenuation and/or scattering spectra of a population
to estimate the related viscoelastic parameters [2], [3]. In
turn, the model predicts the scattering cross section of
the coated bubbles. Although the assumption of a linear
radial response, inherent in the model, is violated when
smaller phospholipid-coated microbubbles are insonified
[4], [5], the method is still widely used, probably because
the possible nonlinear response of single bubbles in the
population is masked by the linear response of others [4].
More recent models also consider possible shell modifica-
tions due to nonlinear effects such as buckling or rupture
[6]–[9]. It should be noted that such models propose a
time-invariant system, not accounting for possible slow
changes in the shell structure and/or gas dissolution,
which could happen when microbubbles are repeatedly
exposed to imaging pulses [10], [11].
To overcome the problems faced in population-based
studies, optical methods are used to resolve the radial re-
sponse of single bubbles to a limited number of excitation
pulses [1], [12]–[15]. In this case, the characterization of
an entire population is assembled by repeating the basic
measurements on bubbles of different radii. Only few ex-
perimental studies address the echo of single microbubbles
(for example, [11], [16]–[20]. In [16] and [17], coated mi-
crobubbles were insonified with low-pressure pulses taking
care to incorporate only bubbles that maintained their
initial size. Bubble images were simultaneously recorded
together with their echo signals.
The objective of this work is to investigate the behav-
ior of single lipid-shelled microbubbles exposed to a long
series of low-pressure US pulses. First, optical recording of
the bubble size during the acoustically induced deflation
allows tracking the dissolution behavior as a function of
insonation parameters. Second, acoustic sampling of the
same bubble while deflating presents a convenient way to
contribute to UCA characterization. In contrast to previ-
ous studies in which a relatively small number of bubble
radii were examined, this approach allows quasicontinuous
recording of both the echo amplitude and phase corre-
sponding to an interval of bubble sizes. Information on the
resonance characteristics and damping are thus obtained.
Microbubble Characterization Through
Acoustically Induced Deflation
Francesco Guidi, Member, IEEE, Hendrik J. Vos, Student Member, IEEE, Riccardo Mori,
Nico de Jong, Associate Member, IEEE, and Piero Tortoli, Senior Member, IEEE
Manuscript received February 25, 2009; accepted October 1, 2009.
F. Guidi, R. Mori, and P. Tortoli are with the Department of Electron-
ics and Telecommunications, Università degli Studi di Firenze, Florence,
Italy (e-mail: Francesco.Guidi@unifi.it).
H. J. Vos and N. de Jong are with the Biomedical Engineering Thorax
Centre, Erasmus Medical Centre, Rotterdam, The Netherlands.
Digital Object Identifier 10.1109/TUFFC.2010.1398
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II. M
A. Experimental Setup
Definity (Lantheus Medical Imaging, North Billerica,
MA) microbubbles were used in the experiments. They
are comprised of a perfluoropropane gas core coated with
a flexible phospholipid shell, and product literature claims
a 1.1-µm and 3.3-µm mean diameter in the population.
The microbubbles under test were contained in a capil-
lary fiber immersed in a water tank at room temperature
(T ≈ 22°C). The cellulose capillary fiber (Cuprophan,
Akzo Nobel Faser AG, Wuppertal, Germany) had an in-
ner diameter of 160 µm and was nearly transparent both
acoustically and optically.
As shown in Fig. 1, the experimental setup combines
an acoustical interrogation and measurement system with
a microscope and a video camera. The acoustical section
consists of the US bubble behavior testing (BBT) system.
This is a custom-integrated electronic board, developed at
the Microelectronic Systems Design Laboratory (Universi-
ty of Florence, Florence, Italy), which includes 2 program-
mable transmitters and 2 low-noise receivers, a real-time
processing section, and a USB 2.0 interface to a host PC
[21]. The transmitters and receivers operate coherently at
64 million samples per second. In this work, the BBT sys-
tem was configured to use one single-element transducer
(PA076 1 inch focus, Precision Acoustics, Dorchester, UK)
as transmitter (TX) and another (C381-SU 1 inch focus,
Panametrics-NDT, Waltham, MA) as receiver (RX). The
2 transducers were positioned cofocally with a relative an-
gle of 100° to intercept the same part of the fiber, i.e., the
region of interest (ROI). The RX circuitry was optimized
to obtain an equivalent input noise of only 0.9 nV/√Hz,
and thus to guarantee the sensitivity requested to detect
the weak echoes produced by single bubbles.
The optical equipment consists of a water-immersion
40 objective (LUMPLFL 40×/W N.A. 0.8, Olympus, To-
kyo, Japan) having the focal plane in the ROI, which is il-
luminated by a continuous light source. The objective was
mounted on the microscope (Olympus BX-FM, 2×/4×
extra zoom), which projected the images on a commer-
cial digital camera (Redlake, MotionPro, San Diego, CA),
configured to store 250 frames/s with a shutter time of
2 ms, and having 4-GB circular memory storage capabil-
ity. The final resolution was up to 13.4 pixels/µm.
The frame acquisition was synchronized with the trans-
mission of the BBT system to guarantee the correlation
between acquired acoustical and optical data. For each
transmitted pulse one frame and the corresponding ra-
diofrequency (RF) bubble echo were stored on a host PC.
The amount of available memory was adequate to record
acousto-optical data over 64 × 1024 insonation pulses
(about 4 min at 250-Hz repetition frequency).
B. Experimental Procedure
UCA vials were prepared according to the instructions
of the manufacturer. A small amount of the agent was
extracted, diluted in Isotone II (Beckman Coulter, Fuller-
ton, CA), shaken, and slightly filtered to remove smaller
bubbles using gravity. The suspension was injected in the
capillary tube. The capillary was flushed using a manual
micro-syringe until optical inspection revealed that a sin-
gle bubble was present in the ROI, with no other bubbles
within ± 1 mm. The procedure requires between a few
minutes and one hour to complete.
The TX transducer was excited by tone bursts hav-
ing a pulse repetition frequency (PRF) of 250 Hz. Each
burst contained 15 cycles at a pressure level of either 49
or 62 kPa, as specified in Table I. The TX frequency was
cyclically changed in steps of 0.5 MHz between subsequent
pulses, covering the frequency range 2 to 4 MHz.
Both the BBT system and the RX transducer have
been characterized to convert the RX voltage readout to a
pressure value at the transducer surface [22].
Special care was taken to remove the contribution of
acoustic clutter echoes and fixed optical image patterns.
In particular, each acquisition was followed by a second
acquisition in which no bubble was present in the ROI,
to get “clutter reference” data to be subtracted from the
raw data.
C. Data Analysis
The available data were divided into different data sets,
i.e., collections of acquisitions obtained with the same fir-
ing conditions (see Table I).
Video frames and corresponding backscattered echoes
were analyzed using Matlab (MathWorks Inc., Natick,
194 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 57, . 1, JANUARY 2010
Fig. 1. Experimental setup. Two US transducers and the microscope are
co-focused on the fiber. The video camera is synchronized to the bubble
behavior testing (BBT) system to acquire one frame per transmitted
acoustic pulse.
TABLE I. N A, F, P
U E D S.
Data set
Number of
acquisitions
Frequencies
(min: max–step)
[MHz]
Acoustic pressure
[kPa]
P1 6
2: 4–0.5
49
P2 43 62
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MA). The bubble radius, R, was estimated from the video
frames using an edge-tracking minimum cost algorithm
[1]. The echo amplitude was evaluated as follows. First, a
time-gating window was applied around the RF echo sig-
nal. The trace was filtered around the first harmonic with
a zero phase second order band-pass Butterworth filter
(bandwidth 500 kHz). Finally, the analytical signal was
extracted, and the envelope peak was converted to units
of Pascals to produce the echo amplitude value, Ps. The
normalized scattering cross section was computed by tak-
ing the ratio of the measured acoustical scattering cross
section (SCS) (i.e., the ratio between the scattered power
and the incident intensity [23]) and the geometrical cross
section,
SCSnorm
s
a
=
P
Pr
R
2
24
4
2
2
p
p,
(1)
with Pa the amplitude of the excitation pressure (at the
location of the microbubble), r the distance to the RX
transducer (equal to 25 mm as obtained with a conven-
tional time-of-flight measurement), and R the equilibrium
radius during the pulse repetition interval (PRI). The nor-
malized SCS can be interpreted as the scattering strength
of the microbubble compared with a geometrical scatterer
having equal size as the microbubble.
The relative echo phase was preliminarily evaluated
as the instantaneous phase of the complex demodulated
samples selected in the central part of each echo signal.
The absolute echo phase values were then estimated by
combining the information obtained through the analysis
of multiple bubbles of a same population, as detailed in
Section III-C.
III. E
A. Deflation Analysis
About 50 microbubbles with arbitrary initial radii were
studied. About 30% of the bubbles either moved out of
the ROI before the end of the experiment or maintained a
stable equilibrium radius over subsequent PRIs. Bubbles
in the latter group typically had radii larger than 3 µm.
The remaining bubbles exhibited similar behavior.
Typically, a gradual bubble size reduction was observed:
the bubbles initially showed slower deflation, which accel-
erated in the intermediate range. At the end of the defla-
tion process, the bubbles assumed a stable radius, which
was insensitive to further insonation.
Fig. 2(a) reports the final stable radii vs. the initial ra-
dii measured for the 2 data sets. Independent of the initial
radius, the final radius was 1.44 ± 0.17 µm (0.4 correla-
tion coefficient). Fig. 2(b) illustrates the final part of the
radius-time curves measured for different bubbles excited
by the 62-kPa pulse sequence P2.
B. Single-Frequency Analysis
Although all the experiments were made using multi-
ple-frequency excitation (Table I), it is useful first showing
the results obtained at 2-MHz insonation. The analysis
related to the other frequencies is presented in Section
III-D.
The deflation of a typical bubble is shown in Fig. 3.
Three video frames and the corresponding acoustic echoes
of the bubble excited by the 49-kPa sequence are shown.
At the start of the experiment (t = 0 s) as illustrated in
Fig. 3(a), the bubble had a spherical shape with a radius
around 2.4 µm. The corresponding echo envelope illus-
trated in Fig. 3(a), bottom, shows stable amplitude after
a transient 2-cycle oscillation.
After about 7 s of pulsed insonation, as illustrated in
Fig. 3(b), the bubble has deflated by about 0.2 µm, and
195 .:
Fig. 2. (a) Final radius vs. initial radius of P1 and P2 data sets (see Table
I); (b) equilibrium radius as function of time for 5 different bubbles ex-
posed to the P2 pulse sequence.
Fig. 3. Images (top) and corresponding full echoes (bottom) of a deflating
Definity bubble, recorded at different times. The bubble was insonified at
250 Hz PRF for about 10 s by the sequence P1. These results, in particu-
lar, show the bubble response to the 2-MHz transmission frequency.
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the echo exhibits a slightly longer rise time followed by a
stable amplitude (close to that observed for the previous
echo). When the bubble was deflated to about 1.8 µm, as
illustrated in Fig. 3(c), the shape was still spherical, and
the backscattered echo was characterized by lower ampli-
tude (about 1 Pa) and longer rise time (about 4 cycles).
Fig. 3 also shows that the observed bubble was displaced
due to radiation force. In all experiments, the actual dis-
placement was small (a few micrometers as observed op-
tically) in comparison with the insonation wavelengths
(> 375 µm). We may therefore ignore any effect due to
the bubble translation.
As described in the previous section, suitable process-
ing of images like those shown in Fig. 3 (top) allowed mea-
surement of the equilibrium bubble radius, while the echo
amplitude and phase were estimated from the full echo-
signals (bottom) received in each pulse repetition interval.
Fig. 4 reports the results of such analysis made between
the 6th and the 10th second of the same acquisition. Fig.
4(a) shows that the bubble deflated from 2.4 µm down
to the minimum radius of 1.7 µm, which was then main-
tained regardless of further insonation. The curve exhibits
a typical sigmoid shape similar to that observed for lipid-
shelled bubbles [10]. As shown in Fig. 4(b), both the am-
plitude and the phase of the acoustic response gradually
changed during 2.5 s of acquisition, which corresponded
to about 600 PRIs. The echo-amplitude curve has a shape
similar to that observed for the radius, scaling from 3 Pa
down to about 1 Pascal. The echo phase shows a shift of
π/2 radians.
For the smallest radius, 1.7 µm, the scattered pressure
has a level of 1 Pa, which is 3 times lower than that ob-
tained for radii between 2.2 and 2.4 µm. This shows the
large size dependency of the scattered pressure. The com-
bination of data shown in Figs. 4(a) and 4(b) allows pre-
sentation of the experimental normalized SCS, as defined
in (1), and phase versus the bubble radius, as illustrated
in Fig. 4(c). The normalized SCS shows a broad peak cen-
tered at a radius of about 2.2 µm, which corresponds to
the 2-MHz resonant size (note that we use the definitions
given in [24] for the undamped natural frequency, damped
frequency, and resonance frequency of a microbubble).
Furthermore, the maximum level is −2 dB. Because this
value can be interpreted as the scattering strength, the
microbubble scatters the ultrasound with a relative power
of 63% compared with a geometrically scattering particle
of the same size. Microbubbles are commonly denoted to
have a high scattering strength due to resonance effects,
but these results suggest that the scattering strength of
a microbubble is low, even at resonance. A general cause
for low scattering would be a large damping of the oscil-
lation, which could also cause the observed broadening
of the resonance peak (for a theoretical example, see Fig.
4.4 in [23]). Note that Sijl et al. [16] report similar scat-
tering strength for another type of phospholipid-coated
microbubbles (BR14, Bracco Research, Geneva, Switzer-
land), but they did not observe resonance behavior.
The observed phase shift ranges over 0.5 π radians in
the size range 1.7 to 2.4 µm. This phase is the relative
phase difference between the excitation wave and the ra-
dial oscillation, and the results shown here actually prove
that the microbubble is a resonant system. The phase de-
creases with increasing microbubble size, consistent with
theory [23]. In addition, in this size range, the phase var-
ies linearly with radius, which could also be explained by
strong damping.
Fig. 5 combines the results obtained for 16 microbub-
bles excited with the 62-kPa sequence, evaluated at the
TX frequency of 2 MHz. Twenty-seven out of the 43 ex-
periments were discarded because of absence of deflation
(17 bubbles), fast bubble movements capable of signifi-
cantly affecting the acoustical response (3 bubbles), and
residual limitations (7 bubbles), such as acoustic inter-
ferences, bubble sticking to the wall, and misalignment
issues. The initial radii of the remaining bubbles were be-
tween 1.2 and 2.7 µm, while the final radii were in a range
compressed around 1.4 µm; see Fig. 2(b).
All bubbles exhibited similar echo-amplitude behavior,
despite their different initial radius and covered radius
196 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 57, . 1, JANUARY 2010
Fig. 5. A 2-MHz normalized scattering cross section (SCS) of 16 bubbles
excited with the P2 sequence. A regression curve (continuous line) and
the confidence bounds (dotted lines) are superimposed.
Fig. 4. Results of the analysis of a Definity bubble insonified by the P1
sequence: (a) bubble radius vs. time; (b) echo amplitude and correspond-
ing echo phase vs. time, at 2-MHz insonation; (c) normalized scattering
cross section (SCS, left axis) and phase vs. radius (right axis) (2 MHz).
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intervals. The normalized SCS clearly exhibits 2 regions
with different trends: for radii larger than 2.2 µm it slowly
decreases with increasing radius, while for radii smaller
than 1.7 µm the normalized SCS shows a slope greater
than 30 dB/µm. In the same graph, a regression curve
with relative confidence bounds (calculated on linearly
scaled data and represented on log scale) were added. This
curve has been computed by a local weighted linear least-
square regression method, using a linear polynomial (“low-
ess” smoothing in Matlab) with a relative span of 0.5. The
confidence interval was derived from the sum of squared
errors using the same weight and sliding of the smoothing
process. The resulting average deviations are 6.1 dB and
2.6 dB for the upper and the lower bounds, respectively.
C. Phase Analysis
The phase relation between the radial oscillation and
the US pressure wave indicates the regimes of bubble
oscillation. It is therefore a useful parameter to detect
resonance effects (as also suggested by Van der Meer [1,
Section II-C, pp. 651]). In particular, a phase lag of π/2
radians indicates an excitation at the undamped natural
frequency. The radius where this occurs can be compared
with the resonant radius (i.e., where the normalized SCS
is maximum) to evaluate the magnitude of the damping.
As will be shown, it is difficult to estimate accurately the
sizes corresponding to the undamped natural frequency
and resonance, but the results can still provide a qualita-
tive estimate of the significance of damping.
The coherence of the TX and RX operations allows
determining the changes in the echo phase. Although a
direct estimation of the “absolute” phase between the
driving pressure and the echo is not available (see Sec-
tion IV-A), its indirect estimate was possible through the
following procedure.
First, the offset of each phase curve was adjusted to
minimize the squared differences in the overlapping re-
gions. Second, a local regression curve was obtained using
the same technique described above. Then the absolute
offset for this composite curve was estimated by one of the
2 following criteria:
1) If the slope of the phase curve at the largest radius
is low, it suggests that such radius is much larger
than resonant: the phase at that point is set to −π
radians.
2) If the slope at the largest radius is non negligible, the
phase value corresponding to the maximum slope is
set to −π/2, according to resonant system theory
[23].
Fig. 6 shows the absolute echo phase responses and the
regression curve obtained with the same data set used in
Fig. 5. It is seen that the slope at 2.5 µm is not zero, pre-
venting application of the first criterion described above.
Hence, the second criterion was adopted, and the phase
at a radius of 1.8 µm, where the curve shows the steepest
slope, was set to −π/2 radians.
D. Multiple-Frequency Analysis
Because we used an excitation sequence with 5 different
TX frequencies, the normalized SCS and phase behavior
were also extracted from the responses to the 2.5-, 3-, 3.5-,
and 4-MHz pulses. Fig. 7 shows the results obtained at all
frequencies. For clarity of presentation, raw data are omit-
ted, and only the regression curves are shown.
The normalized SCSs (Fig. 7, left panels) reveal a peak
at a radius that is larger than 2 µm at 2 MHz and smaller
than 1.8 µm at 4 MHz. The overall excursion of the SCS
is in the range 10 to 20 dB, with typically larger values at
lower frequencies. The confidence bounds are close to the
regression curves, especially when the SCS is high, except
at 2.5 MHz where the confidence interval is over 6 dB also
in the highest value range.
The phase regression curves (Fig. 7, right panels) reveal
a clear trend: at all frequencies, the overall phase excursion
is larger than π/2 radians, covering about 3/4π radians at
2.5 MHz. At the 2.5-, 3-, 3.5-, and 4-MHz frequency, the
slope is low at the largest radii and, according to the cri-
teria described earlier, the phase at largest radius was set
to −π rad. (first criterion), while the 2-MHz curve was set
to −π/2 rad (second criterion). The bubble radius corre-
sponding to the undamped natural frequency [24], produc-
ing π/2 phase lag [1], decreases with increasing frequency,
from about 1.8 µm at 2 MHz to 1.4 µm at 4 MHz.
IV. D
A. Experimental Uncertainties
Insonifying phospholipid-coated microbubbles with
2- to 4-MHz ultrasound pulses at 49- or 62-kPa pressure
amplitude led to slow deflation of the microbubbles. At
250-Hz PRF, it typically covered an interval of several
197 .:
Fig. 6. A 2-MHz absolute phase response of the same bubbles considered
in Fig. 5. A regression curve (continuous line) and the confidence bounds
(dotted lines) are superimposed.
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seconds, enabling dense sampling of the phenomenon. The
current setup satisfied the requirement of large memory
buffers to store the bubble echoes and images during the
full deflation process.
The radius, echo amplitude, and echo phase were di-
rectly extracted from the raw data without averaging
between subsequent images/US pulses. This was possible
thanks to an ultra-low-noise receiver, designed for this
application, combined with a sensitive transducer. In the
echo signals received from very small bubbles (1.2-µm ra-
dius), the signal-to-noise ratio (S/N) was estimated in the
order of 11 dB.
The accurate system calibration is demonstrated by the
good agreement between predicted and experimentally re-
ceived pressure. As a reference, assuming linear scattering
theory in the inertial regime [23], the pressure level scat-
tered by a 2.3-µm radius microbubble excited by 49-kPa
pulses, is 4.5 Pa at 25-mm distance: such value is close to
that reported (3 Pa) in Fig. 3.
Compared with the approach used in another bubble
characterization study in which differently sized bubbles
are subsequently observed [16], a same bubble with vary-
ing radius was considered in the current study. It is im-
plicitly assumed that bubble acoustical or structural prop-
erties do not depend on the initial size. This might not
always be true, though results like those shown in Figs.
5 to 7 seem not to suggest significant changes. The hy-
pothesis is corroborated by the observation that bubbles
with different initial size subjected to the same type of US
excitation show similar deflation profiles, as shown, e.g.,
in Fig. 2(b), and similar acoustical responses, as shown in
Figs. 5 to 7.
This similarity is helpful for the absolute phase compu-
tation. The measured phase is intended as “relative” and
not absolute, because the latter is affected by factors such
as initial bubble position, transducer-fiber alignment, wa-
ter bath temperature, and so on. A phase offset adjust-
ment was thus necessary to remove this phase bias when
estimating the “absolute” phase curves from multiple ex-
periments.
Ideally, the phase curve covers [0, −π] radians if the
bubbles have negligible damping, and when they are de-
flating from well above resonance to well below resonance
[23]. However, the measured phase curves showed less
than π variation, expected to be caused by both a finite
deflation range and damping. Therefore, the availability
of echo data from multiple bubbles behaving similarly
helped in the enlargement of the covered range.
Due to buoyancy, the bubbles float against the upper
fiber wall and stay in contact, as confirmed by the in-
focus sequence of images (see Fig. 3). This capillary wall
proximity was surely not ideal, because it could change
the bubble behavior in terms of oscillation shape [25],
[26], amplitude [26]–[28], and resonance [29]. The influ-
ence of these effects could not be estimated in the cur-
rent study.
198 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 57, . 1, JANUARY 2010
Fig. 7. Normalized scattering cross section (SCS) (left) and phase (right) regression curves evaluated over 16 bubbles excited at 2, 2.5, 3, 3.5, and
4 MHz (from top to bottom), by the P2 sequence.
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Due to radiation force [20], [30], the microbubbles were
slightly displaced parallel to the wall. However, some
bubbles visibly remained still. Such sticking effect is not
understood, although it has been frequently observed in
similar optical studies with the cellulose capillary fiber,
also for nondeflating bubbles (from experience in the past
years in the labs).
Because the experimental procedure was such that
the time between agent-extraction from the vial and the
actual recording could last from few minutes up to one
hour, air could have been dissolved from the bulk into
the microbubbles. Such diffusion would result in an ini-
tial growth of the microbubbles (because air diffusivity is
much larger than that of perfluorocarbon). However, the
microbubbles are not monitored during the dilution after
extraction from the vial, and such possible growth could
not be observed.
Finally, although a single bubble was visible in the in-
spected ROI, the possible presence of bubbles close to but
out of the ROI could not be excluded. When such a pres-
ence was clearly revealed in the echo, the related acqui-
sition was discarded. However, in general, an undesired
interference by proximal bubbles was always possible.
B. Results: Deflation Phenomenon
Most observed bubbles exhibited a similar deflation
behavior, consisting of a gradual size reduction upon in-
sonification that stopped when the bubble achieved a fi-
nal steady-state condition. This happened for all bubbles
with initial radii between 2.7 µm and 1.3 µm, while larger
bubbles needed higher TX power to start deflating.
The TX frequency range was selected to include the
resonance frequencies of bubbles with diameter in the
mean range of the Definity population. Each TX pulse
was long enough to allow ignoring of the transient effects.
A low pulsing frequency was used to extinguish possible
transient oscillations due to the previous TX pulse. The
PRF was, however, high enough to avoid the influence of
slow changes of bubble properties due to natural dissolu-
tion [31], [32].
During deflation, the coating of the bubble can expe-
rience significant changes, such as folding, disruption of
monomolecularity, and shedding of material through ves-
icles and micelles [31], [32]. However, we often found that
the bubbles deflated maintaining a spherical shape (see,
e.g., Fig. 3). This behavior is consistent with observations
reported in [30].
The sigmoid behavior visible in Fig. 4(a), e.g., is in ac-
cordance with the results shown by Borden et al. [10]. The
range of radii of accelerated dissolution corresponds to
the region around resonance, where radial oscillations are
highest and gas pressure fluctuation inside the microbub-
ble is out of phase with the driving US pulse. In such
conditions, the partial gas pressures at opposite sides of
the shell are highest, giving highest potential for gas diffu-
sion. Large radial oscillations are also expected to increase
the rate at which the shell sheds material, increasing the
effective surface tension [6], [31], [33], [34]. In addition,
during the expansion half-cycle of the oscillation, the lipid
coating concentration might be too low to cover the full
bubble surface [6], [34], thus diminishing its resistance to
dissolution. Comparison of the 2 data sets suggests that
the size of the stable final radius was influenced by the
excitation amplitude. This dependency is supported by
the analysis of other data sets (not reported here) with
excitation pressures in the range 49 to 170 kPa. In general,
the higher the pressure, the smaller the final radius.
The fact that the stable final radius did not depend on
the initial value (see Fig. 2) also suggests that lipid mol-
ecules are shed during the deflation. On the other hand,
the existence of a stable radius might be hypothesized to
originate from a dense packing of the phospholipid mol-
ecules at the surface, thus both increasing the resistance
to diffusion and reducing the surface tension [6], [34]. The
lower radial excursion of small bubbles might not be able
to force the shedding.
C. Results: Acoustic Response
The echo changes during deflation (see Fig. 3). At
the larger initial size (left frame) the echo exhibits the
highest amplitude and quasisinusoidal oscillations while,
when the bubble is deflated (right frame), the ampli-
tude decreases and nonlinear contributions can be recog-
nized. After a partial deflation (center frame) the echo
amplitude is similar to that obtained at larger bubble
size. This demonstrates the nonlinear relation between
the geometrical and scattering cross section, which is
also recognized in Fig. 4, comparing the echo amplitude
and radius curves emphasized in Fig. 4(c) through the
normalization. Here the maximum normalized scatter-
ing is not obtained at the maximum bubble size, but at
resonance. The comparison between the results reported
here and those reported by Sijl et al. [16] shows that the
long time to response of the deflating bubble does not
significantly differ from the response of single bubbles of
different constant sizes.
The curves represented in Figs. 5 and 6 obtained from
16 different bubbles highlight a similar behavior, as con-
firmed by the narrow confidence intervals. The small dif-
ferences between the individual curves (up to 6 dB at
2.5 MHz) are consistent with previous studies, showing
that phospholipid-coated microbubbles with equal size
show different acoustic behavior [16], [30], [35]. Hetero-
geneity of phospholipid packing in different bubbles of
the same population [10], [32] might have contributed to
the observed differences. In addition, the phase regression
curves are surely affected by the uncertainty coming from
the recombination of the different curves.
The results shown in Figs. 5 to 7 suggest that the cho-
sen frequency range is sufficient to consider the resonant
behavior of the bubbles. For each transmitted frequency,
2 different resonant radii can be identified, based on the
analysis of the echo-amplitude and of the relative echo
phase, respectively, as explained below.
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The normalized SCS curves in Fig. 5 and Fig. 7 are
nearly constant for large radii (where the oscillation is
mainly mass controlled: inertia dominates the motion [23],
while it rapidly decays when the bubble shrinks toward
the minimum size (the oscillation is mainly stiffness con-
trolled: the elastic force dominates the motion [23]). In be-
tween these states (resistance-controlled oscillation), the
normalized SCS curves show a peak, here defined as the
first harmonic amplitude-resonant radius.
In the echo phase curves, monotonic behavior within
the 0 to −π range was observed. The driving frequency
is coincident with the undamped natural frequency [24]
when the phase is equal to −π/2. The radius correspond-
ing to this condition is here defined as the phase-resonant
radius.
Although the measurements may have limited accuracy
(especially for smaller bubble radii where the S/N ratio
is lower) or may be affected by the subjective criteria
used in giving the reference phase value, they show a clear
trend. In Fig. 7, the amplitude-resonant radii range from
about 2 µm at 2 MHz to less than 1.8 µm at frequen-
cies ≥ 3 MHz. The phase-resonant radii range from about
1.8 µm at 2 MHz to 1.5 µm at 2.5 MHz and about 1.4 µm
at higher frequencies. The difference between these 2 reso-
nant radii, being in the order of 0.3 µm at all excitation
frequencies, is indicative of significant damping of the os-
cillation [24]. Such damping also explains the absence of
visible echo-peaks around resonance and the slow rate of
change of both amplitude and phase curves versus radius
[23].
D. Clinical Implication
The results suggest that if experimental conditions
equivalent to those adopted in the current study were
used in clinical applications, significant consequences
could emerge. Bubbles close to resonance would rapidly
shrink and, after prolonged excitation, only bubbles much
smaller or much larger than the resonant size would pro-
duce a detection signal. Accordingly, in fundamental im-
aging applications, the largest signal is expected to come
from larger bubbles, because size seems more important
than resonance. This is consistent with findings reported
earlier in literature [2], [16], [36].
V. C
Two goals have been simultaneously pursued in this
paper. First, the phenomenon of acousticallyinduced bub-
ble deflation has been described in detail. A final stable
radius was identified that was maintained independent of
further insonation. The acoustic response of the deflat-
ing bubble was strongly correlated to the instantaneous
radius and not related to the initial radius. Second, it
has been shown that a forced decrease of microbubble
radius offers a means to contribute to UCA characteriza-
tion in terms of resonance and damping effects. Significant
damping was indirectly demonstrated by the difference of
amplitude-resonant and phase-resonant radii and by the
absence of large increase of fundamental-frequency scat-
tering for bubbles around resonance.
Future work will be focused on understanding the rela-
tive importance of microbubble size and other properties
in UCA detection schemes. Furthermore, the experimen-
tal setup will be integrated with specialized equipment
like an optical tweezer [27], capable of eliminating residual
interference by the nearby fiber wall, and with an ultra-
fast camera [37] to simultaneously resolve the radial oscil-
lations of deflating microbubbles optically.
A
We would like to acknowledge P. van Neer (Erasmus
MC Rotterdam) and J. Sijl (University of Twente) for the
calibration of the receiving transducer, and Dr. E. Boni
(University of Florence) for his contribution in BBT sys-
tem optimization. We also thank Dr. T. Hay (University
of Twente) for proofreading the manuscript.
R
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Francesco Guidi was born in Portoferraio (LI),
Italy, in 1964. He graduated from the University
of Florence, Italy, with the M.Sc. degree in elec-
tronics engineering and subsequently he received
his Ph.D. degree in electronic systems engineering.
After working in a national company on the de-
sign of a real-time radiologic image processing sys-
tem, he joined the National Institute of Nuclear
Physics (INFN), where he was involved in the de-
sign of real-time software for solid-state particle
detectors. Since 1992, Francesco has held a posi-
tion at the Electronics and Telecommunications Department of the Uni-
versity of Florence. His research interests include the development of
real-time methods for ultrasound blood flow estimation and the investi-
gation of acoustic properties of ultrasound contrast agents.
Hendrik J. Vos received an M.Sc. degree in ap-
plied physics in 2004 from the Delft University of
Technology, the Netherlands. His M.Sc. research
project involved the design and prototyping of a
20 to 40 MHz intravascular ultrasound (IVUS)
transducer. In 2004, he won a grant from the
Dutch VSB foundation for a one-year post-Mas-
ter’s research at the Universitá di Firenze, Italy,
concerning acoustic radiation force on microbub-
bles. Currently, he is in the Department of Bio-
medical Engineering of the Erasmus MC pursuing
a Ph.D. degree (due January 2010). His interests include the acoustical
and optical imaging of single medical contrast bubbles, and biomedical
engineering in general.
Riccardo Mori was born in Florence, Italy, in
1982. He received the Master’s degree in electron-
ic engineering in 2006 from the University of Flor-
ence. He is currently a Ph.D. student in electronic
systems engineering at the University of Florence
and joins a collaboration with the Italian Institute
of Nuclear Physics (INFN). His main research in-
terests include the characterization of ultrasound
contrast agents through optical and acoustical in-
vestigations.
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Nico de Jong graduated from Delft University
of Technology, The Netherlands, in 1978. He re-
ceived his M.Sc. degree in the field of pattern
recognition. Since 1980, he has been a staff
member of the Thoraxcenter of the Erasmus
University Medical Center, Rotterdam, The
Netherlands. At the Department of Biomedical
Engineering, he developed linear and phased-
array ultrasonic probes for medical diagnosis,
especially compound and transesophageal trans-
ducers. In 1986, his interest in ultrasound ap-
plications shifted toward the theoretical and practical background of
ultrasound contrast agents. In 1993, he received his Ph.D. degree for
“Acoustic properties of ultrasound contrast agents.” Dr. De Jong is
the project leader of STW and FOM projects on ultrasound contrast
imaging, molecular imaging and drug delivery systems and partici-
pates with his group in several European projects. Since 1996, to-
gether with Folkert ten Cate, M.D., he has been organizer of the an-
nual European Symposium on Ultrasound Contrast Imaging held in
Rotterdam and attended by approximately 175 scientists from all
over the world.
Since 2003, Nico de Jong has been part-time professor at the Univer-
sity of Twente. He has published more than 100 scientific papers and has
several patents on ultrasound contrast imaging and transducer design.
Piero Tortoli (M’91–SM’96) received the Laurea
degree in electronic engineering from the Univer-
sity of Florence, Italy, in 1978. Since then, he has
been with the Electronics and Telecommunica-
tions Department of the University of Florence,
where he is currently a full professor of Electron-
ics. Piero has been a member of the IEEE Inter-
national Ultrasonics Symposium Technical Pro-
gram Committee since 1999. He organized the
22nd International Symposium on Acoustical Im-
aging (1995) and the 12th New England Doppler
Conference (2003). In 2000, he was nominated to be an Honorary Mem-
ber of the Polish Academy of Sciences. His research activity is centered
on the development of ultrasound research systems and novel imaging/
Doppler methods.
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