Acoustic characterization of monodisperse lipid-coated microbubbles: Relationship between size and shell viscoelastic properties Miguel A. Parrales,a) Juan M. Fernandez, and Miguel Perez-Saborid Aerospace Engineering and Fluid Mechanics Department, University of Seville, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain
Jonathan A. Kopechek and Tyrone M. Porter Mechanical 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, microbubbles samples were generated with a very narrow size distribution by using microfluidics techniques. 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 equilibrium bubble radius. The results showed the great advantage of dealing with monodisperse populations rather than polydisperse populations for the acoustic characterization of ultrasound contrast C 2014 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4890643] agents. V PACS number(s): 43.35.Bf, 43.35.Yb, 43.80.Qf, 43.20.Fn [TGL]
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 applications.1–3 These contrast agents also have a great potential use for drug and gene delivery for treating different diseases.4–6 Due to their compressibility, the microbubbles perform volumetric oscillations, giving rise to a strong resonant echo when driven by an ultrasound field with a specific frequency. Consequently, they scatter more energy than rigid particles of the same size, or even larger liquid-filled particles (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 excitation. 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 a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
J. Acoust. Soc. Am. 136 (3), September 2014
Pages: 1077–1084
dissipation during the oscillatory motion of the coated bubble.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 suspensions13,14 and optical measurements of the oscillatory motion of single microbubbles.15,16 While optical methods are more accurate and sophisticated, they need a considerable investment 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 distribution. In fact, it has been shown that larger microbubbles tend to be the primary source of attenuation in polydispersions, 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 parameters (elasticity and viscosity). Therefore, in order to get a novel generation of monodisperse contrast agents, it is essential 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 characterization methods. To address these needs, researchers began using microfluidic devices to produce monodisperse lipid-coated microbubbles.19,20 Unlike polydisperse microbubble suspensions, monodispersions allow one to measure
0001-4966/2014/136(3)/1077/8/$30.00
C 2014 Acoustical Society of America V
1077
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
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 microbubbles. The theoretical background for these estimations is based on the linearized Rayleigh–Plesset equation modified with the Marmottant model11 to account for the shell rheology. Consequently, in order to assure accurate measurements, we generated monodisperse samples of microbubbles and acquired the acoustic attenuation for different equilibrium radius, thus avoiding the difficulties when using polydisperse contrast agents. We found that the linear viscoelastic parameters 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 experimental 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 symmetrically. The equations of motion describing the radial oscillations 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 surrounding liquid medium, leading to the well-known Rayleigh–Plesset equation,9,22 :: 3 2 1 RR þ R_ ¼ ðpL pa p1 Þ; 2 q1
(1)
where pL stands for the liquid pressure just outside the bubble. This term can be related with the gas pressure inside the bubble pg by setting the normal stress balance across the bound_ ary, pL ¼ pg 2r=R 4lE R=R, where pg ¼ pg0 ðR=Ro Þ3j , where pg0 is the gas pressure at rest and r is the surface tension. 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 lth Þ, 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 q1 x2o R3o =4c1 and lth ¼ pg0 ImU=4xo , respectively, where xo is the characteristic oscillation frequency and c1 is the sound speed in the liquid. We found that both the polytropic coefficient, defined as j ¼ ReU=3, and the thermal viscosity were related to a complex function U, which can be written as25 1078
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
U¼
3c ; p 3ðc 1Þ ffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 1 iPecot iPe 1 iPe
(2)
where c is the adiabatic coefficient and Pe ¼ xo R2o =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 formulation. Assuming that the shell is represented by a thin lipid monolayer with viscoelastic properties, the pressure difference across the bubble wall can now be written as _ þ 4js R=R _ 2; pL ¼ pg 2rðRÞ=R 4lE R=R
(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, considering R ’ Ro ð1 þ XÞ with jXj 1, the linear microbubble radial dynamics equation yields24,25 :: pa X þ 2d X_ þ x2n X ¼ ; q1 R2o
(4)
where d ¼ ð2lE =q1 R2o þ 2js =q1 R3o Þ is the damping factor and xn is the bubble natural frequency, defined by x2n ¼
3jp1 4v þ : 2 q1 Ro q1 R3o
(5)
The differential equation for the radial dynamics shows that the coated microbubble behaves as a damped harmonic oscillator, 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 natural 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 r from the linearly oscillating bubble can be written as :: ps ¼ q1 R3o X ðsÞ=r, where s ¼ ðt r=c1 Þ is the retarded time. Assuming time-harmonic acoustic excitations and oscillations of the form X ¼ X^ expðixo tÞ, we can finally write p^s ¼
eikr eikr ^ ¼ p ; f s a r ðxn =xo Þ2 1 iC r p^a Ro
(6)
where k ¼ xo =c1 is the wavenumber, fs is the omnidirectional 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 bubble 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 Parrales et al.: Viscoelastic properties of coated bubbles
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
rs ¼
ð
jfs j2 dX ¼ 4pjfs j2 ;
(7)
X
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 =q1 xo R2o . 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=Cac Þrs :
(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 ðRo Þ. 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 coefficient is written in terms of the extinction cross section as ð1 nre f ðRo ÞdRo : (9) a¼ 0
Note that, if the microbubble suspension were monodisperse, this parameter would be just a ¼ nre . In this case, the maximum value of the attenuation is reached at the natural frequency 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 experimental 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 microchannels were fabricated in the PDMS device, it was then oxygen 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, microfluidic 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, dipalmitoylphosphatidic 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 maintaining the liquid flow rate and gas pressure constant, we produced 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 independent 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 significantly higher rate of production (see Fig. 2). In order to collect 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 experimental setup for generating monodisperse lipid-coated microbubbles.
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
Parrales et al.: Viscoelastic properties of coated bubbles
1079
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
FIG. 2. Generation of contrast microbubbles. (a) Flow-focusing microdevice (103 lbubbles/s). (b) Co-flow microdevice (105 lbubbles/s). (c) Micrograph of a monodisperse sample with a mean bubble size of approximately 12 lm.
characterization with the theoretical prediction for the attenuation in a contrast microbubble suspension, the measured size distribution was fitted by a Weibull density function (Fig. 3), h K1 K i lK exp lRo =Ro ; (10) f ðRo Þ ¼ lRo =Ro Ro where Ro is the microbubble mean radius and l is a shape parameter defined by l ¼ ½ðK 1Þ=K1=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 agitation/sonication.31,32 B. Acoustic characterization
The experimental setup for measuring frequencydependent attenuation for suspended monodisperse lipidcoated microbubbles is shown in Fig. 4. Monodispersions were dispensed into a sample holder made of polymethylmethacrylate 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
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. 1080
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
12 lm thickness each. The sample holder was submerged in a tank of deionized water and positioned just in front of a stainless 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 transducer (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 arbitrary 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 propagating 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. 4. (Color online) Acoustic experimental setup for measuring the acoustic attenuation of contrast microbubble suspensions. Parrales et al.: Viscoelastic properties of coated bubbles
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
FIG. 5. Acoustic transmission power spectrum for the reference signal, and the measured one for the microbubble monodisperse sample.
Effectively, we observe that the maximum intensity gain was reached at the transducer center frequency. When a contrast 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 1 Iref ; (11) a ¼ ln Isample l 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 lipidcoated microbubbles, with a mean diameter of 5:960:2 lm, as shown in Fig. 3. In Fig. 6, we show the attenuation
FIG. 6. (Color online) Attenuation coefficient in a monodisperse sample at different concentrations n (103 microbubbles/ml). 䊊: n ¼ 1:4, ⵧ: n ¼ 3:5, 䉫: 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 3 108 kg/s. The inset corresponds to a micrograph of the monodisperse coated microbubble suspension. J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
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 corresponding 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 measured for monodispersions was proportional to the microbubble concentration n. This scaling is only valid for low concentration suspensions where multiple scattering between the bubbles 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 coefficient 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, excitation frequency, and, finally, on the viscoelastic properties of the lipid shell, i.e., re ðRo ; xo ; v; js Þ. It is very difficult to measure the shell elasticity and viscosity directly; alternatively, 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 modulus to v ¼ 0:28 N/m and the shell surface viscosity to js ¼ 3 108 kg/s, as shown in Fig. 6. These values were in a very good agreement with those obtained by previous experimental 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 difficulty in identifying both the main resonance frequency peak
FIG. 7. Attenuation coefficient in a polydisperse sample at different concentrations n (105 microbubbles/ml). 䊊: n ¼ 1:2, ⵧ: n ¼ 2:2, 䉫: n ¼ 3:1, and þ: n ¼ 4:5. The inset corresponds to a micrograph of the polydisperse coated microbubble suspension. Parrales et al.: Viscoelastic properties of coated bubbles
1081
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
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.
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 experimental 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 TABLE I. Results obtained for the acoustic characterization and lipid-shell properties estimations using monodisperse contrast agents. Ro (lm) 2.9 3.7 4.8 5.5 6.3
1082
fn (MHz)
v (N/m)
js (108 kg/s)
1.37 1.14 0.84 0.78 0.70
0.28 0.35 0.50 0.76 0.85
3.0 3.6 4.2 5.4 6.0
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
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 microbubble 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 measurements 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 amplitude 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 nonlinear behavior. Moreover, the non-linear correction for the shell viscoelastic model explains theoretically the compression-only behavior observed when lipid-coated microbubbles oscillate with large amplitudes.11,36 Parrales et al.: Viscoelastic properties of coated bubbles
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
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. DPI2011-28356C03-01 and funded by the National Science Foundation (CBET 1134420). 1
FIG. 9. (Color online) Viscoelastic parameters experimental estimation in function of the mean equilibrium microbubble radius from different monodisperse samples. (a) Elastic modulus linear regression: v ¼ 1:8 105 Ro 0:28 N/m. (b) Surface viscosity linear regression: js ¼ 9 103 Ro þ 2:7 109 kg/s.
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 microbubbles rather than polydisperse ones for the acoustic characterization 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 attenuation 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 samples,7,13,14 which are characterized by a very simple instrumentation. More recently, the coating parameters have usually been estimated from optical characterization of single bubbles,15,16,35,36 which avoid the uncertainty related to polydispersity. 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 properties 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 J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
R. Gremiak and P. M. Shah, “Echocardiography of the aortic root,” Invest. Radiol. 3, 356–388 (1968). 2 E. Stride and N. Saffari, “Microbubble ultrasound contrast agents: A review,” Proc. Inst. Mech. Eng., Part H 217, 429–447 (2003). 3 F. Calliada, R. Campani, O. Bottinelli, A. Bozzini, and M. G. Sommaruga, “Ultrasound contrast agents: Basic principles,” Eur. J. Radiol. 27, 157–160 (1998). 4 P. A. Dijkmans, L. J. M. Juffermans, R. J. P. Musters, A. van Wamel, F. J. ten Cate, W. van Gilst, C. A. Visser, N. de Jong, and O. Kamp, “Microbubbles and ultrasound: from diagnosis to therapy,” Eur. J. Echocardiography 5, 245–256 (2004). 5 K. Ferrara, R. Pollard, and M. Borden, “Ultrasound microbubble contrast agents: Fundamentals and application to gene and drug delivery,” Annu. Rev. Biomed. Eng. 9, 415–447 (2007). 6 E. C. Unger, T. Porter, W. Culp, R. Labell, T. Matsunaga, and R. Zutshi, “Therapeutic applications of lipid-coated microbubbles,” Adv. Drug Deliv. Rev. 56, 1291–1314 (2004). 7 L. Hoff, “Acoustic properties of ultrasonic contrast agents,” Ultrasonics. 34, 591–593 (1996). 8 N. de Jong, A. Bouakaz, and P. Frinking, “Basic acoustic properties of microbubbles,” Echocardiography 19, 229–240 (2002). 9 S. Hilgenfeldt, D. Lohse, and M. Zomack, “Response of bubbles to diagnostic ultrasound: A unifying theoretical approach,” Eur. Phys. J. B 4, 247–255 (1998). 10 E. Stride and M. Edirisinghe, “Novel preparation techniques for controlling microbubble uniformity: A comparison,” Med. Biol. Eng. Comput. 47, 883–892 (2009). 11 P. Marmottant, S. van der Meer, M. Emmer, M. Versluis, N. de Jong, S. Hilgenfeldt, and D. Lohse, “A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture,” J. Acoust. Soc. Am. 118, 3499–3505 (2005). 12 A. Doinikov and A. Bouakaz, “Review of shell models for contrast agent microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 981–993 (2011). 13 N. de Jong and L. Hoff, “Absorption and scatter of encapsulated gas filled microspheres,” Ultrasonics 30, 95–103 (1992). 14 J. N. Marsh and C. S. Hall, “Broadband through-transmission signal loss measurements of Albunex suspensions,” J. Acoust. Soc. Am. 101, 1155–1161 (1997). 15 S. van der Meer, B. Dollet, M. Voormolen, C. Chin, A. Bouakaz, N. de Jong, M. Versluis, and D. Lohse, “Microbubble spectroscopy of ultrasound contrast agents,” J. Acoust. Soc. Am. 121, 648–656 (2007). 16 J. Tu, J. Guan, Y. Qiu, and T. Matula, “Estimating the shell parameters of SonoVue microbubbles using light scattering,” J. Acoust. Soc. Am. 126, 2954–2962 (2009). 17 D. E. Goertz, N. de Jong, and A. F. W. van der Steen, “Attenuation and size distribution measurements of Definity and manipulated Definity populations,” Ultrasound Med. Biol. 33, 1376–1388 (2007). 18 J. M. Gorce, M. Arditi, and M. Schneider, “Influence of bubble size distribution on the echogenicity of ultrasound contrast agents: A study of SonoVue,” Invest. Radiol. 35, 661–671 (2000). 19 K. Hettiarachchi, E. Talu, M. L. Longo, P. A. Dayton, and A. P. Lee, “Onchip generation of microbubbles as a practical technology for manufacturing contrast agents for ultrasonic imaging,” Lab Chip. 7, 463–468 (2007). 20 M. Kaya, S. Feingold, K. Hettiarachchi, A. P. Lee, and P. A. Dayton, “Acoustic responses of monodisperse lipid-encapsulated microbubble contrast agents produced by flow focusing,” Bubble Sci. Eng. Technol. 2, 33–40 (2010). 21 Y. Gong, M. Cabodi, and T. Porter, “Relationship between size and frequency dependent attenuation of monodisperse populations of lipid coated microbubbles,” Bubble Sci. Eng. Technol. 2, 41–47 (2010). Parrales et al.: Viscoelastic properties of coated bubbles
1083
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
22
A. Prosperetti and A. Lezzi, “Bubble dynamics in a compressible liquid. Part 1. First-order theory,” J. Fluid Mech. 168, 457–478 (1986). 23 C. Devin, “Survey of thermal, radiation, and viscous damping of pulsating air bubbles in water,” J. Acoust. Soc. Am. 31, 1654–1667 (1959). 24 A. Prosperetti, “Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids,” J. Acoust. Soc. Am. 61, 17–27 (1977). 25 A. Prosperetti, L. Crum, and K. Commander, “Nonlinear bubble dynamics,” J. Acoust. Soc. Am. 83, 502–514 (1988). 26 J. Kopechek, K. Haworth, J. Raymond, T. Douglas-Mast, S. Perrin, M. Klegerman, S. Huang, T. Porter, D. McPherson, and C. Holland, “Acoustic characterization of echogenic liposomes: Frequency-dependent attenuation and backscatter,” J. Acoust. Soc. Am. 130, 3472–3482 (2011). 27 J. M. Gordillo, Z. D. Cheng, A. M. Ganan-Calvo, M. Marquez, and D. A. Weitz, “A new device for the generation of microbubbles,” Phys. Fluids. 16, 2828–2834 (2004). 28 P. Garstecki, H. A. Stone, and G. M. Whitesides, “Mechanism for flowrate controlled breakup in confined geometries: A route to monodisperse emulsions,” Phys. Rev. Lett. 94, 164501 (2005). 29 P. Garstecki, A. M. Ganan-Calvo, and G. M. Whitesides, “Formation of bubbles and droplets in microfluidic systems,” Bull. Pol. Acad. Sci. 53, 361–372 (2005).
1084
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
30
E. Castro-Hernandez, W. van Hoeve, D. Lohse, and J. M. Gordillo, “Microbubble generation in a co-flow device operated in a new regime,” Lab Chip. 11, 2023–2029 (2011). 31 K. Kooiman, M. Emmer, M. Foppen-Harteveld, A. van Wammel, and N. de Jong, “Increasing the endothelial layer permeability through ultrasound activated microbubbles,” IEEE Trans. Biomed. Eng. 57, 29–32 (2010). 32 T. Faez, M. Emmer, K. Kooiman, M. Versluis, A. van der Steen, and N. de Jong, “20 years of ultrasound contrast agents modeling,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 7–20 (2013). 33 N. de Jong, M. Emmer, A. van Wammel, and M. Versluis, “Ultrasonic characterization of ultrasound contrast agents,” Med. Biol. Eng. Comput. 47, 861–873 (2009). 34 K. Sarkar, W. T. Shi, D. Chatterjee, and F. Forsberg, “Characterization of ultrasound contrast microbubbles using in vitro experiments and viscous and viscoelastic interface models for encapsulation,” J. Acoust. Soc. Am. 118, 539–550 (2005). 35 J. Sijl, E. Gaud, P. Frinking, M. Arditi, N. de Jong, D. Lohse, and M. Versluis, “Acoustic characterization of single ultrasound contrast agent microbubbles,” J. Acoust. Soc. Am. 124, 4091–4097 (2008). 36 A. Doinikov, J. Haac, and P. Dayton, “Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles,” Ultrasonics 49, 269–275 (2009).
Parrales et al.: Viscoelastic properties of coated bubbles
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
Jonathan A. Kopechek and Tyrone M. Porter Mechanical 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, microbubbles samples were generated with a very narrow size distribution by using microfluidics techniques. 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 equilibrium bubble radius. The results showed the great advantage of dealing with monodisperse populations rather than polydisperse populations for the acoustic characterization of ultrasound contrast C 2014 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4890643] agents. V PACS number(s): 43.35.Bf, 43.35.Yb, 43.80.Qf, 43.20.Fn [TGL]
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 applications.1–3 These contrast agents also have a great potential use for drug and gene delivery for treating different diseases.4–6 Due to their compressibility, the microbubbles perform volumetric oscillations, giving rise to a strong resonant echo when driven by an ultrasound field with a specific frequency. Consequently, they scatter more energy than rigid particles of the same size, or even larger liquid-filled particles (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 excitation. 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 a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
J. Acoust. Soc. Am. 136 (3), September 2014
Pages: 1077–1084
dissipation during the oscillatory motion of the coated bubble.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 suspensions13,14 and optical measurements of the oscillatory motion of single microbubbles.15,16 While optical methods are more accurate and sophisticated, they need a considerable investment 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 distribution. In fact, it has been shown that larger microbubbles tend to be the primary source of attenuation in polydispersions, 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 parameters (elasticity and viscosity). Therefore, in order to get a novel generation of monodisperse contrast agents, it is essential 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 characterization methods. To address these needs, researchers began using microfluidic devices to produce monodisperse lipid-coated microbubbles.19,20 Unlike polydisperse microbubble suspensions, monodispersions allow one to measure
0001-4966/2014/136(3)/1077/8/$30.00
C 2014 Acoustical Society of America V
1077
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
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 microbubbles. The theoretical background for these estimations is based on the linearized Rayleigh–Plesset equation modified with the Marmottant model11 to account for the shell rheology. Consequently, in order to assure accurate measurements, we generated monodisperse samples of microbubbles and acquired the acoustic attenuation for different equilibrium radius, thus avoiding the difficulties when using polydisperse contrast agents. We found that the linear viscoelastic parameters 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 experimental 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 symmetrically. The equations of motion describing the radial oscillations 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 surrounding liquid medium, leading to the well-known Rayleigh–Plesset equation,9,22 :: 3 2 1 RR þ R_ ¼ ðpL pa p1 Þ; 2 q1
(1)
where pL stands for the liquid pressure just outside the bubble. This term can be related with the gas pressure inside the bubble pg by setting the normal stress balance across the bound_ ary, pL ¼ pg 2r=R 4lE R=R, where pg ¼ pg0 ðR=Ro Þ3j , where pg0 is the gas pressure at rest and r is the surface tension. 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 lth Þ, 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 q1 x2o R3o =4c1 and lth ¼ pg0 ImU=4xo , respectively, where xo is the characteristic oscillation frequency and c1 is the sound speed in the liquid. We found that both the polytropic coefficient, defined as j ¼ ReU=3, and the thermal viscosity were related to a complex function U, which can be written as25 1078
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
U¼
3c ; p 3ðc 1Þ ffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 1 iPecot iPe 1 iPe
(2)
where c is the adiabatic coefficient and Pe ¼ xo R2o =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 formulation. Assuming that the shell is represented by a thin lipid monolayer with viscoelastic properties, the pressure difference across the bubble wall can now be written as _ þ 4js R=R _ 2; pL ¼ pg 2rðRÞ=R 4lE R=R
(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, considering R ’ Ro ð1 þ XÞ with jXj 1, the linear microbubble radial dynamics equation yields24,25 :: pa X þ 2d X_ þ x2n X ¼ ; q1 R2o
(4)
where d ¼ ð2lE =q1 R2o þ 2js =q1 R3o Þ is the damping factor and xn is the bubble natural frequency, defined by x2n ¼
3jp1 4v þ : 2 q1 Ro q1 R3o
(5)
The differential equation for the radial dynamics shows that the coated microbubble behaves as a damped harmonic oscillator, 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 natural 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 r from the linearly oscillating bubble can be written as :: ps ¼ q1 R3o X ðsÞ=r, where s ¼ ðt r=c1 Þ is the retarded time. Assuming time-harmonic acoustic excitations and oscillations of the form X ¼ X^ expðixo tÞ, we can finally write p^s ¼
eikr eikr ^ ¼ p ; f s a r ðxn =xo Þ2 1 iC r p^a Ro
(6)
where k ¼ xo =c1 is the wavenumber, fs is the omnidirectional 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 bubble 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 Parrales et al.: Viscoelastic properties of coated bubbles
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
rs ¼
ð
jfs j2 dX ¼ 4pjfs j2 ;
(7)
X
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 =q1 xo R2o . 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=Cac Þrs :
(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 ðRo Þ. 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 coefficient is written in terms of the extinction cross section as ð1 nre f ðRo ÞdRo : (9) a¼ 0
Note that, if the microbubble suspension were monodisperse, this parameter would be just a ¼ nre . In this case, the maximum value of the attenuation is reached at the natural frequency 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 experimental 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 microchannels were fabricated in the PDMS device, it was then oxygen 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, microfluidic 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, dipalmitoylphosphatidic 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 maintaining the liquid flow rate and gas pressure constant, we produced 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 independent 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 significantly higher rate of production (see Fig. 2). In order to collect 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 experimental setup for generating monodisperse lipid-coated microbubbles.
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
Parrales et al.: Viscoelastic properties of coated bubbles
1079
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
FIG. 2. Generation of contrast microbubbles. (a) Flow-focusing microdevice (103 lbubbles/s). (b) Co-flow microdevice (105 lbubbles/s). (c) Micrograph of a monodisperse sample with a mean bubble size of approximately 12 lm.
characterization with the theoretical prediction for the attenuation in a contrast microbubble suspension, the measured size distribution was fitted by a Weibull density function (Fig. 3), h K1 K i lK exp lRo =Ro ; (10) f ðRo Þ ¼ lRo =Ro Ro where Ro is the microbubble mean radius and l is a shape parameter defined by l ¼ ½ðK 1Þ=K1=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 agitation/sonication.31,32 B. Acoustic characterization
The experimental setup for measuring frequencydependent attenuation for suspended monodisperse lipidcoated microbubbles is shown in Fig. 4. Monodispersions were dispensed into a sample holder made of polymethylmethacrylate 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
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. 1080
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
12 lm thickness each. The sample holder was submerged in a tank of deionized water and positioned just in front of a stainless 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 transducer (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 arbitrary 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 propagating 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. 4. (Color online) Acoustic experimental setup for measuring the acoustic attenuation of contrast microbubble suspensions. Parrales et al.: Viscoelastic properties of coated bubbles
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
FIG. 5. Acoustic transmission power spectrum for the reference signal, and the measured one for the microbubble monodisperse sample.
Effectively, we observe that the maximum intensity gain was reached at the transducer center frequency. When a contrast 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 1 Iref ; (11) a ¼ ln Isample l 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 lipidcoated microbubbles, with a mean diameter of 5:960:2 lm, as shown in Fig. 3. In Fig. 6, we show the attenuation
FIG. 6. (Color online) Attenuation coefficient in a monodisperse sample at different concentrations n (103 microbubbles/ml). 䊊: n ¼ 1:4, ⵧ: n ¼ 3:5, 䉫: 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 3 108 kg/s. The inset corresponds to a micrograph of the monodisperse coated microbubble suspension. J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
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 corresponding 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 measured for monodispersions was proportional to the microbubble concentration n. This scaling is only valid for low concentration suspensions where multiple scattering between the bubbles 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 coefficient 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, excitation frequency, and, finally, on the viscoelastic properties of the lipid shell, i.e., re ðRo ; xo ; v; js Þ. It is very difficult to measure the shell elasticity and viscosity directly; alternatively, 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 modulus to v ¼ 0:28 N/m and the shell surface viscosity to js ¼ 3 108 kg/s, as shown in Fig. 6. These values were in a very good agreement with those obtained by previous experimental 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 difficulty in identifying both the main resonance frequency peak
FIG. 7. Attenuation coefficient in a polydisperse sample at different concentrations n (105 microbubbles/ml). 䊊: n ¼ 1:2, ⵧ: n ¼ 2:2, 䉫: n ¼ 3:1, and þ: n ¼ 4:5. The inset corresponds to a micrograph of the polydisperse coated microbubble suspension. Parrales et al.: Viscoelastic properties of coated bubbles
1081
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
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.
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 experimental 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 TABLE I. Results obtained for the acoustic characterization and lipid-shell properties estimations using monodisperse contrast agents. Ro (lm) 2.9 3.7 4.8 5.5 6.3
1082
fn (MHz)
v (N/m)
js (108 kg/s)
1.37 1.14 0.84 0.78 0.70
0.28 0.35 0.50 0.76 0.85
3.0 3.6 4.2 5.4 6.0
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
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 microbubble 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 measurements 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 amplitude 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 nonlinear behavior. Moreover, the non-linear correction for the shell viscoelastic model explains theoretically the compression-only behavior observed when lipid-coated microbubbles oscillate with large amplitudes.11,36 Parrales et al.: Viscoelastic properties of coated bubbles
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
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. DPI2011-28356C03-01 and funded by the National Science Foundation (CBET 1134420). 1
FIG. 9. (Color online) Viscoelastic parameters experimental estimation in function of the mean equilibrium microbubble radius from different monodisperse samples. (a) Elastic modulus linear regression: v ¼ 1:8 105 Ro 0:28 N/m. (b) Surface viscosity linear regression: js ¼ 9 103 Ro þ 2:7 109 kg/s.
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 microbubbles rather than polydisperse ones for the acoustic characterization 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 attenuation 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 samples,7,13,14 which are characterized by a very simple instrumentation. More recently, the coating parameters have usually been estimated from optical characterization of single bubbles,15,16,35,36 which avoid the uncertainty related to polydispersity. 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 properties 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 J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
R. Gremiak and P. M. Shah, “Echocardiography of the aortic root,” Invest. Radiol. 3, 356–388 (1968). 2 E. Stride and N. Saffari, “Microbubble ultrasound contrast agents: A review,” Proc. Inst. Mech. Eng., Part H 217, 429–447 (2003). 3 F. Calliada, R. Campani, O. Bottinelli, A. Bozzini, and M. G. Sommaruga, “Ultrasound contrast agents: Basic principles,” Eur. J. Radiol. 27, 157–160 (1998). 4 P. A. Dijkmans, L. J. M. Juffermans, R. J. P. Musters, A. van Wamel, F. J. ten Cate, W. van Gilst, C. A. Visser, N. de Jong, and O. Kamp, “Microbubbles and ultrasound: from diagnosis to therapy,” Eur. J. Echocardiography 5, 245–256 (2004). 5 K. Ferrara, R. Pollard, and M. Borden, “Ultrasound microbubble contrast agents: Fundamentals and application to gene and drug delivery,” Annu. Rev. Biomed. Eng. 9, 415–447 (2007). 6 E. C. Unger, T. Porter, W. Culp, R. Labell, T. Matsunaga, and R. Zutshi, “Therapeutic applications of lipid-coated microbubbles,” Adv. Drug Deliv. Rev. 56, 1291–1314 (2004). 7 L. Hoff, “Acoustic properties of ultrasonic contrast agents,” Ultrasonics. 34, 591–593 (1996). 8 N. de Jong, A. Bouakaz, and P. Frinking, “Basic acoustic properties of microbubbles,” Echocardiography 19, 229–240 (2002). 9 S. Hilgenfeldt, D. Lohse, and M. Zomack, “Response of bubbles to diagnostic ultrasound: A unifying theoretical approach,” Eur. Phys. J. B 4, 247–255 (1998). 10 E. Stride and M. Edirisinghe, “Novel preparation techniques for controlling microbubble uniformity: A comparison,” Med. Biol. Eng. Comput. 47, 883–892 (2009). 11 P. Marmottant, S. van der Meer, M. Emmer, M. Versluis, N. de Jong, S. Hilgenfeldt, and D. Lohse, “A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture,” J. Acoust. Soc. Am. 118, 3499–3505 (2005). 12 A. Doinikov and A. Bouakaz, “Review of shell models for contrast agent microbubbles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 981–993 (2011). 13 N. de Jong and L. Hoff, “Absorption and scatter of encapsulated gas filled microspheres,” Ultrasonics 30, 95–103 (1992). 14 J. N. Marsh and C. S. Hall, “Broadband through-transmission signal loss measurements of Albunex suspensions,” J. Acoust. Soc. Am. 101, 1155–1161 (1997). 15 S. van der Meer, B. Dollet, M. Voormolen, C. Chin, A. Bouakaz, N. de Jong, M. Versluis, and D. Lohse, “Microbubble spectroscopy of ultrasound contrast agents,” J. Acoust. Soc. Am. 121, 648–656 (2007). 16 J. Tu, J. Guan, Y. Qiu, and T. Matula, “Estimating the shell parameters of SonoVue microbubbles using light scattering,” J. Acoust. Soc. Am. 126, 2954–2962 (2009). 17 D. E. Goertz, N. de Jong, and A. F. W. van der Steen, “Attenuation and size distribution measurements of Definity and manipulated Definity populations,” Ultrasound Med. Biol. 33, 1376–1388 (2007). 18 J. M. Gorce, M. Arditi, and M. Schneider, “Influence of bubble size distribution on the echogenicity of ultrasound contrast agents: A study of SonoVue,” Invest. Radiol. 35, 661–671 (2000). 19 K. Hettiarachchi, E. Talu, M. L. Longo, P. A. Dayton, and A. P. Lee, “Onchip generation of microbubbles as a practical technology for manufacturing contrast agents for ultrasonic imaging,” Lab Chip. 7, 463–468 (2007). 20 M. Kaya, S. Feingold, K. Hettiarachchi, A. P. Lee, and P. A. Dayton, “Acoustic responses of monodisperse lipid-encapsulated microbubble contrast agents produced by flow focusing,” Bubble Sci. Eng. Technol. 2, 33–40 (2010). 21 Y. Gong, M. Cabodi, and T. Porter, “Relationship between size and frequency dependent attenuation of monodisperse populations of lipid coated microbubbles,” Bubble Sci. Eng. Technol. 2, 41–47 (2010). Parrales et al.: Viscoelastic properties of coated bubbles
1083
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
22
A. Prosperetti and A. Lezzi, “Bubble dynamics in a compressible liquid. Part 1. First-order theory,” J. Fluid Mech. 168, 457–478 (1986). 23 C. Devin, “Survey of thermal, radiation, and viscous damping of pulsating air bubbles in water,” J. Acoust. Soc. Am. 31, 1654–1667 (1959). 24 A. Prosperetti, “Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids,” J. Acoust. Soc. Am. 61, 17–27 (1977). 25 A. Prosperetti, L. Crum, and K. Commander, “Nonlinear bubble dynamics,” J. Acoust. Soc. Am. 83, 502–514 (1988). 26 J. Kopechek, K. Haworth, J. Raymond, T. Douglas-Mast, S. Perrin, M. Klegerman, S. Huang, T. Porter, D. McPherson, and C. Holland, “Acoustic characterization of echogenic liposomes: Frequency-dependent attenuation and backscatter,” J. Acoust. Soc. Am. 130, 3472–3482 (2011). 27 J. M. Gordillo, Z. D. Cheng, A. M. Ganan-Calvo, M. Marquez, and D. A. Weitz, “A new device for the generation of microbubbles,” Phys. Fluids. 16, 2828–2834 (2004). 28 P. Garstecki, H. A. Stone, and G. M. Whitesides, “Mechanism for flowrate controlled breakup in confined geometries: A route to monodisperse emulsions,” Phys. Rev. Lett. 94, 164501 (2005). 29 P. Garstecki, A. M. Ganan-Calvo, and G. M. Whitesides, “Formation of bubbles and droplets in microfluidic systems,” Bull. Pol. Acad. Sci. 53, 361–372 (2005).
1084
J. Acoust. Soc. Am., Vol. 136, No. 3, September 2014
30
E. Castro-Hernandez, W. van Hoeve, D. Lohse, and J. M. Gordillo, “Microbubble generation in a co-flow device operated in a new regime,” Lab Chip. 11, 2023–2029 (2011). 31 K. Kooiman, M. Emmer, M. Foppen-Harteveld, A. van Wammel, and N. de Jong, “Increasing the endothelial layer permeability through ultrasound activated microbubbles,” IEEE Trans. Biomed. Eng. 57, 29–32 (2010). 32 T. Faez, M. Emmer, K. Kooiman, M. Versluis, A. van der Steen, and N. de Jong, “20 years of ultrasound contrast agents modeling,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 7–20 (2013). 33 N. de Jong, M. Emmer, A. van Wammel, and M. Versluis, “Ultrasonic characterization of ultrasound contrast agents,” Med. Biol. Eng. Comput. 47, 861–873 (2009). 34 K. Sarkar, W. T. Shi, D. Chatterjee, and F. Forsberg, “Characterization of ultrasound contrast microbubbles using in vitro experiments and viscous and viscoelastic interface models for encapsulation,” J. Acoust. Soc. Am. 118, 539–550 (2005). 35 J. Sijl, E. Gaud, P. Frinking, M. Arditi, N. de Jong, D. Lohse, and M. Versluis, “Acoustic characterization of single ultrasound contrast agent microbubbles,” J. Acoust. Soc. Am. 124, 4091–4097 (2008). 36 A. Doinikov, J. Haac, and P. Dayton, “Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles,” Ultrasonics 49, 269–275 (2009).
Parrales et al.: Viscoelastic properties of coated bubbles
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.21.35.191 On: Fri, 19 Dec 2014 01:11:32
