6542 DOI: 10.1021/la904088p Langmuir 2010, 26(9), 6542–6548Published on Web 01/12/2010

pubs.acs.org/Langmuir

© 2010 American Chemical Society

Microbubble Dissolution in a Multigas Environment

James J. Kwan and Mark A. Borden*

Chemical Engineering, Columbia University, New York, New York 10027

Received October 27, 2009. Revised Manuscript Received December 1, 2009

Microbubbles occur naturally in the oceans and are used in many industrial and biomedical applications. Here, atheoretical and experimental study was undertaken to determine the fate of a microbubble suddenly suspended in amedium with several gas species as in, for example, the injection of an ultrasound contrast agent into the bloodstream.The model expands on Epstein and Plesset’s analysis to include any number of gases. An experimental system wasdevelopedwhich isolates themicrobubble in a permeable hollow fiber submerged in a perfusion chamber, allowing rapidexchange of the external aqueous medium. Experimental verification of the model was performed with individual sulfurhexafluoride (SF6) microbubbles coated with the soluble surfactant, sodium dodecyl sulfate (SDS). SDS-coatedmicrobubbles suddenly placed in an air-saturated medium initially grew with the influx of O2 andN2 and then dissolvedunder Laplace pressure. SF6-filled microbubbles coated with the highly insoluble lipid, dibehenoylphosphatidylcholine,were found to exhibit significantly different behavior owing to a dynamic surface tension. The initial growth phase wasdiminished, possibly owing to a shell “breakup” tension that exceeded the pure gas/liquid surface tension. Threedissolution regimes were observed: (1) an initial rapid dissolution to the initial diameter followed by (2) steadydissolution with monolayer collapse and finally (3) stabilization below 10 μm diameter. Results indicated that the lipidshell becomes increasingly rigid as the microbubble dissolves, which has important implications on microbubble sizedistribution, stability, and acoustic properties.

Introduction

Microbubbles are gas particles smaller than a 100 μm indiameter suspended in an aqueous medium. Lipid-coated micro-bubbles are ubiquitous in nature; they form in the oceans bybreaking waves and have a profound impact on acoustic proper-ties, solid sedimentation rates, andmass transport rates across theatmosphere-ocean interface.1-5 Microbubbles also have beenused as a source for extreme temperatures in sonochemicalreactions.6 They have been used to increase oxygen delivery infermentation process.7 Microelectromechanical devices utilize anoscillating microbubble to drive mixing on a chip.8 Medicalmicrobubbles less than 10 μm in diameter are being developedfor use as ultrasound contrast agents,9-11 drug/gene deliveryvehicles,12,13 and oxygen carriers.14,15 Microbubble size and life-span are critically important for all of these applications.

The classic Epstein and Plesset (EP) theory predicts the rate ofmicrobubble dissolution in a quiescent medium for a single gascomponent.16 The EP model includes effects of constant surfacetension and undersaturation of the encapsulated gas.Duncan andNeedham17 used a micropipet technique to show that micro-bubbles with an initial radius around 15 μm and stabilized withsoluble surfactant, such as sodiumdodecyl sulfate (SDS), dissolveaccording to the EPmodel. Insoluble surfactant mixtures, such aslipids, deviate from the predictions of Epstein and Plesset.18

Borden and Longo18 accounted for the increase in microbubbledissolution timeby including a finite shell permeability term to theEP model. Kadyar et al.19 applied a dilatational surface elasticityterm in addition to shell permeability to account for long-termstability under saturated conditions.

Situations often arise, however,whenmultiple gases are presentin the bulk medium surrounding the microbubble. In such cases,the initial microbubble may comprise a single gas, but thesurrounding fluid may have several dissolved gases. For example,lipid-coated microbubbles used in medical applications are ex-posed to a multigas environment when they are injected intoblood, which has oxygen, nitrogen, carbon dioxide, and pos-sibly anesthetic gases as well. Naturally occurring microbubblesformed in the ocean and synthetic microbubbles used in bioreac-tors, microfluidic devices, and microfloatation columns also mayexperience multigas environments. In this article, we treat air as atwo-component gas consisting of nitrogen and oxygen, which aretreated independently. For example, blood has a constant con-centration of nitrogen, but depending on the location of themicrobubble (arterial or venous), the partial pressure of oxygenmay vary.

*Corresponding author: Ph 212-854-6955; Fax 212-854-3054; e-mailmb2910@columbia.edu.(1) D’Arrigo, J. S.Stable Gas-in-Liquid Emulsions: Production inNaturalWaters

and Artificial Media, 2nd ed.; Elsevier Science B.V.: Amsterdam, 2003; Chapter 1.(2) Leighton, T. G.TheAcoustic Bubble, 1st ed.; Academic Press: NewYork, 1997;

Chapter 3.(3) Vagle, S.; Burch, H. J. Acoust. Soc. Am. 2005, 117, 153–163.(4) Lozano, M. M.; Talu, E.; Longo, M. L. J. Geophys. Res., [Oceans] 2007,

112, 9.(5) Johnson, B. D.; Cooke, R. C. Science 1981, 213, 209–211.(6) Shchukin, D.G.;Mohwald, H.Phys. Chem. Chem. Phys. 2006, 8, 3496–3506.(7) Weber, J.; Agblevor, F. A. Proc. Biochem. 2005, 40, 669–676.(8) Marmottant, P.; Raven, J. P.; Gardeniers, H.; Bomer, J. G.; Hilgenfeldt, S.

J. Fluid Mech. 2006, 568, 109–118.(9) de Jong, N.; Emmer, M.; van Wamel, A.; Versluis, M. Med. Biol. Eng.

Comput. 2009, 47, 861–873.(10) Qin, S. P.; Caskey, C. F.; Ferrara, K. W. Phys. Med. Biol. 2009, 54,

R27–R57.(11) Lindner, J. R. Nat. Rev. Drug Discovery 2004, 3, 527–532.(12) Sirsi, S. R.; Borden, M. A. Bubble Sci., Eng. Technol. 2009, 1, 3–17.(13) Lentacker, I.; De Smedt, S. C.; Sanders, N. N. Soft Matter 2009, 5, 2161–

2170.(14) Burkard, M. E.; Vanliew, H. D. J. Appl. Physiol. 1994, 77, 2874–2878.(15) Karichev, Z. R.; Muler, A. L.; Itkin, G. P. Theor. Found. Chem. Eng. 1998,

32, 235–240.

(16) Epstein, P. S.; Plesset, M. S. J. Chem. Phys. 1950, 18, 1505–1509.(17) Duncan, P. B.; Needham, D. Langmuir 2004, 20, 2567–2578.(18) Borden, M. A.; Longo, M. L. Langmuir 2002, 18, 9225–9233.(19) Kadyar, A.; Sarkar, K.; Jain, P. J. Colloid Interface Sci. 2009, 336, 519–525.

DOI: 10.1021/la904088p 6543Langmuir 2010, 26(9), 6542–6548

Kwan and Borden Article

Several models have been developed to predict the dissolutionrate of a microbubble in a multigas medium.15,19-23 Kabalnovet al.20 developed a model to explain the in vivo behavior ofmicrobubbles injected into rabbits and pigs. They adapted theEP model to consider two-gas dissolution influenced by a pres-sure schedule due to cardiopulmonary circulation. Dissolutionwas predicted to occur over three stages: (1) an initial growthperiod, (2) steady dissolution, and (3) a vapor-to-liquid phasechange of the low vapor pressure gas acting under Laplacepressure. Sarkar et al.23 derived a modified EP model for a two-gas system for a lipid-coated microbubble accounting for theeffect of shell permeability on the characteristic growth step anddissolution rate.Kadyar et al.19 later applied a dilatational surfaceelasticity to explain longer dissolution times. Air was treated as apseudo-single gas in these studies.

Systems such as blood contain multiple gases which mayindependently varywith time. Burkard andVanLiew21 developeda numerical model to predict multigas growth and decay ofmicrobubbles within tissue. The model incorporated the effectsof blood perfusion on the influx and efflux of gas and used aniterative technique to solve the model.

Here, we present a numerical model, which is not limited to thenumber of gases in the system. Air is treated as two independentgases. The EP equation was separated into two components, themass balance coupled with diffusion and the Laplace pressureequation, thus allowing theEP form to beused for a systemof anyN number of gases. The numerical model allows estimation of theapparent surface tension when the diameter of the microbubble isknown as a function of time. The fit to experimental data givesinsight into the dynamics of the microbubble shell during growthand dissolution.

Several experimental methods have been developed to investi-gate microbubble dissolution. Borden and Longo18 developed amicrobubble dissolution technique using a laminar flowperfusionchamber. Microbubbles were allowed to rise to the top glasscoverslip, where they remained stationary as the solution belowwas exchanged. However, the glass plate was an impermeablebarrier that impeded symmetric gas diffusion, and insufficientmicrobubble immobilization reduced its effectiveness duringrapid medium exchange. Duncan and Needham17 investigatedmicrobubble dissolution using a micropipet technique. A suctionpressure was applied to a glass pipet to hold the microbubble inplace. Once immobilized, the use of a transfer pipet allowedplacement of the microbubble into a different solution. However,the system was open to the atmosphere and therefore not suitablefor a controlled multigas environment. Kabalnov et al.24 usedultrasound contrast attenuation persistence to qualitatively mea-sure dissolution time. This analysis was complicated by otherclearance mechanisms, such as uptake by phagocytes and lungfiltration. In this report, we use a porous hollow microfibersubmerged in a perfusion chamber,whichmaybeused to simulatethe injection of a microbubble into blood. We designed theapparatus to quickly exchange the bulk fluid without dislodgingthemicrobubble. This novel technique allowed direct observationof microbubble growth and dissolution and quantitative verifica-tion of the numerical model.

Theory

For a microbubble instantaneously submerged in a quiescentmedium with N number of gases, the concentration profilearound the microbubble is assumed to develop orders of magni-tude faster than the movement of the bubble wall.17 The randomwalk diffusive velocity of the slowest gas is several orders ofmagnitude faster than the microbubble wall velocity (verified inresults below), which confirms that a fully developed diffusionprofile approximation is appropriate. We assume that no con-vection occurred due to efflux of gas or bulk flow surrounding themicrobubble. The gas components are assumed to behave ideally.The molar flux is written as

Ji ¼ -DDCi

Dr

� �r¼R

¼ -DiCi, 0 -Ci, s

Rð1Þ

where the diffusion zone is equal to the microbubble radius(i.e., Sherwood number = 2 for pure diffusion from a sphere).25

The component balance is

dni

dt¼ -4πR2Ji ð2Þ

where ni is the moles of component i, t is time, R is themicrobubble radius, J is molar flux, D is diffusivity, and C ismolar concentration (subscripts “0” and “s” represent the bulkand surface, respectively). The microbubble gas pressure (Pg) isgiven by the Laplace equation26

Pg ¼ 2σ

Rþ PH ð3Þ

where σ is the effective surface tension and PH is hydrostaticpressure. The total pressure is equal to the sum of partialpressures, which are related to the moles of gas through the idealgas law.

Pg ¼ BT

4

3πR3

XNi¼1

ni ð4Þ

BT

4

3πR3

XNi¼1

ni ¼ 2σ

Rþ PH ð5Þ

where B is the ideal gas constant and T is temperature. Thediffusion of mass and heat inside the microbubble is sufficientlyfast such that the gas core has uniform concentration andtemperature. Assuming the interface is at local thermodynamicequilibrium, Henry’s law relates the gas partial pressure to theconcentration on the fluid side of the boundary. The interfacialconcentration of species i is given by

Ci, s ¼ KH, i2σ

Rþ PH -

3BT

4πR3

XNj¼1

nj

0@

1A where j 6¼ i ð6Þ

whereKH,i is themolarHenry’s constant andP¥,i is the saturationpressure far from the microbubble (under ambient temperature

(20) Kabalnov, A.; Klein, D.; Pelura, T.; Schutt, E.; Weers, J. Ultrasound Med.Biol. 1998, 24, 739–749.(21) Burkard, M. E.; Vanliew, H. D. Respir. Physiol. 1994, 95, 131–145.(22) Yung, C. N.; Dewitt, K. J.; Brockwell, J. L.; McQuillen, J. B.; Chai, A. T.

J. Colloid Interface Sci. 1989, 127, 442–452.(23) Sarkar, K.; Katiyar, A.; Jain, P.UltrasoundMed. Biol. 2009, 35, 1385–1396.(24) Kabalnov, A.; Bradley, J.; Flaim, S.; Klein, D.; Pelura, T.; Peters, B.; Otto,

S.; Reynolds, J.; Schutt, E.; Weers, J. Ultrasound Med. Biol. 1998, 24, 751–760.

(25) Deen, W. M. Analysis of Transport Phenomena, 1st ed.; Oxford UniversityPress: New York, 1998; Chapter 10.

(26) Edwards, D. A.; Brenner, H.; Wasan, D. Interfacial Transport Processesand Rheology, 2nd ed.; Butterworth-Heinemann: Woburn, MA, 1961; Chapter 4.

6544 DOI: 10.1021/la904088p Langmuir 2010, 26(9), 6542–6548

Article Kwan and Borden

and pressure). The saturation fraction (f) relates the bulk partialpressure with the saturation pressure.

Ci, 0 ¼ KH, iP¥, i fi ð7ÞSubstituting eqs 6 and 7 into the molar balance (eq 2) gives

dni

dt¼ -4πRDiKH, i

2σ

R- P¥, i fi þ PH -

3BT

4πR3

XNj¼ 1

nj

0@

1A

where j 6¼ i ð8ÞRearranging eq 3 and applying the ideal gas law gives

0 ¼ 2σR2 þ PHR3 -

3BT

4π

XNi¼1

ni ð9Þ

Equations 8 and 9 are used to construct the numerical model,whichmaybe solved forN number of gases. In the single-gas case,the model reduces to the classic EP model.

Experimental Materials and Methods

Langmuir Isotherms. Filtered phosphate buffer saline (PBS)(Sigma-Aldrich, St. Louis, MO) solution was used as the subphaseon a Langmuir trough (KSV, Monroe, CT). Stock solution of1,2-dibehenoyl-sn-glycero-3-phosphocholine (DBPC) (Avanti PolarLipids,Alabaster,AL) andpoly(ethylene glycol) 40 (PEG40) stearate(Sigma-Aldrich, St. Louis, MO) were dissolved into chloroform at amolar ratioof 9:1andaconcentrationof 1mg/mL.The stock solutionwas then deposited onto the PBS subphase. After the chloroformevaporated (10-15 min), the deposited monolayer was compressedat a rate of 382.5 mm2/min. The monolayer was compressed from8925 to 7548 mm2 and then expanded back to 8925 mm2. Themonolayer elasticity was determined using the following equation27

χ ¼ Adπ

dAð10Þ

where χ is the elastic modulus, π is the surface pressure, and A is thesurface area.

Preparation of SDS Microbubbles. SDS (Sigma-Aldrich,St. Louis, MO) was dissolved to 10 mM in purified water(18 MΩ 3 cm, Milipore, Billerica, MA) filtered through a 0.2 μmfilter (Whatman, Maidstone, England). The solution was placedinto 3 mL serum vials and put under vacuum for 5 min. SF6

(99.8% pure, Airgas, Radnor, PA) was flowed into the vials at agauge pressure of 40 kPa for 5 min. After SF6 was introduced, sixcycles of vacuum and SF6 (40 s per cycle) were applied to ensure

there was no remaining air in the vial. After the last cycle, theserum vial was left under 40 kPa gauge pressure of SF6 for 8 min.Before use, each vial was vented for 4-6 s. A dental amalgamator(Vialmix, Bristol-Myers Squibb) was used to shake the solution toentrain gas and create SDS microbubbles.

Preparation of Lipid Microbubbles. A lipid formulationwas used as an insoluble surfactant system. DBPC was chosenbecause it is the least soluble among commonly used lipids, andPEG40 stearate was added to enhance microbubble production.To prepare the microbubbles, DBPC and PEG40 stearate werefirst dissolved into chloroform. The two solutions were mixedsuch that the molar ratio of lipid to emulsifier was 9 to 1. Thechloroform was allowed to evaporate in a vacuum chamberovernight. The lipid/emulsifier appeared as a white powder filmat the bottom of the vial. PBS solution was used to resuspend thelipid/emulsifier powder to a concentration of 3mg/mL. The lipid/emulsifier was suspended by heated bath sonication. The gasexchange method described above was used to replace air withSF6. Before shaking, the serum vial was brought up to 80 �C,which is above the main phase transition temperature of DBPC.Once shaken, the vial was immediately cooled under flowing tapwater back to room temperature.

Observation of Microbubble Growth and Dissolution.Figure 1 shows the experimental setup. A porous microdialysishollow fiber (18 kDa molecular weight cutoff, Spectra/Por,Rancho Dominguez, CA) was threaded through a modifiedWarner Instruments RC-20 perfusion chamber to trap the micro-bubbles and rapidly exchange the gas concentration aroundthe microbubble. The perfusion chamber had two inlet ports(Figure 1A). One inlet was used as a microbubble injection site,and the other was used to inject the indicated bulk fluid. Themicrobubbles were trapped in the fiber due to buoyancy(Figure 1B). The perfusion chamber (48 μL volume; 1mmheight)was designed to allow flow around the microfiber withoutdisturbing the microbubble inside. A threaded, 500 μL gastightsyringe (Hamilton, Reno, NV) was used tomanipulate the micro-bubble in the microfiber. A syringe pump was used to inject thebulk fluid into the flow chamber at a rate of 5 mL/min for 10 s.Thus, a volume of 83 μL was applied to ensure the previoussolution was fully purged. The flow chamber setup was placedon an Olympus IX71 inverted microscope with a 20� or 50�objective lens (and an additional 1.6� zoom). Time lapse imageswere acquired using a high-resolution CCD camera (Pixelink,Ottawa, ON).

First, SDS-coated SF6 microbubbles were placed in SF6-satu-rated 10mMSDSsolution.Themicrobubblewas allowed to settlewithin the hollow fiber, and time lapse images of microbubbledissolution were obtained. Second, microbubbles were injectedinto an SF6-saturated solution. Once a single microbubble wasfound and trapped with no flow observed within the microfiber,the syringe pump was activated to purge the system of the SF6-saturated solution and replace it with air-saturated solution.

Image Processing. ImageJ (NIH) was used to determine thediameter of each microbubble and in some cases the aspect ratio

Figure 1. Perfusion chamberdiagram. (A)Flowchamber setup showing the injection sites of themicrobubbles andbulk fluid.Themicrofiberwas threaded through the center of the flow chamber to allow rapid exchange of themedium surrounding themicrobubble. (B)A side view ofthe apparatus showing arrangement of the optics and the location of the microbubble in the hollow fiber.

(27) Gaines, G. Insoluble Monolayers at Liquid-Gas Interfaces; John Wiley &Sons: New York, 1966.

DOI: 10.1021/la904088p 6545Langmuir 2010, 26(9), 6542–6548

Kwan and Borden Article

(ratio of themajor andminor axis of a fitted ellipse). Froma singlemicrobubble image, ImageJ processed four different diametermeasurements: (1) diameter based on area, (2) diameter based onperimeter, (3) maximum distance between two points within themicrobubble, and (4) minimum distance between two pointswithin the microbubble. Differences between these four differentmeasurements were used to obtain error bars. The dissolutiontime was based on the final image taken before the microbubblecompletely disappeared because SDS microbubble dissolutiontended to speed up as the microbubble became smaller.

Simulation. Using the initial microbubble radius andgas composition as an initial condition, a forward-wind finite-difference method28 was employed to estimate future molar gascompositions of the microbubble interior, as follows:

niτþ1 ¼ - 4πhRDiKH, i

2σ

R-P¥, i fi þ PH -

3BT

4πR3

XNj¼1

nj

24

35

þ ni where j 6¼ i ð11Þwhere τ is the numerical time step and h is the difference in timebetween ni and ni

τþ1. Using eq 8 for a single-gas system, theprediction is identical to that of the EP model. After determiningthe new composition of the microbubble, a new radius wascalculated using the Newton-Raphson method:29

0 ¼ 8πσ

3BTðRτ þ 1Þ2 þ 4πPH

3BTðRτ þ 1Þ3 -

XNi¼1

niτ þ 1 ð12Þ

Toavoid instability in themodeling, the time stepwasmade variablewith respect to the microbubble radius. The time step was set equalto the time for amolecule of the slowest dissolving gas (diffusivity=Dmin) to diffuse a distance equal to the microbubbles radius.

h ¼ R2

4Dminð13Þ

Table 1 gives the parameters of solubility and diffusion coeffi-cients for oxygen, nitrogen, and sulfur hexafluoride in water usedin the model.

Another algorithmwas developed that used the experimentallydetermined microbubble radius as an input and solved for aneffective surface tension as an output. Use of a dynamic surfacetension accounted for the mechanical properties and diffusionresistance of the lipid monolayer. Equation 11 was solved todetermine the microbubble composition under an assumed sur-face tension. Equation 12 was then used to solve a new surfacetension value using the experimentally determined microbubbleradius. The new surface tension was substituted into eq 11 toredetermine the molar composition. Iterations were performeduntil the two surface tension values were identical.

Results and Discussion

Wereport on the effects of dissolved gas content and surfactantsolubility on microbubble dissolution. First, we observed micro-

bubbles coated with a soluble surfactant in a single-gas environ-ment. We then observed the same microbubbles submerged in amultigas environment. Finally, we observed the dissolution ofmicrobubbles coated with an insoluble surfactant (lipid) in amultigas medium. SDS was chosen as the stabilizing surfactantbecause it provides a constant surface tension and, as a solublesurfactant, stands as a comparison to the highly insoluble DBPClipid. Larger microbubbles were chosen both for experimentalpracticality and for their importance inmany systems. Results areexpected to scale with microbubble diameter.SDS/SF6 Microbubble in an SF6-Saturated Medium.We

used 10 mM SDS as the soluble surfactant because it maintains aconstant surface tension (40 mN/m) above the critical micelleconcentration (cmc).17 Solutions inside and outside the fiber wereat the same SDS concentration in order to maintain a constantchemical potential for the surfactant in the system. SDS-encap-sulated SF6-filled microbubbles were introduced into the poroushollow microfiber, which was submerged in saturated SF6 solu-tion. The solution surrounding the microfiber was not changed inorder to allow surface tension driven dissolution in a single-gasenvironment. Figure 2A shows the experimental dissolution timesof SDS microbubbles of varying diameter. Also shown are thenumerical model prediction values and analytical solution ob-tained by Duncan and Needham.17 To fit the data, a correctionfactor of 1.5 was applied to the solubility (or, equivalently, thediffusivity) of SF6. This factor was used for all subsequentmodeling. The enhanced solubility (or diffusivity) may be dueto SDS micelles present in solution which may act as hydro-phobic reservoirs for facilitated diffusion.30,31 A representativediameter-time curve is shown Figure 2B.SDS/SF6 Microbubble in an Air-Saturated Medium. We

next tested the effect of sudden exposure to an air-saturatedenvironment (i.e., multigas). This experiment simulates the injec-tion of a microbubble into blood. Figure 3 shows the observedmicrobubble diameter changingwith time. Themicrobubbles hadan initial growth phase followed by dissolution (Figure 3A,B).The model predicted a growth phase as a result of the influx ofoxygen and nitrogen, as shown in Figure 3C. The initial influx ofN2 is much larger than O2 due to the higher dissolved concentra-tion in water. Nitrogen and oxygen diluted the SF6 and reducedthe concentration gradient and therefore the dissolution rate.The growthalso caused a reduction in theLaplace pressure, whichis inversely proportional to the microbubbles radius. Thesecombined effects caused the efflux rate of SF6 gas to decreasewith time. Once SF6 effectively exited the microbubble, thediameter-time curve followed the EP model for a quasi-singlecomponent. The SDS-encapsulated microbubble ceased to bean SF6 microbubble and instead became an air-filled microbub-ble, as previously predicted by Sarkar et al.23 These resultsillustrate that microbubbles may exchange their gas core withinseconds of immersion. Furthermore, they indicate that the con-cept of an osmotic gas for microbubbles used as oxygen sub-stitutesmay only be appropriate when themicrobubble is initiallysubmerged.32-34

We assumed that the diffusion profile surrounding the micro-bubble was fully developed during microbubble growth anddissolution. The observed SDS-encapsulated SF6 microbubble

Table 1. Key Parameters for the Different Gases

gas typeHenry’s constant[(g/m3)/Pa] � 104

diffusivity[m2/s] � 109

oxygen [O2] 3.94846 2.4247,48

nitrogen [N2] 1.71346 247,48

sulfur hexafluoride [SF6] 3.459646,49,50 1.2

(28) Farlow, S. J. Partial Differential Equations for Scientists and Engineers;Dover Publications: New York, 1982; Chapter 37.(29) Stewart, J.Calculus, 4th ed.; Brooks/Cole Publishing: Pacific Grove, CA, 1999;

Chapter 4.

(30) Dungan, S. R.; Tai, B. H.; Gerhardt, N. I. Colloids Surf., A 2003, 216,149–166.

(31) Huang, H. L.; Lee, W. M. G. Chemosphere 2001, 44, 963–972.(32) Unger, E. C.; Porter, T.; Culp, W.; Labell, R.; Matsunaga, T.; Zutshi, R.

Adv. Drug Delivery Rev. 2004, 56, 1291–1314.(33) Vanliew, H. D.; Burkard, M. E. J. Appl. Physiol. 1995, 79, 1379–1385.(34) Vanliew, H. D.; Burkard, M. E. Invest. Radiol. 1995, 30, 315–321.

6546 DOI: 10.1021/la904088p Langmuir 2010, 26(9), 6542–6548

Article Kwan and Borden

in Figure 3B had a maximum radial velocity of 0.42 μm/s.Theoretically, the initial growth phase peaked at a maximumvelocity of 1.7 μm/s. A single SF6 gas molecule diffuses at avelocity of 560 μm/s assuming random walk dynamics, which isseveral orders of magnitude faster than the microbubble surfacevelocity. Thus, the quasi-static assumption was valid.

We compared the observed microbubble dissolution times tothe predicted dissolution times to verify the model (Figure 4A).Statistical software (Prism) was used to determine the correlationbetween the observed and predicted values. The coefficient ofdetermination, R2, for the model (with the independently deter-mined correction factor) was 0.9473. The value was near unityand suggests that the model has strong predictive value. Theresidual scatter plot shows that although the residual tends to bepositive, there was no trend associated with it (Figure 4B). Notethat although there is goodagreement between the theoretical andexperimental dissolution times, not all of the simulations tracedthe diameter-time curves as accurately as Figure 3B.Lipid/SF6 Microbubble in an Air-Saturated Medium.We

repeated the air-saturated experiment using the insoluble surfac-tant mixture, DBPC and PEG40S. This experiment most closelysimulated an ultrasound contrast agent being injected into blood.Figures 5 and 6 show selected microscopy images and thediameter-time curve for a typical lipid-coated microbubble.

When subjected to the air-saturated environment, an initial expan-sion phase was observed for the lipid-coated microbubble. However,expansionwasmuch less pronounced than for theSDSmicrobubbles.The shorter growthperiodobserved for the lipid-coatedmicrobubbles

indicated a large dynamic surface tension that resisted expansion.Wetherefore made surface tension a fitting parameter in the model. Thefit required an increase in surface tension during the growth period,with a peak at 520 mN/m (Figure 7). The effective surface tensionwas 7-fold larger than that of the surface tension for an air-waterinterface (73 mN/m). This large tension may be explained by a“breakup” tension, i.e., a tension that resists lipid monolayerexpansion from its fully condensed state. The concept was origin-ally put forward by Marmottant et al.35 for lipid-encapsulatedmicrobubbles sonicated by 2 MHz pulses over 60 ms intervals,which exhibited “compression only” behavior below a thresholdacoustic pressure. For a 1.6 μm diameter BR14 microbubble(Bracco Diagnostics), the breakup tension was estimated to be∼130mN/m.35The higher breakup tension in our systemmayhavearisen due to the larger microbubble size and lower expansion rate.Lipid shell composition and microstructure also may explain thehigher breakup tension. DBPC is well below the main phasetransition temperature (75 �C), and DBPC microbubbles areknown to exhibit high yield shear and surface viscosity.36

The resting microbubble may be assumed to be in the fullycondensed state.36,37 In this state, the lipid molecules are maxi-mally compressed and the intermolecular van derWaals forces aremaximized. The strength of these van der Waal forces is also

Figure 2. Dissolution of SF6-filled SDS-coatedmicrobubbles dissolving in an SF6-saturated aqueous solution. (A) Experimental dissolutiontimes (scatter), numerical model predicted values (open squares), and the analytical prediction from Duncan and Needham17 (line). Acorrection factor of 1.5 was applied to the Henry’s constant (solubility) of SF6 in water. (B) A typical microbubble dissolution curve.

Figure 3. Growth and dissolution of a typical SF6-filled SDS-coated microbubble suddenly exposed to an air-saturated environment.(A)Microscopy images of themicrobubble. Spots on the bubble are artifacts of the CCDcamera used to obtain the images. (B) Experimentaland theoretical diameter-time curves. (C) Predicted gas content inside the microbubble.

(35) Marmottant, P.; van der Meer, S.; Emmer, M.; Versluis, M.; de Jong, N.;Hilgenfeldt, S.; Lohse, D. J. Acoust. Soc. Am. 2005, 118, 3499–3505.

(36) Kim, D. H.; Costello, M. J.; Duncan, P. B.; Needham, D. Langmuir 2003,19, 8455–8466.

(37) Borden, M. A.; Longo, M. L. J. Phys. Chem. B 2004, 108, 6009–6016.

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Kwan and Borden Article

evident by the rigidity36 and low permeability37 of the monolayer.The large breakup tension for the DBPC microbubble may havearisen due to the force required to suddenly overcome the short-range intermolecular forces between the highly compressed lipids.In addition to short-range van der Waals forces, hydrophobicinteractions also may resist monolayer breakup.

Lipid monolayers undergo transitions from liquid to solidphases when compressed.27 During compression, domain forma-tion must overcome electrostatic repulsion between the head

groups and entropic forces to orient and pack the lipid monolayer.Thus, an activation energy is associated with domain formation.38

Upon expansion, surface tension gradients drive the domains todissolve. However, the kinetics of domain dissolution are domi-nated by strong short-range vanderWaals forces. Expansion of themonolayer, therefore, requires work to overcome these lateral vander Waals forces between the hydrophobic tails of the lipid39 andexpose the hydrophobic tails and gas interface to water.

Figure 8 shows a Langmuir isotherm of DBPC and PEG40stearate mixture of the same composition as the lipid-encapsulatedmicrobubbles.Compressionof themonolayer resulted in agraduallyincreasing surface pressure, followed by a sharp rise in elasticity andmonolayer collapse. The monolayer reached a maximum compres-sion elasticity of 171 mN/m. Hysteresis was observed upon expan-sion. The collapse plateau was not tracked back, indicating thatcollapse was irreversible.40 The compression elasticity increased to412mN/m. The difference in elasticity suggested that themonolayerbecame more rigid upon compression. Hysteresis observed incompression-expansion cycles of surface pressure isotherms of lipidmonolayers40 may be due to the difference in activation energybetween domain formation and dissolution.

A parallel may be drawn between lipid shell breakup duringmicrobubble expansion and hysteresis observed on Langmuir iso-therms. The microbubble expansion rate is determined by the influx

Figure 5. Growth and dissolution of a typical lipid-coated SF6-filled microbubble suddenly exposed to an air-saturated environ-ment.Microscopy images show (A) initial size, aspect ratio (AR)=1.021; (B) spherical growth, AR= 1.013; (C) nonspherical dissolu-tion, AR= 1.141; (D) elliptical microbubble, AR= 1.165; and (E)stablemicrobubble,AR=1.041.Spotson thebubble areartifacts ofthe CCD camera used to obtain the images.

Figure 6. Experimental diameter-time curve corresponding tothe microbubble shown in Figure 5. The aspect ratio (AR) is alsoplotted. The labeled growth and dissolution regimes are discussedin the text.

Figure 7. Effective surface tension of the lipid-coated microbub-ble shown in Figure 5. Also shown is the fitted diameter-timecurve.The cartoons showthe suggestedbehavior of the lipidmono-layer shell, as discussed in the text.

Figure 4. Dissolution times of SF6-filled SDS-coatedmicrobubbles in air-saturated solution. (A) Experimental and theoretical values for thedissolution time as a function of the initial diameter. The numerical model assumed that the microbubble had a constant surface tension of40 mN/m in the 10 mM SDS solution. (B) Observed vs predicted dissolution times. Residuals are shown in the inset.

(38) Helm, C. A.; Mohwald, H. J. Phys. Chem. 1988, 92, 1262–1266.(39) Israelachvili, J. Intermolecular and Surface Force, 2nd ed.; Academic Press:

New York, 1991.(40) Nino, M. R. R.; Lucero, A.; Patino, J. M. R. Colloids Surf., A 2008, 320,

260–270.

6548 DOI: 10.1021/la904088p Langmuir 2010, 26(9), 6542–6548

Article Kwan and Borden

of gas into themicrobubble and ranged from110 to 21000mm2/mincompared to the 380 mm2/min of the Langmuir-Blodgett trough.Themicrobubblemay therefore have experienced “nonequilibrium”expansion. That is, the rate of expansionwas greater than the rate oflipid domain dissolution. The domains may have “torn” apart,possibly along the interdomain borders, to relieve the overpressureinside the microbubble. Domain tearing has been observed in othermonolayer systems.41 The tensile force required to tear apart lipiddomains may be the origin of the high breakup tension.

Lipid domain “tearing”may impact the behavior a lipid-coatedmicrobubble under ultrasound pulsing. For example, higherdefect densities within the monolayer shell may reduce thepressure buildup necessary for shell rupture, thus making themicrobubble more compliant. One may then design the shellmicrostructure to amplify or dampen the acoustic response.However, this remains to be tested experimentally.

Dissolution of the lipid-encapsulated microbubble after thegrowth phase appeared to have three regions. In region 1,immediately after monolayer expansion, the microbubble shrankrapidly back to its initial resting diameter (Figure 6). Laplacepressure forced rapid dissolution of the gas core and compressionof the monolayer back to a condensed phase. The surface ten-sion decreased from the breakup tension and plateaued around34 mN/m at the end of microbubble expansion. As the efflux ofgas further drove surface compression, the monolayer reachedmaximum packing and began to collapse.

The onset of region 2 occurred when the microbubble returnedback to its approximate initial size. Region 2was characterized bya nearly constant average microbubble boundary velocity. Non-spherical shapes and rapid jerks in diameter were also observedduring dissolution (Figure 6). Fluctuations in the effective surfacetension suggested that monolayer collapse was discontinuous, as

previously observed in Langmuir monolayers of lipid mixtures.42

Discrete collapse mechanisms such as vesicle formation and lipidmonolayer buckling and folding may have caused the observeddeviations in sphericity and fluctuations in surface tension.42-44

Though the effective surface tension fluctuated, the meansteadily decreased from around 10 mN/m to about 1 mN/m.The decrease in surface tension suggested that the shell wasbecoming increasingly rigid as the microbubble became smaller.The microbubble elliptical shape was characterized by an aspectratio, which peaked around the transition between regions 2 and 3(Figure 6).

In region 3, the diameter of the microbubble quickly droppedfrom 16 to 8 μm in diameter and then stabilized. As the micro-bubble continued to dissolve very slowly, it became more sphe-rical at diameters below∼6 μm. The microbubble may have beencompressed to a point where themolecules or domains in the shellbecame “jammed”,45 thus hindering further collapse. Interest-ingly, microbubble stabilization indicated that the monolayerbecomes increasingly rigid at smaller diameters, suggesting thatsmaller microbubbles are more stable.

Conclusions

SF6microbubbles of 25-100 μminitial diameterwere observedas they were suddenly immersed in single- and multigas environ-ments using a modified perfusion chamber, and results werecompared to a model derived to simulate gas exchange. Micro-bubbles coated with the soluble surfactant, SDS, and kept in asingle-gas environment dissolved under constant surface tensionas predictedby classicEP theory.Microbubbles suddenly exposedto an air-saturated environment initially grew due to the influx ofair and then dissolved under surface tension. The interior gas wasrapidly exchanged. Interestingly, the coating surfactant had astrong effect on the reaction of the microbubble. While SDS-coated microbubbles grew and dissolved as predicted by themodel, lipid-coated microbubbles deviated significantly. Surpris-ingly, the growth regime was less pronounced, and three dissolu-tion regimes were found, including (1) rapid dissolution backto the original diameter, (2) steady dissolution with a nearlyconstant wall velocity, and (3) stabilization near ∼10 μm dia-meter. The results indicate that the surface tension was dynamic,and the behavior can be explained by monolayer breakup,collapse, and jamming. The role of the monolayer in the micro-bubble response has important implications on microbubblestability and size distribution aswell as the fate of themicrobubbleduring intravenous injection and ultrasound insonification.

Acknowledgment. This research was supported by theNew York State Foundation for Science, Technology andInnovation (NYSTAR) grant C020028 to MAB.

Figure 8. Langmuir isotherm of a DBPC:PEG40-stearate mono-layer mixture. The monolayer was compressed and then expandedat a rate of 380mm2/min. Compression and expansion are denotedby arrows on the hysteresis curve. Dotted lines show linear fit todetermine elasticity values. Cartoons show suggested monolayerbehavior, as discussed in the text.

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