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Hydrostatic Pressurization of Lung Surfactant Microbubbles: Observation of a Strain-Rate Dependent Elasticity Alec N. Thomas, and Mark Andrew Borden Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03307 • Publication Date (Web): 24 Oct 2017 Downloaded from http://pubs.acs.org on November 2, 2017

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Hydrostatic Pressurization of Lung Surfactant

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Microbubbles: Observation of a Strain-Rate

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Dependent Elasticity

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Alec N. Thomas1 and Mark A. Borden*1,2

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Department of Mechanical Engineering, 2Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA

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*Corresponding Author Mark A. Borden, PhD University of Colorado 1111 Engineering Drive Boulder, CO 80309-0427 Phone: 303.492.7750 Fax: 303.492.3498 Email: [email protected]

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KEYWORDS: Survanta, DPPC, perfluorobutane, dissolution, monolayer collapse

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Abstract

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The microbubble offers a unique platform to study lung surfactant mechanics at physiologically

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relevant geometry and length scale. In this study, we compared the response of microbubbles

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(~15 µm initial radius) coated with pure dipalmitoyl-phosphatidylcholine (DPPC) versus

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naturally derived lung surfactant (Survanta®) when subjected to linearly increasing hydrostatic

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pressure at different rates (0.5 to 2.3 kPa/s) at room temperature. The microbubbles contained

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perfluorobutane gas and were submerged in buffered saline saturated with perfluorobutane at

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atmospheric pressure. Bright-field microscopy showed that DPPC microbubbles compressed

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spherically and smoothly, whereas Survanta microbubbles exhibited wrinkling and smoothing

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cycles associated with buckling and collapse.

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collapse amplitude was constant, but collapse rate increased with pressurization rate.

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analysis of the pressure-volume curves indicated that the dilatational elasticity increased during

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compression for both shell types. The initial dilatational elasticity for Survanta was nearly twice

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that of DPPC at higher pressurization rates (>1.5 kPa/s), producing a pressure drop of up to 60

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kPa across the film prior to condensation of the perfluorobutane core. The strain-rate dependent

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stiffening of Survanta shells likely arises from its composition and microstructure, which

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provides enhanced in-plane monolayer rigidity and lateral repulsion from surface-associated

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collapse structures. Overall, these results provide new insights into lung surfactant mechanics

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and collapse behavior during compression.

Seismograph analysis showed that Survanta An

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Introduction

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The pulmonary system is a complex network of interconnected structures terminating at

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microscopic alveolar sacs lined with lung surfactant (LS) at the air/water interface.1

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comprises lipids and proteins working in concert to maintain a low surface tension throughout

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the dynamic breathing cycle.1–3 Low surface tension is necessary to prevent alveolar collapse and

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reduce the required work to expand the lungs by the thoracic muscles. A hallmark of acute

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respiratory distress syndrome (ARDS) is the inactivation of LS, rendering the film incapable of

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dynamic mechanical stability and leading to alveolar collapse and low blood oxygenation.4,5

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Direct instillation of lung surfactant replacement therapy (LSRT) has substantially improved

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survival rates for neonatal respiratory distress syndrome (NRDS), and it is the current standard

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practice of care.6,7 More recently, researchers have attempted to formulate LSRTs to treat ARDS

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more generally, and to mitigate the risks of animal-derived LSRT by creating purely synthetic

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surfactant formulations.8,9,2

LS

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The typical human lung contains ~170 alveoli per mL of lung parenchyma,10 and each alveolus

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is quasi-spherical in shape with an average diameter of ~100 µm.11 Owing to the complexity of

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the lung and difficulty imaging it without inducing artifacts, the exact physiological structure of

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LS and the mechanics at the alveolar air/water interface during inflation/deflation are not yet

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fully understood.11,12 This makes it challenging to strictly define physiological values for strain

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and strain rate. A recent review lists values for the linear strain ( =  −  /, where 

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and  are initial and final radii) to be ~5-25% during normal breathing.11 A recent in vivo x-ray

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imaging study in mice reported a similar range of strains.13 Given the respiratory rate for an

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adult human of ~12-20 breaths/min, the alveolar strain rate is estimated to be ~1-10 %/s. This

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value can vary significantly between different regions of the lung, and for different tidal volumes

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and respiratory rates.

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Development and application of a functional LSRT relies on an understanding of LS

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mechanics during compression.14–16 During inhalation, the diaphragm and intercostal muscles

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expand the chest cavity to induce a negative pressure that draws air in. During exhalation, the

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muscles induce a positive pressure that drives air out, thus compressing the alveolar surface area

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and collapsing the surfactant film. Langmuir trough experiments have shown that natural and

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synthetic LS films can achieve high surface pressure (near zero surface tension) prior to

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collapse.17–19 Collapse is evident as a plateau in the surface pressure-area isotherm, indicating a

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very low film elasticity. Unfortunately, the Wilhelmy plate method of measuring surface tension

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loses accuracy as the film transitions into a solid.20

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measurements have shown similar results for LS films between spreading and collapse.21,22

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However, the mechanical properties of LS films during compression beyond the onset of

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collapse is poorly understood and rarely investigated. The post-collapse mechanics may be

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critical to the development of efficacious LSRTs since alveoli experience a wide range of strains

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dependent on their location in the lung.

Captive bubble and pendant drop

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A microbubble is a small, gas-filled particle (1-100 µm diameter) stabilized by a surfactant

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shell that inhibits coalescence and surface tension-induced dissolution. Microbubbles have been

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widely studied for use as ultrasound contrast agents, drug/gene delivery vehicles and injectable

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oxygen carriers.23–25

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microbubbles for these applications.26–28 In this study, we used a custom microscopy chamber to

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monitor the response of individual microbubbles coated with Survanta® (a commercially

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available LSRT), versus those coated with pure dipalmitoyl-phosphatidylcholine (DPPC) (the

Our group has previously demonstrated the synthesis and use of LS

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main component of LS), to a linear pressure increase. In this sense, we use the microbubble as a

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sort of film balance to study LS mechanics. This idea is in part inspired by the original work of

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R.E. Pattle,29 who discovered LS by the observation of highly stable microbubbles liberated from

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the aspirated lung.30 We caution that an individual microbubble does not completely mimic the

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complex interconnected nature of the pulmonary system. However, many of the properties of the

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microbubble are similar to those of an isolated lung alveolus. For example, the spherical shape

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of a microbubble provides a similar geometry and curvature. This curvature is relevant because

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the surfactant molecules are known to assemble into microdomains within the monolayer

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plane,31 and alveolar deformation is on the order of microns during normal breathing. By

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following the response of a microbubble to pressurization, one may determine physiologically

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relevant physical properties, such as surface elasticity and gas permeability.

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In this study, we first observed the bubble shape as it compressed under the hydrostatic load

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and analyzed collapse events by plotting the corresponding seismograms. We then analyzed the

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pressure-volume behavior of each microbubble with an analytical model that accounts for both

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compression and dissolution. The analysis provided an estimation of the initial dilatational

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elasticity of the shell (  ), which serves to characterize the mechanical response of Survanta and

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DPPC shells.

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Theory

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Here, an analytical model is derived for the compression and dissolution of a microbubble

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subjected to a linear increase in hydrostatic pressure. Fick’s law describes the accumulation of

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gas in the bubble over time,

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=  −  ,

(1)

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where  is the number of moles,  is time,  is the mass transfer coefficient,  is the bubble

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surface area,  is the dissolved gas concentration at the bubble surface, and  is the dissolved

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gas concentration in the bulk medium. Henry’s law relates the dissolved gas concentration to the

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partial pressure for dilute solutions at equilibrium, =

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,

(2)

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where  is Henry’s constant (in this form, the “Ostwald coefficient”) and  is the dissolved gas

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concentration. The molar gas concentration,  = , is determined by the ideal gas law, where

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 is the gas partial pressure,



is the gas constant, ! is the temperature. Substitution gives,

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=

"#$ 

 −  .

(3)

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Before pressurization begins, the medium is equilibrated with the gas at atmospheric pressure  .

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For a single gas component, the partial pressure is equal to the total pressure inside the bubble

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(),

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=

"#$ 

 − .

(4)

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The shell interfacial rheology has been shown to significantly influence the microbubble

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response to pressure changes.32,33 Here, we adopt the exponential elasticity model by Paul et

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al.34 to describe the surface dilatational elasticity, , of the shell:

=  ∙ exp−)*,

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(5)

" /

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where  is the initial dilatational elasticity, * = +," . − 11 is the fractional change in area

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from the unstrained state, and ) is a constant equal 1.5.34 The surface tension, 2, of the film is

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then determined by,

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-

2 = 2 + ∙ *,

(6)

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where 2 is the equilibrium surface tension. The microbubble is modeled as a sphere on which

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the interfacial stresses cause a jump (pressure drop) in the normal stress at the interface. Sarkar

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et al.35 previously defined this pressure jump at the interface as the dynamic boundary condition:

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78 9:78 /< /= 7 /  = 4 + 46 + ; + - + +, . − 11, 7

7

7

7

7-

(7)

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where 4 is the hydrostatic pressure, 6 is the medium viscosity and > is the surface dilatational

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viscosity. For the pressurization rates used in this study, the viscous normal stress in the medium

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(water) and the dilatational viscosity contribution of the lipid shell (of order ~µN/m36) can be

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neglected. Additionally, the initial surface tension is set to zero for an initially stable (non-

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dissolving) microbubble.37,38 The dynamic boundary condition then reduces to the well-known

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Laplace pressure equation with the surface dilatational elasticity contribution,

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 = 4 +

/= 7

7 /

+,7 . − 11 . -

(8)

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Equations (5), (6) and (8) was solved numerically using the backward-difference method with

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 as the single fitting parameter to the experimental data using a least-squares regression.

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Experimental Section

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Materials. Survanta® (beractant, AbbVie Inc., Chicago, IL, USA) was purchased and stored

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at 4 °C, as directed. Special care was taken to ensure sterility during the use of the product.

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Survanta is a naturally derived bovine lung surfactant that is fortified to standardize each batch

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with the following components: DPPC, palmitic acid and tripalmitin. The concentrations of

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components are listed on the package insert as 25 mg/mL phospholipid (primarily DPPC), 0.5-

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1.75 mg/mL triglycerides, 1.4-3.5 mg/mL fatty acids and less than 1.0 mg/mL proteins (SP-B,

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SP-C). Though Survanta is naturally derived, the extraction and purification process alters the

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composition to reduce hydrophobic surfactant proteins SP-B and SP-C and eliminate cholesterol

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and the hydrophilic surfactant proteins. DPPC was purchased from Avanti (Alabaster, AL) in

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lyophilized dry powder form of greater than 99% purity and stored at -20°C with a nitrogen gas

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head space. Perfluorobutane (PFB) was purchased from FluoroMed (Round Rock, TX). PFB

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was chosen as the filling gas because it generated a higher yield of microbubbles and was less

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susceptible to dissolution during pressurization than air microbubbles. Supplemental Figure 1

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shows that even at the lowest pressurization rate an air microbubble dissolves rapidly, yielding

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strain rates beyond the physiological range and making it difficult to analyze the surfactant

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mechanics. Phosphate buffered saline (PBS) 137 mM NaCl, pH 7.4 (ThermoFischer Scientific,

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Fair Lawn, NJ) was purchased and used as directed.

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Microbubble Synthesis. Survanta microbubbles were produced as follows: the 20-mL stock

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vial of Survanta was warmed to room temperature and gently swirled to homogenize the

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contents.

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phospholipid in 0.2-µm filtered PBS (137 mM NaCl) made from purified water (18.2 MΩ cm

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resistivity; Direct-Q, Millipore, Billerica, MA, USA). To ensure a well-mixed solution, each

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batch was bath sonicated for 10 min at 37 oC. Then 2-mL aliquots were dispensed in 3-mL glass

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serum vials, immediately capped, the air headspace was exchanged with PFB, and the vial was

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stored at 4 oC.

The Survanta material was extracted by sterile syringe and diluted to 2 mg/mL

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DPPC microbubbles were made as follows: Lipid was rehydrated in PBS to a concentration of

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2 mg/mL and then homogenized by tip sonication until the solution appeared translucent.

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During sonication, the temperature was periodically monitored to ensure the temperature did not

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exceed 10 °C past the main phase transition temperature (41 °C). 2-mL aliquots were dispensed

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into 3-mL glass serum vials, the air headspace was exchanged with PFB, and the vial was stored

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at 4 oC.

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All microbubbles were produced by securing a serum vial in a shaker device (VialMix, Bristol-

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Myers Squib) and activating for 45 s. The suspension was extracted with a 3-mL syringe, and

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larger microbubbles were isolated by inverting the syringe for 10 s, discarding the sub-phase, and

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refilling the syringe with fresh PFB-saturated PBS to dilute the microbubbles.

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Pressurization Chamber. Survanta and DPPC microbubbles were observed at six separate

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linear pressurization rates (0.5, 0.8, 1.1, 1.5, 1.9 and 2.3 kPa/s) using a custom chamber fastened

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to a microscope stage (Olympus BX52, Center Valley, PA, USA) at room temperature (21 °C ±

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1 °C). The chamber was outfitted with a pressure transducer (Transducers Direct TDH40

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Cincinnati, OH, USA) and a type-K thermocouple insulated wire (Omega HSTC-TT-K-24S-36,

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Stamford, CT, USA), which was tethered and sealed through the thermocouple port.

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performed experiments at room temperature to establish a baseline response of the surfactant

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films undergoing compression during microbubble pressurization. Several prior studies have

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also investigated lung surfactant films at room temperature,39–42 and the results obtained at this

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temperature remain relevant to technologies employing these types of surfactant films, such as

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microbubbles used for drug delivery and oxygenation.29 The chamber was outfitted with a

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pressure transducer (Transducers Direct TDH40 Cincinnati, OH, USA) and a type-K

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thermocouple insulated wire (Omega HSTC-TT-K-24S-36, Stamford, CT, USA), which was

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tethered and sealed through the thermocouple port. The thermocouple tip was secured adjacent

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to the optical window to obtain an accurate reading of the microbubble temperature. Images

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were captured in bright-field mode on an upright microscope with a digital camera (Q-Imaging

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Q-Click, Surrey, BC, Canada) at 10 Hz sampling frame rate. All data were acquired through a

We

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data acquisition device (USB-6000, National Instruments, Austin, TX, USA) by a custom

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LabVIEW (National Instruments) program.

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Figure 1. Illustration of the chamber design. The chamber pressure was controlled by a syringe

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pump (Harvard Apparatus, Holliston, MA) programmed to deliver a calibrated volumetric flow

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rate. A metal syringe (KD Scientific, Holliston, MA) filled with PFB-saturated PBS was used to

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ensure uniform pressurization during the entire experiment.

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The experiment commenced by first filling the chamber with PFB-saturated PBS to maintain a

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saturated environment. Then microbubbles were injected into the chamber and floated to the top

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coverslip. The outlet valve was shut off and the inlet valve was opened to the metal syringe.

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The syringe pump was programmed to achieve the desired pressurization rate, and data

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acquisition was started approximately one minute before the onset of pressurization to verify that

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bubble volume remained constant before the onset of pressurization.

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Image Analysis. Digital images were processed through a custom MATLAB (Mathworks,

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Natick, MA) program. Briefly, each acquired frame was converted to a binary image and

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analyzed to measure the cross sectional area, perimeter and eccentricity of the microbubble

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during pressurization. The grayscale pixel threshold was automatically generated using the

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MATLAB function graythresh.

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deviation, unless otherwise noted. The largest microbubble radius change was 8 µm (mean 4 ± 2

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µm) before the onset of condensation. The imaging plane was not altered during the experiment,

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and the depth of focus of our imaging system was ~17 µm. Thus, each microbubble remained in

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focus during the experiment.

All measured values are presented as mean ± standard

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Statistical Analysis. A two-way Analysis of Variance was performed on the fitted initial

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dilatational elasticities for Survanta and DPPC. The population means for the initial dilatational

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elasticity of the shell types were compared against each other at each pressurization rate using

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the Tukey method in order to quantify the comparisons. A significance level of p < 0.05 was

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used. The statistical results are reported in Supplemental Table 1.

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Results and Discussion

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Microbubble Morphology. The spherical microbubble shape is a consequence of surface

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tension acting to minimize surface area. In our experiments, all microbubbles were initially

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observed to have a spherical shape (n ≥ 20 microbubbles for each shell type and pressurization

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rate). Examples are shown in Figure 2. The initial tension of these microbubbles must have

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been quite low, however, or they would have spontaneously dissolved under their own Laplace

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pressure.37,38,43 Rather, we observed that the bubbles were stable in size for at least several

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minutes prior to hydrostatic pressurization.

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Figure 2A shows typical microscope images of Survanta microbubbles during pressurization at

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the slowest and fastest rates. In general, the cross section remained highly circular during the

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initial compression. After a linear strain of ~9 ± 2 %, however, Survanta shells deviated from

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circularity and appeared to wrinkle and smooth in cycles. This wrinkling is seen on the image at

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249.2 s on the top panel, and at 86.7 s on the bottom panel of Figure 2A. Within one video

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frame (0.1 s), the microbubble rapidly smoothed and regained circularity.

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wrinkling/smoothing behavior was observed for Survanta microbubbles at all pressurization

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rates. This behavior is reminiscent of the “clicking” behavior observed by Pattle on liberated

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lung bubbles44 and by Schürch et al. on the captive bubble surfactometer,45 as well as the “jerks”

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observed on Langmuir films40 of model lung surfactant. The wrinkling of Survanta shells

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suggested that the surface was rigid enough to deform out-of-plane as a mechanism to sustain the

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increasing surface stress. The shape change indicated that the shells achieved states of very low,

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perhaps even negative, surface tension. Furthermore, the sudden shape change suggested that

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Survanta shells experienced a buckling instability and collapsed.42,46 The return to a more

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circular shape at these collapse transitions was consistent with a transient increase in surface

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tension.

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perfluorobutane gas core condensed at a hydrostatic pressure of 272 ± 9 kPa (mean ± standard

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deviation), which was ~60 kPa above the equilibrium saturation curve.47

Similar

The wrinkling/smoothing process repeated itself during pressurization until the

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Figure 2. Images acquired for Survanta (A) and DPPC (B) microbubbles during pressurization at

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0.5 kPa/s (top row of each panel) and 2.3 kPa/s (bottom row of each panel). The scale bar is 10

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µm.

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Figure 2B shows a similarly sized DPPC bubble undergoing pressurization at the same rates.

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In general, DPPC microbubbles remained circular throughout the pressurization process, for all

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pressurization rates. These microbubbles were not observed to wrinkle. The smooth, spherical

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shape of DPPC shells indicated that they were not able to buckle and collapse in the same

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manner as Survanta shells. On average, DPPC microbubbles condensed at a slightly lower

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hydrostatic pressure of 262 ± 8 kPa, which was ~50 kPa above the equilibrium saturation curve,

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Collapse Phenomena. Figure 3 shows typical plots of microbubble cross sectional area as a

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function of time for the slowest and fastest pressurization rates. The Survanta microbubbles

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initially had a relatively smooth and steep area reduction until the onset of collapse (denoted by

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the first arrow in Fig. 3A). These microbubbles continued to experience buckling/collapse

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cycles until just before condensation (denoted by the second arrow in Fig. 3A). The sharp

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collapse events indicated a series of elastic compression and singular failure events.

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supports our assumption that the dilatational elasticity dominates over dilatational viscosity.

This

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Figure 3. Cross-sectional areas of typical Survanta (black curve) and DPPC (red curve)

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microbubbles, along with the chamber pressure (blue curve). (A) Pressurization rate of 0.5 kPa/s

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and (B) pressurization rate of 2.3 kPa/s. The arrows indicate the first and last buckling events for

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the Survanta microbubbles.

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Typical DPPC microbubbles are shown in Figure 3B. These microbubbles exhibited a smooth

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reduction in cross sectional area, absent of discontinuities, throughout the pressurization process.

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Similar to Survanta, the cross section of DPPC microbubbles initially decreased rapidly and then

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plateaued, and an abrupt decrease in area was observed upon condensation of the core.

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Figure 4 compares seismograms for the Survanta and DPPC microbubbles shown in Figure 3.

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This analysis follows that by Gopal et al.40 for Langmuir films and by Kwan et al.48 for

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microbubbles coated with long acyl-chain lipids. Here, we define a collapse event as a spike in

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the cross-sectional area velocity (−∆A /∆). The cross-sectional area velocity of DPPC never

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exceeded the threshold value of 15 µm2/s. Survanta shells, on the other hand, showed several

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spikes in the seismograms, indicating buckling/collapse transitions. The left arrow denotes the

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first collapse event for Survanta, while the right arrow marks the final collapse event before

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condensation. The first collapse event occurred at a linear strain of 9 ± 2 % (mean ± standard

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deviation), independent of pressurization rate. Interestingly, the seismogram did not exhibit a

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trend for either collapse frequency or amplitude as a function of time (and therefore size).

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294 295

Figure 4. A representative seismogram for compression of Survanta (black) and DPPC (red)

296

shelled microbubbles at 0.5 kPa/s, corresponding to the area-time curves in Figure 3. The dashed

297

line indicates the area velocity threshold arbitrarily assigned to define a buckling event. The blue

298

arrows correspond to the first and last buckling events.

299 300

Figure 5A shows the collapse amplitude for Survanta microbubbles at each pressurization rate.

301

Collapse amplitude was calculated as the surface area difference between consecutive collapse

302

events (−∆ ) to indicate the amount of ejected material. Prior research suggests this material

303

remains associated to the microbubble surface as folds and vesicles.28 The average value of ∆

304

was 20.7 ± 3.1 µm2 (mean ± standard deviation) at all pressurization rates. The magnitude of

305

collapse was found to be independent of both microbubble size and compression rate.

306

Figure 5B shows the average collapse frequency at each pressurization rate for Survanta

307

microbubbles. To determine the collapse frequency (BA ), the total number of collapse events

308

exceeding the threshold was divided by the pressurization time, up to condensation. As might be

309

expected from the constant collapse amplitude, the frequency monotonically increased with

310

pressurization rate. The trend was approximately linear, which is unexpected for isothermal

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311

compression of an ideal gas. This result indicated that microbubble pressurization at these rates

312

is a complex process involving both compression and dissolution.

313

314 315

Figure 5. (A) The average surface area reduction between consecutive collapse events versus

316

pressurization rate for Survanta shelled microbubbles. The dashed line indicates the average

317

surface area loss. (B) Collapse frequency versus pressurization rate. The red line is a linear

318

regression trend-line (R2=0.98).

319 320

Pressure-Volume Behavior. To examine the relative degree of compression and dissolution,

321

we compared the experimental data to theoretical curves for each process, respectively (Figure

322

6). The experimental normalized volume, C/C, is shown for each shell at the slowest and

323

fastest pressurization rates (mean ± standard deviation). The upper curves in each plot were

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324

calculated from the ideal gas law assuming isothermal compression without dissolution of the

325

gas core and that the bubble pressure was equal to the hydrostatic pressure,  = 4 .

326

Surprisingly, the experimental data for Survanta shells were above the isothermal compression

327

curves for the first ~50 s at the slowest rate and ~20 s at the fastest rate. This result cannot be

328

explained by gas diffusion into the bubble because the chemical potential gradient in this case

329

favors a net transfer of gas molecules in the opposite direction. Thus, the pressure  inside the

330

gas core must have been less than the measured hydrostatic pressure for these microbubbles. A

331

pressure drop suggests that Survanta shells are capable of sustaining stress (i.e., negative surface

332

tension) under these conditions.

333

simulations, which showed that model lung surfactant membranes are capable of sustaining a

334

negative surface tension under compression.49

335

Eventually, the experimental normalized volume dropped below the isothermal compression

336

curve, indicating that gas dissolution is significant for both Survanta and DPPC microbubbles at

337

each pressurization rate.

This effect is supported by previous molecular dynamics

This effect was not observed for DPPC.

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Figure 6. Normalized volume-time curves. A) Survanta (left) and DPPC (right) microbubbles at

340

the slowest pressurization rate (n ≥ 20). B) Similar plots at the fastest pressurization rate (n ≥

341

20). The upper (red) curves were calculated assuming isothermal compression without

342

dissolution. The bottom (green) curves were calculated by use of equation (4) for pure

343

dissolution without shell resistance to gas permeation.

344 345

The lower curves in each plot of Figure 6 were calculated from equation (4) assuming that the

346

mass transfer coefficient is equal to that for a purely diffusing sphere with no shell resistance:

347

 = D/, where D is the diffusivity of perfluorobutane in water (7×10-10 m2/s); and bubble

348

pressure was set equal to the hydrostatic value. The experimental data were always above these

349

“pure dissolution” curves, indicating that gas dissolution was hindered by the shell.

Two

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350

mechanisms may explain this result: First, the shell may have been able to sustain stress (as

351

indicated above), leading to a pressure drop across the shell that diminished the concentration

352

gradient. Second, the shell material may have impeded gas transport. These mechanisms are

353

investigated in detail below.

354

Model analysis. The results above suggest that Survanta and DPPC microbubbles compressed

355

and dissolved as the surrounding hydrostatic pressure was increased. We therefore modeled the

356

bubble response to pressurization using equations (3)-(8), which explicitly account for

357

dissolution. Unfortunately, the model failed to fit the experimental data accurately with the mass

358

transfer coefficient set to a constant value. To better fit the data, we introduced an empirical

359

relation for the mass transfer coefficient to account for the effect of convection. The relation

360

forced a linear increase in  with increasing rate of change in the radius E8 E:

361

 =  + E8 E,

362

where  is the mass transfer coefficient in the quasi-static case and  is an empirical constant.

363

The quasi-static mass transfer coefficient is given by the equation:

364

1/ = /D + F4GHH ,

(9)

(10)

365

where D is the diffusivity of PFB in water and F4GHH is the shell resistance to gas permeation

366

(107 s/m).25 The empirical constant  was set to 103.

367

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Figure 7. Model results from representative Survanta shelled microbubbles at (A) the slowest

370

pressurization rate and (B) the fastest pressurization rate. The first column shows the theoretical

371

volume of the bubble using E0 as the fitting parameter. The second column is the elasticity of

372

the shell during the pressurization experiment using the exponential elasticity model. The third

373

column compares the hydrostatic pressure to the apparent bubble pressure.

374 375

Figure 7 shows results from representative Survanta microbubbles at the slowest (top) and

376

fastest (bottom) pressurization rates. The calculated volume fits the experimental data well.

377

According to the model, the surface dilatational elasticity monotonically increased with time and

378

then plateaued prior to condensation (Fig. 7B). The elasticity values fall within the range of

379

experimentally reported surface dilatational elasticity values for DPPC of 0.03 – 2.5 N/m.35,50–53

380

The model also predicted an increasing pressure drop across the shell (negative surface tension)

381

that followed the increasing elasticity.

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382

Figure 8 shows the results of representative DPPC microbubbles. The general shape of the

383

elasticity-time curves were similar for DPPC and Survanta, but the pressure drop across the

384

DPPC shell was significantly less. At the slowest pressurization rate, the estimated pressure drop

385

was 40.4 ± 11.1 kPa (mean ± standard deviation) for Survanta and 21.8 ± 12.7 kPa for DPPC. At

386

the fastest rate, the pressure drop was 62.7 ± 9.9 kPa for Survanta and 27.3 ± 11.3 kPa for DPPC.

387

Mountford et al.47 reported condensation for PFB gas inside DPPC microbubbles at 25–75 kPa

388

greater than the equilibrium saturation curve across a wide temperature range.

389

observed condensation at similarly high hydrostatic pressures, providing confidence in the

390

theoretical model applied here to analyze compression and dissolution. Taken together, these

391

results suggest that Survanta shells can absorb more stress than their pure DPPC counterparts.

Here, we

392

On the other hand, Survanta shells did not significantly affect gas transport. At the end of

393

compression, prior to condensation, the model estimated that the fraction of gas remaining in the

394

bubble compared to that at the onset of pressurization (/ ) was 0.60 ± 0.027 and 0.61 ± 0.031

395

for Survanta and DPPC, respectively, at the slowest pressurization rate. At the fastest rate, the

396

ratio was 0.66 ± 0.030 and 0.66 ± 0.025 for Survanta and DPPC, respectively, indicating that

397

mass transport was nearly identical for the two shell compositions.

398

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Figure 8. Model results from representative DPPC shelled microbubbles at (A) the slowest

401

pressurization rate and (B) the fastest pressurization rate. The first column shows the theoretical

402

volume of the bubble using E0 as the fitting parameter. The second column is the elasticity of

403

the shell during the pressurization experiment using the exponential elasticity model. The third

404

column compares the hydrostatic pressure to the apparent bubble pressure.

405 406

Figure 9 shows a comparison of the initial dilatational elasticity values for both shell types.

407

Survanta shells gave statistically similar  values to DPPC at the three slowest rages. At the

408

three fastest pressurization rates, however, the value of  for Survanta was significantly larger

409

than for DPPC (p < 0.05). This difference can be explained by the multi-component composition

410

of Survanta, which contains both saturated and unsaturated lipids as well as hydrophobic

411

surfactant proteins SP-B and SP-C. This composition provides microstructure that enables the

412

shell to better sustain in-plane stress.42 Additionally, Survanta microbubbles have been shown to

413

form surface associated folds after a compression event, and lung surfactant at the alveolar

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414

air/water interface is believed to form lipid reservoirs in the hypophase connected to the film

415

surface as multilamellar lipid stacks. Patashinski et al.54 showed that a monolayer must form a

416

multilayered structure to sustain negative surface tension. Survanta is uniquely capable of

417

forming and sustaining the necessary multilayers because of the presence of the hydrophobic

418

proteins SP-B and SP-C. We therefore speculate that the increased  for Survanta at higher

419

compression rates resulted from both in-plane monolayer rigidity and lateral repulsion between

420

surface-associated structures.

421

422 423

Figure 9. The initial dilatational elasticity, E0, for the two shell types versus pressurization rate

424

(mean I standard error, n ≥ 20). The black dashed line indicates the average elasticity value for

425

DPPC shells. The red line is a sigmoidal fit of the Survanta data, and is shown to help guide the

426

eye. The difference of the means between DPPC and Survanta at the three fastest pressurization

427

rates is significant (p < 0.05).

428 429

Conclusion

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430

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In this study, we examine LS mechanics by the use of individual microbubbles subjected

431

to linear pressurization at room temperature.

432

remained

433

wrinkling/smoothing cycles indicative of monolayer buckling and collapse. Pressure-volume

434

results suggested that Survanta shells support a negative surface tension, and that both Survanta

435

and DPPC microbubbles dissolve as they are pressurized. We employed an empirical model to

436

account for the simultaneous effects of isothermal compression and gas dissolution, in order to

437

better analyze the effects of surfactant film mechanics.

438

dilatational elasticity  of Survanta shells diverges from that of DPPC shells as strain rate

439

increases. We speculate that the higher elasticity of Survanta shells is a consequence of in-plane

440

monolayer rigidity and interactions between surface-associated folds and vesicles. Overall, this

441

technique reveals new physical insights into surfactant film mechanics and collapse behavior

442

during compression.

443

Acknowledgements. This work was funded by NSF grant DMR-1409972 and NIH grant R21

444

RHL129144.

spherical

during

pressurization,

We observed that pure DPPC microbubbles while

Survanta

microbubbles

exhibited

Analysis showed that the initial

445 446

Supporting Information. The Supporting Information is available free of charge on the ACS

447

Publications website: (i) normalized volume-time pressurization curve for an air-filled

448

microbubble, (ii) PFB microbubble condensation pressures, (iii) onset pressures for the first

449

Survanta buckling-collapse event, (iv) histograms for initial elasticity  , (v) normalized

450

volume-time curves for Survanta and DPPC, and (vi) curve-fitting statistics for the model fit to

451

experimental data.

452

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References

454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496

(1) (2) (3) (4) (5) (6)

(7)

(8)

(9)

(10)

(11) (12)

(13)

(14) (15) (16)

(17)

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(52) Kotula, A. P.; Anna, S. L. Insoluble Layer Deposition and Dilatational Rheology at a Microscale Spherical Cap Interface. Soft Matter 2016, 12 (33), 7038–7055. (53) Lum, J. S.; Dove, J. D.; Murray, T. W.; Borden, M. A. Single Microbubble Measurements of Lipid Monolayer Viscoelastic Properties for Small-Amplitude Oscillations. Langmuir 2016, 32 (37), 9410–9417. (54) Patashinski, A. Z.; Orlik, R.; Paclawski, K.; Ratner, M. A.; Grzybowski, B. A. The Unstable and Expanding Interface between Reacting Liquids: Theoretical Interpretation of Negative Surface Tension. Soft Matter 2012, 8 (5), 1601–1608.

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Figure 1. Illustration of the chamber design. The chamber pressure was controlled by a syringe pump (Harvard Apparatus, Holliston, MA) programmed to deliver a calibrated volumetric flow rate. A metal syringe (KD Scientific, Holliston, MA) filled with PFB-saturated PBS was used to ensure uniform pressurization during the entire experiment. 66x43mm (300 x 300 DPI)

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Figure 2. Images acquired for Survanta (A) and DPPC (B) microbubbles during pressurization at 0.5 kPa/s (top row of each panel) and 2.3 kPa/s (bottom row of each panel). The scale bar is 10 µm. 188x174mm (300 x 300 DPI)

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Figure 3. Cross-sectional areas of typical Survanta (black curve) and DPPC (red curve) microbubbles, along with the chamber pressure (blue curve). (A) Pressurization rate of 0.5 kPa/s and (B) pressurization rate of 2.3 kPa/s. The arrows indicate the first and last buckling events for the Survanta microbubbles. 137x185mm (300 x 300 DPI)

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Figure 4. A representative seismogram for compression of Survanta (black) and DPPC (red) shelled microbubbles at 0.5 kPa/s, corresponding to the area-time curves in Figure 3. The dashed line indicates the area velocity threshold arbitrarily assigned to define a buckling event. The blue arrows correspond to the first and last buckling events. 77x59mm (300 x 300 DPI)

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Figure 5. (A) The average surface area reduction between consecutive collapse events versus pressurization rate for Survanta shelled microbubbles. The dashed line indicates the average surface area loss. (B) Collapse frequency versus pressurization rate. The red line is a linear regression trend-line (R¬2=0.98). 138x188mm (300 x 300 DPI)

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Figure 6. Normalized volume-time curves. A) Survanta (left) and DPPC (right) microbubbles at the slowest pressurization rate (n ≥ 20). B) Similar plots at the fastest pressurization rate (n ≥ 20). The upper (red) curves were calculated assuming isothermal compression without dissolution. The bottom (green) curves were calculated by use of equation (4) for pure dissolution without shell resistance to gas permeation. 158x123mm (300 x 300 DPI)

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Figure 7. Model results from representative Survanta shelled microbubbles at (A) the slowest pressurization rate and (B) the fastest pressurization rate. The first column shows the theoretical volume of the bubble using E0 as the fitting parameter. The second column is the elasticity of the shell during the pressurization experiment using the exponential elasticity model. The third column compares the hydrostatic pressure to the apparent bubble pressure. 110x59mm (300 x 300 DPI)

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Figure 8. Model results from representative DPPC shelled microbubbles at (A) the slowest pressurization rate and (B) the fastest pressurization rate. The first column shows the theoretical volume of the bubble using E0 as the fitting parameter. The second column is the elasticity of the shell during the pressurization experiment using the exponential elasticity model. The third column compares the hydrostatic pressure to the apparent bubble pressure. 110x60mm (300 x 300 DPI)

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Figure 9. The initial dilatational elasticity, E0, for the two shell types versus pressurization rate (mean ± standard error, n ≥ 20). The black dashed line indicates the average elasticity value for DPPC shells. The red line is a sigmoidal fit of the Survanta data, and is shown to help guide the eye. The difference of the means between DPPC and Survanta at the three fastest pressurization rates is significant (p < 0.05). 71x49mm (300 x 300 DPI)

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TOC figure 41x22mm (300 x 300 DPI)

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