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Surfactant Properties Differentially Influence Intravascular Gas Embolism Mechanics

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Abstract

Gas bubble motion in a blood vessel causes temporal and spatial gradients of shear stress at the cell surface lining the vessel wall as the bubble approaches the cell, moves over it and passes it by. Rapid reversals occur in the sign of the shear stress imparted to the cell surface during this motion. These may result in injury to the cell. The presence of a soluble surfactant in the bulk medium reduces the level of the shear stress gradients imparted to the cell surface as compared to an equivalent surfactant-free system and is an important therapeutic aid. This is particularly true for a very small vessel. In this study, we analyze various physical and chemical properties of any given soluble surfactant to ascertain the relative significance of the property of the surfactant on the reduction in the level of the shear stress gradients imparted to the cell surface in such a vessel. While adsorption, desorption, and maximum possible monolayer interface surfactant concentration significantly impact the shear stress levels, physical properties such as the bulk or surface diffusivity do not appear to have large effects. At a given diameter, surfactants with \(k_{\rm a}/(k_{\rm d} d) >{{\mathcal{O}}}(10^{-5})\) and \({\Upgamma_\infty/C_0d}\,>\,9.5 \times 10^{-4}\) are noted to be preferable from the point of view of an increased gap size between the bubble and vessel wall, and a corresponding reduction in the shear stress level imparted to an endothelial cell. The shear stress characteristics of nearly occluding bubbles, in contrast with smaller sized bubbles under identical conditions, are most affected by the introduction of a surfactant in regard to shear stress levels. These observations could form a basis for choosing surfactants in treating gas embolism related illnesses.

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Acknowledgments

This work was sponsored by the Office of Naval Research Grant No. N00014-08-1-0436 and NIH Grant No. R01-HL067986.

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Authors and Affiliations

  1. Department of Anesthesiology and Critical Care, University of Pennsylvania, Philadelphia, PA, USA

    T. N. Swaminathan & D. M. Eckmann

  2. Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA

    T. N. Swaminathan & P. S. Ayyaswamy

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  1. T. N. Swaminathan
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  2. P. S. Ayyaswamy
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Correspondence to P. S. Ayyaswamy.

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Associate Editor Stefan Jockenhoevel oversaw the review of this article.

Appendix A: Validation

Appendix A: Validation

In addition to the validation of the numerical scheme done previously, in this appendix, we compare the rise velocity of an air bubble in human blood plasma by performing experiments and numerical calculations. The bubble motion and bubble shape cannot be visualized adequately using whole blood. Thus, we examine terminal bubble rise velocity using freshly prepared human blood plasma. Following an approved Institutional Review Board protocol, whole blood was obtained by venipuncture from healthy adult volunteer donors. Samples were immediately citrated (9 parts blood to 1 part citrate) and spun in a Sorvall Super T21 centrifuge (Thermo Electron Corporation, Asheville, NC, USA) at 2600 rpm (1500 g) for 15 min to obtain platelet poor plasma.11 Plasma was used to fill a 180-cm length of TYGON® R-3603 AAC00003 tubing (Saint-Gobain Performance Plastics Akron, OH, USA) having an inner diameter of 1.5875 mm. The tubing, which was affixed taughtly alongside a ruler onto a vertical frame, was open to atmosphere on top and closed via a blunt-tip connector attached to a three-way stopcock on the bottom. Bubbles were introduced into the liquid by slow injection using a microsyringe (Hamilton Company, Reno, NV, USA) and allowed to rise freely under buoyancy.

Bubbles were viewed in the upper-most (last) 20 cm of tubing using a video imaging system consisting of a high resolution black and white video camera (JE12HMV, Javelin Systems, Torrance, CA), a video image marker-measurement system (Model VIA-170, Boeckeler Instruments, Tucson, AZ, USA), monitor (Model PVM-1343MD, Sony, Tokyo, Japan), and video cassette recorder (Sony SVO-9500 MD S-VHS, Sony Corporation, Tokyo, Japan) operating at a standard 30 frames per second.3,5,6,9,10 Post-experiment measurements of bubble dimensions and terminal rise velocity were made by reviewing the videotape calibrated for distance with the ruler included in the video image and by counting the number of video frames elapsed for a minimum vertical bubble displacement of 20 mm.

A comparison of the rise velocity of bubble under identical conditions is shown in Fig. 16. The diameter of the bubble (d bubble) has been normalized with the diameter of the tube (d tube) and the velocity has been normalized with the Mendelsen equation28 \(\sqrt{2\sigma/\rho_{\rm l}d_{\rm tube}+g d_{\rm tube}/2}.\) For the numerical simulation, the evaluation of surface tension in Lampe et al.,23 gives the value of σ for the air–plasma interface as ∼54 mN/m. The viscosity of plasma is obtained from Sharan and Popel48 as 1.2 cP. The predicted numerical results are compared with our experimental values. It can be seen that the two results agree well (<15% error), noting that our experiments are carried out in a very long open tube. This comparison thus serves to additionally validate our numerical procedure.

Figure 16
figure 16

Comparison of the numerical results of the rise of an air bubble in a tube containing human blood plasma with that of our experimental results. Here, d tube = 1.5875 mm is the tube diameter

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Swaminathan, T.N., Ayyaswamy, P.S. & Eckmann, D.M. Surfactant Properties Differentially Influence Intravascular Gas Embolism Mechanics. Ann Biomed Eng 38, 3649–3663 (2010). https://doi.org/10.1007/s10439-010-0120-5

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