Theory of Red Blood Cell Oscillations in an Ultrasound Field
DOI:
https://doi.org/10.1515/aoa-2017-0013Keywords:
Spatio--temporal cell dynamics, Rayleigh--Plesset equation, spherical cell, red blood cell, erythrocyteAbstract
Manipulating particles in the blood pool with noninvasive methods has been of great interest in therapeutic delivery. Recently, it was demonstrated experimentally that red blood cells can be forced to translate and accumulate in an ultrasound field. This acoustic response of the red blood cells has been attributed to sonophores, gas pockets that are formed under the influence of a sound field in the inner-membrane leaflets of biological cells. In this paper, we propose a simpler model: that of the compressible membrane. We derive the spatio-temporal cell dynamics for a spherically symmetric single cell, whilst regarding the cell bilayer membrane as two monolayer Newtonian viscous liquids, separated by a thin gas void. When applying the newly-derived equations to a red blood cell, it is observed that the void inside the bilayer expands to multiples of its original thickness, even at clinically safe acoustic pressure amplitudes. For causing permanent cell rupture during expansion, however, the acoustic pressure amplitudes needed would have to surpass the inertial cavitation threshold by a factor 10. Given the incompressibility of the inner monolayer, the radial oscillations of a cell are governed by the same set of equations as those of a forced antibubble. Evidently, these equations must hold for liposomes under sonication, as well.References
Apfel R.E., Holland C.K. (1991), Gauging the likelihood of cavitation from short-pulse, low-duty cycle diagnostic ultrasound, Ultrasound in Medicine & Biology, 17, 2, 179–185.
Bao S., Thrall B.D., Miller D.L. (1997), Transfection of a reporter plasmid into cultured cells by sonoporation in vitro, Ultrasound in Medicine & Biology, 23, 6, 953–959.
Boal D. (2012), Mechanics of the Cell, University Press, Cambridge.
Church C.C. (1995), The effects of an elastic solid surface layer on the radial pulsations of gas bubbles, Journal of the Acoustical Society of America, 97, 3, 1510–1521.
Delalande A., Kotopoulis S., Rovers T., Pichon C., Postema M. (2011), Sonoporation at a low mechanical index, Bubble Science, Engineering and Technology, 3, 1, 3–11.
Delalande A., Postema M., Mignet N., Midoux P., Pichon C. (2012), Ultrasound and microbubble-assisted gene delivery: recent advances and ongoing challenges, Therapeutic Delivery, 3, 10, 1199–1215.
Doinikov A.A., Dayton P.A. (2007), Maxwell rheological model for lipid-shelled ultrasound microbubble contrast agents, Journal of the Acoustical Society of America, 121, 6, 3331–3340.
Isenberg C. (1992), The science of soap films and soap bubbles, Dover edition, General Publishing Company, Don Mills.
Kotopoulis S., Johansen K., Gilja O.H., Poortinga A.T., Postema M. (2015), Acoustically active antibubbles, Acta Physica Polonica A, 127, 1, 99–102.
Krasovitski B., Frenkel V. Shoham S., Kimmel E. (2011), Intramembrane cavitation as a unifying mechanism for ultrasound-induced bioeffects, Proceedings of the National Academy of Sciences, 108, 8, 3258–3263.
Kudo N., Okada K., Yamamoto K. (2009), Sonoporation by single-shot pulsed ultrasound with microbubbles adjacent to cells, Biophysical Journal, 96, 12, 4866–4876.
Landau L., Lifshitz E. (1986), Theory of Elasticity, Butterworth-Heinemann, Oxford.
Leighton T.G. (1994), The Acoustic Bubble, Academic Press, London.
Li F., Chan C.U., Ohl C.D. (2013), Yield strength of human erythrocyte membranes to impulsive stretching, Biophysical Journal, 105, 4, 872–879.
Mazzawi N., Postema M., Kimmel E. (2015), Bubble-like response of living blood cells and microparticles in an ultrasound field, Acta Physica Polonica A, 127, 1, 103–105.
Postema M. (2011), Fundamentals of Medical Ultrasonics, Spon Press, London.
Prentice P., Cuschieri A., Dholakia K., Prausnitz M., Campbell P. (2005), Membrane disruption by optically controlled microbubble cavitation, Nature Physics, 1, 107–110.
Tran-Son-Tay R., Sutera S.P., Rao P.R. (1984), Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion, Biophysical Journal, 46, 1, 65–72.
van Wamel A., Kooiman K., Harteveld M., Emmer M., ten Cate F.J., Versluis M., de Jong N.
(2006), Vibrating microbubbles poking individual cells: drug transfer into cells via sonoporation, Journal of Controlled Release, 112, 2, 149–155.
Walther T., Postema M. (2016), Device for the identification, separation and/or cell type-specific manipulation of at least one cell of a cellular system, United States Patent Application US 2016/0060615 A1.
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