Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-28T20:13:57.929Z Has data issue: false hasContentIssue false
  • English
  • Français

A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles

Published online by Cambridge University Press:  19 December 2017

Achim Guckenberger Open the ORCID record for Achim Guckenberger [Opens in a new window]  and
Stephan Gekle Open the ORCID record for Stephan Gekle [Opens in a new window]
Achim Guckenberger*
Affiliation:
Biofluid Simulation and Modeling, Fachbereich Physik, Universität Bayreuth, 95440 Bayreuth, Germany
Stephan Gekle
Affiliation:
Biofluid Simulation and Modeling, Fachbereich Physik, Universität Bayreuth, 95440 Bayreuth, Germany
*
†Email address for correspondence: achim.guckenberger@uni-bayreuth.de
Get access Rights & Permissions [Opens in a new window]

Abstract

A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof contains as a subset the simpler boundary integral equation without volume-changing objects (such as red blood cell or capsule suspensions) which is widely used but for which a formal proof in periodic domains has not been published to date. In the second part, we apply our method to study microbubbles for targeted drug delivery. The ideal drug delivery agent should stay away from the biochemically active vessel walls during circulation. However, upon reaching its target it should attain a near-wall position for efficient drug uptake. Though seemingly contradictory, we show that lipid-coated microbubbles in conjunction with a localized ultrasound pulse possess precisely these two properties. This ultrasound-triggered margination is due to hydrodynamic interactions between the red blood cells and the oscillating lipid-coated microbubbles which alternate between a soft and a stiff state. We find that the effect is very robust, existing even if the duration in the stiff state is more than three times lower than the opposing time in the soft state.

JFM classification

Biological Fluid Dynamics: Blood flow Low-Reynolds-number flows: Boundary integral methods Biological Fluid Dynamics: Capsule/cell dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 952 - 997
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aarts, P. A., van den Broek, S. A., Prins, G. W., Kuiken, G. D., Sixma, J. J. & Heethaar, R. M. 1988 Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood. Arterioscler. Thromb. Vasc. Biol. 8 (6), 819–824.Google Scholar
Bächer, C., Schrack, L. & Gekle, S. 2017 Clustering of microscopic particles in constricted blood flow. Phys. Rev. Fluids 2 (1), 013102.Google Scholar
Blake, J. R. 1971 A note on the image system for a Stokeslet in a no-slip boundary. Math. Proc. Camb. Phil. Soc. 70 (2), 303–310.CrossRefGoogle Scholar
Blawzdziewicz, J. 2007 Boundary integral methods for Stokes flows. In Computational Methods for Multiphase Flow (ed. Andrea, P. & Gretar, T.), pp. 193–236. Cambridge University Press.Google Scholar
Bogacki, P. & Shampine, L. F. 1989 A 3(2) pair of Runge–Kutta formulas. Appl. Maths Lett. 2 (4), 321–325.CrossRefGoogle Scholar
Borden, M. A., Kruse, D. E., Caskey, C. F., Zhao, S., Dayton, P. A. & Ferrara, K. W. 2005 Influence of lipid shell physicochemical properties on ultrasound-induced microbubble destruction. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52 (11), 1992–2002.CrossRefGoogle ScholarPubMed
Canham, P. B. 1970 The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theor. Biol. 26 (1), 61–81.Google Scholar
Cash, J. R. & Karp, A. H. 1990 A variable order Runge–Kutta method for initial value problems with rapidly varying right-hand sides. ACM Trans. Math. Softw. 16 (3), 201–222.Google Scholar
Chien, S., Usami, S., Taylor, H. M., Lundberg, J. L. & Gregersen, M. I. 1966 Effects of hematocrit and plasma proteins on human blood rheology at low shear rates. J. Appl. Phys. 21 (1), 81–87.Google ScholarPubMed
Cortez, R. & Hoffmann, F. 2014 A fast numerical method for computing doubly-periodic regularized Stokes flow in 3D. J. Comput. Phys. 258, 1–14.Google Scholar
Couture, O., Foley, J., Kassell, N. F., Larrat, B. & Aubry, J.-F. 2014 Review of ultrasound mediated drug delivery for cancer treatment: updates from pre-clinical studies. Transl. Cancer Res. 3 (5), 494–511.Google Scholar
Cowper, G. R. 1973 Gaussian quadrature formulas for triangles. Intl J. Numer. Meth. Engng 7 (3), 405–408.Google Scholar
Daddi-Moussa-Ider, A. & Gekle, S. 2016 Hydrodynamic interaction between particles near elastic interfaces. J. Chem. Phys. 145 (1), 014905.Google Scholar
Daddi-Moussa-Ider, A. & Gekle, S. 2017 Hydrodynamic mobility of a solid particle near a spherical elastic membrane: axisymmetric motion. Phys. Rev. E 95 (1), 013108.Google Scholar
Daddi-Moussa-Ider, A., Guckenberger, A. & Gekle, S. 2016a Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles. Phys. Rev. E 93 (1), 012612.Google Scholar
Daddi-Moussa-Ider, A., Guckenberger, A. & Gekle, S. 2016b Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation. Phys. Fluids 28 (7), 071903.Google Scholar
Daddi-Moussa-Ider, A., Lisicki, M. & Gekle, S. 2017a Hydrodynamic mobility of a solid particle near a spherical elastic membrane. Part II. Asymmetric motion. Phys. Rev. E 95 (5), 053117.Google Scholar
Daddi-Moussa-Ider, A., Lisicki, M. & Gekle, S. 2017b Mobility of an axisymmetric particle near an elastic interface. J. Fluid Mech. 811, 210–233.Google Scholar
D’Apolito, R., Tomaiuolo, G., Taraballi, F., Minardi, S., Kirui, D., Liu, X., Cevenini, A., Palomba, R., Ferrari, M., Salvatore, F. et al. 2015 Red blood cells affect the margination of microparticles in synthetic microcapillaries and intravital microcirculation as a function of their size and shape. J. Control. Release 217, 263–272.Google Scholar
Dayton, P., Klibanov, A., Brandenburger, G. & Ferrara, K. 1999 Acoustic radiation force in vivo: a mechanism to assist targeting of microbubbles. Ultrasound Med. Biol. 25 (8), 1195–1201.CrossRefGoogle ScholarPubMed
Doinikov, A. A. & Bouakaz, A. 2011 Review of shell models for contrast agent microbubbles. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58 (5), 981–993.Google Scholar
Evans, E. & Fung, Y.-C. 1972 Improved measurements of the erythrocyte geometry. Microvasc. Res. 4 (4), 335–347.Google Scholar
Faez, T., Emmer, M., Kooiman, K., Versluis, M., van der Steen, A. F. W. & de Jong, N. 2013 20 years of ultrasound contrast agent modeling. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60 (1), 7–20.Google Scholar
Fan, X.-J., Phan-Thien, N. & Zheng, R. 1998 Completed double layer boundary element method for periodic suspensions. Z. angew. Math. Phys. 49 (2), 167–193.Google Scholar
Farutin, A., Biben, T. & Misbah, C. 2014 3D numerical simulations of vesicle and inextensible capsule dynamics. J. Comput. Phys. 275, 539–568.Google Scholar
Farutin, A. & Misbah, C. 2013 Analytical and numerical study of three main migration laws for vesicles under flow. Phys. Rev. Lett. 110 (10).Google Scholar
Fedosov, D. A. & Gompper, G. 2014 White blood cell margination in microcirculation. Soft Matt. 10 (17), 2961–2970.Google Scholar
Fedosov, D. A., Pan, W., Caswell, B., Gompper, G. & Karniadakis, G. E. 2011 Predicting human blood viscosity in silico. Proc. Natl Acad. Sci. USA 108 (29), 11772–11777.Google Scholar
Ferrara, K., Pollard, R. & Borden, M. 2007 Ultrasound microbubble contrast agents: fundamentals and application to gene and drug delivery. Annu. Rev. Biomed. Engng 9 (1), 415–447.CrossRefGoogle ScholarPubMed
Fitzgibbon, S., Spann, A. P., Qi, Q. M. & Shaqfeh, E. S. G. 2015 In vitro measurement of particle margination in the microchannel flow: effect of varying hematocrit. Biophys. J. 108 (10), 2601–2608.CrossRefGoogle ScholarPubMed
Freund, J. B. 2007 Leukocyte margination in a model microvessel. Phys. Fluids 19 (2), 023301.Google Scholar
Freund, J. B. 2013 The flow of red blood cells through a narrow spleen-like slit. Phys. Fluids 25 (11), 110807.CrossRefGoogle Scholar
Freund, J. B. 2014 Numerical simulation of flowing blood cells. Annu. Rev. Fluid Mech. 46 (1), 67–95.Google Scholar
Freund, J. B. & Orescanin, M. M. 2011 Cellular flow in a small blood vessel. J. Fluid Mech. 671, 466–490.Google Scholar
Freund, J. B. & Shapiro, B. 2012 Transport of particles by magnetic forces and cellular blood flow in a model microvessel. Phys. Fluids 24 (5), 051904.Google Scholar
Freund, J. B. & Vermot, J. 2014 The wall-stress footprint of blood cells flowing in microvessels. Biophys. J. 106 (3), 752–762.Google Scholar
Frinking, P. J. A., Gaud, E., Brochot, J. & Arditi, M. 2010 Subharmonic scattering of phospholipid-shell microbubbles at low acoustic pressure amplitudes. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 (8), 1762–1771.Google Scholar
Gekle, S. 2016 Strongly accelerated margination of active particles in blood flow. Biophys. J. 110 (2), 514–520.Google Scholar
Greengard, L. & Kropinski, M. C. 2004 Integral equation methods for Stokes flow in doubly-periodic domains. J. Engng Maths 48 (2), 157–170.Google Scholar
Guckenberger, A. & Gekle, S. 2017 Theory and algorithms to compute Helfrich bending forces: a review. J. Phys.: Condens. Matter 29 (20), 203001.Google Scholar
Guckenberger, A., Schraml, M. P., Chen, P. G., Leonetti, M. & Gekle, S. 2016 On the bending algorithms for soft objects in flows. Comput. Phys. Commun. 207, 1–23.CrossRefGoogle Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5 (2), 317–328.Google Scholar
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28 (11–12), 693–703.Google Scholar
Hernández-Ortiz, J. P., de Pablo, J. J. & Graham, M. D. 2007 Fast computation of many-particle hydrodynamic and electrostatic interactions in a confined geometry. Phys. Rev. Lett. 98 (14), 140602.Google Scholar
House, S. D. & Lipowsky, H. H. 1987 Microvascular hematocrit and red cell flux in rat cremaster muscle. Am. J. Phys. 252 (1), H211–H222.Google Scholar
Huang, L. R., Cox, E. C., Austin, R. H. & Sturm, J. C. 2004 Continuous particle separation through deterministic lateral displacement. Science 304 (5673), 987–990.Google Scholar
Janssen, P. J. A. & Anderson, P. D. 2008 A boundary-integral model for drop deformation between two parallel plates with non-unit viscosity ratio drops. J. Comput. Phys. 227 (20), 8807–8819.Google Scholar
Johnson, K. A., Vormohr, H. R., Doinikov, A. A., Bouakaz, A., Shields, C. W., López, G. P. & Dayton, P. A. 2016 Experimental verification of theoretical equations for acoustic radiation force on compressible spherical particles in traveling waves. Phys. Rev. E 93 (5), 053109.Google Scholar
de Jong, N., Emmer, M., Chin, C. T., Bouakaz, A., Mastik, F., Lohse, D. & Versluis, M. 2007 ‘Compression-only’ behavior of phospholipid-coated contrast bubbles. Ultrasound Med. Biol. 33 (4), 653–656.Google Scholar
Karrila, S. J. & Kim, S. 1989 Integral equations of the second kind for Stokes flow: direct solution for physical variables and removal of inherent accuracy limitations. Chem. Engng Commun. 82 (1), 123–161.CrossRefGoogle Scholar
Katanov, D., Gompper, G. & Fedosov, D. A. 2015 Microvascular blood flow resistance: role of red blood cell migration and dispersion. Microvasc. Res. 99, 57–66.Google Scholar
Kilroy, J. P., Klibanov, A. L., Wamhoff, B. R., Bowles, D. K. & Hossack, J. A. 2014 Localized in vivo model drug delivery with intravascular ultrasound and microbubbles. Ultrasound Med. Biol. 40 (10), 2458–2467.Google Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth–Heinemann.Google Scholar
Klibanov, A. L. 2002 Ultrasound contrast agents: development of the field and current status. In Topics in Current Chemistry (ed. Werner, K.), vol. 222, pp. 73–106. Springer.Google Scholar
af Klinteberg, L. & Tornberg, A.-K. 2014 Fast Ewald summation for Stokesian particle suspensions. Intl J. Numer. Meth. Fluids 76 (10), 669–698.Google Scholar
af Klinteberg, L. & Tornberg, A.-K. 2016 A fast integral equation method for solid particles in viscous flow using quadrature by expansion. J. Comput. Phys. 326, 420–445.Google Scholar
Klitzman, B. & Duling, B. R. 1979 Microvascular hematocrit and red cell flow in resting and contracting striated muscle. Am. J. Phys. 237 (4), H481–H490.Google Scholar
Kohr, M. & Pop, I. 2004 Viscous Incompressible Flow for Low Reynolds Numbers, Advances in Boundary Elements, vol. 16. WIT Press.Google Scholar
Kooiman, K., Vos, H. J., Versluis, M. & de Jong, N. 2014 Acoustic behavior of microbubbles and implications for drug delivery. Adv. Drug Deliv. Rev. 72, 28–48.Google Scholar
Kotopoulis, S., Dimcevski, G., Cormack, E. M., Postema, M., Gjertsen, B. T. & Gilja, O. H. 2016 Ultrasound- and microbubble-enhanced chemotherapy for treating pancreatic cancer: a phase I clinical trial. J. Acoust. Soc. Am. 139 (4), 2092–2092.CrossRefGoogle Scholar
Kress, R. 2014 Linear Integral Equations, 3rd edn. Applied Mathematical Sciences, vol. 82. Springer.Google Scholar
Kretz, M. & Lindenstruth, V. 2012 Vc: a C++ library for explicit vectorization. Softw. Pract. Exp. 42 (11), 1409–1430.Google Scholar
Krüger, T. 2012 Computer Simulation Study of Collective Phenomena in Dense Suspensions of Red Blood Cells Under Shear. Vieweg and Teubner.Google Scholar
Krüger, T., Holmes, D. & Coveney, P. V. 2014 Deformability-based red blood cell separation in deterministic lateral displacement devices: a simulation study. Biomicrofluidics 8 (5).Google Scholar
Kumar, A. & Graham, M. D. 2011 Segregation by membrane rigidity in flowing binary suspensions of elastic capsules. Phys. Rev. E 84 (6), 066316.Google ScholarPubMed
Kumar, A. & Graham, M. D. 2012 Accelerated boundary integral method for multiphase flow in non-periodic geometries. J. Comput. Phys. 231 (20), 6682–6713.Google Scholar
Kumar, A., Henríquez Rivera, R. G. & Graham, M. D. 2014 Flow-induced segregation in confined multicomponent suspensions: effects of particle size and rigidity. J. Fluid Mech. 738, 423–462.Google Scholar
Ladyzhenskaya, O. A. 1969 The Mathematical Theory of Viscous Incompressible Flow, 2nd edn. Gordon & Breach.Google Scholar
Lammertink, B. H. A., Bos, C., Deckers, R., Storm, G., Moonen, C. T. W. & Escoffre, J.-M. 2015 Sonochemotherapy: from bench to bedside. Front. Pharmacol. 6 (138).Google Scholar
Li, X., Zhou, H. & Pozrikidis, C. 1995 A numerical study of the shearing motion of emulsions and foams. J. Fluid Mech. 286, 379–404.Google Scholar
Lindbo, D. & Tornberg, A.-K. 2010 Spectrally accurate fast summation for periodic Stokes potentials. J. Comput. Phys. 229 (23), 8994–9010.CrossRefGoogle Scholar
Lindner, J. R. 2004 Microbubbles in medical imaging: current applications and future directions. Natl Rev. Drug Discov. 3 (6), 527–533.Google Scholar
Lindner, J. R., Song, J., Jayaweera, A. R., Sklenar, J. & Kaul, S. 2002 Microvascular rheology of definity microbubbles after intra-arterial and intravenous administration. J. Am. Soc. Echocardiogr. 15 (5), 396–403.Google Scholar
Liron, N. & Mochon, S. 1976 Stokes flow for a Stokeslet between two parallel flat plates. J. Engng Maths 10 (4), 287–303.Google Scholar
Loewenberg, M. & Hinch, E. J. 1996 Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 321, 395–419.Google Scholar
Marin, O., Gustavsson, K. & Tornberg, A.-K. 2012 A highly accurate boundary treatment for confined Stokes flow. Comput. Fluids 66, 215–230.Google Scholar
Marmottant, P., van der Meer, S., Emmer, M., Versluis, M., de Jong, N., Hilgenfeldt, S. & Lohse, D. 2005 A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture. J. Acoust. Soc. Am. 118 (6), 3499–3505.CrossRefGoogle Scholar
McWhirter, J. L., Noguchi, H. & Gompper, G. 2009 Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries. Proc. Natl Acad. Sci. USA 106 (15), 6039–6043.Google Scholar
Mehrabadi, M., Ku, D. N. & Aidun, C. K. 2016 Effects of shear rate, confinement, and particle parameters on margination in blood flow. Phys. Rev. E 93 (2), 023109.Google Scholar
Misbah, C. 2012 Vesicles, capsules and red blood cells under flow. J. Phys.: Conf. Ser. 392, 012005.Google Scholar
Mukherjee, S. & Sarkar, K. 2013 Effects of matrix viscoelasticity on the lateral migration of a deformable drop in a wall-bounded shear. J. Fluid Mech. 727, 318–345.CrossRefGoogle Scholar
Mukherjee, S. & Sarkar, K. 2014 Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall. Phys. Fluids 26 (10), 103102.Google Scholar
Müller, K., Fedosov, D. A. & Gompper, G. 2014 Margination of micro- and nano-particles in blood flow and its effect on drug delivery. Sci. Rep. 4, 4871.Google Scholar
Müller, K., Fedosov, D. A. & Gompper, G. 2015 Smoothed dissipative particle dynamics with angular momentum conservation. J. Comput. Phys. 281, 301–315.Google Scholar
Müller, K., Fedosov, D. A. & Gompper, G. 2016 Understanding particle margination in blood flow: a step toward optimized drug delivery systems. Med. Engng Phys. 38 (1), 2–10.Google Scholar
Namdee, K., Thompson, A. J., Charoenphol, P. & Eniola-Adefeso, O. 2013 Margination propensity of vascular-targeted spheres from blood flow in a microfluidic model of human microvessels. Langmuir 29 (8), 2530–2535.Google Scholar
Nie, Q., Tanveer, S., Dupont, T. F. & Li, X. 2002 Singularity formation in free-surface Stokes flows. In Recent Advances in Numerical Methods for Partial Differential Equations and Applications (ed. Xiaobing, F. & Schulze, T. P.), Contemporary Mathematics, vol. 306, pp. 147–165. AMS.Google Scholar
Noguchi, H. & Gompper, G. 2005 Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations. Phys. Rev. E 72 (1), 011901.Google Scholar
Odqvist, F. K. G. 1930 Über die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten. Math. Z. 32 (1), 329–375.Google Scholar
Overvelde, M., Garbin, V., Sijl, J., Dollet, B., de Jong, N., Lohse, D. & Versluis, M. 2010 Nonlinear shell behavior of phospholipid-coated microbubbles. Ultrasound Med. Biol. 36 (12), 2080–2092.Google Scholar
Owen, J., Grove, P., Rademeyer, P. & Stride, E. 2014 The influence of blood on targeted microbubbles. J. R. Soc. Interface 11 (100), 20140622.Google Scholar
Park, Y., Best, C. A., Badizadegan, K., Dasari, R. R., Feld, M. S., Kuriabova, T., Henle, M. L., Levine, A. J. & Popescu, G. 2010 Measurement of red blood cell mechanics during morphological changes. Proc. Natl Acad. Sci. USA 107 (15), 6731–6736.Google Scholar
Paul, S., Katiyar, A., Sarkar, K., Chatterjee, D., Shi, W. T. & Forsberg, F. 2010 Material characterization of the encapsulation of an ultrasound contrast microbubble and its subharmonic response: strain-softening interfacial elasticity model. J. Acoust. Soc. Am. 127 (6), 3846–3857.Google Scholar
Phan-Thien, N., Tran-Cong, T. & Graham, A. L. 1991 Shear flow of periodic arrays of particle clusters: a boundary-element method. J. Fluid Mech. 228, 275–293.Google Scholar
Popel, A. S. & Johnson, P. C. 2005 Microcirculation and hemorheology. Annu. Rev. Fluid Mech. 37 (1), 43–69.Google Scholar
Power, H. 1992 The low Reynolds number deformation of a gas bubble in shear flow: a general approach via integral equations. Engng Anal. Bound. Elem. 9 (1), 31–37.Google Scholar
Power, H. 1996 A second kind integral equation formulation for the low Reynolds number interaction between a solid particle and a viscous drop. J. Engng Maths 30 (1–2), 225–237.CrossRefGoogle Scholar
Power, H. & Miranda, G. 1987 Second kind integral equation formulation of Stokes’ flows past a particle of arbitrary shape. SIAM J. Appl. Maths 47 (4), 689–698.Google Scholar
Power, H. & de Power, B. F. 1992 The completed second kind boundary integral equation method for the deformation of a gas bubble due to low Reynolds number flow. In Boundary Element Technology VII (ed. Brebbia, C. A. & Ingber, M. S.), pp. 193–210. Springer.Google Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge Texts in Applied Mathematics, vol. 8. Cambridge University Press.Google Scholar
Pozrikidis, C. 1993 On the transient motion of ordered suspensions of liquid drops. J. Fluid Mech. 246, 301–320.CrossRefGoogle Scholar
Pozrikidis, C. 1995 Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J. Fluid Mech. 297, 123–152.Google Scholar
Pozrikidis, C. 1996 Computation of periodic Green’s functions of Stokes flow. J. Engng Maths 30 (1–2), 79–96.CrossRefGoogle Scholar
Pozrikidis, C. 1999 A spectral-element method for particulate Stokes flow. J. Comput. Phys. 156 (2), 360–381.Google Scholar
Pozrikidis, C. 2001 Interfacial dynamics for Stokes flow. J. Comput. Phys. 169 (2), 250–301.CrossRefGoogle Scholar
Pranay, P., Anekal, S. G., Hernandez-Ortiz, J. P. & Graham, M. D. 2010 Pair collisions of fluid-filled elastic capsules in shear flow: effects of membrane properties and polymer additives. Phys. Fluids 22 (12), 123103.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 2007 Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press.Google Scholar
Qi, Q. M. & Shaqfeh, E. S. G. 2017 Theory to predict particle migration and margination in the pressure-driven channel flow of blood. Phys. Rev. Fluids 2 (9), 093102.Google Scholar
Quint, S., Christ, A. F., Guckenberger, A., Himbert, S., Kaestner, L., Gekle, S. & Wagner, C. 2017 3D tomography of cells in micro-channels. Appl. Phys. Lett. 111 (10), 103701.Google Scholar
Rivara, M. C. 1984 Algorithms for refining triangular grids suitable for adaptive and multigrid techniques. Intl J. Numer. Meth. Engng 20 (4), 745–756.Google Scholar
Rychak, J. J., Klibanov, A. L. & Hossack, J. A. 2005 Acoustic radiation force enhances targeted delivery of ultrasound contrast microbubbles: in vitro verification. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52 (3), 421–433.Google Scholar
Rychak, J. J., Klibanov, A. L., Ley, K. F. & Hossack, J. A. 2007 Enhanced targeting of ultrasound contrast agents using acoustic radiation force. Ultrasound Med. Biol. 33 (7), 1132–1139.Google Scholar
Rychak, J. J., Lindner, J. R., Ley, K. & Klibanov, A. L. 2006 Deformable gas-filled microbubbles targeted to P-selectin. J. Control. Release 114 (3), 288–299.CrossRefGoogle ScholarPubMed
Saad, Y. & Schultz, M. 1986 GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (3), 856–869.Google Scholar
Saintillan, D., Darve, E. & Shaqfeh, E. S. G. 2005 A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: the sedimentation of fibers. Phys. Fluids 17 (3), 033301.CrossRefGoogle Scholar
Sarkar, K., Shi, W. T., Chatterjee, D. & Forsberg, F. 2005 Characterization of ultrasound contrast microbubbles using in vitro experiments and viscous and viscoelastic interface models for encapsulation. J. Acoust. Soc. Am. 118 (1), 539–550.Google Scholar
Sijl, J., Overvelde, M., Dollet, B., Garbin, V., de Jong, N., Lohse, D. & Versluis, M. 2011 ‘Compression-only’ behavior: a second-order nonlinear response of ultrasound contrast agent microbubbles. J. Acoust. Soc. Am. 129 (4), 1729–1739.Google Scholar
Singh, R. K., Li, X. & Sarkar, K. 2014 Lateral migration of a capsule in plane shear near a wall. J. Fluid Mech. 739, 421–443.Google Scholar
Sinha, K. & Graham, M. D. 2015 Dynamics of a single red blood cell in simple shear flow. Phys. Rev. E 92 (4), 042710.Google Scholar
Sinha, K. & Graham, M. D. 2016 Shape-mediated margination and demargination in flowing multicomponent suspensions of deformable capsules. Soft Matt. 12 (6), 1683–1700.CrossRefGoogle ScholarPubMed
Skalak, R., Ozkaya, N. & Skalak, T. C. 1989 Biofluid mechanics. Annu. Rev. Fluid Mech. 21 (1), 167–200.Google Scholar
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13 (3), 245–264.Google Scholar
Smart, J. R. & Leighton, D. T. 1991 Measurement of the drift of a droplet due to the presence of a plane. Phys. Fluids Fluid Dyn. 3 (1), 21–28.Google Scholar
Spann, A. P., Campbell, J. E., Fitzgibbon, S. R., Rodriguez, A., Cap, A. P., Blackbourne, L. H. & Shaqfeh, E. S. G. 2016 The effect of hematocrit on platelet adhesion: experiments and simulations. Biophys. J. 111 (3), 577–588.CrossRefGoogle ScholarPubMed
Staben, M. E., Zinchenko, A. Z. & Davis, R. H. 2003 Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Phys. Fluids 15 (6), 1711–1733.Google Scholar
Unger, E., Porter, T., Lindner, J. & Grayburn, P. 2014 Cardiovascular drug delivery with ultrasound and microbubbles. Adv. Drug Deliv. Rev. 72, 110–126.Google Scholar
Unnikrishnan, S. & Klibanov, A. L. 2012 Microbubbles as ultrasound contrast agents for molecular imaging: preparation and application. Am. J. Roentgenol. 199 (2), 292–299.Google Scholar
Vahidkhah, K. & Bagchi, P. 2015 Microparticle shape effects on margination, near-wall dynamics and adhesion in a three-dimensional simulation of red blood cell suspension. Soft Matt. 11 (11), 2097–2109.Google Scholar
van der Vorst, H. 1992 Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13 (2), 631–644.Google Scholar
Wang, W., Diacovo, T. G., Chen, J., Freund, J. B. & King, M. R. 2013 Simulation of platelet, thrombus and erythrocyte hydrodynamic interactions in a 3D arteriole with in vivo comparison. PLoS ONE 8 (10), e76949.Google Scholar
Yoon, Y.-Z., Kotar, J., Yoon, G. & Cicuta, P. 2008 The nonlinear mechanical response of the red blood cell. Phys. Biol. 5 (3), 036007.Google Scholar
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69 (2), 377–403.Google Scholar
Youngren, G. K. & Acrivos, A. 1976 On the shape of a gas bubble in a viscous extensional flow. J. Fluid Mech. 76 (3), 433–442.Google Scholar
Zhang, C. & Chen, T. 2001 Efficient feature extraction for 2D/3D objects in mesh representation. In Proceedings ICIP 2001, vol. 3, pp. 935–938. IEEE Signal Processing Society.Google Scholar
Zhang, Z., Henry, E., Gompper, G. & Fedosov, D. A. 2015 Behavior of rigid and deformable particles in deterministic lateral displacement devices with different post shapes. J. Chem. Phys. 143 (24), 243145.CrossRefGoogle ScholarPubMed
Zhao, H., Isfahani, A. H. G., Olson, L. N. & Freund, J. B. 2010 A spectral boundary integral method for flowing blood cells. J. Comput. Phys. 229 (10), 3726–3744.Google Scholar
Zhao, H. & Shaqfeh, E. S. G. 2011 Shear-induced platelet margination in a microchannel. Phys. Rev. E 83 (6).Google Scholar
Zhao, H., Shaqfeh, E. S. G. & Narsimhan, V. 2012 Shear-induced particle migration and margination in a cellular suspension. Phys. Fluids 24 (1), 011902.Google Scholar
Zhao, X., Li, J., Jiang, X., Karpeev, D., Heinonen, O., Smith, B., Hernandez-Ortiz, J. P. & de Pablo, J. J. 2017 Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries. J. Chem. Phys. 146 (24), 244114.Google Scholar
Zhu, L., Rabault, J. & Brandt, L. 2015 The dynamics of a capsule in a wall-bounded oscillating shear flow. Phys. Fluids 27 (7), 071902.Google Scholar
Zick, A. A. & Homsy, G. M. 1982 Stokes flow through periodic arrays of spheres. J. Fluid Mech. 115, 13–26.CrossRefGoogle Scholar
Zinchenko, A. Z. & Davis, R. H. 2000 An efficient algorithm for hydrodynamical interaction of many deformable drops. J. Comput. Phys. 157 (2), 539–587.Google Scholar
Zinchenko, A. Z., Rother, M. A. & Davis, R. H. 1997 A novel boundary-integral algorithm for viscous interaction of deformable drops. Phys. Fluids 9 (6), 1493–1511.CrossRefGoogle Scholar

Guckenberger and Gekle supplementary movie

Video showing an excerpt from the simulation depicted in fig. 4 (a) in the main text. The ultrasound is switched on at around 4s.

Download Guckenberger and Gekle supplementary movie(Video)
Video 198.3 MB
Supplementary material: PDF

Guckenberger and Gekle supplementary material

Supplementary Information

Download Guckenberger and Gekle supplementary material(PDF)
PDF 4.2 MB