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Multi-scale modeling of hemodynamics in the cardiovascular system. (English) Zbl 1342.92061

Summary: The human cardiovascular system is a closed-loop and complex vascular network with multi-scaled heterogeneous hemodynamic phenomena. Here, we give a selective review of recent progress in macro-hemodynamic modeling, with a focus on geometrical multi-scale modeling of the vascular network, micro-hemodynamic modeling of microcirculation, as well as blood cellular, subcellular, endothelial biomechanics, and their interaction with arterial vessel mechanics. We describe in detail the methodology of hemodynamic modeling and its potential applications in cardiovascular research and clinical practice. In addition, we present major topics for future study: recent progress of patient-specific hemodynamic modeling in clinical applications, micro-hemodynamic modeling in capillaries and blood cells, and the importance and potential of the multi-scale hemodynamic modeling.

MSC:

92C35 Physiological flow
76Z05 Physiological flows
Full Text: DOI

References:

[1] Taylor, C.A., Figueroa, C.A.: Patient-specific modeling of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 11, 109-134 (2009) · doi:10.1146/annurev.bioeng.10.061807.160521
[2] van de Vosse, F., Stergiopulos, N.: Pulse wave propagation in the arterial tree. Annu. Rev. Fluid Mech. 43, 467-499 (2011) · Zbl 1299.76328 · doi:10.1146/annurev-fluid-122109-160730
[3] Holzapfel, G.A., Ogden, R.W.: Constitutive modelling of arteries. Proc. R. Soc. Lond. A 466, 1551-1597 (2010) · Zbl 1228.35239 · doi:10.1098/rspa.2010.0058
[4] Taelman, L., Degroote, J., Verdonck, P., et al.: Modeling hemodynamics in vascular networks using a geometrical multiscale approach: numerical aspects. Ann. Biomed. Eng. 41, 1445-1458 (2013) · doi:10.1007/s10439-012-0717-y
[5] Popel, A.S., Johnson, P.C.: Microcirculation and hemorheology. Annu. Rev. Fluid Mech. 37, 43-69 (2005) · Zbl 1117.76078 · doi:10.1146/annurev.fluid.37.042604.133933
[6] Perktold, K., Rappitsch, G.: Mathematical modeling of arterial blood flow and correlation to atherosclerosis. Technol. Health Care 3, 139-151 (1995) · Zbl 0833.76099
[7] Formaggia, L., Gerbeau, J.F., Nobile, F., et al.: On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191, 561-582 (2001) · Zbl 1007.74035 · doi:10.1016/S0045-7825(01)00302-4
[8] Wolters, B.J.B.M., Ruttern, M.C.M., Schurink, G.W.H., et al.: A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms. Med. Eng. Phys. 27, 871-883 (2005) · doi:10.1016/j.medengphy.2005.06.008
[9] Peskin, C.S.: The immersed boundary method. Acta Numer. 11, 479-517 (2002) · Zbl 1123.74309 · doi:10.1017/S0962492902000077
[10] Vigmond, E.J., Hughes, M., Plank, G., et al.: Computational tools for modeling electrical activity in cardiac tissue. J. Electrocardiol. 36, 69-74 (2003) · doi:10.1016/j.jelectrocard.2003.09.017
[11] Glowinski, R., Pan, T.W., Hesla, T.I., et al.: A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys. 169, 363-426 (2001) · Zbl 1047.76097 · doi:10.1006/jcph.2000.6542
[12] Hart, J.D., Peters, G.W.M., Schreurs, P.J.G., et al.: A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. J. Biomech. 36, 103-112 (2003) · doi:10.1016/S0021-9290(02)00244-0
[13] Figueroa, C.A., Vignon-Clementel, I.E., Jansen, K.E., et al.: A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput. Methods Appl. Mech. Eng. 194, 5685-5706 (2006) · Zbl 1126.76029 · doi:10.1016/j.cma.2005.11.011
[14] Reymond, P., Crosetto, P., Deparis, S., et al.: Physiological simulation of blood flow in the aorta: comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models. Med. Eng. Phys. 35, 784-791 (2013) · doi:10.1016/j.medengphy.2012.08.009
[15] Sughimoto, K., Takahara, Y., Mogi, K., et al.: Blood flow dynamic improvement with aneurysm repair detected by a patient-specific model of multiple aortic aneurysms. Heart Vessels 29, 404-412 (2014) · doi:10.1007/s00380-013-0381-7
[16] Sherwin, S.J., Formaggia, L., Peiro, J., et al.: Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. Int. J. Numer. Methods Fluids 43, 673-700 (2003) · Zbl 1032.76729 · doi:10.1002/fld.543
[17] Formaggia, L., Lamponi, D., Tuveri, M., et al.: Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Comput. Methods Biomech. Biomed. Eng. 9, 273-288 (2006) · doi:10.1080/10255840600857767
[18] Liang, F.Y., Takagi, S., Himeno, R., et al.: Biomechanical characterization of ventricular-arterial coupling during aging: a multi-scale model study. J. Biomech. 42, 692-704 (2009) · doi:10.1016/j.jbiomech.2009.01.010
[19] Liang, F.Y., Takagi, S., Himeno, R., et al.: Multi-scale modeling of the human cardiovascular system with applications to aortic valvular and arterial stenosis. Med. Biol. Eng. Comput. 47, 743-755 (2009) · doi:10.1007/s11517-009-0449-9
[20] Devault, K., Gremaud, P.A., Novak, V., et al.: Blood flow in the circle of Willis: modeling and calibration. Multiscale Model. Simul. 7, 888-909 (2008) · Zbl 1277.76131 · doi:10.1137/07070231X
[21] Bessems, D., Rutten, M., van de Vosse, F.: A wave propagation model of blood flow in large vessels using an approximate velocity profile function. J. Fluid Mech. 580, 145-168 (2007) · Zbl 1175.76171 · doi:10.1017/S0022112007005344
[22] Reymond, P., Merenda, F., Perren, F., et al.: Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. 297, 208-222 (2009)
[23] Huo, Y., Kassab, G.S.: A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree. Am. J. Physiol. Heart Circ. Physiol. 292, H2623-H2633 (2007) · doi:10.1152/ajpheart.00987.2006
[24] Alastruey, J., Parker, K.H., Peiro, J., et al.: Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J. Biomech. 40, 1794-1805 (2007) · doi:10.1016/j.jbiomech.2006.07.008
[25] Müller, L.O., Toro, E.F.: A global multiscale mathematical model for the human circulation with emphasis on the venous system. Int. J. Numer. Methods Biomed. Eng. 30, 681-725 (2014) · doi:10.1002/cnm.2622
[26] Liang, F.Y., Takagi, S., Himeno, R., et al.: A computational model of the cardiovascular system coupled with an upper-arm oscillometric cuff and its application to studying the suprasystolic cuff oscillation wave concerning its value in assessing arterial stiffness. Comput. Methods Biomech. Biomed. Eng. 16, 141-157 (2013) · doi:10.1080/10255842.2011.610305
[27] Pan, Q., Wang, R., Reglin, B., et al.: A one-dimensional mathematical model for studying the pulsatile flow in microvascular networks. J. Biomech. Eng. 136, 011009 (2014) · doi:10.1115/1.4025879
[28] Frank, O.: Die grundform des arteriellen pulses. Z. Biol. 37, 483-526 (1899)
[29] Westerhof, N., Lankhaar, J.W., Westerhof, B.E.: The arterial windkessel. Med. Biol. Eng. Comput. 47, 131-141 (2009) · doi:10.1007/s11517-008-0359-2
[30] Westerhof, N., Bosman, F., De Vries, C.J., et al.: Analog studies of the human systemic arterial tree. J. Biomech. 2, 121-143 (1969) · doi:10.1016/0021-9290(69)90024-4
[31] Stergiopulos, N., Westerhof, B.E., Westerhof, N.: Total arterial inertance as the fourth element of the windkessel model. Am. J. Physiol. 276, H81-H88 (1999)
[32] Liang, F.Y., Liu, H.: Simulation of hemodynamic responses to the valsalva maneuver: an integrative computational model of the cardiovascular system and the autonomic nervous system. J. Physiol. Sci. 56, 45-65 (2006) · doi:10.2170/physiolsci.RP001305
[33] Lu, K., Clark, J.W.J., Ghorbel, F.H., et al.: A human cardiopulmonary system model applied to the analysis of the valsalva maneuver. Am. J. Physiol. Heart Circ. Physiol. 281, H2661-H2679 (2001)
[34] Stergiopulos, N., Young, D.F., Rogge, T.: Computer simulation of arterial flow with applications to arterial and aortic stenosis. J. Biomech. 25, 1477-1488 (1992) · doi:10.1016/0021-9290(92)90060-E
[35] Olufsen, M.S., Peskin, C.S., Kim, W.Y., et al.: Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann. Biomed. Eng. 28, 1281-1299 (2000) · doi:10.1114/1.1326031
[36] Heywood, J.G., Rannacher, R., Turek, S.: Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods. Fluids. 22, 325-352 (1996) · Zbl 0863.76016 · doi:10.1002/(SICI)1097-0363(19960315)22:5<325::AID-FLD307>3.0.CO;2-Y
[37] Formaggia, L., Moura, A., Nobile, F.: On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. ESAIM Math. Model. Numer. Anal. 41, 743-769 (2007) · Zbl 1139.92009 · doi:10.1051/m2an:2007039
[38] Leiva, J.S., Blanco, P.J., Buscaglia, G.C.: Iterative strong coupling of dimensionally heterogeneous models. Int. J. Numer. Methods Eng. 81, 1558-1580 (2009) · Zbl 1183.76838
[39] Leiva, J.S., Blanco, P.J., Buscaglia, G.C.: Partitioned analysis for dimensionally-heterogeneous hydraulic networks. Multiscale Model. Simul. 9, 872-903 (2011) · Zbl 1300.76011 · doi:10.1137/100809301
[40] Vignon-Clementel, I.E., Figueroa, C.A., Jansen, K.E., et al.: Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods Appl. Mech. Eng. 195, 3776-3796 (2006) · Zbl 1175.76098 · doi:10.1016/j.cma.2005.04.014
[41] Blanco, P.J., Pivello, M.R., Urquiza, S.A., et al.: On the potentialities of 3D-1D coupled models in hemodynamics simulations. J. Biomech. 42, 919-930 (2009) · doi:10.1016/j.jbiomech.2009.01.034
[42] Hsia, T.Y., Cosentino, D., Corsini, C., et al.: Use of mathematical modeling to compare and predict hemodynamic effects between hybrid and surgical Norwood palliations for hypoplastic left heart syndrome. Circulation 124, S204-S210 (2011) · doi:10.1161/CIRCULATIONAHA.110.010769
[43] Mahler, F., Muheim, M.H., Intaglietta, M., et al.: Blood pressure fluctuations in human nailfold capillaries. Am. J. Physiol. Heart Circ. Physiol. 236, H888-H893 (1979)
[44] Nakano, T., Tominaga, R., Nagano, I., et al.: Pulsatile flow enhances endothelium-derived nitric oxide release in the peripheral vasculature. Am. J. Physiol. Heart Circ. Physiol. 278, H1098-H1104 (2000)
[45] Li, Y., Zheng, J., Bird, I.M., et al.: Effects of pulsatile shear stress on nitric oxide production and endothelial cell nitric oxide synthase expression by ovine fetoplacental artery endothelial cells. Biol. Reprod. 69, 1053-1059 (2003)
[46] Uryash, A., Wu, H., Bassuk, J., et al.: Low-amplitude pulses to the circulation through periodic acceleration induces endothelial-dependent vasodilatation. J. Appl. Physiol. 106, 1840-1847 (2009)
[47] Sezai, A., Shiono, M., Orime, Y., et al.: Renal circulation and cellular metabolism during left ventricular assisted circulation: comparison study of pulsatile and nonpulsatile assists. Artif. Organs. 21, 830-835 (1997)
[48] Orime, Y., Shiono, M., Nakata, et al.: The role of pulsatility in end-organ microcirculation after cardiogenic shock. ASAIO J. 42, M724-728 (1996)
[49] O’Neil, M.P., Fleming, J.C., Badhwar, A., et al.: Pulsatile versus nonpulsatile flow during cardiopulmonary bypass: microcirculatory and systemic effects. Ann. Thorac. Surg. 94, 2046-2053 (2012)
[50] Mittal, N., Zhou, Y., Linares, C., et al.: Analysis of blood flow in the entire coronary arterial tree. Am. J. Physiol. Heart Circ. Physiol. 289, H439-H446 (2005)
[51] Lipowsky, H.H., Zweifach, B.W.: Network analysis of microcirculation of cat mesentery. Microvasc. Res. 7, 73-83 (1974) · doi:10.1016/0026-2862(74)90038-7
[52] Pries, A.R., Secomb, T.W., Gaehtgens, P., et al.: Blood flow in microvascular networks. Experiments and simulation. Circ. Res. 67, 826-834 (1990) · doi:10.1161/01.RES.67.4.826
[53] Grinberg, L., Cheever, E., Anor, T., et al.: Modeling blood flow circulation in intracranial arterial networks: a comparative 3D/1D simulation study. Ann. Biomed. Eng. 39, 297-309 (2011) · Zbl 1175.76098
[54] Shi, Y., Lawford, P., Hose, R.: Review of zero-D and 1-D models of blood flow in the cardiovascular system. Biomed. Eng. Online 10, 33 (2011) · doi:10.1186/1475-925X-10-33
[55] Ganesan, P., He, S., Xu, H.: Modelling of pulsatile blood flow in arterial trees of retinal vasculature. Med. Eng. Phys. 33, 810-823 (2011) · doi:10.1016/j.medengphy.2010.10.004
[56] Lee, J., Smith, N.: Development and application of a one-dimensional blood flow model for microvascular networks. Proc. Inst. Mech. Eng. Part H 222, 487-511 (2008) · doi:10.1243/09544119JEIM308
[57] Seki, J.: Flow pulsation and network structure in mesenteric microvasculature of rats. Am. J. Physiol. Heart Circ. Physiol. 266, H811-H821 (1994)
[58] Pries, A.R., Ley, K., Gaehtgens, P.: Generalization of the Fahraeus principle for microvessel networks. Am. J. Physiol. Heart Circ. Physiol. 251, H1324-1332 (1986)
[59] Nakano, A., Sugii, Y., Minamiyama, M., et al.: Measurement of red cell velocity in microvessels using particle image velocimetry (PIV). Clin. Hemorheol. Microcirc. 29, 445-455 (2003)
[60] Golub, A.S., Barker, M.C., Pittman, R.N.: Microvascular oxygen tension in the rat mesentery. Am. J. Physiol. Heart Circ. Physiol. 294, H21-H28 (2008) · doi:10.1152/ajpheart.00861.2007
[61] Pries, A.R., Secomb, T.W.: Origins of heterogeneity in tissue perfusion and metabolism. Cardiovasc. Res. 81, 328-335 (2009) · doi:10.1093/cvr/cvn318
[62] Tuma, R.F., Duran, W.N., Ley, K.: Microcirculation. Academic Press, New York (2008)
[63] Fung, Y.C., Zweifach, B.W., Intaglietta, M.: Elastic environment of the capillary bed. Circ. Res. 19, 441-461 (1966) · doi:10.1161/01.RES.19.2.441
[64] Pries, A.R., Secomb, T.W., Gaehtgens, P.: Biophysical aspects of blood flow in the microvasculature. Cardiovasc. Res. 32, 654-667 (1996) · doi:10.1016/0008-6363(96)00065-X
[65] Alastruey, J., Parker, K.H., Peiro, J., et al.: Lumped parameter outflow models for 1-D blood flow simulations: effect on pulse waves and parameter estimation. Commun. Comput. Phys. 4, 317-336 (2008) · Zbl 1364.76248
[66] Dao, M., Lim, C.T., Suresh, S.: Mechanics of the human red blood cell deformed by optical tweezers. J. Mech. Phys. Solids 51, 2259-2280 (2003) · doi:10.1016/j.jmps.2003.09.019
[67] Tsubota, K., Wada, S.: Elastic force of red blood cell membrane during tank-treading motion: consideration of the membrane’s natural state. Int. J. Mech. Sci. 52, 356-364 (2010) · doi:10.1016/j.ijmecsci.2009.10.007
[68] Tsubota, K., Wada, S.: Effect of the natural state of an elastic cellular membrane on tank-treading and tumbling motions of a single red blood cell. Phys. Rev. E. 81, 011910 (2010) · doi:10.1103/PhysRevE.81.011910
[69] Tsubota, K., Wada, S., Liu, H.: Elastic behavior of a red blood cell with the membrane’s nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion. Biomech. Model. Mechanobiol. 13, 735-746 (2014) · doi:10.1007/s10237-013-0530-z
[70] Skalak, R., Tozeren, A., Zarda, R.P., et al.: Strain energy function of red blood cell membranes. Biophys. J. 13, 245-264 (1973)
[71] Helfrich, W.: Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C. 28, 693-703 (1973)
[72] Tsubota, K.: Short note on the bending models for a membrane in capsule mechanics: comparison between continuum and discrete models. J. Comput. Phys. 277, 320-328 (2014) · Zbl 1349.74263 · doi:10.1016/j.jcp.2014.08.007
[73] Kamada, H., Tsubota, K., Nakamura, M., et al.: A three-dimensional particle simulation of the formation and collapse of a primary thrombus. Int. J. Numer. Methods Biomed. Eng. 26, 488-500 (2010) · Zbl 1183.92047
[74] Kamada, H., Tsubota, K., Nakamura, M., et al.: Computational study on effect of stenosis on primary thrombus formation. Biorheology 48, 99-114 (2011) · Zbl 1277.76131
[75] Miyoshi, H., Tsubota, K., Hoyano, T., et al.: Three-dimensional modulation of cortical plasticity during pseudopodial protrusion of mouse leukocytes. Biochem. Biophys. Res. Commun. 438, 594-599 (2013)
[76] Tsubota, K., Wada, S., Yamaguchi, T.: Simulation study on effects of hematocrit on blood flow properties using particle method. J. Biomech. Sci. Eng. 1, 159-170 (2006) · doi:10.1299/jbse.1.159
[77] Morishita, Y., Iwasa, Y.: Growth based morphogenesis of vertebrate limb bud. Bull. Math. Biol. 70, 1957-1978 (2008) · Zbl 1147.92302 · doi:10.1007/s11538-008-9334-1
[78] Morishita, Y., Suzuki, T.: Bayesian inference of whole-organ deformation dynamics from limited space-time point data. J. Theor. Biol. 357, 74-85 (2014) · Zbl 1412.92020 · doi:10.1016/j.jtbi.2014.04.027
[79] Ishihara, S., Sugimura, K.: Baysian inference of force dynamics during morphogenesis. J. Theor. Biol. 313, 201-211 (2012) · Zbl 1337.92021 · doi:10.1016/j.jtbi.2012.08.017
[80] Okuda, S., Inoue, Y., Eiraku, M., et al.: Reversible network reconnection model for simulating large deformation in dynamic tissue morphogenesis. Biomech. Model. Mechanobiol. 12, 627-644 (2013)
[81] Ridley, A.J., Schwartz, M.A., Burridge, K., et al.: Cell migration: integrating signals from front to back. Science 302, 1704-1709 (2003)
[82] Mullins, R.D., Heuser, J.A., Pollard, T.D.: The interaction of Arp2/3 complex with actin: nucleation, high affinity pointed end capping, and formation of branching networks of filaments. Proc. Natl. Acad. Sci. USA 95, 6181-6186 (1998) · doi:10.1073/pnas.95.11.6181
[83] Svitkina, T.M., Borisy, G.G.: Arp2/3 complex and actin depolymerizing factor/cofilin in dendritic organization and treadmilling of actin filament array in lamellipodia. J. Cell Biol. 145, 1009-1026 (1999) · doi:10.1083/jcb.145.5.1009
[84] Pollard, T.D., Blanchoin, L., Mullins, D.: Molecular mechanisms controlling actin filament dynamics in nonmuscle cells. Annu. Rev. Biophys. Biomol. Struct. 29, 545-576 (2000) · doi:10.1146/annurev.biophys.29.1.545
[85] Small, J.V., Stradal, T., Vignal, E., et al.: The lamellipodium: where motility begins. Trends Cell Biol. 12, 112-120 (2002)
[86] Chhabra, E.S., Higgs, H.N.: The many faces of actin: matching assembly factors with cellular structures. Nat. Cell Biol. 9, 1110-1121 (2007) · doi:10.1038/ncb1007-1110
[87] Lazarides, E., Burridge, \[K.: \alpha\] α-Actinin: immunofluorescent localization of a muscle structural protein in nonmuscle cells. Cell 6, 289-298 (1975) · doi:10.1016/0092-8674(75)90180-4
[88] Weber, K., Groeschel-Stewart, U.: Antibody to myosin: the specific bisualization of myosin-containing filaments in nonmuscle cells. Proc. Natl. Acad. Sci. USA 71, 4561-4564 (1974) · doi:10.1073/pnas.71.11.4561
[89] Small, J.V., Rottner, K., Kaverina, I., et al.: Assembling an actin cytoskeleton for cell attachment and movement. Biochim. Biophys. Acta 1404, 271-281 (1998) · Zbl 1117.76078
[90] Hotulainen, P., Lappalainen, P.: Stress fibers are generated by two distinct actin assembly mechanisms in motile cells. J. Cell Biol. 173, 383-394 (2006) · doi:10.1083/jcb.200511093
[91] Pellegrin, S., Mellor, H.: Actin stress fibres. J. Cell Sci. 120, 3491-3499 (2007) · doi:10.1242/jcs.018473
[92] Chiu, J.J., Chien, S.: Effects of disturbed flow on vascular endothelium: pathophysiological basis and clinical perspectives. Physiol. Rev. 91, 327-387 (2011)
[93] Ward, M.R., Pasterkamp, G., Yeung, A.C., et al.: Arterial remodeling: mechanisms and clinical implications. Circulation 102, 1186-1191 (2000) · Zbl 1197.74075
[94] Wojciak-Stothard, B., Ridley, A.J.: Shear stress-induced endothelial cell polarization is mediated by Rho and Rac but not Cdc42 or PI 3-kinases. J. Cell Biol. 161, 429-439 (2003) · doi:10.1083/jcb.200210135
[95] Ingber, D.E.: Tensegrity II: how structure networks influence cellular information processing networks. J. Cell Sci. 116, 1397-1408 (2003) · doi:10.1242/jcs.00360
[96] Schwartz, E.A., Gerristen, M.E., Bizios, R.: Effects of Hydrostatic Pressure on Endothelial Cells. In: Lelkes, P. I. (ed.) Endothelium and Mechanical Forces, chapter 13, pp. 275-290. Harwood Academic Publishers, London, England (1999) · Zbl 1299.76328
[97] Chien, S.: Effects of disturbed flow on endothelial cells. Ann. Biomed. Eng. 36, 554-562 (2008) · doi:10.1007/s10439-007-9426-3
[98] Azuma, N., Aydin Duzgan, S., Ikeda, M., et al.: Endothelial cell response to different mechanical forces. J. Vasc. Surg. 32, 789-794 (2000) · Zbl 1197.74075
[99] Davies, P.F., Tripathi, S.C.: Mechanical stress mechanisms and the cell. An endothelial paradigm. Circ. Res. 72, 239-245 (1993) · doi:10.1161/01.RES.72.2.239
[100] Chicurel, M.E., Chen, C.S., Ingber, D.E.: Cellular control lies in the balance of forces. Curr. Opin. Cell Biol. 10, 232-239 (1998) · doi:10.1016/S0955-0674(98)80145-2
[101] Seneviratne, A., Hulsmans, M., Holvoet, P., et al.: Biomechanical factors and macrophages in plaque stability. Cardiovasc. Res. 99, 284-293 (2013)
[102] Gao, H., Long, Q.: Atherosclerosis Plaque Stress Analysis: A Review, vol. XIX. Springer, New York (2014)
[103] Yim, P., DeMarco, K., Castro, M.A., et al.: Characterization of shear stress on the wall of the carotid artery using magnetic resonance imaging and computational fluid dynamics. Stud. Health Technol. Inform. 113, 412-442 (2005)
[104] Barbee, K.A., Davies, P.F., Lal, R.: Shear stress-induced reorganization of the surface topography of living endothelial cells imaged by atomic force microscopy. Circ. Res. 74, 163-171 (1994) · doi:10.1161/01.RES.74.1.163
[105] Wei, T., Nackman, G.B., Voorhees, A.: Experiments show importance of flow-induced pressure on endothelial cell shape and alignment. Proc. R. Soc. A 463, 1409-1419 (2007) · doi:10.1098/rspa.2006.1805
[106] Liu, S.Q., Yen, M., Fung, Y.C.: On measuring the third dimension of cultured endothelial cells in shear flow. Proc. Natl. Acad. Sci. USA 91, 8782-9796 (1994) · doi:10.1073/pnas.91.19.8782
[107] Hazel, A.L., Pedley, T.J.: Vascular endothelial cells minimize the total force on their nuclei. Biophys. J. 78, 47-54 (2000) · doi:10.1016/S0006-3495(00)76571-4
[108] Waché, P., Wang, X., Maurice, et al.: Calcul numérique de la déformation mécanique d’un modèle de cellule endothéliale. C. R. Acad. Sci. Paris Bioméch./Biomech. 328, 633-638 (2000) (in German) · Zbl 1093.76555
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