Popel, AS, Johnson, PC. Microcirculation and hemorheology. Annu Rev Fluid Mech 2005, 37:43–69.
Lipowsky, HH. Microvascular rheology and hemodynamics. Microcirculation 2005, 12:5–15.
Pries, AR, Secomb, TW. Blood flow in microvascular networks. In: Tuma, RF, Duran, WN, Ley, K, eds. Handbook of Physiology, The Cardiovascular System, Microcirculation. San Diego, CA: Academic Press; 2008, 3–36.
Secomb, TW, Pries, AR. The microcirculation: physiology at the mesoscale. J Physiol 2011, 589:1047–1052.
Pries, AR, Secomb, TW, Gaehtgens, P. Biophysical aspects of blood flow in the microvasculature. Cardiovasc Res 1996, 32:654–667.
Pries, AR, Secomb, TW. Rheology of the microcirculation. Clin Hemorheol Microcirc 2003, 29:143–148.
Fåhraeus, R. The suspension stability of the blood. Physiol Rev 1929, 9:241–274.
Fåhraeus, R, Lindqvist, T. The viscosity of the blood in narrow capillary tubes. Am J Phys 1931, 96:562–568.
Reinke, W, Gaehtgens, P, Johnson, PC. Blood viscosity in small tubes: effect of shear rate, aggregation, and sedimentation. Am J Physiol 1987, 253:H540–H547.
Pries, AR, Neuhaus, D, Gaehtgens, P. Blood viscosity in tube flow: dependence on diameter and hematocrit. Am J Physiol 1992, 263:H1770–H1778.
Goldsmith, HL, Cokelet, GR, Gaehtgens, P. Robin Fahraeus: evolution of his concepts in cardiovascular physiology. Am J Physiol 1989, 257:H1005–H1015.
Cokelet, GR, Goldsmith, HL. Decreased hydrodynamic resistance in the two‐phase flow of blood through small vertical tubes at low flow rates. Circ Res 1991, 68:1–17.
Cantat, I, Misbah, C. Lift force and dynamical unbinding of adhering vesicles under shear flow. Phys Rev Lett 1999, 83:880–883.
Abkarian, M, Lartigue, C, Viallat, A. Tank treading and unbinding of deformable vesicles in shear flow: determination of the lift force. Phys Rev Lett 2002, 88:068103.
Klitzman, B, Duling, BR. Microvascular hematocrit and red cell flow in resting and contracting striated muscle. Am J Physiol 1979, 237:H481–H490.
Schmid‐Schönbein, GW, Skalak, R, Usami, S, Chien, S. Cell distribution in capillary networks. Microvasc Res 1980, 19:18–44.
Lipowsky, HH, Usami, S, Chien, S. In vivo measurements of “apparent viscosity” and microvessel hematocrit in the mesentery of the cat. Microvasc Res 1980, 19:297–319.
Pries, AR, Ley, K, Gaehtgens, P. Generalization of the Fahraeus principle for microvessel networks. Am J Physiol 1986, 251:H1324–H1332.
Pries, AR, Ley, K, Claassen, M, Gaehtgens, P. Red cell distribution at microvascular bifurcations. Microvasc Res 1989, 38:81–101.
Pries, AR, Secomb, TW, Gessner, T, Sperandio, MB, Gross, JF, Gaehtgens, P. Resistance to blood flow in microvessels in vivo. Circ Res 1994, 75:904–915.
Maeda, N, Suzuki, Y, Tanaka, J, Tateishi, N. Erythrocyte flow and elasticity of microvessels evaluated by marginal cell‐free layer and flow resistance. Am J Physiol 1996, 271:H2454–H2461.
Kim, S, Kong, RL, Popel, AS, Intaglietta, M, Johnson, PC. Temporal and spatial variations of cell‐free layer width in arterioles. Am J Physiol 2007, 293:H1526–H1535.
Pries, AR, Secomb, TW. Microvascular blood viscosity in vivo and the endothelial surface layer. Am J Physiol 2005, 289:H2657–H2664.
Vink, H, Duling, BR. Identification of distinct luminal domains for macromolecules, erythrocytes, and leukocytes within mammalian capillaries. Circ Res 1996, 79:581–589.
Pries, AR, Secomb, TW, Gaehtgens, P. The endothelial surface layer. Pflugers Arch 2000, 440:653–666.
Weinbaum, S, Tarbell, JM, Damiano, ER. The structure and function of the endothelial glycocalyx layer. Annu Rev Biomed Eng 2007, 9:121–167.
Yen, W‐Y, Cai, B, Zeng, M, Tarbell, JM, Fu, BM. Quantification of the endothelial surface glycocalyx on rat and mouse blood vessels. Microvasc Res 2012, 83:337–346.
Lemley, KV, Zimmerhackl, B, Jamison, RL, Kriz, W. The shape of renal vasa recta capillaries and its effect on calculation of single capillary blood flow. Microvasc Res 1986, 32:1–20.
Pries, AR, Schönfeld, D, Gaehtgens, P, Kiani, MF, Cokelet, GR. Diameter variability and microvascular flow resistance. Am J Physiol 1997, 272:H2716–H2725.
Secomb, TW, Hsu, R. Resistance to blood flow in nonuniform capillaries. Microcirculation 1997, 4:421–427.
Secomb, TW, Hsu, R. Motion of red blood cells in capillaries with variable cross‐sections. J Biomech Eng 1996, 118:538–544.
Enden, G, Popel, AS. A numerical study of plasma skimming in small vascular bifurcations. J Biomech Eng 1994, 116:79–88.
Ong, PK, Jain, S, Kim, S. Spatio‐temporal variations in cell‐free layer formation near bifurcations of small arterioles. Microvasc Res 2012, 83:118–125.
Katanov, D, Gompper, G, Fedosov, DA. Microvascular blood flow resistance: role of red blood cell migration and dispersion. Microvasc Res 2015, 99:57–66.
Pries, AR, Secomb, TW, Jacobs, H, Sperandio, M, Osterloh, K, Gaehtgens, P. Microvascular blood flow resistance: role of endothelial surface layer. Am J Physiol 1997, 273:H2272–H2279.
Damiano, ER. The effect of the endothelial‐cell glycocalyx on the motion of red blood cells through capillaries. Microvasc Res 1998, 55:77–91.
Secomb, TW, Hsu, R, Pries, AR. Motion of red blood cells in a capillary with an endothelial surface layer: effect of flow velocity. Am J Physiol 2001, 281:H629–H636.
Secomb, TW, Hsu, R, Pries, AR. Blood flow and red blood cell deformation in nonuniform capillaries: effects of the endothelial surface layer. Microcirculation 2002, 9:189–196.
Deng, M, Li, X, Liang, H, Caswell, B, Karniadakis, GE. Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres. J Fluid Mech 2012, 711:192–211.
Römer, F, Fedosov, DA. Dense brushes of stiff polymers or filaments in fluid flow. Europhys Lett 2015, 109:68001.
Sun, C, Munn, LL. Particulate nature of blood determines macroscopic rheology: a 2D lattice‐Boltzmann analysis. Biophys J 2005, 88:1635–1645.
Bagchi, P. Mesoscale simulation of blood flow in small vessels. Biophys J 2007, 92:1858–1877.
Secomb, TW, Styp‐Rekowska, B, Pries, AR. Two‐dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann Biomed Eng 2007, 35:755–765.
Zhang, J, Johnson, PC, Popel, AS. Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows. Microvasc Res 2009, 77:265–272.
Liu, Y, Liu, WK. Rheology of red blood cell aggregation by computer simulation. J Comput Phys 2006, 220:139–154.
Dupin, MM, Halliday, I, Care, CM, Munn, LL. Lattice Boltzmann modelling of blood cell dynamics. Int J Comput Fluid Dyn 2008, 22:481–492.
McWhirter, JL, Noguchi, H, Gompper, G. Flow‐induced clustering and alignment of vesicles and red blood cells in microcapillaries. Proc Natl Acad Sci USA 2009, 106:6039–6043.
Fedosov, DA, Caswell, B, Popel, AS, Karniadakis, GE. Blood flow and cell‐free layer in microvessels. Microcirculation 2010, 17:615–628.
Freund, JB, Orescanin, MM. Cellular flow in a small blood vessel. J Fluid Mech 2011, 671:466–490.
Wendt, JF, ed. Computational Fluid Dynamics. 3rd ed. Berlin: Springer; 2009.
Pivkin, IV, Caswell, B, Karniadakis, GE. Dissipative particle dynamics. In: Lipkowitz, KB, ed. Reviews in Computational Chemistry, vol. 27. Hoboken, NJ: John Wiley %26 Sons, Inc.; 2011, 85–110.
Gompper, G, Ihle, T, Kroll, DM, Winkler, RG. Multi‐particle collision dynamics: a particle‐based mesoscale simulation approach to the hydrodynamics of complex fluids. Adv Polym Sci 2009, 221:1–87.
Monaghan, JJ. Smoothed particle hydrodynamics. Rep Prog Phys 2005, 68:1703–1759.
Discher, DE, Boal, DH, Boey, SK. Simulations of the erythrocyte cytoskeleton at large deformation. II: Micropipette aspiration. Biophys J 1998, 75:1584–1597.
Noguchi, H, Gompper, G. Shape transitions of fluid vesicles and red blood cells in capillary flows. Proc Natl Acad Sci USA 2005, 102:14159–14164.
Pivkin, IV, Karniadakis, GE. Accurate coarse‐grained modeling of red blood cells. Phys Rev Lett 2008, 101:118105.
Fedosov, DA, Caswell, B, Karniadakis, GE. A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys J 2010, 98:2215–2225.
Peng, Z, Li, X, Pivkin, IV, Dao, M, Karniadakis, GE, Suresh, S. Lipid bilayer and cytoskeletal interactions in a red blood cell. Proc Natl Acad Sci USA 2013, 110:13356–13361.
Zhao, H, Isfahani, AHG, Olson, LN, Freund, JB. A spectral boundary integral method for flowing blood cells. J Comput Phys 2010, 229:3726–3744.
Doddi, SK, Bagchi, P. Three‐dimensional computational modeling of multiple deformable cells flowing in microvessels. Phys Rev E 2009, 79:046318.
Li, X, Vlahovska, PM, Karniadakis, GE. Continuum‐ and particle‐based modeling of shapes and dynamics of red blood cells in health and disease. Soft Matter 2013, 9:28–37.
Ju, M, Ye, SS, Namgung, B, Cho, S, Low, HT, Leo, HL, Kim, S. A review of numerical methods for red blood cell flow simulation. Comput Methods Biomech Biomed Eng 2015, 18:130–140.
Fedosov, DA, Noguchi, H, Gompper, G. Multiscale modeling of blood flow: from single cells to blood rheology. Biomech Model Mechanobiol 2014, 13:239–258.
Freund, JB. Numerical simulation of flowing blood cells. Annu Rev Fluid Mech 2014, 46:67–95.
Fedosov, DA, Dao, M, Karniadakis, GE, Suresh, S. Computational biorheology of human blood flow in health and disease. Ann Biomed Eng 2014, 42:368–387.
Omori, T, Imai, Y, Kikuchi, K, Ishikawa, T, Yamaguchi, T. Hemodynamics in the microcirculation and in microfluidics. Ann Biomed Eng 2015, 43:238–257.
Lei, H, Fedosov, DA, Caswell, B, Karniadakis, GE. Blood flow in small tubes: quantifying the transition to the non‐continuum regime. J Fluid Mech 2013, 722:214–239.
Alizadehrad, D, Imai, Y, Nakaaki, K, Ishikawa, T, Yamaguchi, T. Quantification of red blood cell deformation at high‐hematocrit blood flow in microvessels. J Biomech 2012, 45:2684–2689.
Soutani, M, Suzuki, Y, Tateishi, N, Maeda, N. Quantitative evaluation of flow dynamics of erythrocytes in microvessels: influence of erythrocyte aggregation. Am J Physiol 1995, 268:H1959–H1965.
Fedosov, DA, Gompper, G. White blood cell margination in microcirculation. Soft Matter 2014, 10:2961–2970.
Kumar, A, Graham, MD. Mechanism of margination in confined flows of blood and other multicomponent suspensions. Phys Rev Lett 2012, 109:108102.
Zhao, H, Shaqfeh, ESG, Narsimhan, V. Shear‐induced particle migration and margination in a cellular suspension. Phys Fluids 2012, 24:011902.
Kumar, A, Henriquez‐Rivera, RG, Graham, MD. Flow‐induced segregation in confined multicomponent suspensions: effects of particle size and rigidity. J Fluid Mech 2014, 738:423–462.
Freund, JB. Leukocyte margination in a model microvessel. Phys Fluids 2007, 19:023301.
Fedosov, DA, Fornleitner, J, Gompper, G. Margination of white blood cells in microcapillary flow. Phys Rev Lett 2012, 108:028104.
Crowl, L, Fogelson, AL. Analysis of mechanisms for platelet near‐wall excess under arterial blood flow conditions. J Fluid Mech 2011, 676:348–375.
Zhao, H, Shaqfeh, ESG. Shear‐induced platelet margination in a microchannel. Phys Rev E 2011, 83:061924.
Vahidkhah, K, Diamond, SL, Bagchi, P. Platelet dynamics in three‐dimensional simulation of whole blood. Biophys J 2014, 106:2529–2540.
Müller, K, Fedosov, DA, Gompper, G. Margination of micro‐ and nano‐particles in blood flow and its effect on drug delivery. Sci Rep 2014, 4:4871.
Fitzgibbon, S, Spann, AP, Qi, QM, Shaqfeh, ESG. In vitro measurement of particle margination in the microchannel flow: effect of varying hematocrit. Biophys J 2015, 108:2601–2608.
Müller, K, Fedosov, DA, Gompper, G. Understanding particle margination in blood flow—a step toward optimized drug delivery systems. Med Eng Phys. In press. DOI: 10.1016/j.medengphy.2015.08.009.
Barber, JO, Alberding, JP, Restrepo, JM, Secomb, TW. Simulated two‐dimensional red blood cell motion, deformation, and partitioning in microvessel bifurcations. Ann Biomed Eng 2008, 36:1690–1698.
Xiong, W, Zhang, J. Two‐dimensional lattice Boltzmann study of red blood cell motion through microvascular bifurcation: cell deformability and suspending viscosity effects. Biomech Model Mechanobiol 2012, 11:575–583.
Lykov, K, Li, X, Lei, H, Pivkin, IV, Karniadakis, GE. Inflow/outflow boundary conditions for particle‐based blood flow simulations: application to arterial bifurcations and trees. PLoS Comput Biol 2015, 11:e1004410.
Li, X, Popel, AS, Karniadakis, GE. Blood‐plasma separation in Y‐shaped bifurcating microfluidic channels: a dissipative particle dynamics simulation study. Phys Biol 2012, 9:026010.
Hyakutake, T, Nagai, S. Numerical simulation of red blood cell distributions in three‐dimensional microvascular bifurcations. Microvasc Res 2015, 97:115–123.
Tousi, N, Wang, B, Pant, K, Kiani, MF, Prabhakarpandian, B. Preferential adhesion of leukocytes near bifurcations is endothelium independent. Microvasc Res 2010, 80:384–388.
Pries, AR, Secomb, TW, Gaehtgens, P, Gross, JF. Blood flow in microvascular networks: experiments and simulation. Circ Res 1990, 67:826–834.
Pries, AR, Secomb, TW. Microcirculatory network structures and models. Ann Biomed Eng 2000, 28:916–921.
Kiani, MF, Pries, AR, Hsu, LL, Sarelius, IH, Cokelet, GR. Fluctuations in microvascular blood flow parameters caused by hemodynamic mechanisms. Am J Physiol 1994, 266:H1822–H1828.
Carr, RT, Lacoin, M. Nonlinear dynamics of microvascular blood flow. Ann Biomed Eng 2000, 28:641–652.
Guibert, R, Fonta, C, Plouraboue, F. Cerebral blood flow modeling in primate cortex. J Cereb Blood Flow Metab 2010, 30:1860–1873.
Fraser, GM, Goldman, D, Ellis, CG. Microvascular flow modeling using in vivo hemodynamic measurements in reconstructed 3D capillary networks. Microcirculation 2012, 19:510–520.
Fry, BC, Lee, J, Smith, NP, Secomb, TW. Estimation of blood flow rates in large microvascular networks. Microcirculation 2012, 19:530–538.
Secomb, TW, Hsu, R. Simulation of O2 transport in skeletal muscle: diffusive exchange between arterioles and capillaries. Am J Physiol 1994, 267:H1214–H1221.
Goldman, D, Popel, AS. Computational modeling of oxygen transport from complex capillary networks. Adv Exp Med Biol 1999, 471:555–563.
Pries, AR, Höpfner, M, le Noble, F, Dewhirst, MW, Secomb, TW. The shunt problem: control of functional shunting in normal and tumour vasculature. Nat Rev Cancer 2010, 10:587–593.
Sefidgar, M, Soltani, M, Raahemifar, K, Sadeghi, M, Bazmara, H, Bazargan, M, Naeenian, MM. Numerical modeling of drug delivery in a dynamic solid tumor microvasculature. Microvasc Res 2015, 99:43–56.
Soltani, M, Chen, P. Numerical modeling of interstitial fluid flow coupled with blood flow through a remodeled solid tumor microvascular network. PLoS One 2013, 8:e67025.
Kim, E, Stamatelos, S, Cebulla, J, Bhujwalla, ZM, Popel, AS, Pathak, AP. Multiscale imaging and computational modeling of blood flow in the tumor vasculature. Ann Biomed Eng 2012, 40:2425–2441.
Stamatelos, SK, Kim, E, Pathak, AP, Popel, AS. A bioimage informatics based reconstruction of breast tumor microvasculature with computational blood flow predictions. Microvasc Res 2014, 91:8–21.
Welter, M, Rieger, H. Interstitial fluid flow and drug delivery in vascularized tumors: a computational model. PLoS ONE 2013, 8:e70395.
Rieger, H, Welter, M. Integrative models of vascular remodeling during tumor growth. WIREs Syst Biol Med 2015, 7:113–129.
Warren, BA. The vascular morphology of tumors. In: Petersen, HI, ed. Tumor Blood Circulation. Boca Raton, FL: CRC Press; 1979, 1–47.
Shubik, PW. Vascularization of tumors: a review. J Cancer Res Clin Oncol 1982, 103:211–226.
Jain, RK. Determinants of tumor blood flow: a review. Cancer Res 1988, 48:2641–2658.
Less, JR, Skalak, TC, Sevick, EM, Jain, RK. Microvascular architecture in a mammary carcinoma: branching patterns and vessel dimensions. Cancer Res 1991, 51:265–273.
Dvorak, HF. Tumors: wounds that do not heal. N Engl J Med 1986, 315:1650–1659.
Hashizume, H, Baluk, P, Morikawa, S, McLean, JW, Thurston, G, Roberge, S, Jain, RK, McDonald, DM. Openings between defective endothelial cells explain tumor vessel leakiness. Am J Pathol 2000, 156:1363–1380.
Arciero, JC, Carlson, BE, Secomb, TW. Theoretical model of metabolic blood flow regulation: roles of ATP release by red blood cells and conducted responses. Am J Physiol 2008, 295:H1562–H1571.
Carlson, BE, Arciero, JC, Secomb, TW. Theoretical model of blood flow autoregulation: roles of myogenic, shear‐dependent, and metabolic responses. Am J Physiol 2008, 295:H1572–H1579.
Secomb, TW. Theoretical models for regulation of blood flow. Microcirculation 2008, 15:765–775.
Forouzan, O, Yang, X, Sosa, JM, Burns, JM, Shevkoplyas, SS. Spontaneous oscillations of capillary blood flow in artificial microvascular networks. Microvasc Res 2012, 84:123–132.
Song, JW, Bazou, D, Munn, LL. Anastomosis of endothelial sprouts forms new vessels in a tissue analogue of angiogenesis. Integr Biol 2012, 4:857–862.