54
Views
0
CrossRef citations to date
0
Altmetric
Articles

Theoretical Modeling in Hemodynamics of Microcirculation

&
Pages 699-714 | Received 14 Apr 2008, Published online: 10 Jul 2009

References

  • Alarcon T, Byrne HM, Maini PK. A design principle for vascular beds: The effects of complex blood rheology. Microvasc Res 2005; 69: 156–172
  • Audet DM, Olbricht WL. The motion of model cells at capillary bifurcations. Microvasc Res 1987; 33: 377–396
  • Bagchi P. Mesoscale simulation of blood flow in small vessels. Biophys J 2007; 92: 1858–1877
  • Bagchi P, Johnson PC, Popel AS. Computational fluid dynamic simulation of aggregations of deformable cells in a shear flow. J Biomech Eng 2005; 127: 1070–1080
  • Beighley PE, Thomas PJ, Jorgensen SM, Ritman EL. 3D architecture of myocardial microcirculation in intact rat heart: A study with micro-CT. Analytical and Quantitative Dardiology, S Sideman, R Beyar. Plenum Press New York. 1997; 165–175
  • Boryczko K, Dzwinel W, Yuen DA. Modeling fibrin aggregation in blood flow with discrete-particles. Comp Meth Prog Biomed 2004; 75: 181–194
  • Bugliarello G, Hsiao GCC. Phase separation in suspensions flowing through bifurcations: A simplified hemodynamic model. Science 1964; 143: 469–471
  • Cabel M, Meiselman HJ, Popel AS, Johnson PC. Contribution of red blood cell aggregation to venous vascular resistance in skeletal muscle. Amer J Physiol 1997; 272: H1020–H1032
  • Carr RT, Geddes JB, Wu F. Oscillations in a simple microvascular network. Ann Biomed Eng 2005; 33: 764–771
  • Carr RT, Lacoin M. Nonlinear dynamics of microvascular blood flow. Ann Biomed Eng 2000; 28: 641–652
  • Cassot F, Lauwers F, Fouard C, Prohaska S, Lauwers-Cances V. A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex. Microcirculation 2006; 13: 1–18
  • Chen H, Chen S, Matthaeus WH. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys Rev A 1992; 45: R5339–R5342
  • Chien S, Jan KM. Ultrastructural basis of the mechanism of rouleaux formation. Microvasc Res 1973; 5: 155–166
  • Cokelet GR. Viscometric, in vitro and in vivo blood viscosity relationships: How are they related?. Biorheology 1999; 36: 343–358
  • Cokelet GR, Pries AR, Kiani MF. Observations on the accuracy of photometric techniques used to measure some in vivo microvascular blood flow parameters. Microcirculation 1998; 5: 61–70
  • Cristini V, Blawzdzewics J, Lowenberg M. An adaptive mesh algorithm for evolving surfaces: Simulations of drop breakup and coalescence. J Computa Physics 2001; 168: 445–463
  • Damiano ER, Stace TM. A mechano-electrochemical model of radial deformation of the capillary glycocalyx. Biophys J 2002; 82: 1153–1175
  • Dao M, Lim CT, Suresh S. Mechanics of the human red blood cell deformed by optical tweezers. J Mech Physics Solids 2003; 51: 2259–2280
  • Das B, Bishop JJ, Kim S, Meiselman HJ, Johnson PC, Popel AS. Red blood cell velocity profiles in skeletal muscle venules at low flow rates are described by the Casson model. Clin Hemorheol Microcirc 2007; 36: 217–233
  • Discher DE. New insights into erythrocyte membrane organization and microelasticity. Curr Opin Hematol 2000; 7: 117–122
  • Discher DE, Boal DH, Boey SK. Simulations of the erythrocyte cytoskeleton at large deformation. II. micropipette aspiration. Biophys J 1998; 75: 1584–1597
  • Dupin MM, Halliday I, Care CM, Alboul L, Munn LL. Modeling the flow of dense suspensions of deformable particles in three dimensions. Physical Review. E, statistical. nonlinear and soft matter physics 2007; 75: 066707066707–17
  • Dzwinel W, Boryczko K, Yuen DA. A discrete-particle model of blood dynamics in capillary vessels. J Colloid Interface Sci 2003; 258: 163–173
  • Eggleton CD, Popel AS. Large deformation of red blood cell ghosts in a simple shear flow. Physics Fluids 1998; 10: 1834–1845
  • El-Kareh AW, Secomb TW. A model for red blood cell motion in bifurcating microvessels. Intern J Multiphase Flow 2000; 26: 1545–1564
  • Ellsworth ML, Liu A, Dawant B, Popel AS, Pittman RN. Analysis of vascular pattern and dimensions in arteriolar networks of the retractor muscle in young hamsters. Microvasc Res 1987; 34: 168–183
  • Enden G, Popel A. A numerical study of the shape of the surface separating flow into two branches in microvascular bifurcations. J Biomech Eng 1992; 114: 398–405
  • Engelson ET, Skalak TC, Schmid-Schonbein GW. The microvasculature in skeletal muscle I. Arteriolar network in rat spinotrapezius muscle. Microvasc Res 1985; 30: 29–44
  • Evans EA. Structure and deformation properties of red blood cells: Concepts and quantitative methods. Meth Enzymol 1989; 173: 3–35
  • Evans EA, Hochmuth RM. Membrane viscoelasticity. Biophys J 1976; 16: 1–11
  • Evans EA Skalak R. 1980. Mechanics and Thermodynamics of Biomembranes. CRC. Boca Raton, FL.
  • Fahraeus R. The suspension stability of blood. Physiol Rev 1929; 9: 241–274
  • Fahraeus R, Lindqvist T. The viscosity of the blood in narrow capillary tubes. Amer J Physiol 1931; 96: 562–568
  • Fang J, Owens RG. Numerical simulations of pulsatile blood flow using a new constitutive model. Biorheology 2006; 43: 637–660
  • Feng J, Weinbaum S. Lubrication theory in highly compressible porous media: The mechanics of skiing, from red cells to humans. J Fluid Mech 2000; 422: 281–317
  • Fenton BM, Carr RT, Cokelet GR. Nonuniform red cell distribution in 20 to 100 (m bifurcations. Microvasc Res 1985; 29: 103–126
  • Fibich G, Lanir Y, Libron N. Mathematical model of blood flow in a coronary capillary. Amer J Physiol 1993; 265: H1829–H1840
  • Fischer TM, Stohr-Lissen M, Schmid-Schönbein GW. The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 1978; 202: 894–896
  • Formaggia L, Nobile F, Quarteroni A, Veneziani A. Multiscale modelling of the circulatory system: A preliminary analysis. Comp Visua. Sci 1999; 2: 75–83
  • Frame MDS, Sarelius IH. Arteriolar bifurcation angles vary with position and when flow is changed. Microvasc Res 1993; 46: 190–205
  • Frame MDS, Sarelius IH. Energy optimization and bifurcation angles in the microcirculation. Microvasc Res 1995; 50: 301–310
  • Garcia-Sanz A, Rodriguez-Barbero A, Bentley MD, Ritman EL, Romero JC. Three-dimensional microcomputed tomography of renal vasculature in rats. Hypertension 1998; 31: 440–444
  • Gerneke DA, Sands GB, Ganesalingam R, Joshi P, Caldwell BJ, Smaill BH, Legrice IJ. Surface imaging microscopy using an ultramiller for large volume 3D reconstruction of wax- and resin-embedded tissues. Microscopy Res Tech 2007; 70: 886–894
  • Groner W Winkelman JW Harris AGI Can Bouma GJ Messmer K Nadeau RG. 1999. Orthogonal polarization spectral imaging: A new method for study of the microcirculation. Nature Me 5:1209–1213.
  • Halpern D, Secomb TW. The squeezing of red blood cells through capillaries with near-minimal diameters. J Fluid Mech 1989; 203: 381–400
  • Haynes RH. Physical basis of the dependence of blood viscosity on tube radius. Amer J Physiol 1960; 198: 1193–1200
  • Heinzer S, Krucker T, Stampanoni M, Abela R, Meyer EP, Schuler A, Schneider P, Muller R. Hierarchical microimaging for multiscale analysis of large vascular networks. NeuroImage 2006; 32: 626–636
  • Hiller KH, Waller C, Voll S, Haase A, Ertl G, Bauer WR. Combined high-speed NMR imaging of perfusion and microscopic coronary conductance vessels in the isolated rat heart. Microvasc Res 2001; 62: 327–334
  • Hochmuth RM, Worthy PR, Evans EA. Red cell extensional recovery and the determination of membrane viscosity. Biophys J 1979; 26: 101–114
  • Hsu R, Secomb TW. Motion of nonaxisymmetric red blood cells in cylindrical capillaries. J Biomech Eng 1989; 111: 147–151
  • Jadhav S, Eggleton CD, Konstantopoulos K. Mathematical modeling of cell adhesion in shear flow: Application to targeted drug delivery in inflammation and cancer metastasis. Curr Pharm Des 2007; 13: 1511–1526
  • Jorgensen SM, Demirkaya O, Ritman EL. Three-dimensional imaging of vasculature and parenchyma in intact rodent organs with X-ray micro-CT. Amer J Physiol 1998; 275: H1103–H1114
  • Kamgoue A, Ohayon J, Tracgui P. Estimation of cell Young's modulus of adherent cells probed by optical and magnetic tweezers: Influence of cell thickness and bead immersion. J Biomech Eng 2007; 129: 523–530
  • Kassab GS. Scaling laws of vascular trees: of form and function. Amer J Physiol (Heart Circ. Physiol. 2006; 290: H894–H903
  • Kassab GS, Rider CA, Tang NJ, Fung YC. Morphometry of pig coronary arterial trees. Amer J Physiol 1993; 265: H350–H365
  • Keller SR, Skalak R. Motion of a tank-treading ellipsoidal particle in a shear flow. J Fluid Mech 1982; 120: 27–47
  • Kiani MF, Pries AR, Hsu R, Sarelius IH, Cokelet GR. Fluctuations in microvascular blood flow parameters caused by hemodynamic mechanisms. Amer J Physiol 1994; 266: H1822–H1828
  • Koller A, Dawant B, Liu A, Popel AS, Johnson PC. Quantitative analysis of arteriolar network architecture in cat sartorius muscle. Amer J Physiol 1987; 253: H154–H164
  • Krogh A. The Anatomy and Physiology of Capillaries. New Haven, Ct: Yale University Press. 1922
  • LaBarbera M. Principles of design of fluid transport systems in zoology. Science 1990; 249: 992–1000
  • Landis EM. Poiseuille's law and the capillary circulation. Amer J Physiol 1933; 103: 432–443
  • Laughlin MH. Skeletal muscle blood flow capacity: Role of muscle pump in exercise hyperemia. Amer J Physiol 1987; 253: H993–H1004
  • Lee J, Salathe EP, Schmid-Schönbein GW. Fluid exchange in skeletal muscle with viscoelastic blood vessels. Amer J Physiol 1987; 253: H1548–H1556
  • Lee JC-M, Wong DT, Discher DE. Direct measures of large, anisotropic strains in deformation of the erythrocyte cytoskeleton. Biophysical Journal 1999; 77: 853–864
  • Lee JCJ, Beighley PE, Ritman EL, Smith NP. Automatic segmentation of 3D micro-CT coronary vascular images. Med Image Anal 2007; 11: 630–647
  • Lee JCJ, Smith NP. Development and application of 1D blood flow model for microvascular networks. J Eng Med 2007; 222: 487–512
  • Lee S-Y, Schmid-Schönbein GW. Pulsatile pressure and flow in the skeletal muscle microcirculation. J Biomech Eng 1990; 112: 437–443
  • Ley K, Pries AR, Gaehtgens P. Topological structure of rat mesenteric microvessel networks. Microvasc Res 1986; 32: 315–332
  • Li J, Dao M, Lim CT, Suresh S. Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys J 2005; 88: 3707–3719
  • Li X, Barth‘es-Biesel D, Helmy A. Large deformation and burst of a capsule suspended in an elongational flow. J Fluid Mec 1988; 187: 179–196
  • Lipowsky HH. Microvascular rheology and hemodynamics. Microcirculation 2005; 12: 5–15
  • 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
  • Lipowsky HH, Zweifach BW. Methods for the simultaneous measurement of pressure differentials and flow in single unbranched vessels of the microcirculation for rheological studies. Microvasc Res 1977; 14: 345–361
  • Lipowsky HH, Zweifach BW. Network analysis of microcirculation of cat mesentery. Microvasc Res 1974; 7: 73–83
  • Liu Y, Kassab GS. Vascular metabolic dissipation in Murray's law. Amer J Physiol 2007; 292: H1336–H1339
  • McCormick BH. Brain tissue scanner enables brain microstructure surveys. Neurocomputing 2002; 44–46: 1113–1118
  • Merrill EW, Gilliland ER, Lee TS, Salzman EW. Blood rheology: effect of fibrinogen deduced by addition. Circ Res 1966; 18: 437–446
  • Mohandas N, Evans EA. Mechanical properties of the red cell membrane in relation to molecular structure and genetic defects. Ann Rev Biophys Biomolec Struc 1994; 23: 787–818
  • Murray CD. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc Natl Acad Sci USA 1926; 12: 207–214
  • N'Dri NA, Shyy W, Liu H, Tran-Son-Tay R. Multi-scale modeling spanning from cell surface receptors to blood flow in arteries. Modeling and Simulation of Capsules and Biological Cells, C. Pozrikidis. Chapman & Hall/CRC, Boca Raton, FL 2003
  • Neofytou P. Comparison of blood rheological models for physiological flow simulation. Biorheology 2004; 41: 693–714
  • Noguchi H, Gompper G. Shape transitions of fluid vesicles and red blood cells in capillary flows. PNAS 2005; 102: 14159–14164
  • Nordsletten DA, Blackett S, Bentley MD, Ritman EL, Smith NP. Structural morphology of renal vasculature. Amer J Physiol 2006; 291: H296–H309
  • Owens RG. A new microstructure-based constitutive model for human blood. J Non-Newtonian Fluid Mech 2006; 140: 57–70
  • Painter PR, Eden P, Bengtsson H-U. Pulsatile blood flow, shear force, energy dissipation and Murray's law. Theore Biol Med Model 2006; 3: 31
  • Papenfuss HD, Gross JF. Microhemodynamics of capillary networks. Biorheology 1981; 18: 673–692
  • Paszynski M, Schaefer R. The modified fluid particle model for non-linear Casson fluid and its parallel distributed implementation. Comp Meth Appl Mech Eng 2005; 194: 4386–4410
  • Plouraboue F, Cloetens P, Fonta C, Steyer A, Lauwers F, Macr-Vergnes JP. X-ray high-resolution vascular network imaging. J Microscopy 2004; 215: 139–148
  • Poiseuille JLM. Recherches experimentales sur le mouvement des liquides dans les tubes de tres petits diametres. CR Acad Sci 1840; 11: 961–967
  • Popel AS, Johnson PC. Microcirculation and hemorheology. Ann Rev Fluid Mech 2005; 37: 43–69
  • Pozrikidis C. The axisymmetric deformation of a red blood cell in uniaxial straining Stokes flow. J Fluid Mech 1990; 216: 213–254
  • Pozrikidis C. Numerical simulation of cell motion in tube flow. Ann Biomed Eng 2005; 33: 165–178
  • Pozrikidis C. Numerical simulation of the flow-induced deformation of red blood cells. Ann Biomed Eng 2003; 31: 1194–1205
  • Pries AR, Albrecht KH, Gaehtgens P. Model studies on phase separation at a capillary orifice. Biorheology 1981; 18: 355–367
  • Pries AR, Ley K, Claassen M, Gaehtgens P. Red cell distribution at microvascular bifurcations. Microvasc Res 1989; 38: 81–101
  • Pries AR, Neuhaus D, Gaehtgens P. Blood viscosity in tube flow: dependence on diameter and hematocrit. Amer J Physiol Heart Circ Physiol 1992; 263: H1770–H1778
  • Pries AR, Schonfeld D, Gaehtgens P, Kiani MF, Cokelet GR. Diameter variability and microvascular flow resistance. Amer J Physiol 1997; 272: H2716–H2725
  • Pries AR, Secomb TW. Microvascular blood viscosity in vivo and the endothelial surface layer. Amer J Physiol 2005; 289: H2657–H2664
  • Pries AR, Secomb TW, Gaehtgens P. Biophysical aspects of blood flow in the microvasculature. Cardiovasc Res 1996; 32: 654–667
  • Pries AR, Secomb TW, Gaehtgens P. Design principles of vascular beds. Circ Res 1995; 77: 1017–1023
  • Pries AR, Secomb TW, Gaehtgens P. The endothelial surface layer. Pflugers Arch 2000; 440: 653–666
  • Pries AR, Secomb TW, Gaehtgens P. Relationship between structural and hemodynamic heterogeneity in microvascular networks. Ame J Physiol 1996; 270: H545–H553
  • Pries AR, Secomb TW, Gaehtgens P. Structure and hemodynamics of microvascular networks: Heterogeneity and correlations. Amer J Physiol 1995; 269: H1713–H1722
  • 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, Gessner T, Sperandio MB, Gross JF, Gaehtgens P. Resistance to blood flow in microvessels in vivo. Circ Res 1994; 75: 904–915
  • Queguiner C, Barthes-Biesel D. Axisymmetric motion of capsules through cylindrical channels. J Fluid Mech 1997; 348: 349–376
  • Ramanujan S, Pozrikidis C. Deformation of liquid capsules enclosed by elastic membrane in simple shear flow: lLarge deformation and effect of fluids viscosities. J Fluid Mech 1998; 361: 117–143
  • Rief M, Pascual J, Saraste M, Gaub HE. Single molecule force spectroscopy of spectrin repeats: Low unfolding forces in helix bundles. J Molec Biol 1999; 286: 553–561
  • Rodriguez A, Ehlenberger DB, Hof PR, Wearne SL. Rayburst sampling, an algorithm for automated three-dimensional shape analysis from laser scanning microscopy images. Nature Prot 2006; 1: 2152–2161
  • Sands GB, Gerneke DA, Hooks DA, Green CR, Smaill BH, Legrice IJ. Automated imaging of extended tissue volumes using confocal microscopy. Microscopy Res Technique 2005; 67: 227–239
  • Schmid-Schönbein GW. Analysis of inflammation. Ann Rev Biomed Eng 2006; 8: 93–151
  • Schmid-Schönbein GW. A theory of blood flow in skeletal muscle. J Biomech Eng 1988; 110: 20–26
  • Schmid-Schönbein GW, Skalak R, Usami S, Chien S. Cell distribution in capillary networks. Microvasc Res 1980; 19: 18–44
  • Secomb TW. Mechanics of red blood cells and blood flowing narrow tubes. Modeling and Simulation of Capsules and Biological Cells. Boca Raton, FL: Chapman & Hall/CRC, C. Pozrikidis, 2003; 163–196
  • Secomb TW 2008. Theoretical models for regulation of blood flow. Microcirculation doi: 10.1080/10739680802229076.
  • Secomb TW, Hsu R, Pries AR. A model for red blood cell motion in glycocalyx-lined capillaries. Amer J Physiol 1998; 274: H1016–H1022
  • Secomb TW, Hsu R, Pries AR. Motion of red blood cells in a capillary with an endothelial surface layer: Effect of flow velocity. Amer J Physiol 2001; 281: H629–H636
  • Secomb TW, Skalak R, Ozkaya N, Gross JF. Flow of axisymmetric red blood cells in narrow capillaries. J Fluid Mech 1986; 163: 405–423
  • Secomb TW, Styp-Rekowska, Pries AR. Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann BiomedEngineer 2007; 35: 755–765
  • Seki J, Satomura Y, Ooi Y, Yanagida T, Seiyama A. Velocity profiles in the rat cerebral microvessels measured by optical coherence tomography. Clin Hemorheol Microcirc 2006; 34: 233–239
  • Sharan M, Popel AS. A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall. Biorheology 2001; 38: 415–428
  • Shen BW, Josephs R, Steck TL. Ultrastructure of the intact skeleton of the human erythrocyte membrane. J Cell Bio 1986; 102: 997–1006
  • Sherman TF. On connecting large vessels to small-The meaning of Murray's Law. J Gen Physiol 1981; 78: 431–453
  • Sherman TF Popel AS Koller A Johnson PC. 1989. The cost of departure from optimal radii in microvascular networks. J Theor Bio l136:245–265.
  • Sherwin SJ, Franke V, Peiro J, Parker K. One-dimensional modelling of a vascular network in space-time variables. J Engineer Math 2003; 47: 217–250
  • Simoens P, De Schaepdrijver L, Lauwers H. Morphologic and clinical study of the retinal circulation in the miniature pig. A: Morphology of the retinal microvasculature. Exper Eye Res 1992; 54: 965–973
  • Simon SI, Green CE. Molecular mechanics and dynamics of leukocyte recruitment during inflammation. Ann Rev Biomed Engineer 2005; 7: 151–185
  • Skalak R, Branemark PI. Deformation of red blood cells in capillaries. Science 1969; 164: 283–287
  • Skalak TC, Schmid-Schönbein GW. Viscoelastic properties of microvessels in rat spinotrapezius muscle. J BiomechEng 1986; 108: 193–200
  • Smith NP, Pullan AJ, Hunter PJ. An anatomically based model of transient coronary blood flow in the heart. SIAM J Appl Math 2002; 62: 990–1018
  • Soltanian-Zadeh H, Shahrokni A, Khalighi M-M, Zhang ZG, Zoroofi RA, Maddah M, Chopp M. 3-D quantification and visualization of vascular structures from confocal microscopic images using skeletonization and voxel-coding. Comp Biol Med 2005; 35: 791–813
  • Sun C, Munn LL. Particulate nature of blood determines macroscopic rheology: A 2-D lattice Boltzmann analysis. Biophys J 2005; 88: 1635–1645
  • Taber LA. An optimization principle for vascular radius including the effects of smooth muscle tone. Biophys J 1998; 74: 109–114
  • Thurston GB. Elastic effects in pulsatile blood flow. Microvasc Res 1975; 9: 145–157
  • Thurston GB. The viscosity and viscoelasticity of blood in small diameter tubes. Microvasc Res 1976; 11: 133–146
  • Toyota E, Fujimoto K, Ogasawara Y, Kajita T, Shigeto F, Matsumoto T, Goto M, Kajiya F. Dynamic changes in three-dimensional architecture and vascular volume of transmural coronary microvasculature between diastolic- and systolic-arrested rat hearts. Circulation 2002; 105: 621–626
  • Toyota E, Ogasawara Y, Hiramatsu O, Tachibana H, Kajiya F, Yamamori S, Chilian WM. Dynamics of flow velocities in endocardial and epicardial coronary arterioles. AmerJ Physiol 2005; 288: H1598–H1603
  • Tschakovsky ME, Sheriff DD. Immediate exercise hyperemia: Contributions of the muscle pump vs. rapid vasodilation. J ApplPhysiol 2004; 97: 739–747
  • Tsubota K-I, Wada S, Yamaguchi T. Particle method for computer simulation of red blood cell motion in blood flow. Comp Meth Prog Biomed 2006; 83: 139–146
  • van Oss CJ, Arnold K, Coakley WT. Depletion flocculation and depletion stabilization of erythrocytes. Cell Biophys 1990; 17: 1–10
  • vanTeeffelen JWGE, Brands J, Stroes ES, Vink H. Endothelial glycocalyx: Sweet shield of blood vessels. Trends Cardiovas Med 2007; 17: 101–105
  • Vejlens G. 1938. The distribution of leukocytes in the vascular system. Acta Pathol Microbiol Scand, Suppl 3–239.
  • Wagner RC, Czymmek K, Hossler FE. Confocal microscopy, computer modeling, and quantification of glomerular vascular corrosion casts. Microscopy Microanal 2006; 12: 262–268
  • Westerhof N, Boer C, Lamberts RR, Sipkema P. Cross-talk between cardiac muscle and coronary vasculature. Physiol Rev 2006; 86: 1263–1308
  • Yedgar S, Koshkaryev A, Barshtein G. The red blood cell in vascular occlusion. Pathophys Haemostasis Thromb 2002; 32: 263–268
  • Zamir M. Shear forces and blood vessel radii in the cardiovascular system. J GenPhysiol 1977; 69: 449–461
  • Zarda PR, Chien S, Skalak R. Interaction of viscous incompressible fluid with an elastic body. Computational Methods for Fluid-Solid Interaction Problems, T Belytschko, TL Geers. American Society of Mechanical Engineers, New York 1977; 65–82
  • Zhou Y, Kassab GS, Molloi S. On the design of the coronary arterial tree: a generalization of Murray's law. Phys Med Biol 1999; 44: 2929–2945
  • Zhou Y, Toga AW. Efficient skeletonization of volumetric objects. IEEE Trans Visual Comp Graphics 1999; 5: 196–209

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.