Numerical simulation of the coagulation dynamics of blood

References

• Anand , M. and Rajagopal , K.R. 2004 . A shear-thinning viscoelastic fluid model for describing the flow of blood . Int. J. Cardiovas. Med. Sci. , 4 ( 2 ) : 59 – 68 .
   Google Scholar
• M. Anand and K.R. Rajagopal, A model for the formation and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency, submitted (2007)
   Google Scholar
• Anand , M. , Rajagopal , K. and Rajagopal , K.R. 2003 . A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood . J. Theor. Med. , 5 ( 3–4 ) : 183 – 218 .
   Google Scholar
• Anand , M. , Rajagopal , K. and Rajagopal , K.R. 2005 . A model for the formation and lysis of blood clots . Pathophysiol. Haemost. Thromb. , 34 : 109 – 120 .
   PubMedGoogle Scholar
• Ataullakhanov , F. , Zarnitsina , V. , Pokhilko , A. , Lobanov , A. and Morozova , O. 2002 . Spatio-temporal dynamics of blood coagulation and pattern formation. A theoretical approach . Int. J. Bifur. Chaos , 12 ( 9 ) : 1985 – 2002 .
   Google Scholar
• Butenas , S. and Mann , K.G. 2002 . Blood coagulation . Biochemistry (Moscow) , 67 ( 1 ) : 3 – 12 . (translated from Biokhimiya, Vol. 67, No. 1, 2002, pp. 5–15.)
   PubMed Web of Science ®Google Scholar
• Charm , S.E. and Kurland , G.S. 1965 . Viscometry of human blood for shear rates of 0–100,000 sec− 1 . Nature , 206 : 617 – 618 .
   PubMedGoogle Scholar
• Chien , S. , Usami , S. , Taylor , H.M. , Lundberg , J.L. and Gregersen , M.I. 1966 . Effect of hematocrit and plasma proteins on human blood rheology at low shear rates . J. Appl. Physiol. , 21 : 81 – 87 .
   PubMed Web of Science ®Google Scholar
• Chien , S. , Usami , S. , Dellenback , R. and Gregersen , M. 1970 . Shear-dependent deformation of erythrocytes in rheology of human blood . Am. J. Physiol. , 219 : 136 – 142 .
   PubMed Web of Science ®Google Scholar
• Colantuoni , G. , Hellums , J. , Moake , J. and Alfre , C. 1977 . The response of human platelets to shear stress at short exposure times . Trans. Amer. Soc. Artificial Int. Organs , 23 : 626 – 631 .
   Google Scholar
• Engquist , B. , Lötstedt , P. and Sjögreen , B. 1989 . Nonlinear filters for efficient shock computation . Math. Comput. , 52 ( 186 ) : 509 – 537 .
   Google Scholar
• Fogelson , A.L. 1992 . Continuum models of platelet aggregation: Formulation and mechanical properties . SIAM J. Appl. Math. , 52 : 1089 – 1110 .
   Web of Science ®Google Scholar
• Jameson , A. 1991 . “ Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings ” . In Proceedings of the AIAA 10th Computational Fluid Dynamics Conference, Honolulu June (aIAA Paper 91–1596)
   Google Scholar
• Jameson , A. , Schmidt , W. and Turkel , E. 1981 . “ Numerical solutions of the Euler equations by finite volume methods using Runge–Kutta time-stepping Schemes ” . In Proceedings of the AIAA 14th Fluid and Plasma Dynamic Conference, Palo Alto, CA June (aIAA paper 81–1259)
   Google Scholar
• Kroll , H. , Hellums , J. , McIntire , L. , Schafer , A.I. and Moake , J. 1996 . Platelets and shear stresss . Blood , 88 : 1525 – 1541 .
   PubMed Web of Science ®Google Scholar
• Kuharsky , A.L. and Fogelson , A.L. 2001 . Surface-mediated control of blood coagulation: The role of binding site densities and platelet deposition . Biophys. J. , 80 : 1050 – 1074 .
   PubMed Web of Science ®Google Scholar
• Leuprecht , A. and Perktold , K. 2001 . Computer simulation of non-Newtonian effects of blood flow in large arteries . Comput. Meth. Biomech. Biomech. Eng. , 4 : 149 – 163 .
   PubMedGoogle Scholar
• Mann , K. , Brummel-Ziedins , K. , Orfeo , T. and Butenas , S. 2006 . Models of blood coagulation . Blood Cells, Mol. Dis. , 36 : 108 – 117 .
   PubMed Web of Science ®Google Scholar
• Nägele , S. and Wittum , G. 2007 . On the influence of different stabilisation methods for the incompressible Navier–Stokes equations . J. Comp. Phys. , 224 : 100 – 116 .
   Google Scholar
• Rajagopal , K. and Lawson , J. 2007 . “ Regulation of hemostatic system function by biochemical and mechanical factors ” . In Modeling of Biological Materials , 179 – 210 . Boston : Birkhäuser .
   Google Scholar
• Riha , P. , Wang , X. , Liao , R. and Stoltz , J. 1999 . Elasticity and fracture strain of blood clots . Clin. Hemorheol. Microcirc. , 21 ( 1 ) : 45 – 49 .
   PubMed Web of Science ®Google Scholar
• Robertson , A. , Sequeira , A. and Kameneva , M. 2008 . “ Hemorheology ” . In Hemodynamical Flows: Modelling, Analysis and Simulation , Boston : Oberwolfach Seminars Series. Birkhäuser .
   Google Scholar
• Robertson , A. , Sequeira , A. and Owens , R. 2008 . “ Rheological models for blood ” . In Cardiovascular Mathematics , Berlin : Springer . (to appear)
   Google Scholar
• Schenone , M. and Furie , B. 2004 . The blood coagulation cascade . Curr. Opin. Hematol. , 11 : 272 – 277 .
   PubMed Web of Science ®Google Scholar
• Schmid-Schönbein , H. and Wells , R. 1969 . Fluid drop-like transition of erythrocytes under shear . Science , 165 : 288 – 291 .
   PubMed Web of Science ®Google Scholar
• Shyy , W. , Chen , M.H. , Mittal , R. and Udaykumar , H.S. 1992 . On the suppression of numerical oscillations using a non-linear filter . J. Comput. Phys. , 102 : 49 – 62 .
   Web of Science ®Google Scholar
• Thurston , G.B. 1973 . Frequency and shear rate dependence of viscoelasticity of human blood . Biorheology , 10 : 375 – 381 .
   PubMedGoogle Scholar
• Vierendeels , J. , Riemslagh , K. and Dick , E. 1999 . A multigrid semi-implicit line-method for viscous incompressible and low-Mach-number flows on high aspect ratio grids . J. Comput. Phys. , 154 : 310 – 344 .
   Google Scholar
• Wang , N. and Fogelson , A.L. 1999 . Computational methods for continuum models of platelet aggregation . J. Comput. Phys. , 151 : 649 – 675 .
   Google Scholar
• Yeleswarapu , K. , Kameneva , M. , Rajagopal , K. and Antaki , J. 1998 . The flow of blood in tubes: Theory and experiments . Mech. Res. Commun. , 25 ( 3 ) : 257 – 262 .
   Web of Science ®Google Scholar
• Zarnitsina , V.I. , Pokhilko , A.V. and Ataullakhanov , F.I. 1996a . A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation – I. The model description . Thromb. Res. , 84 ( 4 ) : 225 – 236 .
   PubMed Web of Science ®Google Scholar
• Zarnitsina , V.I. , Pokhilko , A.V. and Ataullakhanov , F.I. 1996b . A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation – II. Results . Thromb. Res. , 84 ( 5 ) : 333 – 344 .
   Google Scholar