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Blood coagulation dynamics: mathematical modeling and stability results
1.  Department of Mathematics and CEMAT/IST, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049001 Lisboa, Portugal 
2.  Department of Mathematics and CEMAT/IST, Faculty of Sciences and Technology, University of Algarve, Campus de Gambelas 8005139 Faro, Portugal 
3.  Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University, Náměstí 13, 121 35 Prague 2, Czech Republic 
References:
[1] 
M. Anand, K. Rajagopal and K. R. Rajagopal, A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood, J. of Theoretical Medicine, 5 (2003), 183218. doi: 10.1080/10273660412331317415. 
[2] 
M. Anand, K. Rajagopal and K. R. Rajagopal, A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency, J. of Theoretical Biology, 253 (2008), 725738. doi: 10.1016/j.jtbi.2008.04.015. 
[3] 
F. I. Ataullakhanov and M. A. Panteleev, Mathematical modeling and computer simulation in blood coagulation, Pathophysiol. Haemost. Thromb., 34 (2005), 6070. doi: 10.1159/000089927. 
[4] 
S. P. Bhat and D. S. Bernstein, Nontangencybased Lyapunov tests for convergence and stability in systems having a continuum of equilibria, SIAM J. Control Optim., 42 (2003), 17451775. doi: 10.1137/S0363012902407119. 
[5] 
T. Bodnár and A. Sequeira, Numerical simulation of the coagulation dynamics of blood, Comp. Math. Methods in Medicine, 9 (2008), 83104. doi: 10.1080/17486700701852784. 
[6] 
I. Borsi, A. Farina, A. Fasano and K. R. Rajagopal, Modelling the combined chemical and mechanical action for blood clotting, In "Nonlinear Phenomena with Energy Dissipation," volume 29 of GAKUTO Internat. Ser. Math. Sci. Appl., pages 5372. Gakkōtosho, Tokyo, 2008. 
[7] 
S. L. Campbell and N. J. Rose, Singular perturbations of autonomous linear systems, SIAM Journal Math. Anal., 10 (1979), 542551. doi: 10.1137/0510051. 
[8] 
M. H. Kroll, J. D. Hellums, L. V. McIntire, A. I. Schafer and J. L. Moake, Platelets and shear stress, Blood, 88 (1996), 15251541. 
[9] 
A. L. Kuharsky and A. L. Fogelson, Surfacemediated control of blood coagulation: The role of binding site densities and platelet deposition, Biophys. J., 80 (2001), 10501074. doi: 10.1016/S00063495(01)760857. 
[10] 
A. Leuprecht and K. Perktold, Computer simulation of nonNewtonian effects of blood flow in large arteries, Computer Methods in Biomechanics and Biomech. Eng., 4 (2001), 149163. 
[11] 
L. Michaelis and M. L. Menten, Die kinetik der invertinwirkung, Biochem Z., 49 (1913), 333369. 
[12] 
Y. H. Qiao, J. L. Liu and Y. J. Zeng, A kinetic model for simulation of blood coagulation and inhibition in the intrinsic path, J. of Medical Eng. and Technology, 29 (2005), 7074. doi: 10.1080/03091900410001709079. 
[13] 
A. M. Robertson, A. Sequeira and M. V. Kameneva, Hemorheology, In "Hemodynamical Flows: Modeling, Analysis and Simulation (Oberwolfach Seminars)," volume 37, G.P. Galdi, R. Rannacher, A. M. Robertson, and S. Turek (Eds.), Birkhäuser Verlag, 2008, 63120. 
[14] 
M. Schenone, B. C. Furie and B. Furie, The blood coagulation cascade, Curr. Opin. Hematol., 11 (2004), 272277. doi: 10.1097/01.moh.0000130308.37353.d4. 
[15] 
L. A. Segel and M. Slemrod, The quasysteadystate assumption: A case study in perturbation, SIAM Review, 32 (1989), 446477. doi: 10.1137/1031091. 
[16] 
N. T. Wang and A. L. Fogelson, Computational methods for continuum models of platelet aggregation, J. Comput. Phys., 151 (1999), 649675. doi: 10.1006/jcph.1999.6212. 
show all references
References:
[1] 
M. Anand, K. Rajagopal and K. R. Rajagopal, A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood, J. of Theoretical Medicine, 5 (2003), 183218. doi: 10.1080/10273660412331317415. 
[2] 
M. Anand, K. Rajagopal and K. R. Rajagopal, A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency, J. of Theoretical Biology, 253 (2008), 725738. doi: 10.1016/j.jtbi.2008.04.015. 
[3] 
F. I. Ataullakhanov and M. A. Panteleev, Mathematical modeling and computer simulation in blood coagulation, Pathophysiol. Haemost. Thromb., 34 (2005), 6070. doi: 10.1159/000089927. 
[4] 
S. P. Bhat and D. S. Bernstein, Nontangencybased Lyapunov tests for convergence and stability in systems having a continuum of equilibria, SIAM J. Control Optim., 42 (2003), 17451775. doi: 10.1137/S0363012902407119. 
[5] 
T. Bodnár and A. Sequeira, Numerical simulation of the coagulation dynamics of blood, Comp. Math. Methods in Medicine, 9 (2008), 83104. doi: 10.1080/17486700701852784. 
[6] 
I. Borsi, A. Farina, A. Fasano and K. R. Rajagopal, Modelling the combined chemical and mechanical action for blood clotting, In "Nonlinear Phenomena with Energy Dissipation," volume 29 of GAKUTO Internat. Ser. Math. Sci. Appl., pages 5372. Gakkōtosho, Tokyo, 2008. 
[7] 
S. L. Campbell and N. J. Rose, Singular perturbations of autonomous linear systems, SIAM Journal Math. Anal., 10 (1979), 542551. doi: 10.1137/0510051. 
[8] 
M. H. Kroll, J. D. Hellums, L. V. McIntire, A. I. Schafer and J. L. Moake, Platelets and shear stress, Blood, 88 (1996), 15251541. 
[9] 
A. L. Kuharsky and A. L. Fogelson, Surfacemediated control of blood coagulation: The role of binding site densities and platelet deposition, Biophys. J., 80 (2001), 10501074. doi: 10.1016/S00063495(01)760857. 
[10] 
A. Leuprecht and K. Perktold, Computer simulation of nonNewtonian effects of blood flow in large arteries, Computer Methods in Biomechanics and Biomech. Eng., 4 (2001), 149163. 
[11] 
L. Michaelis and M. L. Menten, Die kinetik der invertinwirkung, Biochem Z., 49 (1913), 333369. 
[12] 
Y. H. Qiao, J. L. Liu and Y. J. Zeng, A kinetic model for simulation of blood coagulation and inhibition in the intrinsic path, J. of Medical Eng. and Technology, 29 (2005), 7074. doi: 10.1080/03091900410001709079. 
[13] 
A. M. Robertson, A. Sequeira and M. V. Kameneva, Hemorheology, In "Hemodynamical Flows: Modeling, Analysis and Simulation (Oberwolfach Seminars)," volume 37, G.P. Galdi, R. Rannacher, A. M. Robertson, and S. Turek (Eds.), Birkhäuser Verlag, 2008, 63120. 
[14] 
M. Schenone, B. C. Furie and B. Furie, The blood coagulation cascade, Curr. Opin. Hematol., 11 (2004), 272277. doi: 10.1097/01.moh.0000130308.37353.d4. 
[15] 
L. A. Segel and M. Slemrod, The quasysteadystate assumption: A case study in perturbation, SIAM Review, 32 (1989), 446477. doi: 10.1137/1031091. 
[16] 
N. T. Wang and A. L. Fogelson, Computational methods for continuum models of platelet aggregation, J. Comput. Phys., 151 (1999), 649675. doi: 10.1006/jcph.1999.6212. 
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