{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T15:08:19Z","timestamp":1766848099133},"publisher-location":"Dordrecht","reference-count":58,"publisher":"Springer Netherlands","isbn-type":[{"type":"print","value":"9781402056895"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-1-4020-5690-1_4","type":"book-chapter","created":{"date-parts":[[2007,11,24]],"date-time":"2007-11-24T02:56:17Z","timestamp":1195872977000},"page":"65-87","source":"Crossref","is-referenced-by-count":29,"title":["An Overview of Some Mathematical Models of Blood Rheology"],"prefix":"10.1007","author":[{"given":"Ad\u00e9lia","family":"Sequeira","sequence":"first","affiliation":[]},{"given":"Jo\u00e3o","family":"Janela","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"4_CR1","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1016\/S1631-0721(02)01501-2","volume":"330","author":"M. Anand","year":"2002","unstructured":"M. Anand, K. R. Rajagopal, A mathematical model to describe the change in the constitutive character of blood due to platelet activation, C.R. M\u00e9canique, 330, 2002, pp. 557\u2013562.","journal-title":"C.R. M\u00e9canique"},{"key":"4_CR2","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1080\/10273660412331317415","volume":"5","author":"M. Anand","year":"2003","unstructured":"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, pp. 183\u2013218.","journal-title":"J. of Theoretical Medicine"},{"key":"4_CR3","first-page":"59","volume":"4","author":"M. Anand","year":"2004","unstructured":"M. Anand and K. R. Rajagopal, A shear-thinning viscoelastic fluid model for describing the flow of blood, Int. J. Cardiovascular Medicine and Science, 4, 2004, pp. 59\u201368.","journal-title":"Int. J. Cardiovascular Medicine and Science"},{"issue":"9","key":"4_CR4","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1142\/S0218202503002921","volume":"13","author":"N. Arada","year":"2003","unstructured":"N. Arada, and A. Sequeira, Strong Steady Solutions for a generalized Oldroyd-B Model with Shear-Dependent Viscosity in a Bounded Domain, Mathematical Models & Mehods in Applided Sciences, 13, no.9, 2003, pp. 1303\u20131323.","journal-title":"Mathematical Models & Mehods in Applided Sciences"},{"key":"4_CR5","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1055\/s-2003-44551","volume":"29","author":"O. K. Baskurt","year":"2003","unstructured":"O. K. Baskurt and H. J. Meiselman, Blood rheology and hemodynamics, Seminars in Thrombosis and Hemostasis, 29, 2003, pp. 435\u2013450.","journal-title":"Seminars in Thrombosis and Hemostasis"},{"key":"4_CR6","first-page":"109","volume":"177","author":"C. G. Caro","year":"1971","unstructured":"C. G. Caro, J. M. Fitz-Gerald and R. C. Schroter, Atheroma and arterial wall shear: observation, correlation and proposal of a shear dependent mass transfer mechanism of artherogenesis, Proc. Royal Soc. London, 177, 1971, pp. 109\u2013159.","journal-title":"Proc. Royal Soc. London"},{"key":"4_CR7","volume-title":"The Mechanics of the Circulation","author":"C. G. Caro","year":"1978","unstructured":"C. G. Caro, T. J. Pedley, R. C. Schroter and W. A. Seed, The Mechanics of the Circulation, Oxford University Press, Oxford, 1978."},{"key":"4_CR8","unstructured":"P. J. Carreau, PhD Thesis, University of Wisconsin, Madison, 1968."},{"key":"4_CR9","unstructured":"I. Chatziprodromoua, A. Tricolia, D. Poulikakosa and Y. Ventikos, Haemodynamics and wall remodelling of a growing cerebral aneurysm: A computational model, Journal of Biomechanics, accepted December 2005, in press."},{"issue":"3790","key":"4_CR10","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1126\/science.157.3790.827","volume":"157","author":"S. Chien","year":"1967","unstructured":"S. Chien, S. Usami, R. J. Dellenback, M. I. Gregersen, Blood viscosity: Influence of erythrocyte deformation, Science, 157(3790), 1967, pp. 827\u2013829.","journal-title":"Science"},{"issue":"3790","key":"4_CR11","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1126\/science.157.3790.829","volume":"157","author":"S. Chien","year":"1967","unstructured":"S. Chien, S. Usami, R. J. Dellenback, M. I. Gregersen, Blood viscosity: Influence of erythrocyte aggregation, Science, 157(3790), 1967, pp. 829\u2013831.","journal-title":"Science"},{"key":"4_CR12","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1152\/ajplegacy.1970.219.1.136","volume":"219","author":"S. Chien","year":"1970","unstructured":"S. Chien, S. Usami, R. J. Dellenback, M. I. Gregersen, Shear-dependent deformation of erythrocytes in rheology of human blood, American Journal of Physiology, 219, 1970, pp. 136\u2013142.","journal-title":"American Journal of Physiology"},{"key":"4_CR13","doi-asserted-by":"crossref","first-page":"241","DOI":"10.3233\/BIR-1991-283-415","volume":"28","author":"Y. I. Cho","year":"1991","unstructured":"Y. I. Cho and K. R. Kensey, Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part I: Steady flows, Biorheology, 28, 1991, pp. 241\u2013262.","journal-title":"Biorheology"},{"key":"4_CR14","unstructured":"G. R, Cokelet, The rheology of human blood. In: Y. C. Fung and M. Anliker (Eds.), Biomechanics: its foundations and objectives, Ch. 4, Prentice Hall, 1972."},{"key":"4_CR15","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/0095-8522(52)90078-0","volume":"7","author":"A. L. Copley","year":"1952","unstructured":"A. L. Copley, The rheology of blood. A survey, J. Colloid Sci., 7, 1952, pp. 323\u2013333.","journal-title":"J. Colloid Sci."},{"key":"4_CR16","doi-asserted-by":"crossref","first-page":"117","DOI":"10.3233\/CH-1981-1202","volume":"1","author":"A. L. Copley","year":"1981","unstructured":"A. L. Copley and G. V. F. Seaman, The meaning of the terms rheology, biorheology and hemorheology, Clinical Hemorheology, 1, 1981, pp. 117\u2013119.","journal-title":"Clinical Hemorheology"},{"issue":"12","key":"4_CR17","doi-asserted-by":"publisher","first-page":"1724","DOI":"10.1007\/s10439-005-8776-y","volume":"33","author":"V. Cristini","year":"2005","unstructured":"V. Cristini and G. S. Kassab, Computer modeling of red blood cell rheology in the microcirculation: a brief overview, Annals of Biomedical Engineering, 33, n.12, 2005, pp. 1724\u20131727.","journal-title":"Annals of Biomedical Engineering"},{"key":"4_CR18","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1016\/0095-8522(65)90022-X","volume":"20","author":"M. M. Cross","year":"1965","unstructured":"M. M. Cross, Rheology of non-Newtonian fluids: a new flow equation for pseudo-plastic systems, J. Colloid Sci., 20, 1965, pp. 417\u2013437.","journal-title":"J. Colloid Sci."},{"key":"4_CR19","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1007\/BF01738786","volume":"7","author":"R. F\u00e5hraeus","year":"1928","unstructured":"R. F\u00e5hraeus, Die Str\u00f6mungsverh\u00e4ltnisse und die Verteilung der Blutzellen im Gef\u00e4sssystem, Klin. Wschr., 7, 1928, pp. 100\u2013106.","journal-title":"Klin. Wschr."},{"key":"4_CR20","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1152\/ajplegacy.1931.96.3.562","volume":"96","author":"R. F\u00e5hraeus","year":"1931","unstructured":"R. F\u00e5hraeus and T. Lindqvist, The viscosity of blood in narrow capillary tubes, Am. J. Physiol. 96. 1931, pp. 562\u2013568.","journal-title":"Am. J. Physiol."},{"key":"4_CR21","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1137\/0152064","volume":"52","author":"A. L. Fogelson","year":"1992","unstructured":"A. L. Fogelson, Continuum models of platelet aggregation: formulation and mechanical properties, SIAM J. Appl. Math., 52, 1992, 1089\u20131110.","journal-title":"SIAM J. Appl. Math."},{"key":"4_CR22","unstructured":"P. J. Frey, G\u00e9n\u00e9ration et adaptation de maillages de surfaces \u00e0 partir de donn\u00e9es anatomiques discr\u00e8tes, Rapport de Recherche, 4764, INRIA, 2003."},{"key":"4_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite Element Methods for the navier-Stokes Equations","author":"V. Girault","year":"1986","unstructured":"V. Girault and P.-A. Raviart, Finite Element Methods for the navier-Stokes Equations, Springer-Verlag Berlin, Heidelberg, New York, Tokyo, 1986."},{"key":"4_CR24","volume-title":"Incompressible Flow and the Finite Element Method","author":"P. M. Gresho","year":"2000","unstructured":"P. M. Gresho and R. L. Sani, Incompressible Flow and the Finite Element Method, Vol.2, Jphn Wiley and Sons, Chichester, 2000."},{"key":"4_CR25","doi-asserted-by":"crossref","first-page":"279","DOI":"10.3233\/BIR-1975-12505","volume":"12","author":"C. R. Huang","year":"1975","unstructured":"C. R. Huang, N. Siskovic, R. W. Robertson, W. Fabisiak, E. H. Smith-Berg and A. L. Copley, Quantitative characterization of thixotropy of whole human blood, Biorheology, 12, 1975, pp. 279\u2013282.","journal-title":"Biorheology"},{"key":"4_CR26","unstructured":"R. Keunings, A survey of computational rheology, in: Proceedings of the XIIIth International Congress on Rheology (D.M. Binding et al. ed.), British Soc. Rheol., 1, 2000, pp. 7\u201314."},{"key":"4_CR27","unstructured":"A. Kuharsky, Mathematical modeling of blood coagulation, PhD Thesis, Univ. of Utah, 1998."},{"issue":"3","key":"4_CR28","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1016\/S0006-3495(01)76085-7","volume":"80","author":"A. Kuharsky","year":"2001","unstructured":"A. Kuharsky, A. L. Fogelson, Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition, Biophys. J., 80(3), 2001, pp. 1050\u20131074.","journal-title":"Biophys. J."},{"key":"4_CR29","volume-title":"Clinical Blood Rheology","author":"D. O. Lowe","year":"1998","unstructured":"D. O. Lowe, Clinical Blood Rheology, Vol. I, II, CRC Press, Boca Raton, Florida, 1998."},{"key":"4_CR30","doi-asserted-by":"crossref","unstructured":"D. E. McMillan, J. Strigberger and N. G. Utterback, Rapidly recovered transient flow resistance: a newly discovered property of blood, American Journal of Physiology, 253, pp. 919\u2013926.","DOI":"10.1152\/ajpheart.1987.253.4.H919"},{"key":"4_CR31","doi-asserted-by":"crossref","DOI":"10.1142\/p160","volume-title":"Computational Rheology","author":"R. G. Owens","year":"2002","unstructured":"R. G. Owens and T. N. Phillips, Computational Rheology, Imperial College Press\/World Scientific, London, UK, 2002."},{"key":"4_CR32","doi-asserted-by":"crossref","unstructured":"R. G. Owens, A new microstructure-based constitutive model for human blood, J. Non-Newtonian Fluid Mech., 2006, to appear.","DOI":"10.1016\/j.jnnfm.2006.01.015"},{"key":"4_CR33","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1053\/ejvs.2001.1313","volume":"21","author":"M. J. Perko","year":"2001","unstructured":"M. J. Perko, Duplex Ultrasound for Assessment of Superior Mesenteric Artery Blood Flow, European Journal of Vascular and Endovascular Surgery, 21, 2001, pp. 106\u2013117.","journal-title":"European Journal of Vascular and Endovascular Surgery"},{"key":"4_CR34","doi-asserted-by":"crossref","unstructured":"K. Perktold and M. Prosi, Computational models of arterial flow and mass transport, in:Cardiovascular Fluid Mechanics (G. Pedrizzetti, K. Perktold, Eds.), CISM Courses and Lectures n.446, Springer-Verlag, pp. 73\u2013136, 2003.","DOI":"10.1007\/978-3-7091-2542-7_2"},{"issue":"6","key":"4_CR35","doi-asserted-by":"crossref","first-page":"383","DOI":"10.3233\/BIR-1975-12609","volume":"12","author":"W. M. Phillips","year":"1975","unstructured":"W. M. Phillips, S. Deutsch, Towards a constitutive equation for blood, Biorheology, 12(6), 1975, pp. 383\u2013389.","journal-title":"Biorheology"},{"key":"4_CR36","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1146\/annurev.fluid.37.042604.133933","volume":"37","author":"A. S. Popel","year":"2005","unstructured":"A. S. Popel and P. C. Johnson, Microcirculation and hemorheology, Annu. Rev. Fluid Mech., 37, 2005, pp. 43\u201369.","journal-title":"Annu. Rev. Fluid Mech."},{"key":"4_CR37","first-page":"143","volume":"29","author":"A. R. Pries","year":"2003","unstructured":"A. R. Pries and T. W. Secomb, Rheology of the microcirculation, Clinical Hemorheology and Microcirculation, 29, 2003, pp. 143\u2013148.","journal-title":"Clinical Hemorheology and Microcirculation"},{"issue":"3\u20134","key":"4_CR38","doi-asserted-by":"crossref","first-page":"253","DOI":"10.3233\/BIR-1993-303-410","volume":"30","author":"D. A. Quemada","year":"1993","unstructured":"D. A. Quemada, A non-linear Maxwell model of biofluids-Application to normal blood, Biorheology, 30(3\u20134), 1993, pp. 253\u2013265.","journal-title":"Biorheology"},{"key":"4_CR39","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-85268-1","volume-title":"Numerical Approximation of Partial Differential Equations","author":"A. Quarteroni","year":"1994","unstructured":"A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer-Verlag, Heidelberg, 1994."},{"key":"4_CR40","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/S0377-0257(99)00023-3","volume":"88","author":"K. R. Rajagopal","year":"2000","unstructured":"K. R. Rajagopal, A. Srinivasa, A thermodynamic framework for rate type fluid models, J. of Non-Newtonian Fluid Mech., 88, 2000, pp. 207\u2013228.","journal-title":"J. of Non-Newtonian Fluid Mech."},{"key":"4_CR41","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1002\/(SICI)1097-0363(19971015)25:7<847::AID-FLD590>3.0.CO;2-1","volume":"25","author":"G. Rappitsch","year":"1997","unstructured":"G. Rappitsch, K. Perktold and E. Pernkopf, Numerical modelling of shear-dependent mass transfer in large arteries, Int. J. Numer. Meth. Fluids, 25, 1997, pp. 847\u2013857.","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"4_CR42","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1002\/zamm.19850650919","volume":"65","author":"M. Renardy","year":"1985","unstructured":"M. Renardy, Existence of slow steady flows of viscoelastic fluids with a differential constitutive equation, Z. Angew. Math. Mech., 65, 1985, pp. 449\u2013451.","journal-title":"Z. Angew. Math. Mech."},{"key":"4_CR43","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719413","volume-title":"Mathematical Analysis of Viscoelastic Flows","author":"M. Renardy","year":"2000","unstructured":"M. Renardy, Mathematical Analysis of Viscoelastic Flows, CBMS 73, SIAM, Philadelphia, 2000."},{"key":"4_CR44","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1038\/183613a0","volume":"183","author":"G. W. Scott-Blair","year":"1959","unstructured":"G. W. Scott-Blair, An equation for the flow of blood, plasma and serum through glass capillaries, Nature, 183, 1959, pp. 613\u2013614.","journal-title":"Nature"},{"issue":"2","key":"4_CR45","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/S1056-8719(00)00123-4","volume":"44","author":"R. Tabrizchi","year":"2000","unstructured":"R. Tabrizchi and M. K. Pugsley, Methods of blood flow measurement in the arterial circulatory system, Journal of Pharmacological and Toxicological Methods, 44(2), 2000, pp. 375\u2013384.","journal-title":"Journal of Pharmacological and Toxicological Methods"},{"issue":"5","key":"4_CR46","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1002\/(SICI)1097-0150(1999)4:5<231::AID-IGS1>3.0.CO;2-Z","volume":"4","author":"C. A. Taylor","year":"1999","unstructured":"C. A. Taylor, M. T. Draney, J. P. Ku, D. Parker, B. N. Steele, K. Wang, C. K. Zarins, Predictive medicine: Computational techniques in therapeutic decision-making, Computed Aided Surgery, 4(5), 1999, pp.231\u2013247.","journal-title":"Computed Aided Surgery"},{"key":"4_CR47","volume-title":"Navier-Stokes Equations, Theory and Numerical Analysis","author":"R. Temam","year":"1984","unstructured":"R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis, North Holland, Amsterdam, 1984."},{"key":"4_CR48","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1016\/S0006-3495(72)86156-3","volume":"12","author":"G. B. Thurston","year":"1972","unstructured":"G. B. Thurston, Viscoelasticity of human blood, Biophys. J., 12, 1972, 1205\u20131217.","journal-title":"Biophys. J."},{"key":"4_CR49","doi-asserted-by":"crossref","first-page":"149","DOI":"10.3233\/BIR-1979-16303","volume":"16","author":"G. B. Thurston","year":"1979","unstructured":"G. B. Thurston, Rheological parameters for the viscosity, viscoelasticity and thixotropy of blood, Biorheology, 16, 1979, pp. 149\u2013162.","journal-title":"Biorheology"},{"key":"4_CR50","doi-asserted-by":"crossref","first-page":"685","DOI":"10.3233\/BIR-1990-27506","volume":"27","author":"G. B. Thurston","year":"1990","unstructured":"G. B. Thurston, Light transmission through blood in oscillatory flow, Biorheology, 27, 1990, pp. 685\u2013700.","journal-title":"Biorheology"},{"issue":"2","key":"4_CR51","doi-asserted-by":"crossref","first-page":"179","DOI":"10.3233\/BIR-1994-31206","volume":"31","author":"G. B. Thurston","year":"1994","unstructured":"G. B. Thurston, Non-Newtonian viscosity of human blood: flow-induced changes in microstructure, Biorheology, 31(2), 1994, pp. 179\u2013192.","journal-title":"Biorheology"},{"key":"4_CR52","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.ics.2005.03.275","volume":"1281","author":"R. Unterhinninghofen","year":"2005","unstructured":"R. Unterhinninghofen, J. Albers, W. Hosch, C. Vahl and R. Dillmann, Flow quantification from time-resolved MRI vector fields, International Congress Series, 1281, 2005, pp. 126\u2013130.","journal-title":"International Congress Series"},{"issue":"1","key":"4_CR53","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0006-355X(97)00002-4","volume":"34","author":"G. Vlastos","year":"1997","unstructured":"G. Vlastos, D. Lerche, B. Koch, The superimposition of steady and oscillatory shear and its effect on the viscoelasticity of human blood and a blood-like model fluid, Biorheology, 34(1), 1997, pp. 19\u201336.","journal-title":"Biorheology"},{"key":"4_CR54","doi-asserted-by":"crossref","first-page":"201","DOI":"10.3233\/BIR-1976-13307","volume":"13","author":"F. J. Walburn","year":"1976","unstructured":"F. J. Walburn, D. J. Schneck, A constitutive equation for whole human blood, Biorheology, 13, 1976, pp. 201\u2013210.","journal-title":"Biorheology"},{"key":"4_CR55","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1006\/jcph.1999.6212","volume":"151","author":"N. T. Wang","year":"1999","unstructured":"N. T. Wang, A. L. Fogelson, Computational methods for continuum models of platelet aggregation, J. Comput. Phys., 151, 1999, pp. 649\u2013675.","journal-title":"J. Comput. Phys."},{"key":"4_CR56","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1016\/j.medengphy.2005.06.008","volume":"27","author":"B. J. B. M. Wolters","year":"2005","unstructured":"B. J. B. M. Wolters, M. C. M. Rutten, G.W. H. Schurink, U. Kose, J. de Hart and F. N. van de Vosse, A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms, Medical Engineering & Physics, 27, 2005, pp. 871\u2013883.","journal-title":"Medical Engineering & Physics"},{"issue":"3","key":"4_CR57","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/S0093-6413(98)00036-6","volume":"25","author":"K. K. Yelesvarapu","year":"1998","unstructured":"K. K. Yelesvarapu, M. V. Kameneva, K. R. Rajagopal, J. F. Antaki, The flow of blood in tubes: theory and experiment,Mech. Res. Comm, 25(3), 1998, pp. 257\u2013262.","journal-title":"Mech. Res. Comm"},{"key":"4_CR58","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/S0021-9290(99)00101-3","volume":"33","author":"J.-B. Zhang","year":"2000","unstructured":"J.-B. Zhang and Z.-B. Kuang, Study on blood constitutive parameters in different blood constitutive equations, J. Biomechanics, 33, 2000, pp. 355\u2013360.","journal-title":"J. Biomechanics"}],"container-title":["A Portrait of State-of-the-Art Research at the Technical University of Lisbon"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4020-5690-1_4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T21:59:26Z","timestamp":1605650366000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-1-4020-5690-1_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9781402056895"],"references-count":58,"URL":"https:\/\/doi.org\/10.1007\/978-1-4020-5690-1_4","relation":{},"subject":[]}}