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A review of computational fluid dynamics analysis of blood pumps

  • M. BEHBAHANI (a1), M. BEHR (a1), M. HORMES (a2), U. STEINSEIFER (a2), D. ARORA (a3), O. CORONADO (a3) and M. PASQUALI (a3)...

Ventricular assist devices (VADs) provide long- and short-term support to chronically ill heart disease patients; these devices are expected to match the remarkable functionality of the natural heart, which makes their design a very challenging task. Blood pumps, the principal component of the VADs, must operate over a wide range of flow rates and pressure heads and minimise the damage to blood cells in the process. They should also be small to allow easy implantation in both children and adults. Mathematical methods and computational fluid dynamics (CFD) have recently emerged as powerful design tools in this context; a review of the recent advances in the field is presented here. This review focusses on the CFD-based design strategies applied to blood flow in blood pumps and other blood-handling devices. Both simulation methods for blood flow and blood damage models are reviewed. The literature is put into context with a discussion of the chronological development in the field. The review is illustrated with specific examples drawn from our group's Galerkin/least squares (GLS) finite-element simulations of the basic Newtonian flow problem for the continuous-flow centrifugal GYRO blood pump. The GLS formulation is outlined, and modifications to include models that better represent blood rheology are shown. Haemocompatibility analysis of the pump is reviewed in the context of haemolysis estimations based on different blood damage models. Our strain-based blood damage model that accounts for the viscoleasticity associated with the red blood cells is reviewed in detail. The viability of design improvement based on trial and error and complete simulation-based design optimisation schemes are also discussed.

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[1]Abraham, F., Behr, M. & Heinkenschloss, M. (2005) Shape optimization in steady blood flow: A numerical study of non-Newtonian effects. Comp. Meth. Biomech. Biomed. Eng. 8 (2), 127137.
[2]Abraham, F., Behr, M. & Heinkenschloss, M. (2005) Shape optimization in unsteady blood flow: A numerical study of non-Newtonian effects. Comp. Meth. Biomech. Biomed. Eng. 8 (3), 201212.
[3]Allaire, P. E., Wood, H. G., Awad, R. S. & Olsen, D. B. (1999) Blood flow in a continuous flow ventricular assist device. Artif. Organs 23 (8), 769773.
[4]The American Heart Association. (2006) Heart disease and stroke statistics: 2006. Circulation 113, 85151.
[5]American Society for Testing and Materials. (1997) Standard practice for assessment of hemolysis in continuous flow blood pumps. Standard F 1841-97, ASTM.
[6]Amsden, A. A. & Harlow, F. H. (1970) The SMAC method: A numerical technique for calculating incompressible fluid flows. Technical Report LA-4370, Los Alamos Scientific Lab., New Mexico.
[7]Anand, M. & Rajagopal, K. R. (2004) A shear-thinning fluid model for describing the flow of blood. Int. J. Cardiovasc. Med. Sci. 4 (2), 5968.
[8]Anderson, D. W. (2001) Blood pumps: Technologies and markets in transformation. Artif. Organs 25 (5), 406410.
[9]Anderson, J. B., Wood, H. G., Allaire, P. E., Bearnson, G. & Khanwilkar, P. (2000) Computational flow study of the continuous flow ventricular assist device, prototype number 3 blood pump. Artif. Organs 24 (5), 377385.
[10]Antaki, J. F., Ghattas, O., Burgreen, G. W. & He, B. (1995) Computational flow optimization of rotary blood pump components. Artif. Organs 19 (7), 608615.
[11]Apel, J., Neudel, F. & Reul, H. (2001) Computational fluid dynamics and experimental validation of a microaxial blood pump. ASAIO 47, 552558.
[12]Apel, J., Paul, R., Klaus, S., Siess, T. & Reul, H. (2001) Assessment of hemolysis related quantities in a microaxial blood pump by computational fluid dynamics. Artif. Organs 25 (5), 341347.
[13]Arora, D. (2005) Computational Hemodynamics: Hemolysis and Viscoelasticity. PhD thesis, Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX.
[14]Arora, D., Behr, M. & Pasquali, M. (2004) A tensor-based measure for estimating blood damage. Artif. Organs 28 (11), 10021015.
[15]Arora, D., Behr, M. & Pasquali, M. (2006) Hemolysis estimation in a centrifugal blood pump using a tensor-based measure. Artif. Organs 30, 539547.
[16]Arvand, A., Hahn, N., Hormes, M., Akdis, M., Martin, M. & Reul, H. (2004) Comparison of hydraulic and hemolytic properties of different impeller designs of an implantable rotary blood pump by computational fluid dynamics. Artif. Organs 28 (10), 892898.
[17]Arvand, A., Hormes, M. & Reul, H. (2005) A validated computational fluid dynamics model to estimate hemolysis in a rotary blood pump. Artif. Organs 29 (7), 531540.
[18]Avrahami, I., Einav, S., Rosenfeld, M. & Affeld, K. (2001) Hemodynamic aspects of the Berlin ventricle assist device. In: Proceedings of the 23rd Annual EMBS International Conference, October 25–28, IEEE Press: Istanbul, Turkey, pp. 468472.
[19]Baaijens, F. P. T. (1998) Mixed finite element methods for viscoelastic flow analysis: A review. J. Non-Newton. Fluid Mech. 79, 361385.
[20]Bagchi, P., Johnson, P. C. & Popel, A. S. (2005) Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. J. Biomech. Eng. 127, 10701080.
[21]Barthès-Biesel, D. & Sgaier, H. (1985) Role of membrane viscosity in the orientation and deformation of a spherical capsule suspended in shear flows. J. Fluid Mech. 160, 119135.
[22]Behr, M. (1992) Stabilized Finite Element Methods for Incompressible Flows With Emphasis on Moving Boundaries and Interfaces. PhD thesis, Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN.
[23]Behr, M. & Arora, D. (2003) Shear-slip mesh update method: Implementation and applications. Comp. Meth. Biomech. Biomed. Eng. 6 (2), 113123.
[24]Behr, M., Arora, D., Coronado, O. & Pasquali, M. (2005) GLS-type finite element methods for viscoelastic fluid flow simulation. In: Bathe, K. J. (editor), Proceedings of the Third MIT Conference on Computational Fluid and Solid Mechanics, Elsevier Science Ltd., Camebridge, MA, pp. 586589.
[25]Behr, M., Arora, D., Nosé, Y. & Motomura, T. (2004) Performance analysis of ventricular assist devices using finite element flow simulation. Int. J. Numer. Meth. Fluids 46, 12011210.
[26]Behr, M. & Tezduyar, T. E. (1994) Finite element solution strategies for large-scale flow simulations. Comp. Meth. Appl. Mech. Eng. 112, 324.
[27]Beris, A. N. & Edwards, B. J. (1994) Thermodynamics of Flowing Systems With Internal Microstructure, 1st edn., Oxford University Press, Oxford.
[28]Bertram, C. D., Qian, Y. & Reizes, J. A. (2001) Computational fluid dynamics performance prediction of the hydrodynamic bearings of the VentrAssist rotary blood pump. Artif. Organs 25 (5), 348357.
[29]Blackshear, P. L. & Blackshear, G. L. (1987) Mechanical hemolysis. In: Skalak, R. & Chien, S. (editors), Handbook of Bioengineering, McGraw-Hill, New York, pp. 15.115.19.
[30]Bludszuweit, C. (1995) Model for a general mechanical blood damage prediction. Artif. Organs 19 (7), 583589.
[31]Bludszuweit, C. (1995) Three-dimensional numerical prediction of stress loading of blood particles in a centrifugal pump. Artif. Organs 19 (7), 590596.
[32]Bludszuweit, C. (1997) Evaluation and optimization of artificial organs by computational fluid dynamics. In: Proceedings of 1997 ASME Fluids Engineering Division Summer Meeting. Vancouver, British Columbia, Canada, ASME. June 22–26, 1997.
[33]Blümich, B. (2005) Essential NMR. Springer, Berlin.
[34]Boryczko, K., Dzwinel, W. & Yuen, D. A. (2003) Dynamical clustering of red blood cells in capillary vessels. J. Mol. Model. 9, 1633.
[35]Brooks, A. N. & Hughes, T. J. R. (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. CMNA 32, 199259.
[36]Burgreen, G. W., Antaki, J. F., Wu, Z. J. & Holmes, A. J. (2001) Computational fluid dynamics as a development tool for rotary blood pumps. Artif. Organs 25 (5), 336340.
[37]Chan, W. K., Wong, Y. W., Ding, Y., Chua, L. P. & Yu, S. C. M. (2002) Numerical investigation of the effect of blade geometry on blood trauma in a centrifugal blood pump. Artif. Organs 26 (9), 785793.
[38]Chan, W. K., Wong, Y. W., Ong, W., Koh, S.-Y. & Chong, V. (2005) Numerical investigation of the effects of the clearance gap between the inducer and impeller of an axial blood pump. Artif. Organs 29 (3), 250258.
[39]Chien, S. (1970) Shear dependence of effective cell volume as determinant of blood viscosity. Science 168, 977979.
[40]Chien, S., Usami, S., Dellenback, R. J. & Gregersen, M. I. (1967) Blood viscosity: Influence of erythrocyte aggregation. Science 157, 827829.
[41]Chien, S., Usami, S., Dellenback, R. J. & Gregersen, M. I. (1967) Blood viscosity: Influence of erythrocyte deformation. Science 157, 829831.
[42]Coronado, O. M., Arora, D., Behr, M. & Pasquali, M. (2006) Four-field Galerkin/least-squares formulation for viscoelastic fluids. J. Non-Newton. Fluid Mech. 140, 132144.
[43]Couillette, C. & Pozrikidis, C. (1998) Motion of an array of drops through a cylindrical tube. J. Fluid Mech. 358, 128.
[44]Cristini, V. & Kassab, G. S. (2005) Computer modeling of red blood cell rheology in the microcirculation: a brief overview. Ann. Biomed. Eng. 33, 17241727.
[45]Crochet, M. J., Davies, A. R. & Walters, K. (1984) Numerical Simulation of Non-Newtonian Flow, Elsevier, New York.
[46]Curtas, A. R., Wood, H. G., Allaire, P. E., McDaniel, J. C., Day, S. W. & Olsen, D. B. (2002) Computational fluid dynamics modeling of impeller designs for the HeartQuest left ventricular assist device. ASAIO 48, 552561.
[47]Curtis, J. J. & Wagner-Mann, C. (2000) Cardiac Assist Devices, Futura, Armonk, NY.
[48]Davie, E. W. (2005) A brief historical review of the waterfall/cascade of blood coagulation. J. Biol. Chem. 278, 5081950832.
[49]Day, S. W., & McDaniel, J. C. (2005) PIV measurements of flow in a centrifugal blood pump: Time varying flow. ASME 127, 254263.
[50]De Wachter, D. & Verdonck, P. (2002) Numerical calculation of hemolysis levels in peripheral hemodialysis cannulas. Artif. Organs 26 (7), 576582.
[51]DeBakey, M. E. (2000) The odyssey of the artificial heart. Artif. Organs 24 (6), 405411.
[52]Ding, W. & Nakamura, S. (1998) Three-dimensional single passage simulation for the IVAS centrifugal heart pump. In: Proceedings of 1998 ASME Fluids Engineering Division Summer Meeting. June 21–25, Washington, DC, ASME.
[53]Easthope, P. L. & Brooks, D. E. (1980) A comparison of rheological and constitutive functions for whole human blood. Biorheology 17, 235247.
[54]Eckmann, D. M. (2000) Hematocrit, volume expander, temperature, and shear rate effects on blood viscosity. Anesth. Analg. 91, 539545.
[55]Eggleton, C. D. & Popel, A. S. (1998) Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids 10 (8), 18341845.
[56]Evans, E. A. & LaCelle, P. L. (1975) Intrinsic material properties of the erythrocyte membrane indicated by mechanical analysis of deformation. Blood 45, 2943.
[57]Franca, L. P. & Frey, S. L. (1992) Stabilized finite element methods: II. The incompressible Navier-Stokes equations. CMAME 99, 209233.
[58]Franca, L. P., Frey, S. L. & Hughes, T. J. R. (1992) Stabilized finite element methods. Part I. Application to the advective-diffusive model. CMAME 95, 253276.
[59]Fung, Y. C.Biomechanics: Mechanical Properties of Living Tissue, Springer, New York.
[60]Gauthier, F. J., Goldsmith, H. L. & Mason, S. G. (1972) Flow of suspensions through tubes. Part X. Liquid drops as models of erythrocytes. Biorheology 9, 205224.
[61]Gawaz, M. P. (1856) Das Blutplättchen. Medinger Sohn, Frankfurt.
[62]Giersiepen, M., Wurzinger, L. J., Opitz, R. & Reul, H. (1990) Estimation of shear stress-related blood damage in heart valve prostheses: In vitro comparison of 25 aortic valves. Int. J. Artif. Organs 13 (5), 300306.
[63]Gijsen, F. J. H., van de Vosse, F. N. & Janssen, J. D. (1999) The influence of the non-Newtonian properties of blood on the flow in large arteries: Steady flow in a carotid bifurcation model. J. Biomech. 32, 601608.
[64]Goubergrits, L. & Affeld, K. (2004) Numerical estimation of blood damage in artificial organs. Artif. Organs 28 (5), 499507.
[65]Grigioni, M., Daniele, C., Morbiducci, U., D'Avenio, G., Di Benedetto, G. & Barbaro, V. (2004) The power-law mathematical model for blood damage prediction: Analytical developments and physical inconsistencies. Artif. Organs 28 (5), 467475.
[66]Grmela, M. & Carreau, P. J. (1987) Conformation tensor rheological models. J. Non-Newton. Fluid Mech. 23, 271294.
[67]Gu, L. & Smith, W. A. (2005) Evaluation of computational models for hemolysis estimation. ASAIO 51, 202207.
[68]Guénette, R., Abdelmalek, Z., Fortin, A., Carreau, P. & Grmela, M. (1992) Simulation of viscoelastic flows using a conformation tensor model. J. Non-Newton. Fluid Mech. 45, 187208.
[69]Han, S., Marseille, O., Gehlen, C. & Blümich, B. (2001) Rheology of blood by NMR. J. Magn. Reson. 152, 8794.
[70]Hellums, J. D. & Brown, C. H. III,. Blood cell damage by mechanical forces. In: Hwang, N. H. C & Normann, N. A. (editors), Cardiovascular Flow Dynamics and Measurements, University Park Press, Baltimore, MD, pp. 799823.
[71]Hénon, S., Lenormand, G., Richert, A. & Gallet, F. (1999) A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. Biophys. J. 76, 11451151.
[72]Hetzer, R., Müller, J., Weng, Y., Wallukat, G., Spiegelsberger, S. & Loebe, M. (1999) Cardiac recovery in dilated cardiomyopathy by unloading with a left ventricular assist device. Ann. Thorac. Surg. 68, 742749.
[73]Heuser, G. & Opitz, R. (1980) A Couette viscometer for short time shearing of blood. Biorheology 17, 1724.
[74]Ho, K. K., Anderson, K.M., Kannel, W. B., Grossman, W. & Levy, D. (1993) Survival after the onset of congestive heart failure in Framingham heart study subjects. Circulation 88, 107115.
[75]Hoffmann, J. I. & Christianson, R. (1978) Congenital heart disease in a cohort of 19,502 births with long-term follow-up. Am. J. Cardiol. 42 (4), 641647.
[76]Hughes, T. J. R., & Brooks, A. N. (1979) A multi-dimensional upwind scheme with no crosswind diffusion. In: Hughes, T. J. R. (editor), Finite Element Methods for Convection Dominated Flows, vol. 34, ASME, New York, pp. 1935.
[77]Hughes, T. J. R., Franca, L. P. & Hulbert, G. M. (1989) A new finite element formulation for computational fluid dynamics. Part 8. The Galerkin/least-squares method for advective–diffusive equations. CMAME 73, 173189.
[78]Hulsen, M. A., Fattal, R. & Kupferman, R. (2005) Flow of viscoelastic fluids past a cylinder at high Weissenberg number: Stabilized simulations using matrix logarithms. J Non-Newton. Fluid Mech. 127, 2739.
[79]Johnson, W. (1973) Engineering Plasticity, VNR, London.
[80]Kameneva, M. V., Burgreen, G. W., Kono, K., Repko, B., Antaki, J. F. & Umezu, M. (2004) Effects of turbulent stresses upon mechanical hemolysis: Experimental and computational analysis. ASAIO J. 50 (5), 418423.
[81]Keunings, R. (2001) Advances in the computer modeling of the flow of polymetric liquids. Comput. Fluid Dyn. 9, 448458.
[82]Klaus, S., Paul, R., Mottaghy, K., Reul, H. & Glasmacher, B. (2001) Investigation of flow and material induced hemolysis with a Couette type high shear system. Materialwissenschaft Werkzeugtech. 32, 922925.
[83]Knierbein, B., Reul, H., Eilers, R., Lange, M., Kaufmann, R. & Rau, G. (1992) Compact mock loops of the systemic and pulmonary circulation for blood testing. Int. J. Artif. Organs 15 (1), 4048.
[84]Lee, S. S., Ahn, K. H., Lee, S. J., Sun, K., Goedhart, P. T. & Hardeman, M. R. (2004) Shear induced damage of red blood cells monitored by the decrease of their deformability. Korea–Aust. Rheol. J. 16 (3), 141146.
[85]Leuprecht, A. & Perktold, K. (2001) Computer simulation of non-Newtonian effects on blood flow in large arteries. Comp. Meth. Biomech. Biomed. Eng. 4, 149163.
[86]Leverett, L. B., Hellums, J. D., Alfrey, C. P. & Lynch, E. C. (1972) Red blood cell damage by shear stress. Biophys. J. 12, 257273.
[87]Maffettone, P. L. & Minale, M. (1998) Equation of change for ellipsoidal drops in viscous flow. J. Non-Newton. Fluid Mech. 78, 227241.
[88]Masuzawa, T., Tsukiya, T., Endo, S., Tatsumi, E., Taenaka, Y., Takano, H., Yamane, T., Nishida, M., Asztalos, B., Miyazoe, Y., Ito, K., Sawairi, T. & Konishi, Y. (1999) Development of design methods for a centrifugal blood pump with a fluid dynamic approach: Results in hemolysis tests. Artif. Organs 23 (8), 757761.
[89]Minami, K., Schulte-Eistrup, S., El-Banayosy, A. & Koerfer, R. (2004) Impact of regulatory affairs on the development of artificial organs, particularly ventricular assist devices. Artif. Organs 25 (5), 860864.
[90]Mitoh, A., Yano, T., Sekine, K., Mitamura, Y., Okamoto, E., Kim, D., Yozu, R. & Kawada, S. (2003) Computational fluid dynamics analysis of an intra-cardiac axial flow pump. Artif. Organs 27 (1), 3440.
[91]Miyazoe, Y., Sawairi, T., Ito, K., Konishi, Y., Yamane, T., Nishida, M., Asztalos, B., Masuzawa, T., Tsukiya, T., Endo, S. & Taenaka, Y. (1999) Computational fluid dynamics analysis to establish the design process of a centrifugal blood pump: Second report. Artif. Organs 23 (8), 762768.
[92]Murakami, T., Golding, L. R., Jacobs, G., Takatani, S., Sukalac, R., Harasaki, H. & Nosé, Y. (1979) Nonpulsatile biventricular bypass using centrifugal blood pumps. Jap. Soc. Artif Organs 8, 636639.
[93]Nakamura, S. (1997) Options and selection of numerical algorithms for unsteady incompressible Navier–Stokes equations. Proceedings of the ASME Fluid Engineering Division Summer Meeting, FEDSM97-3666, New York: American Society of Mechanical Engineers.
[94]Nakamura, S. & Yano, K. (1999) Computational simulation of flows in an entire centrifugal blood pump. Artif. Organs 23 (6), 572575.
[95]Ng, B. T., Chan, W. K. & Li, H. D. (2000) Experimental and computational studies of the relative flow field in a centrifugal pump. Crit. Rev. Biomed. Eng. 28 (1), 119125.
[96]Nonaka, K., Linneweber, J., Ichikawa, S., Yoshikawa, M., Kawahito, S., Mikami, M., Motomura, T., Ishitoya, H., Nishimura, I., Oestmann, D., Glueck, J., Schima, H., Wolner, E., Shinohara, T. & Nosé, Y. (2001) Development of the Baylor Gyro permanently implantable centrifugal blood pump as a biventricular assist device. Artif. Organs 25 (9), 675682.
[97]Nosé, Y. (1998) Design and development strategy for the rotary blood pump. Artif. Organs 22 (6), 438446.
[98]Nosé, Y. (2005) Is it a mistake to develop a totally implantable blood pump for destination therapy? Artif. Organs 29 (2), 9394.
[99]Nosé, Y., Yoshikawa, M., Murabayashi, S. & Takano, T. (2000) Development of rotary blood pump technology: Past, present, and future. Artif. Organs 24 (6), 412420.
[100]Okamoto, E., Hashimoto, T. & Inoue, T. (2003) Blood compatible design of a pulsatile blood pump using computational fluid dynamics and computer-aided design and manufacturing technology. Artif. Organs 27 (1), 6167.
[101]Olsen, D. B. (1999) Rotary blood pumps: A new horizon. Artif. Organs 23 (8), 695696.
[102]Olsen, D. B. (2000) The history of continuous-flow blood pumps. Artif. Organs 24 (6), 401404.
[103]Owens, R. G. (2006) A new microstructure-based constitutive model for human blood. J. Non-Newton. Fluid Mech. 140:5770.
[104]Owens, R. G. & Phillips, T. N. (2002) Computational Rheology, Imperial College Press, London.
[105]Papantonis, D. (1991) Numerical prediction of the shear stresses and the mean exposure time for radial flow impellers. In: Schima, Thoma (editor), Proceedings of the International Workshop on Rotary Blood Pumps, Vienna, pp. 6369.
[106]Papantonis, D. & Croba, D. (1988) Numerical calculation of the performances and shear stresses developed on centrifugal blood pumps. In: Schima, Thoma (editor), Proceedings of the International Workshop on Rotary Blood Pumps, Vienna, pp. 5359.
[107]Pasquali, M. & Scriven, L. E. (2002) Free surface flows of polymer solutions with models based on the conformation tensor. J. Non-Newton. Fluid Mech. 108, 363409.
[108]Pasquali, M. & Scriven, L. E. (2004) Theoretical modeling of microstructured liquids: A simple thermodynamic approach. J. Non-Newton. Fluid Mech. 120, 101135.
[109]Perktold, K., Karner, G., Leuprecht, A. & Hofer, M. (1999) Influence of non-Newtonian flow behavior on local hemodynamics. Z. Angew. Math. Mech. 79, 187190.
[110]Pinotti, M. & Rosa, E. S. (1991) CFD simulation on the performance of parallel corotating disks as a heart assist device. In: Proceedings of the Sixth Mediterranean Conference on Medical and Biological Engineering, Capri, Italia: International Federation of Medical and Biological Engineering, V. 1, pp. 429432.
[111]Pinotti, M. & Rosa, E. S. (1995) Computational prediction of hemolysis in a centrifugal ventricular assist device. Artif. Organs 19 (3), 267273.
[112]Pozrikidis, C. (2003) Modeling and Simulation of Capsules and Biological Cells, Chapman Hall, Boca Raton, FL.
[113]Pozrikidis, C. (2004) Numerical simulation of cell motion in tube flow. Ann. Biomed. Eng. 33, 165178.
[114]Pozrikidis, C. (2003) Numerical simulation of the flow-induced deformation of red blood cells. Ann. Biomed. Eng. 31, 11941205.
[115]Qian, Y. & Bertram, C. D. (2000) Computational fluid dynamics analysis of hydrodynamic bearings of the VentrAssist rotary blood pump. Artif. Organs 24 (6), 488491.
[116]Rose, E. A., Gelijns, A. C., Moskowitz, A. J., Heitjan, D. F., Stevenson, L. W., Dembitsky, W., Long, J. W., Ascheim, D. D., Tierney, A. R., Levitan, R. G., Watson, J. T., Meier, P., Ronan, N. S., Shapiro, P. A., Lazar, R. M., Miller, L. W., Gupta, L., Frazier, O. H., Desvigne-Nickens, P., Oz, M. C. & Poirier, V. L.for the Randomized Evaluation of Mechanical Assistance for the Treatment of Congestive Heart Failure (REMATCH) Study Group. (2001) Long-term use of a left ventricular assistance for end-stage heart failure. New Engl. J. Med. 345, 1435–43.
[117]Rossi Neto, J. M. (2004) A dimensão do problema da insufficiěncia cardíaca do Brazil e do mundo. Revista Soc. Cardiol. Estado São Paulo 14 (1), 110.
[118]Saad, Y. & Schultz, M. (1986) GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Scient. Stat. Comput. 7, 856869.
[119]Schaefer, E. J. (2002) Lipoproteins, nutrition, and heart disease. Am. J. Clin. Nutr. 75, 191212.
[120]Schmid-Schönbein, H. & Wells, R. (1969) Fluid drop-like transition of erythrocytes under shear. Science 165 (3890), 288291.
[121]Scott, M. (2005) The Modeling of Blood Rheology in Small Vessels. PhD Thesis, Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada.
[122]Secomb, T. W., Hsu, R. & Pries, A. R. (1998) A model for red blood cell motion in glycocalyx-lined capillaries. Model. Physiol. 274, 10161022.
[123]Snabre, P. & Mills, P. (1996) Rheology of weakly flocculated suspensions of viscoelastic particles. J. Phys. III France 6, 18351855.
[124]Song, X., Throckmorton, A., Wood, H. G., Antaki, J. & Olsen, D. B. (2004) Quantitative evaluation of blood damage in a centrifugal VAD by computational fluid dynamics. ASME 126, 410418.
[125]Song, X., Throckmorton, A. L., Untaroiu, A., Patel, S., Allaire, P. E., Wood, H. G. & Olsen, D. B. (2003) Axial flow blood pumps. ASAIO 49 (4), 355364.
[126]Song, X., Wood, H. G., Day, S. W. & Olsen, D. B. (2003) Studies of turbulence models in a computational fluid dynamics model of a blood pump. Artif. Organs 27 (10), 935937.
[127]Song, X., Wood, H. G. & Olsen, D. B. (2004) Computational fluid dynamics (CFD) study of the fourth generation prototype of a continuous flow ventricular assist device (VAD). J. Biomed. Eng. 126, 180187.
[128]Stepanoff, A. (1957) Centrifugal and Axial Flow Pumps, Krieger, New York.
[129]Sun, J., Smith, M. D., Armstrong, R. C. & Brown, R. A. (1999) Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method: DAVSS-G/DG. J. Non-Newton. Fluid Mech. 86, 281307.
[130]Takatani, S. (2001) Can rotary blood pumps replace pulsatile devices? Artif. Organs 25 (9), 671674.
[131]Takatani, S., Ozawa, K., Golding, L., Jacobs, G., Murakami, T., Valdes, F., Harasaki, H., Kiraly, R. & Nosé, Y. (1980) Comparative evaluation of nonpulsatile and pulsatile cardiac prostheses. Trans. Am. Soc. Artif. Intern. Organs 26, 438443.
[132]Takiura, K., Masuzawa, T., Endo, S., Wakisaka, Y., Tatsumi, E., Taenaka, Y., Takano, H., Yamane, T., Nishida, M., Asztalos, B., Konishi, Y., Miyazoe, Y. & Ito, K. (1998) Development of design methods of a centrifugal blood pump with in vitro tests, flow visualization, and computational fluid dynamics: Results in hemolysis tests. Artif. Organs 22 (5), 393398.
[133]Tezduyar, T. E., Mittal, S., Ray, S. E. & Shih, R. (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity–pressure elements. CMAME 95, 221242.
[134]Throckmorton, A., Untaroiu, A., Allaire, P. E., Wood, H. G., Matherne, G. P., Lim, D. S., Peeler, B. B. & Olsen, D. B. (2004) Computational analysis of an axial flow pediatric ventricular assist device. Artif. Organs 28 (10), 881891.
[135]Throckmorton, A. L., Wood, H. G., Day, S. W., Song, X., Click, P. C., Allaire, P. E. & Olsen, D. B. (2003) Design of a continuous flow centrifugal pediatric ventricular assist device. Int. J. Artif. Organs, 26 (11), 10151031.
[136]Thurston, G. B. (1979) Rheological parameters for the viscosity, viscoelasticity and thixotropy of blood. Biorheology 16, 149162.
[137]Ündar, A. (2004) Myths and truths of pulsatile and nonpulsatile perfusion during acute and chronic cardiac support. Artif. Organs 28 (5), 439443.
[138]Untaroiu, A., Wood, H. G., Allaire, P. E., Throckmorton, A. L., Day, S., Patel, S. M., Ellman, P., Tribble, C. & Olsen, D. B. (2005) Computational design and experimental testing of a novel axial flow LVAD. ASAIO 51, 702710.
[139]Virchow, R. (1856) Gesammelte Abhandlungen zur Wissenschaftlichen Medicin, Medinger Sohn, Frankfurt.
[140]Watanabe, N., Karsak, O., Neudel, F., Kink, T., Apel, J., Fujimoto, T., Reul, H. & Takatani, S. (2001) Simulation of the BP-80 blood pump. Artificial Organs 25 (9), 733739.
[141]Watanabe, N., Masuda, T., Iida, T., Kataoka, H., Fujimoto, T. & Takatani, S. (2005) Quantification of the secondary flow in a radial coupled centrifugal blood pump based on particle tracking velocimetry. Artificial Organs 29 (1), 2635.
[142]Waugh, R. E. & Hochmuth, R. M. (1995) Mechanics and deformability of hematocytes. In: Bronzino, J. D. (editor), Handbook of Bioengineering, CRC Press, Boca Raton, FL, pp. 474486.
[143]Wood, H. G, Throckmorton, A. L., Untaroiu, A. & Song, X. (2005) The medical physics of ventricular assist devices. Rep. Prog. Phys. 68, 545576.
[144]Wootton, D. M. & Ku, D. N. (1999) Fluid mechanics of vascular systems, diseases, and thrombosis. Annu. Rev. Biomed. Eng. 1999.01, 299–329.
[145]Wu, J., Antaki, J. F., Wagner, W. R., Snyder, T. A., Paden, B. E. & Borovetz, H. S. (2005) Elimination of adverse leakage flow in a miniature pediatric centrifugal blood pump by computational fluid dynamics-based design optimization. ASAIO 51, 636643.
[146]Wu, Y., Allaire, P. & Tao, G. (2003) An adaptive speed/flow controller for a continuous flow left ventricular asssist device. In: Proceedings of the American Control Conference, Denver, CO, IEEE.
[147]Wurzinger, L. J., Opitz, R. & Eckstein, H. (1986) Mechanical blood trauma: An overview. Angeiologie 38 (3), 8197.
[148]Yamaguchi, T., Ishikawa, T., Tsubota, K., Imai, Y., Nakamura, M. & Fukui, T. (2006) Computational blood flow analysis – new trends and methods. J. Biomech. Sci. Eng. 1, 2950.
[149]Yamane, T., Asztalos, B., Nishida, M., Masuzawa, T., Takiura, K., Taenaka, Y., Konishi, Y., Miyazoe, Y. & Ito, K. (1998) Flow visualization as a complementary tool to hemolysis testing in the development of centrifugal blood pumps. Artif. Organs 22 (5), 375380.
[150]Yamane, T., Miyamoto, Y., Tajima, K. & Yamazaki, K. (2004) A comparative study between flow visualization and computational fluid dynamic analysis for the Sun Medical centrifugal blood pump. Artif. Organs 28 (5), 458466.
[151]Yano, K. & Nakamura, S. (1997) Flow simulation of the IVAS heart pump using a parallel computer, T3D. In Proceedings of ASME Fluids Engineering Division Summer Meeting, Vancouver, Canada, IEEE.
[152]Yano, T., Sekine, K., Mitoh, A., Mitamura, Y., Okamoto, E., Kim, D.-W., Nishimura, I., Murabayashi, S. & Yozu, R. (2003) An estimation method of hemolysis within an axial flow blood pump by computational fluid dynamics analysis. Artif. Organs 27 (10), 920925.
[153]Yasuda, T., Shimokasa, K., Funakubo, A., Higami, T., Kawamura, T. & Fukui, Y. (2000) An investigation of blood flow behavior and hemolysis in artificial organs. ASAIO 46 (5), 527531.
[154]Yeleswarapu, K. K.Evaluation of Continuum Models for Characterizing the Constitutive Behavior of Blood, PhD Thesis, Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA.
[155]Yeleswarapu, K. K., Antaki, J. F., Kameneva, M. V. & Rajagopal, K. R. (1995) A mathematical model for shear-induced hemolysis. Artif. Organs 19 (7), 576582.
[156]Yeleswarapu, K. K., Kameneva, M. V., Rajagopal, K. R. & Antaki, J. F. (1998) The flow of blood in tubes: Theory and experiments. Mech. Res. Comm. 25 (3), 257262.
[157]Yoshikawa, M., Nonaka, K., Linneweber, J., Kawahito, S., Ohtsuka, G., Nakata, K., Takano, T., Schulte-Eistrup, S., Glueck, J., Schima, H., Wolner, E. & Nosé, Y. (2000). Development of the NEDO implantable ventricular assist device with Gyro centrifugal pump. Artif. Organs 24 (6), 459467.
[158]Yozu, R., Golding, L. R., Jacobs, G., Harasaki, H. & Nosé, Y. (1985) Experimental results and future prospects for a nonpulsatile cardiac prosthesis. World J. Surg. 9 (1), 116127.
[159]Yu, S. C. M., Ng, B. T. H., Chan, W. K. & Chau, L. P. (2000) The flow patterns within the impeller passage of a centrifugal blood pump model. Med. Eng. Phys. 22, 381393.
[160]Yuri, K., Iwahashi, H., Motomura, T., Hata, A., Asai, T., Nosé, Y., Arora, D., Behr, M. & Pasquali, M. (2004) ASAIO 50th anniversary conference abstracts: Different levels of hemolysis occurred by a centrifugal blood pump in various clinical conditions. ASAIO J. 50 (2), 121.
[161]Zhang, J., Gellman, B., Koert, A., Dasse, K. A., Gilbert, R. J., Griffith, B. P. & Wu, Z. J. (2006) Computational and experimental evaluation of the fluid dynamics and hemocompatibility of the CentriMag blood pump. Artif. Organs 30 (3), 168177.
[162]Zhang, J. B. & Kuang, Z. B.Study on blood constitutive parameters in different blood constitutive equations. J. Biomech. 33, 355360.
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European Journal of Applied Mathematics
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