0
Review Article

A Review of Computational Hemodynamics in Middle Cerebral Aneurysms and Rheological Models for Blood Flow

[+] Author and Article Information
Laura Campo-Deaño

Departamento de Engenharia Mecânica,
CEFT,
Faculdade de Engenharia,
Universidade do Porto,
Rua Dr. Roberto Frias,
Porto 4200-465, Portugal
e-mail: campo@fe.up.pt

Mónica S. N. Oliveira

James Weir Fluids Laboratory,
Mechanical and Aerospace Engineering,
University of Strathclyde,
Glasgow G1 1XJ, UK
e-mail: monica.oliveira@strath.ac.uk

Fernando T. Pinho

Departamento de Engenharia Mecânica,
CEFT,
Faculdade de Engenharia,
Universidade do Porto,
Rua Dr. Roberto Frias,
Porto 4200-465, Portugal
e-mail: fpinho@fe.up.pt

1Corresponding author.

Manuscript received January 13, 2014; final manuscript received October 22, 2014; published online January 15, 2015. Assoc. Editor: Gianluca Iaccarino.

Appl. Mech. Rev 67(3), 030801 (May 01, 2015) (16 pages) Paper No: AMR-14-1007; doi: 10.1115/1.4028946 History: Received January 13, 2014; Revised October 22, 2014; Online January 15, 2015

Cerebrovascular accidents are the third most common cause of death in developed countries. Over recent years, CFD simulations using medical image-based anatomical vascular geometries have been shown to have great potential as a tool for diagnostic and treatment of brain aneurysms, in particular to help advise on the best treatment options. This work aims to present a state of the art review of the different models used in CFD, focusing in particular on modeling blood as a viscoelastic non-Newtonian fluid in order to help understand the role of the complex rheological nature of blood upon the dynamics of middle cerebral aneurysms. Moreover, since the mechanical properties of the vessel walls also play an important role in the cardiovascular system, different models for the arterial structure are reviewed in order to couple CFD and computational solid dynamics to allow the study of the fluidstructure interaction (FSI).

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Deaton, C., Froelicher, E. S., Wu, L. H., Ho, C., Shishani, K., and Jaarsma, T., 2011, “The Global Burden of Cardiovascular Disease,” J. Cardiovasc. Nurs., 26, pp. S5–S14. [CrossRef] [PubMed]
Zarins, C. K., Giddens, D. P., Bharadvaj, B. K., Sottiurai, V. S., Mabon, R. F., and Glagov, S., 1983, “Carotid Bifurcation Atherosclerosis: Quantitative Correlation of Plaque Localization With Flow Velocity Profiles and Wall Shear Stress,” Circ. Res., 53(4), pp. 502–514. [CrossRef] [PubMed]
Thubrikar, M. J., Al-Soudi, J., and Robicsek, F., 2001, “Wall Stress Studies of Abdominal Aortic Aneurysm in a Clinical Model,” Ann. Vasc. Surg., 15(3), pp. 355–366. [CrossRef] [PubMed]
Ujiie, H., Tamano, Y., Sasaki, K., and Hori, T., 2001, “Is the Aspect Ratio a Reliable Index for Predicting the Rupture of a Saccular Aneurysm?,” Neurosurgery, 48(3), pp. 495–502. [CrossRef] [PubMed]
Szikora, I., Páal, G., and Ugron, A., 2008, “Impact of Aneurysmal Geometry on Intraaneurysmal Flow: A Computerized Flow Simulation Study,” Neuroradiology, 50(5), pp. 411–421. [CrossRef] [PubMed]
Imbesi, S. G., and Kerber, C. W., 1999, “Analysis of Slipstream Flow in Two Tuptured Intracranial Cerebral Aneurysms,” Am. J. Neuroradiol., 20(9), pp. 1703–1705.
Moyers-Gonzalez, M., Owens, R. G., and Fang, J., 2008, “A Non-Homogeneous Constitutive Model for Human Blood. Part III. Oscillatory Flow,” J. Non-Newtonian Fluid Mech., 155(3), pp. 161–173. [CrossRef]
Eckmann, D. M., Bowers, S., Stecker, M., and Cheung, A. T., 2000, “Hematocrit, Volume Expander, Temperature, and Shear Rate Effects on Blood Viscosity,” Anesth. Analg., 91(3), pp. 539–545. [CrossRef] [PubMed]
Merrill, E. W., 1969, “Rheology of Blood,” Physiol. Rev., 49, pp. 863–888. [PubMed]
Thurston, G. B., 1979, “Rheological Parameters for the Viscosity, Viscoelasticity and Thixotropy of Blood,” Biorheology, 16, pp. 149–162. [PubMed]
Dintenfass, L., 1963, “Blood Rheology in Cardio-Vascular Diseases,” Nature, 199, pp. 813–815. [CrossRef] [PubMed]
Langstroth, L., 1919, “Blood Viscosity. I Conditions Affecting the Viscosity of Blood After Withdrawal From the Body,” J. Exp. Med., 30(6), pp. 597–606. [CrossRef] [PubMed]
Chien, S., Usami, S., Dellenback, R. J., and Gregersen, M. I., 1967, “Blood Viscosity: Influence of Erythrocyte Deformation,” Science, 157(3790), pp. 827–829. [CrossRef] [PubMed]
Chien, S., Usami, S., Dellenback, R. J., Gregersen, M. I., Nanninga, L. B., and Guest, M. M., 1967, “Blood Viscosity: Influence of Erythrocyte Aggregation,” Science, 157(3790), pp. 829–831. [CrossRef] [PubMed]
Morrison, F. A., 2001, Understanding Rheology, Oxford University, Inc., New York.
Campo-Deaño, L., Dullens, R. P. A., Aarts, D. G. L. A., Pinho, F. T., and Oliveira, M. S. N., 2013, “Viscoelasticity of Blood and Viscoelastic Blood Analogues for Use in Polydymethylsiloxane in Vitro Models of the Circulatory System,” Biomicrofluidics, 7(3), p. 034102. [CrossRef]
Poole, R. J., 2012, “The Deborah and Weissenberg Numbers,” British Soc. Rheol. Rheol. Bull., 53, pp. 32–39.
Galindo-Rosales, F. J., Campo-Deaño, L., Sousa, P. C., Ribeiro, V. M., Oliveira, M. S. N., Alves, M. A., and Pinho, F. T., 2014, “Viscoelastic Instabilities in Micro-Scale Flows,” Experimental Thermal and Fluid Science, 59, pp. 128–129. [CrossRef]
Gijsen, F. J. H., van de Vosse, F. N., and 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(6), pp. 601–608. [CrossRef] [PubMed]
Owens, R. G., 2006, “A New Microstructure-Based Constitutive Model for Human Blood,” J. Non-Newtonian Fluid Mech., 140(1–3), pp. 57–70. [CrossRef]
Moyers-Gonzalez, M., Owens, R. G., and Fang, J., 2008, “A Non-Homogeneous Constitutive Model for Human Blood. Part I. Model Derivation and Steady Flow,” J. Fluid Mech., 617, pp. 327–354. [CrossRef]
Moyers-Gonzalez, M., and Owens, R. G., 2008, “A Non-Homogeneous Constitutive Model for Human Blood. Part II. Asymptotic Solution for Large Péclet Numbers,” J. Non-Newtonian Fluid Mech., 155(3), pp. 146–160. [CrossRef]
Sforza, D. M., Putman, C. M., and Cebral, J. R., 2012, “Computational Fluid Dynamics in Brain Aneurysms,” Int. J. Numer. Methods Biomed. Eng., 28(6–7), pp. 801–808. [CrossRef]
Markwalder, T. M., Grolimund, P., Seiler, R. W., Roth, F., and Aaslid, R., 1984, “Dependency of Blood Flow Velocity in the Middle Cerebral Artery on End-Tidal Carbon Dioxide Partial Pressure- A Transcranial Ultrasound Doppler Study,” J. Cereb. Blood Flow Metab., 4(3), pp. 368–372. [CrossRef] [PubMed]
Vlachos, N. S., and Whitelaw, J. H., 1974, “The Measurement of Blood Velocity With Laser Anemometry,” Proceedings, Volume 1, No. A76-10426 01-35, Purdue University, West Lafayette, IN, pp. 521–540., In: International Workshop on Laser Velocimetry, 2nd, West Lafayette, Ind., March 27–29, 1974.
Lasheras, J. C., 2007, “The Biomechanics of Arterial Aneurysms,” Annu. Rev. Fluid Mech., 39(1), pp. 293–319. [CrossRef]
Sforza, D. M., Putman, C. M., and Cebral, J. R., 2009, “Hemodynamics of Cerebral Aneurysms,” Annu. Rev. Fluid Mech., 41, pp. 91–107. [CrossRef] [PubMed]
Withers, K., Carolan-Rees, G., and Dale, M., 2013, “PipelineTM Embolization Device for the Treatment of Complex Intracranial Aneurysms. A NICE Medical Technology Guidance,” Appl. Health Econ. Health Policy, 11, pp. 5–13. [CrossRef] [PubMed]
Foutrakis, G. N., Yonas, H., and Sclabassi, R. J., 1999, “Saccular Aneurysm Formation in Curved and Bifurcating Arteries,” Am. J. Neuroradiol., 20(7), pp. 1309–1317.
Massoud, T. F., Turjman, F., Ji, C., Viũela, F., Guglielmi, G., Gobin, Y. P., and Duckwiler, G. R., 1995, “Endovascular Treatment of Fusiform Aneurysms With Stents and Coils: Technical Feasibility in a Swine Model,” Am. J. Neuroradiol., 16(10), pp. 1953–1963.
Raghavan, M. L., Ma, B., and Harbaugh, R. E., 2005, “Quantified Aneurysm Shape and Rupture Risk,” J. Neurosurg., 102(2), pp. 355–362. [CrossRef] [PubMed]
Parlea, L., Fahrig, R., Holdsworth, D. W., and Lownie, S. P., 1999, “An Analysis of the Geometry of Saccular Intracranial Aneurysms,” Am. J. Neuroradiol., 20(6), pp. 1079–1089.
Ma, B., Harbaugh, R. B., and Raghavan, M. L., 2004, “Three-Dimensional Geometrical Characterization of Cerebral Aneurysms,” Ann. Biomed. Eng., 32(2), pp. 264–273. [CrossRef] [PubMed]
Lauric, A., Miller, E. L., Baharoglu, M. I., and Malek, A. M., 2011, “3D Shape Analysis of Intracranial Aneurysms Using the Writhe Number as a Discriminant for Rupture,” Ann. Biomed. Eng., 39(5), pp. 1457–1469. [CrossRef] [PubMed]
Hoh, B. L., Sistrom, C. L., Firment, C. S., Fautheree, G. L., Velat, G. J., Whiting, J. H., Reavey-Cantwell, J. F., and Lewis, S. B., 2007, “Bottleneck Factor and Height-Width Ratio: Association With Ruptured Aneurysms in Patients With Multiple Cerebral Aneurysms,” Neurosurgery, 61(4), pp. 716–723. [CrossRef] [PubMed]
Ujiie, H., Tachibana, H., Hiramatsu, O., Hazel, A. L., Matsumoto, T., Ogasawara, Y., Nakajima, H., Hori, T., Takakura, K., and Kajiya, F., 1999, “Effects of Size and Shape (Aspect Ratio) on the Hemodynamics of Saccular Aneurysms: A Possible Index for Surgical Treatment of Intracranial Aneurysms,” Neurosurgery, 45(1), pp. 119–130. [CrossRef] [PubMed]
Fuller, F. B., 1971, “The Writhing Number of a Space Curve,” Proc. Natl. Acad. Sci. U.S.A., 68(4), pp. 815–819. [CrossRef] [PubMed]
Tremmel, M., Dhar, S., Levy, E., Mocco, J., and Meng, H., 2009, “Influence of Intracranial Aneurysms-to-Parent Vessel Size Ratio on Hemodynamics and Implication for Rupture: Results From a Virtual Experimental Study,” Neurosurgery, 64(4), pp. 622–631. [CrossRef] [PubMed]
Ku, D. N., Giddens, D. P., Zarins, C. K., and Glagov, S., 1985, “Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation. Positive Correlation Between Plaque Location and Low and Oscillating Shear Stress,” Arterioscler., Thromb., Vasc. Biol., 5(3), pp. 293–302. [CrossRef]
Mantha, A., Karmonik, C., Benndorf, G., Strother, C., and Metcalfe, R., 2006, “Hemodynamics in a Cerebral Artery Before and After the Formation of an Aneurysm,” Am. J. Neuroradiol., 27(5), pp. 1113–1118.
Shimogonya, Y., Ishikawa, T., Imai, Y., Matsuki, N., and Yamaguchi, T., 2009, “Can Temporal Fluctuation in Spatial Wall Shear Stress Gradient Initiate a Cerebral Aneurysm? A Proposed Novel Hemodynamic Index, the Gradient Oscillatory Number (GON),” J. Biomech., 42(4), pp. 550–554. [CrossRef] [PubMed]
Jou, L.-D., and Mawad, M. E., 2011, “Timing and Size of Flow Impingement in a Giant Intracranial Aneurysm at the Internal Carotid Artery,” Med. Biol. Eng. Comput., 49(8), pp. 891–899. [CrossRef] [PubMed]
Zuleger, D. I., Poulikakos, D., Valavanis, A., and Kollias, S. S., 2010, “Combining Magnetic Resonance Measurements With Numerical Simulations – Extracting Blood Flow Physiology Information Relevant to the Investigation of Intracranial Aneurysms in the Circle of Willis,” Int. J. Heat Fluid Flow, 31(6), pp. 1032–1039. [CrossRef]
Kojima, M., Irie, K., Keda, S., Fukuda, T., Arai, F., Hirose, Y., and Negoro, M., 2012, “The Hemodynamic Study for Growth Factor Evaluation of Rupture Cerebral Aneurysm Followed up for Five Years,” J. Biomed. Sci. Eng., 5(12A), pp. 884–891. [CrossRef]
Irie, K., Anzai, H., Kojima, M., Honjo, N., Ohta, M., Hirose, Y., and Negoro, M., 2012, “Computational Fluid Dynamic Analysis Following Recurrence of Cerebral Aneurysm After Coil Embolization,” Asian J. Neurosurg., 7(3), pp. 109–115. [CrossRef] [PubMed]
Sforza, D. M., Putman, C. M., Tateshima, S., Viñuela, F., and Cebral, J. R., 2012, “Effects of Perianeurysmal Environment During the Growth of Cerebral Aneurysms: A Case Study,” Am. J. Neuroradiol., 33(6), pp. 1115–1120. [CrossRef]
Tanoue, T., Tateshima, S., Villablanca, J. P., Viñuela, F., and Tanishita, K., 2011, “Wall Shear Stress Distribution Inside Growing Cerebral Aneurysm,” Am. J. Neuroradiol., 32(9), pp. 1732–1737. [CrossRef]
Boussel, L., Rayz, V., McCulloch, C., Martin, A., Acevedo-Bolton, G., Lawton, M., Higashida, R., Smith, W. S., Young, W. L., and Saloner, D., 2008, “Aneurysm Growth Occurs at Region of Low Wall Shear Stress: Patient-Specific Correlation of Hemodynamics and Growth in a Longitudinal Study,” Stroke, 39(11), pp. 2997–3002. [CrossRef] [PubMed]
Jou, L.-D., Wong, G., Dispensa, B., Lawton, M. T., Higashida, R. T., Young, W. L., and Saloner, D., 2005, “Correlation Between Lumenal Geometry Changes and Hemodynamics in Fusiform Intracranial Aneurysms,” Am. J. Neuroradiol., 26(9), pp. 2357–2363.
Rayz, V. L., Boussel, L., Ge, L., Leach, J. R., Martin, A. J., Lawton, M. T., McCulloch, C., and Saloner, D., 2010, “Flow Residence Time and Regions of Intraluminal Thrombus Deposition in Intracranial Aneurysms,” Ann. Biomed. Eng., 38(10), pp. 3058–3069. [CrossRef] [PubMed]
Valant, A. Z., Ziberna, L., Papaharilaou, Y., Anayiotos, A., and Georgiou, G. C., 2011, “The Influence of Temperature on Rheological Properties of Blood Mixtures With Different Volume Expanders—Implications in Numerical Arterial Hemodynamics Simulations,” Rheol. Acta, 50(4), pp. 389–402. [CrossRef]
Caro, C. G., Pedley, T. J., Schroter, R. C., and Seed, W. A., 2012, The Mechanics of the Circulation, Cambridge University, New York. [CrossRef]
Vlastos, G., Lerche, D., Koch, B., Samba, O., and Pohl, M., 1997, “The Effect of Parallel Combined Steady and Oscillatory Shear Flows on Blood and Polymer Solutions,” Rheol. Acta, 36(2), pp. 160–172. [CrossRef]
Sousa, P. C., Carneiro, J., Vaz, R., Cerejo, A., Pinho, F. T., Alves, M. A., and Oliveira, M. S. N., 2013, “Shear Viscosity and Nonlinear Behavior of Whole Blood Under Large Amplitude Oscillatory Shear,” Biorheology, 50(5–6), pp. 269–282. [PubMed]
Boyd, J., Buick, J. M., and Green, S., 2007, “Analysis of the Casson and Carreau-Yasuda Non-Newtonian Blood Models in Steady and Oscillatory Flows Using the Lattice Boltzmann Method,” Phys. Fluids, 19(9), p. 093103. [CrossRef]
Razavi, A., Shirani, E., and Sadeghi, M. R., 2011, “Numerical Simulation of Blood Pulsatile Flow in a Stenosed Carotid Artery Using Different Rheological Models,” J. Biomech., 44(11), pp. 2021–2030. [CrossRef] [PubMed]
Molla, M. M., and Paul, M. C., 2012, “LES of Non-Newtonian Physiological Blood Flow in a Model of Arterial Stenosis,” Med. Eng. Phys., 34(8), pp. 1079–1087. [CrossRef] [PubMed]
Valencia, A., Morales, H., Rivera, R., Bravo, E., and Galvez, M., 2008, “Blood Flow Dynamics in Patient-Specific Cerebral Aneurysm Models: The Relationship Between Wall Shear Stress and Aneurysm Area Index,” Med. Eng. Phys., 30(3), pp. 329–340. [CrossRef] [PubMed]
Amornsamankul, S., Wiwatanapataphee, B., Wu, Y. H., and Lenbury, Y., 2005, “Effect of Non-Newtonian Behavior of Blood on Pulsatile Flows in Stenotic Arteries,” Int. J. Biol. Life Sci., 1, pp. 42–46.
Anand, M., and Rajagopal, K. R., 2004, “A Shear-Thinning Viscoelastic Fluid Model for Describing the Flow of Blood,” Int. J. Cardiovasc. Med. Sci., 4, pp. 59–68.
Robertson, A. M., Sequeira, A., and Owens, R. G., 2009, “Rheological Models for Blood,” Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System, L.Formaggia, A.Quarteroni, A.Veneziani, eds., Springer-Verlag, Milano, Italy. [CrossRef]
Bodnár, T., Sequeira, A., and Pirkl, L., 2009, “Numerical Simulations of Blood Flow in a Stenosed Vessel Under Different Flow Rates Using a Generalized Oldroyd-B Model,” International Conference on Numerical Analysis and Applied Mathematics, Rethymno, Crete, Sept. 18–22, Vol. 2, pp. 645–648. [CrossRef]
Yilmaz, F., and Gundogdu, M. Y., 2008, “A Critical Review on Blood Flow in Large Arteries; Relevance to Blood Rheology, Viscosity Models, and Physiologic Conditions,” Korea-Australia Rheol. J., 20, pp. 197–211.
Stuart, J., and Kenny, M. W., 1980, “Blood Rheology,” J. Clin. Pathol., 33(5), pp. 417–429. [CrossRef] [PubMed]
Antonova, N., 2012, “On Some Mathematical Models in Hemorheology,” Biotechnol. Biotechnol. Equip., 26(5), pp. 3286–3291. [CrossRef]
Giesekus, H., 1982, “A Simple Constitutive Equation for Polymer Fluids Based on the Concept of Deformation-Dependent Tensorial Mobility,” J. Non-Newtonain Fluid Mech., 11(1–2), pp. 69–109. [CrossRef]
Phan-Thien, N., and Tanner, R. I., 1977, “A New Constitutive Equation Derived From Network Theory,” J. Non-Newtonain Fluid Mech., 2(4), pp. 353–365. [CrossRef]
Bureau, M., Healy, J. C., Bourgoin, D., and Joly, M., 1980, “Rheological Hysteresis of Blood at Low Shear Rate,” Biorheology, 17(1–2), pp. 191–203. [PubMed]
Oldroyd, J. G., 1950, “On the Formulation of Rheological Equation of State,” Proc. R. Soc. London, Ser. A., 200(1063), pp. 523–541. [CrossRef]
Javadzadegan, J., Esmaeili, M., Majidi, S., and Fakhimghanbarzadeh, B., 2009, “Pulsatile Flow of Viscous and Viscoelastic Fluids in Constricted Tubes,” J. Mech. Sci. Technol., 23(9), pp. 2456–2467. [CrossRef]
Yeleswarapu, K. K., Kameneva, M. V., Rajagopal, K. R., and Antaki, J. F., 1998, “The Flow of Blood in Tubes: Theory and Experiment,” Mech. Res. Commun., 25(3), pp. 257–262. [CrossRef]
Ku, D. N., 1997, “Blood Flow in Arteries,” Annu. Rev. Fluid Mech., 29(1), pp. 399–434. [CrossRef]
Elad, D., and Einav, S., 2004, “Physical and Flow Properties of Blood. Source,” Standard Handbook of Biomedical Engineering and Design, pp. 1–25.
Xiao, N., Humphrey, J. D., and Figueroa, C. A., 2013, “Multi-Scale Computational Model of Three-Dimensional Hemodynamics Within a Deformable Full-Body Arterial Network,” J. Comput. Phys., 244, pp. 22–40. [CrossRef] [PubMed]
Smith, N. P., Pullan, A. J., and Hunter, P. J., 2002, “An Anatomically Based Model of Transient Coronary Blood Flow in the Heart,” SIAM J. Appl. Math., 62(3), pp. 990–1018. [CrossRef]
Womersley, J. R., 1955, “Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries When the Pressure Gradient is Known,” J. Physiol., 127(2), pp. 553–563. [CrossRef] [PubMed]
Fung, Y., 1996, Biomechanics Circulation, Springer, Berlin, Germany.
Banerjee, M. K., Ganguly, R., and Datta, A., 2012, “Effect of Pulsatile Flow Waveform and Womersley Number on the Flow in Stenosed Arterial Geometry,” ISRN Biomath., 2012, p. 853056. [CrossRef]
Campbell, I. C., Ries, J., Dhawan, S. S., Quyyumi, A. A., Taylor, W. R., and Oshinski, J. N., 2012, “Effect of Inlet Velocity Profiles on Patient-Specific Computational Fluid Dynamics Simulations of the Carotid Bifurcation,” ASME J. Biomech. Eng., 134(5), p. 051001. [CrossRef]
Grinberg, L., and Karniadakis, G., 2008, “Outflow Boundary Conditions for Arterial Networks With Multiple Outlets,” Ann. Biomed. Eng., 36(9), pp. 1496–1514. [CrossRef] [PubMed]
Ramalho, S., Moura, A., Gambaruto, A. M., and Sequeira, A., 2012, “Sensitivity to Outflow Boundary Conditions and Level of Geometry Description for a Cerebral Aneurysm,” Int. J. Numer. Methods Biomed. Eng., 28(6–7), pp. 697–713. [CrossRef]
Papanastasiou, T. C., Malamataris, N., and Ellwood, K., 1992, “A New Outflow Boundary Condition,” Int. J. Numer. Methods Fluids, 14(5), pp. 587–608. [CrossRef]
Malamataris, N. T., and Papanastasiou, T. C., 1991, “Unsteady Free Surface Flows on Truncated Domains,” Ind. Eng. Chem. Res., 30(9), pp. 2211–2219. [CrossRef]
Griffiths, D. F., 1997, “The ‘No Boundary Condition’ Outflow Boundary Condition,” Int. J. Numer. Methods Fluids, 24(4), pp. 393–411. [CrossRef]
Renardy, M., 1997, “Imposing No Boundary Condition at Outflow: Why Does It Work?,” Int. J. Numer. Methods Fluids, 24(4), pp. 413–417. [CrossRef]
Park, S. J., and Lee, S. J., 1999, “On the Use of the Open Boundary Condition Method in the Numerical Simulation of Nonisothermal Viscoelastic Flow,” J. Non-Newtonian Fluid Mech., 87(2–3), pp. 197–214. [CrossRef]
Moon, J. Y., Suh, D. C., Lee, Y. S., Kim, Y. W., and Lee, J. S., 2014, “Considerations of Blood Properties, Outlet Boundary Conditions and Energy Loss Approaches in Computational Fluid Dynamics Modeling,” Neurointervention, 9(1), pp. 1–8. [CrossRef] [PubMed]
Vignon-Clementel, I. E., Figueroa, C. A., Jansen, K. E., and Taylor, C. A., 2006, “Outflow Boundary Conditions for Three-Dimensional Finite Element Modeling of Blood Flow and Pressure in Arteries,” Comput. Methods Appl. Mech. Eng., 195(29–32), pp. 3776–3796. [CrossRef]
Vignon, I. E., and Taylor, C. A., 2004, “Outflow Boundary Conditions for One-Dimensional Finite Element Modeling of Blood Flow and Pressure Waves in Arteries,” Wave Motion, 39(4), pp. 361–374. [CrossRef]
Figueroa, C. A., Vignon-Clementel, I. E., Jansen, K. E., Hughes, T. J. R., and Taylor, C. A., 2006, “A Coupled Momentum Method for Modeling Blood Flow in Three-Dimensional Deformable Arteries,” Comput. Methods Appl. Mech. Eng., 195(41–43), pp. 5685–5706. [CrossRef]
Westerhof, N., Bosman, F., DeVries, C. J., and Noordergraaf, A., 1969, “Analogue Studies of the Human Systemic Arterial Tree,” J. Biomech., 2(2), pp. 121–143. [CrossRef] [PubMed]
Olufsen, M. S., and Nadim, A., 2004, “On Deriving Lumped Models for Blood Flow and Pressure in the Systemic Arteries,” Math. Biosci. Eng., 1(1), pp. 61–80. [CrossRef] [PubMed]
Vignon-Clementel, I. E., Figueroa, C. A., Jansen, K. E., and Taylor, C. A., 2010, “Outflow Boundary Conditions for 3D Simulations of Non-Periodic Blood Flow and Pressure Fields in Deformable Arteries,” Comput. Methods Biomech. Biomed. Eng., 13(5), pp. 625–640. [CrossRef]
Esmaily-Moghadam, M., Vignon-Clementel, I. E., Figliola, R., and Marsden, A. L., f. t. M. O. C. H. A. M. I., 2013, “A Modular Numerical Method for Implicit 0D/3D Coupling in Cardiovascular Finite Element Simulations,” J. Comput. Phys., 244, pp. 63–79. [CrossRef]
O'Rourke, M. F., Staessen, J. A., Vlachopoulos, C., Duprez, D., and Plante, G. E., 2002, “Clinical Applications of Arterial Stiffness; Definitions and Reference Values,” Am. J. Hypertens., 15(5), pp. 426–444. [CrossRef] [PubMed]
Couade, M., Pernot, M., Prada, C., Messas, E., Emmerich, J., Bruneval, P., Criton, A., Fink, M., and Tanter, M., 2010, “Quantitative Assessment of Arterial Wall Biomechanical Properties Using Shear Wave Imaging,” Ultrasound Med. Biol., 36(10), pp. 1662–1676. [CrossRef] [PubMed]
Deng, S. X., Tomioka, J., Debes, J. C., and Fung, Y. C., 1994, “New Experiments on Shear Modulus of Elasticity of Arteries,” Am. J. Physiol. Heart Circ. Physiol., 266(1 Pt 2), pp. H1–H10.
Balzani, D., Brinkhues, S., and Holzapfel, G. A., 2012, “Constitutive Framework for the Modeling of Damage in Collagenous Soft Tissues With Application to Arterial Walls,” Comput. Methods Appl. Mech. Eng., 213–216, pp. 139–151. [CrossRef]
Tezduyar, T. E., and Sathe, S., 2007, “Modeling of Fluid-Structure Interactions With Space-Time Finite Elements: Solution Techniques,” Int. J. Numer. Methods Fluids, 54(6–8), pp. 855–900. [CrossRef]
Tezduyar, T. E., Sathe, S., Schwaab, M., and Conklin, B. S., 2008, “Arterial Fluid Mechanics Modeling With the Stabilized Space-Time Fluid-Structure Interaction Technique,” Int. J. Numer. Methods Fluids, 57(5), pp. 601–629. [CrossRef]
Fung, Y., 1993, Biomechanics: Mechanical Properties of Living Tissues, 2nd ed., Springer, Berlin.
Mooney, M., 1940, “A Theory of Large Elastic Deformation,” J. Appl. Phys., 11(9), pp. 582–592. [CrossRef]
Rivlin, R. S., 1948, “Large Elastic Deformations of Isotropic Materials. IV. Further Developments of the General Theory,” Philos. Trans. R. Soc. London, Ser. A, 241(835), pp. 379–397. [CrossRef]
Torii, R., Oshima, M., Kobayashi, T., Takagi, K., and Tezduyar, T. E., 2008, “Fluid-Structure Interaction Modeling of a Patient-Specific Cerebral Aneurysm: Influence of Structural Modeling,” Comput. Mech., 43(1), pp. 151–159. [CrossRef]
Hou, G., Wang, J., and Layton, A., 2012, “Numerical Methods for Fluid-Structure Interaction—A Review,” Commun. Comput. Phys., 12(2), pp. 337–377. [CrossRef]
Valencia, A., Burdiles, P., Ignat, M., Mura, J., Bravo, E., Rivera, R., and Sordo, J., 2013, “Fluid Structural Analysis of Human Cerebral Aneurysm Using Their Own Wall Mechanical Properties,” Comput. Math. Method Med., 2013(5), p. 293128. [CrossRef]
Lee, C. J., Zhang, Y., Takao, H., Murayama, Y., and Qian, Y., 2013, “A Fluid-Structure Interaction Study Using Patient-Specific Ruptured and Unruptured Aneurysm: The Effect of Aneurysm Morphology, Hypertension and Elasticity,” J. Biomech., 46(14), pp. 2402–2410. [CrossRef] [PubMed]
Valencia, A., and Solis, F., 2006, “Blood Flow Dynamics and Arterial Wall Interaction in a Saccular Aneurysm Model of the Basilar Artery,” Comput. Struct., 84(21), pp. 1326–1337. [CrossRef]
Degroote, J., Bathe, K.-J., and Vierendeels, J., 2009, “Performance of a New Partitioned Procedure Versus a Monolithic Procedure in Fluid-Structure Interaction,” Comput. Struct., 87(11–12), pp. 793–801. [CrossRef]
Young, Y. L., Chae, E. J., and Akcabay, D. T., 2012, “Hybrid Algorithm for Modeling of Fluid-Structure Interaction in Incompressible, Viscous Flows,” Acta Mech. Sin., 28(4), pp. 1030–1041. [CrossRef]
Peskin, C. S., 2002, “The Immersed Boundary Method,” Acta Numer., 11, pp. 479–517. [CrossRef]
Jendoubi, A., Yakoubi, D., Fortin, A., and Tibirna, C., 2014, “An Immersed Boundary Method for Fluid Flows Around Rigid Objects,” Int. J. Numer. Methods Fluids, 75(1), pp. 63–80. [CrossRef]
Mittal, R., and Iaccarino, G., 2005, “Immersed Boundary Methods,” Annu. Rev. Fluid Mech., 37(1), pp. 239–261. [CrossRef]
Tezduyar, T. E., Sathe, S., Cragin, T., Nanna, B., Conklin, B. S., Pausewang, J., and Schwaab, M., 2007, “Modeling of Fluid-Structure Interactions With Space-Time Finite Elements: Arterial Fluid Mechanics,” Int. J. Numer. Methpds Fluids, 54(6–8), pp. 901–922. [CrossRef]
Takizawa, K., Moorman, C., Wright, S., Purdue, J., Mcphail, T., Chen, P. R., Warren, J., and Tezduyar, T. E., 2011, “Patient-Specific Arterial Fluid-Structure Interaction Modeling of Cerebral Aneurysms,” Int. J. Numer. Methods Fluids, 65(1–3), pp. 308–323. [CrossRef]
Tezduyar, T. E., T. K., Brummer, T., and Chen, P. R., 2011, “Space-Time Fluid-Structure Interaction Modeling of Patient-Specific Cerebral Aneurysms,” Int. J. Numer. Methods Biomed. Eng., 27(11), pp. 1665–1710. [CrossRef]
Mittal, S., and Tezduyar, T. E., 1995, “Parallel Finite Element Simulation of 3D Incompressible Flows-Fluid-Structure Interactions,” Int. J. Numer. Methods Fluids, 21(10), pp. 933–953. [CrossRef]
Neal, M. L., and Kerckhoffs, R., 2010, “Current Progress in Patient-Specific Modeling,” Briefings Bioinf., 11(1), pp. 111–126. [CrossRef]
Cebral, J. R., Castro, M. A., Burgess, J. E., Pergolizzi, R. S., Sheridan, M. J., and Putman, C. M., 2005, “Characterization of Cerebral Aneurysms for Assessing Risk of Rupture by Using Patient-Specific Computational Hemodynamics Models,” Am. J. Neuroradiol., 26(10), pp. 2550–2559.
Karmonik, C., Klucznik, R., and Benndorf, G., 2008, “Comparison of Velocity Patterns in an AComA Aneurysm Measured With 2D Phase Contrast MRI and Simulated With CFD,” Technol. Health Care, 16(2), pp. 119–128. [PubMed]
Ford, M. D., Nikolov, H. N., Milner, J. S., Lownie, S. P., DeMont, E. M., Kalata, W., Loth, F., Holdsworth, D. W., and Steinman, D. A., 2008, “PIV-Measured Versus CFD-Predicted Flow Dynamics in Anatomically Realistic Cerebral Aneurysm Models,” ASME J. Biomech. Eng., 130(2), p. 021015. [CrossRef]
Potočnik, B., Heric, D., Zazula, D., Cigale, B., and Bernad, D., 2005, “Construction of Patient Specific Virtual Models of Medical Phenomena,” Informatica, 29, pp. 209–218.
Augsburger, L., Reymond, P., Fonck, E., Kulcsar, Z., Farhat, M., Ohta, M., Stergiopulos, N., and Rüfenacht, D. A., 2009, “Methodologies to Assess Blood Flow in Cerebral Aneurysms: Current State of Research and Perspectives,” J. Neuroradiol., 36(5), pp. 270–277. [CrossRef] [PubMed]
Hollnagel, D. I., Summers, P. E., Poulikakos, D., and Kollias, S. S., 2009, “Comparative Velocity Investigations in Cerebral Arteries and Aneurysms: 3D Phase-Contrast MR Angiography, Laser Doppler Velocimetry and Computational Fluid Dynamics,” NMR Biomed., 22(8), pp. 795–808. [CrossRef] [PubMed]
Jeong, W., and Rhee, K., 2012, “Hemodynamics of Cerebral Aneurysms: Computational Analyses of Aneurysm Progress and Treatment,” Comput. Math. Methods Med., 2012(4), pp. 1–11. [CrossRef]
Castro, M. A., Putman, C. M., and Cebral, J. R., 2006, “Patient-Specific Computational Modeling of Cerebral Aneurysms With Multiple Avenues of Flow From 3D Rotational Angiography Images,” Acad. Radiol., 13(7), pp. 811–821. [CrossRef] [PubMed]
Castro, M. A., Putman, C. M., and Cebral, J. R., 2006, “Computational Fluid Dynamics Modeling of Intracranial Aneurysms: Effects of Parent Artery Segmentation on Intra-Aneurysmal Hemodynamics,” Am. J. Neuroradiol., 27(8), pp. 1703–1709.
Marzo, A., Singh, P., Reymond, P., Stergiopulos, N., Patel, U., and Hose, R., 2009, “Influence of Inlet Boundary Conditions on the Local Haemodynamics of Intracranial Aneurysms,” Comput. Methods Biomech. Biomed. Eng., 12(4), pp. 431–444. [CrossRef]
Marzo, A., Singh, P., Larrabide, I., Radaelli, A., Coley, S., Gwilliam, M., Wilkinson, I. D., Lawford, P., Reymond, P., Patel, U., Frangi, A., and Hose, D. R., 2011, “Computational Hemodynamics in Cerebral Aneurysms: The Effects of Modeled Versus Measured Boundary Conditions,” Ann. Biomed. Eng., 39(2), pp. 884–896. [CrossRef] [PubMed]
Shojima, M., Oshima, M., Takagi, K., Torii, R., Hayakawa, M., Katada, K., Morita, A., and Kirino, T., 2004, “Magnitude and Role of Wall Shear Stress on Cerebral Aneurysm: Computational Fluid Dynamic Study of 20 Middle Cerebral Artery Aneurysms,” Stroke, 35(11), pp. 2500–2505. [CrossRef] [PubMed]
Bazilevs, Y., Hsu, M.-C., Zhang, Y., Wang, W., Liang, X., Kvamsdal, T., Brekken, R., and Isaksen, J. G., 2010, “A Fully-Coupled Fluid-Structure Interaction Simulation of Cerebral Aneurysms,” Comput. Mech., 46(1), pp. 3–16. [CrossRef]
Raschi, M., Mut, F., Byrne, G., Putman, C. M., Tateshima, S., Viñuela, F., Tanoue, T., and Tanishita, K., 2012, “CFD and PIV Analysis of Hemodynamics in a Growing Intracranial Aneurysm,” Int. J. Numer. Methods Biomed. Eng., 28(2), pp. 214–228. [CrossRef]
Miura, Y., Ishida, F., Umeda, Y., Tanemura, H., Suzuki, H., Matsushima, S., Shimosaka, S., and Taki, W., 2013, “Low Wall Shear Stress is Independently Associated With the Rupture Status of Middle Cerebral Artery Aneurysms,” Stroke, 44, pp. 519–521. [CrossRef] [PubMed]
Omodaka, S., Sugiyama, S.-I., Inoue, T., Funamoto, K., Fujimura, M., Shimizu, H., Hayase, T., Takahashi, A., and Tominaga, T., 2012, “Local Hemodynamics at the Rupture Point of Cerebral Aneurysms Determined by Computational Fluid Dynamics Analysis,” Cerebrovasc. Dis. (Basel, Switzerland), 34(2), pp. 121–129. [CrossRef]
Fisher, C., and Rossmann, J. S., 2009, “Effect of Non-Newtonian Behavior on the Hemodynamics of Cerebral Aneurysm,” ASME J. Biomech. Eng., 131(9), p. 091004. [CrossRef]
Perktold, K., Peter, R., and Resch, M., 1989, “Pulsatile Non-Newtonian Blood Flow Simulation Through a Bifurcation With an Aneurysm,” Biorheology, 26, pp. 1011–1030. [PubMed]
Valencia, A., Zarate, A., Galvez, M., and Badilla, L., 2006, “Non-Newtonian Blood Flow Dynamics in a Right Internal Carotid Artery With a Saccular Aneurysm,” Int. J. Numer. Methods Fluids, 50(6), pp. 751–764. [CrossRef]
Wang, S. Z., Chen, J. L., Ding, G. H., Lu, G., and Zhang, X. L., 2010, “Non-Newtonian Computational Hemodynamics in Two Patient-Specific Cerebral Aneurysms With Daughter Saccules,” J. Hydrodyn., 22(5), pp. 639–646. [CrossRef]
Bernabeu, M. O., Nash, R. W., Groen, D., Carver, H. B., Hetherington, J., Krüger, T., and Coveney, P. T., 2013, “Impact of Blood Rheology on Wall Shear Stress in a Model of the Middle Cerebral Artery,” Interface Focus, 3(3), p. 20120094. [CrossRef] [PubMed]
Valencia, A., Guzmán, A. M., Finol, E. A., and Amon, C. H., 2006, “Blood Flow Dynamics in Saccular Aneurysm Models of the Basilar Artery,” ASME J. Biomech. Eng., 128(4), pp. 516–526. [CrossRef]
Evju, O., Valen-Sendstad, K., and Mardal, K. A., 2013, “A Study of Wall Shear Stress in 12 Aneurysms With Respect to Different Viscosity Models and Flow Conditions,” J. Biomech., 46(16), pp. 2802–2808. [CrossRef] [PubMed]
Dimakopoulos, Y., Syrakos, A., Georgios, G. C., Papadopoulos, K., and Tsamopoulos, J., 2014, “Effect of RBC Migration Phenomena on the Hemodynamics in Stenotic Microvessels Under Pulsating Flow Conditions,” Book of Abstracts of the 9th Annual European Rheology Conference, Karlsruhe, Germany, Apr. 8–11, Vol. 75, p. 58.
Steinman, D. A., Hoi, Y., Fahy, P., Morris, L., Walsh, M. T., Aristokleous, N., Anayiotos, A. S., Papaharilaou, Y., Arzani, A., Shadden, S. C., Berg, P., Janiga, G., Bols, J., Segers, P., Bressloff, N. W., Cibis, M., Gijsen, F. H., Cito, S., Pallarés, J., Browne, L. D., Costelloe, J. A., Lynch, A. G., Degroote, J., Vierendeels, J., Fu, W., Qiao, A., Hodis, S., Kallmes, D. F., Kalsi, H., Long, Q., Kheyfets, V. O., Finol, E. A., Kono, K., Malek, A. M., Lauric, A., Menon, P. G., Pekkan, K., Moghadam, M. E., Marsden, A. L., Oshima, M., Katagiri, K., Peiffer, V., Mohamied, Y., Sherwin, S. J., Schaller, J., Goubergrits, L., Usera, G., Mendina, M., Valen-Sendstad, K., Habets, D. F., Xiang, J., Meng, H., Yu, Y., Karniadakis, G. E., Shaffer, N., and Loth, F., 2013, “Variability of Computational Fluid Dynamics Solutions for Pressure and Flow in a Giant Aneurysm: The ASME 2012 Summer Bioengineering Conference CFD Challenge,” ASME J. Biomech. Eng., 135(2), p. 021016. [CrossRef]
Valen-Sendstad, K., and Steinman, D. A., 2014, “Mind the Gap: Impact of Computational Fluid Dynamics Solution Strategy on Prediction of Intracranial Aneurysm Hemodynamics and Rupture Status Indicators,” Am. J. Neuroradiol., 35(3), pp. 544–545. [CrossRef]
Janela, J., Moura, A., and Sequeira, A., 2010, “Towards a Geometrical Multiscale Approach to Non-Newtonian Blood Flow Simulations,” Advances in Mathematical Fluid Mechanics, R. Rannacher, A. Sequeira (eds) Springer, Berlin, pp. 295–09.
Forsyth, A. M., Wan, J., Owrutsky, P. D., Abkarian, M., and Stone, H. A., 2011, “Multiscale Approach to Link Red Blood Cell Dynamics, Shear Viscosity, and ATP Release,” Proc. Natl. Acad. Sci. U.S.A, 108, pp. 10986–10991. [CrossRef] [PubMed]
Xu, Z., Chen, N., Shadden, S. C., Marsden, J. E., Kamocka, M. M., Rosen, E. D., and Alber, M., 2009, “Study of Blood Flow Impact on Growth of Thrombi Using a Multiscale Model,” Soft Matter, 5, pp. 769–779. [CrossRef]
Grinberg, L., Fedosov, D. A., and Karniadakis, G. E., 2013, “Parallel Multiscale Simulations of a Brain Aneurysm,” J. Comput. Phys., 244, pp. 131–147. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Shapes of aneurysms: (a) saccular aneurysm and (b) fusiform aneurysm. (Reprinted with permission from Withers, K., et al. [28]. Copyright 2013 2.5 CC-BY-NC).

Grahic Jump Location
Fig. 2

Representation of the aneurysms dimensions

Grahic Jump Location
Fig. 3

Schematic representation of the main processes in handling computational hemodynamics

Grahic Jump Location
Fig. 4

Shear rheology of whole blood measured experimentally. (a) Steady shear viscosity (η) curve [51]. (b) Storage (solid circles) and loss (open circles) moduli (adapted from Campo-Deano et al. [16]).

Grahic Jump Location
Fig. 5

Average viscosity of whole blood measured experimentally by Valant et al. [51], compared to the different constitutive models described in Table 2. The experimental viscosity values are an average over blood samples of Hct ranging between 36% and 49%. The error bars correspond to the standard deviation of the averaged viscosity values.

Grahic Jump Location
Fig. 6

Pressure and flow waves at multiple sites in the full body model. (Reprinted with permission from Xiao, et al. [74]. Copyright 2013 Elsevier).

Grahic Jump Location
Fig. 7

Cyclic uniaxial tension tests of the media of a human carotid artery in circumferential (1) and axial (2) directions. (Reprinted with permission from Balzani, D., et al. [98] Copyright 2012 Elsevier).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In