Abstract
Disease in human physiology is often related to cardiovascular mechanics. Impressively, strokes are one of the leading causes of death in developed countries, and they might occur as a result of an aneurysm rupture, which is a sudden event in the majority of cases. On the basis of several autopsy and angiography series, it is estimated that 0.4–6 % of the general population harbors one or more intracranial aneurysms, and on average the incidence of an aneurysmal rupture is of 10 per 100,000 population per year, with tendency to increase in patients with multiple aneurysms [14, 20].
Keywords
- Outflow Boundary Conditions
- WSS Gradient (WSSG)
- Clip Geometry
- Viscosity Function
- Idealized Geometries
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Anand, M., Rajagopal, K.R.: A shear-thinning viscoelastic fluid model for describing the flow of blood. Int. J. Cardiovasc. Med. Sci. 4(2), 59–68 (2004)
Antiga, L., Piccinelli, M., Botti, L., Ene-Iordache, B., Remuzzi, A., Steinman, D.A.: An image-based modeling framework for patient-specific computational hemodynamics. Med. Biol. Eng. Comput. 46(11), 1097–1112 (2008)
Balossino, R., Pennati, G., Migliavacca, F., Formaggia, L., Veneziani, A., Tuveri, M., Dubini, G.: Influence of boundary conditions on fluid dynamics in models of the cardiovascular system: A multiscale approach applied to the carotid bifurcation. Comput. Meth. Biomech. Biomed. Eng. 12(1) (2009)
Cebral, J.R., Castro, M.A., Appanaboyina, S., Putman, C.M., Millan, D., Frangi, A.F.: Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: Technique and sensitivity. IEEE Trans.Med. Imag. 24(4), 457–467 (2005)
Cebral, J.R., Castro, M.A., Putman, C.M., Alperin, N.: Flow–area relationship in internal carotid and vertebral arteries. Physiol. Meas. 29, 585 (2008)
Formaggia, L., Veneziani, A.: Reduced and multiscale models for the human cardiovascular system. Lecture Notes VKI Lecture Series 7 (2003)
Formaggia, L., Moura, A., Nobile, F.: On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. Math. Model. Numer. Anal. 41(4), 743–769 (2007)
Gambaruto, A.M., Peiró, J., Doorly, D.J., Radaelli, A.G.: Reconstruction of shape and its effect on flow in arterial conduits. Int. J. Numer. Meth. Fluid. 57(5), 495–517 (2008)
Gambaruto, A.M., Janela, J., Moura, A., Sequeira, A.: Sensitivity of hemodynamics in patient specific cerebral aneurysms to vascular geometry and blood rheology. Math. Biosci. Eng. 8(2), 409–423 (2011)
Goljan, E.F.: Rapid Review Pathology. Mosby/Elsevier, Philadelphia (2010)
Hassan, T., Timofeev, E.V., Saito, T., Shimizu, H., Ezura, M., Matsumoto, Y., Takayama, K., Tominaga, T., Takahashi, A.: A proposed parent vessel geometry based categorization of saccular intracranial aneurysms: Computational flow dynamics analysis of the risk factors for lesion rupture. J. Neurosurg. Pediatr. 103(4) (2005)
Heywood, J.G., Rannacher, R., Turek, S.: Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluid. 22(5), 325–352 (1996)
Janela, J., Moura, A., Sequeira, A.: Absorbing boundary conditions for a 3D non-Newtonian fluid–structure interaction model for blood flow in arteries. Int. J. Eng. Sci. 48(11), 1332–1349 (2010)
Krex, D., Schackert, H.K., Schackert, G.: Genesis of cerebral aneurysms–an update. Acta Neurochir. 143(5), 429–449 (2001)
Ku, D.N.: Blood flow in arteries. Annu. Rev. Fluid Mech. 29(1), 399–434 (1997)
Moura, A.: The geometrical multiscale modelling of the cardiovascular system: Coupling 3D and 1D FSI models. PhD thesis, Politecnico di Milano (2007)
Nunes, D., Ramalho, S.: 1D hyperbolic models for blood flow in arteries. Internal Report, CEMAT (2009)
Quarteroni, A.M., Valli, A.: Numerical Approximation of Partial Differential Equations. Springer, Berlin (2008)
Ramalho, S., Moura, A., Gambaruto, A.M., Sequeira, A.: Sensitivity to outflow boundary conditions and level of geometry description for a cerebral aneurysm. Int. J. Numer. Meth. Biomed. Eng. 28(6-7), 697–713 (2012)
Rinkel, G.J.E., Djibuti, M., Algra, A., Van Gijn, J.: Prevalence and risk of rupture of intracranial aneurysms: A systematic review. Stroke 29(1), 251 (1998)
Robertson, A.M.: Review of Relevant Continuum Mechanics. In: Galdi, G.P., Rannacher, R., Robertson, A.M., Turek, S. (eds.) Hemodynamical Flows: Modeling, Analysis and Simulation, pp. 1–62. Birkhäuser, Boston (2008)
Robertson, A.M., Sequeira, A., Kameneva, M.V.: Hemorheology. In Galdi, G.P., Rannacher, R., Robertson, A.M., Turek, S., editors, Hemodynamical Flows: Modeling, Analysis and Simulation, pages 63–120. Birkhäuser, Boston (2008)
Sazonov, I., Yeo, S.Y., Bevan, R.L.T., Xie, X., van Loon, R., Nithiarasu, P.: Modelling pipeline for subject-specific arterial blood flow - a review. Int. J. Numer. Meth. Biomed. Eng. (2011) DOI: 10.1002/cnm.1446.
Sequeira, A., Janela, J.: An overview of some mathematical models of blood rheology. In: Pereira, M.S. (ed.) A Portrait of Research at the Technical University of Lisbon, pp. 65–87. Springer, Berlin (2007)
Sequeira, A., Moura, A., Janela, J.: Towards a geometrical multiscale approach to non-Newtonian blood flow simulations. In: Sequeira, A., Rannacher, R. (eds.) Advances in Mathematical Fluid Mechanics - dedicated to G.P. Galdi on his 60th birthday, chapter 295–309. Springer, Berlin (2009)
Sezgin, M., Sankur, B.: Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imag. 13(1), 146–165 (2004)
Tu, C., Deville, M.: Pulsatile flow of non-Newtonian fluids through arterial stenosis. J. Biomech. 29(7), 899–908 (1996)
Wulandana, R., Robertson, A.M.: An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomech. Model. Mechanobiol. 4(4), 235–248 (2005)
Acknowledgements
We greatly acknowledge Prof. Jorge Campos and his team from the Faculty of Medicine of the University of Lisbon, for providing us the in vivo rotational CTA scans of a specific patient. This work has been partially funded by FCT (Fundação para a Ciência e a Tecnologia, Portugal) through grants SFRH/BPD/34273/2006 and SFRH/BPD/44478/2008 and through the project UT Austin/CA/0047/2008.
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Ramalho, S., Moura, A.B., Gambaruto, A.M., Sequeira, A. (2013). Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms. In: Ledzewicz, U., Schättler, H., Friedman, A., Kashdan, E. (eds) Mathematical Methods and Models in Biomedicine. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4178-6_6
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