2011, 8(2): 409-423. doi: 10.3934/mbe.2011.8.409

Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology

1. 

Dept. of Mathematics and CEMAT/IST, Av Rovisco Pais 1, 1049-001 Lisboa, Portugal, Portugal

2. 

Dept. of Mathematics ISEG, UTL and CEMAT/IST, Rua do Quelhas 6, 1200-781 Lisboa, Portugal

3. 

Department of Mathematics and CEMAT/IST, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa

Received  March 2010 Revised  October 2010 Published  April 2011

Newtonian and generalized Newtonian mathematical models for blood flow are compared in two different reconstructions of an anatomically realistic geometry of a saccular aneurysm, obtained from rotational CTA and differing to within image resolution. The sensitivity of the flow field is sought with respect to geometry reconstruction procedure and mathematical model choice in numerical simulations.
   Taking as example a patient specific intracranial aneurysm located on an outer bend under steady state simulations, it is found that the sensitivity to geometry variability is greater, but comparable, to the one of the rheological model. These sensitivities are not quantifiable a priori. The flow field exhibits a wide range of shear stresses and slow recirculation regions that emphasize the need for careful choice of constitutive models for the blood. On the other hand, the complex geometrical shape of the vessels is found to be sensitive to small scale perturbations within medical imaging resolution.
   The sensitivity to mathematical modeling and geometry definition are important when performing numerical simulations from in vivo data, and should be taken into account when discussing patient specific studies since differences in wall shear stress range from 3% to 18%.
Citation: Alberto M. Gambaruto, João Janela, Alexandra Moura, Adélia Sequeira. Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology. Mathematical Biosciences & Engineering, 2011, 8 (2) : 409-423. doi: 10.3934/mbe.2011.8.409
References:
[1]

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), 59.   Google Scholar

[2]

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi and D. A. Steinman, An image-based modeling framework for patient-specific computational hemodynamics,, Med. Biol. Eng. Comput., 46 (2008), 1097.  doi: 10.1007/s11517-008-0420-1.  Google Scholar

[3]

T. Bodnár and A. Sequeira, Numerical study of the significance of the non-Newtonian nature of blood in steady flow through a stenosed vessel,, In, (2010), 83.   Google Scholar

[4]

E. Burman and M. A. Fernández, Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: Space discretization and convergence,, Numerische Mathematik, 107 (2007), 39.  doi: 10.1007/s00211-007-0070-5.  Google Scholar

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J. R. Cebral, M. A. Castro, S. Appanaboyina, C. M. Putman, D. Millan and A. Frangi, Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: Technique and sensitivity,, IEEE Transactions on Medical Imaging, 24 (2005), 457.  doi: 10.1109/TMI.2005.844159.  Google Scholar

[7]

J. R. Cebral, M. A. Castro, J. E. Burgess, R. S. Pergolizzi, M. J. Sheridan and C. M. Putman, Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models,, Am. J. Neuroradiol., 26 (2005), 2550.   Google Scholar

[8]

Y. I. Cho and K. R. Kensey, Effects of non-Newtonian viscosity of blood on flows in a diseased vessel, part I: Steady flows,, Biorheology, 28 (1991), 241.   Google Scholar

[9]

L. Formaggia, A. M. Quarteroni and A. Veneziani (eds), "Cardiovascular Mathematics. Modeling and Simulation of the Circulatory System,", Series: MS&A Vol. \textbf{1}, 1 (2009).   Google Scholar

[10]

J. Frösen, A. Piippo, A. Paetau, M. Kangasniemi, M. Niemela, J. Hernesniemi and J. Jääskeläinen, Remodeling of saccular cerebral artery aneurysm wall is associated with rupture: Histological analysis of 24 unruptured and 42 ruptured cases,, Stroke, 35 (2004), 2287.  doi: 10.1161/01.STR.0000140636.30204.da.  Google Scholar

[11]

A. M. Gambaruto, A. Moura and A. Sequeira, Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty,, International Journal for Numerical Methods in Biomedical Engineering, 26 (2010), 926.   Google Scholar

[12]

Y. P. Gobin, J. L. Counard and P. Flaud, In vitro study of haemodynamics in a giant saccular aneurysm model: Influence of flow dynamics in the parent vessel and effects of coil embolization,, Neuroradiology, 36 (1994), 530.  doi: 10.1007/BF00593516.  Google Scholar

[13]

G. J. Hademenos and T. F. Massoud, "The Physics of Cerebrovascular Diseases: Biophysical Mechanisms of Development, Diagnosis and Therapy,", Biological Physics Series, (1998).   Google Scholar

[14]

T. Hassan, E. V. Timofeev, T. Saito, H. Shimizu, M. Ezura, Y. Matsumoto, K. Takayama, T. Tominaga and A. Takahashi, A proposed parent vessel geometry-based categorization of saccular intracranial aneurysms: Computational flow dynamics analysis of the risk factors for lesion rupture,, J. Neurosurg., 103 (2005), 662.  doi: 10.3171/jns.2005.103.4.0662.  Google Scholar

[15]

Y. Hoi, H. Meng, S. H. Woodward, B. R. Bendok, R. A. Hanel, L. R. Guterman and L. N. Hopkins, Effects of arterial geometry on aneurysm growth: Three-dimensional fluid dynamics study,, J. Neurosurg., 101 (2004), 676.  doi: 10.3171/jns.2004.101.4.0676.  Google Scholar

[16]

G. D. O. Lowe (ed.), "Clinical Blood Rheology,", CRC Press, (1988).   Google Scholar

[17]

H. Meng, Z. Wang, Y. Hoi, L. Gao, E. Metaxa, D. D. Swartz and J. Kolega, Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation,, Stroke, 38 (2007), 1924.  doi: 10.1161/STROKEAHA.106.481234.  Google Scholar

[18]

S. Moore, T. David, J. G. Chase, J. Arnold and J. Fink, 3D models of blood flow in the cerebral vasculature,, Journal of Biomechanics, 39 (2006), 1454.  doi: 10.1016/j.jbiomech.2005.04.005.  Google Scholar

[19]

J. Nocedal and S. J. Wright, "Numerical Optimization,", Springer Series in Operations Research, (1999).   Google Scholar

[20]

S. O. Oktara, C. Yücela, D. Karaosmanoglua, K. Akkana, H. Ozdemira, N. Tokgoza and T. Talia, Blood-flow volume quantification in internal carotid and vertebral arteries: Comparison of 3 different ultrasound techniques with phase-contrast MR imaging,, American Journal of Neuroradiology, 27 (2006), 363.   Google Scholar

[21]

A. M. Robertson, A. Sequeira and M. Kameneva, Hemorheology,, in, 37 (2008), 63.   Google Scholar

[22]

L. M. Sangalli, P. Secchi, S. Vantini and A. Veneziani, A case study in exploratory functional data analysis: Geometrical features of the internal carotid artery,, Journal of the American Statistical Association, 104 (2009), 37.  doi: 10.1198/jasa.2009.0002.  Google Scholar

[23]

Y. Shimogonya, T. Ishikawa, Y. Imai, N. Matsuki and T. Yamaguchi, Can temporal fluctuation in spatial wall shear stress gradient initiate a cerebral aneurysm? A proposed novel hemodynamic index, the gradient oscillatory number (GON),, Journal of Biomechanics, 42 (2009), 550.  doi: 10.1016/j.jbiomech.2008.10.006.  Google Scholar

[24]

C. M. Strother, V. B. Graves and A. Rappe, Aneurysm hemodynamics: An experimental study,, AJNR American Journal of Neuroradiology, 13 (1992), 1089.   Google Scholar

show all references

References:
[1]

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), 59.   Google Scholar

[2]

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi and D. A. Steinman, An image-based modeling framework for patient-specific computational hemodynamics,, Med. Biol. Eng. Comput., 46 (2008), 1097.  doi: 10.1007/s11517-008-0420-1.  Google Scholar

[3]

T. Bodnár and A. Sequeira, Numerical study of the significance of the non-Newtonian nature of blood in steady flow through a stenosed vessel,, In, (2010), 83.   Google Scholar

[4]

E. Burman and M. A. Fernández, Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: Space discretization and convergence,, Numerische Mathematik, 107 (2007), 39.  doi: 10.1007/s00211-007-0070-5.  Google Scholar

[5]

M. A. Castro, C. M. Putman and J. R. Cebral, Computational fluid dynamics modeling of intracranial aneurysms: Effects of parent artery segmentation on intra-ineurysmal hemodynamics,, Am. J. Neuroradiol., 27 (2007), 1703.   Google Scholar

[6]

J. R. Cebral, M. A. Castro, S. Appanaboyina, C. M. Putman, D. Millan and A. Frangi, Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: Technique and sensitivity,, IEEE Transactions on Medical Imaging, 24 (2005), 457.  doi: 10.1109/TMI.2005.844159.  Google Scholar

[7]

J. R. Cebral, M. A. Castro, J. E. Burgess, R. S. Pergolizzi, M. J. Sheridan and C. M. Putman, Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models,, Am. J. Neuroradiol., 26 (2005), 2550.   Google Scholar

[8]

Y. I. Cho and K. R. Kensey, Effects of non-Newtonian viscosity of blood on flows in a diseased vessel, part I: Steady flows,, Biorheology, 28 (1991), 241.   Google Scholar

[9]

L. Formaggia, A. M. Quarteroni and A. Veneziani (eds), "Cardiovascular Mathematics. Modeling and Simulation of the Circulatory System,", Series: MS&A Vol. \textbf{1}, 1 (2009).   Google Scholar

[10]

J. Frösen, A. Piippo, A. Paetau, M. Kangasniemi, M. Niemela, J. Hernesniemi and J. Jääskeläinen, Remodeling of saccular cerebral artery aneurysm wall is associated with rupture: Histological analysis of 24 unruptured and 42 ruptured cases,, Stroke, 35 (2004), 2287.  doi: 10.1161/01.STR.0000140636.30204.da.  Google Scholar

[11]

A. M. Gambaruto, A. Moura and A. Sequeira, Topological flow structures and stir mixing for steady flow in a peripheral bypass graft with uncertainty,, International Journal for Numerical Methods in Biomedical Engineering, 26 (2010), 926.   Google Scholar

[12]

Y. P. Gobin, J. L. Counard and P. Flaud, In vitro study of haemodynamics in a giant saccular aneurysm model: Influence of flow dynamics in the parent vessel and effects of coil embolization,, Neuroradiology, 36 (1994), 530.  doi: 10.1007/BF00593516.  Google Scholar

[13]

G. J. Hademenos and T. F. Massoud, "The Physics of Cerebrovascular Diseases: Biophysical Mechanisms of Development, Diagnosis and Therapy,", Biological Physics Series, (1998).   Google Scholar

[14]

T. Hassan, E. V. Timofeev, T. Saito, H. Shimizu, M. Ezura, Y. Matsumoto, K. Takayama, T. Tominaga and A. Takahashi, A proposed parent vessel geometry-based categorization of saccular intracranial aneurysms: Computational flow dynamics analysis of the risk factors for lesion rupture,, J. Neurosurg., 103 (2005), 662.  doi: 10.3171/jns.2005.103.4.0662.  Google Scholar

[15]

Y. Hoi, H. Meng, S. H. Woodward, B. R. Bendok, R. A. Hanel, L. R. Guterman and L. N. Hopkins, Effects of arterial geometry on aneurysm growth: Three-dimensional fluid dynamics study,, J. Neurosurg., 101 (2004), 676.  doi: 10.3171/jns.2004.101.4.0676.  Google Scholar

[16]

G. D. O. Lowe (ed.), "Clinical Blood Rheology,", CRC Press, (1988).   Google Scholar

[17]

H. Meng, Z. Wang, Y. Hoi, L. Gao, E. Metaxa, D. D. Swartz and J. Kolega, Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation,, Stroke, 38 (2007), 1924.  doi: 10.1161/STROKEAHA.106.481234.  Google Scholar

[18]

S. Moore, T. David, J. G. Chase, J. Arnold and J. Fink, 3D models of blood flow in the cerebral vasculature,, Journal of Biomechanics, 39 (2006), 1454.  doi: 10.1016/j.jbiomech.2005.04.005.  Google Scholar

[19]

J. Nocedal and S. J. Wright, "Numerical Optimization,", Springer Series in Operations Research, (1999).   Google Scholar

[20]

S. O. Oktara, C. Yücela, D. Karaosmanoglua, K. Akkana, H. Ozdemira, N. Tokgoza and T. Talia, Blood-flow volume quantification in internal carotid and vertebral arteries: Comparison of 3 different ultrasound techniques with phase-contrast MR imaging,, American Journal of Neuroradiology, 27 (2006), 363.   Google Scholar

[21]

A. M. Robertson, A. Sequeira and M. Kameneva, Hemorheology,, in, 37 (2008), 63.   Google Scholar

[22]

L. M. Sangalli, P. Secchi, S. Vantini and A. Veneziani, A case study in exploratory functional data analysis: Geometrical features of the internal carotid artery,, Journal of the American Statistical Association, 104 (2009), 37.  doi: 10.1198/jasa.2009.0002.  Google Scholar

[23]

Y. Shimogonya, T. Ishikawa, Y. Imai, N. Matsuki and T. Yamaguchi, Can temporal fluctuation in spatial wall shear stress gradient initiate a cerebral aneurysm? A proposed novel hemodynamic index, the gradient oscillatory number (GON),, Journal of Biomechanics, 42 (2009), 550.  doi: 10.1016/j.jbiomech.2008.10.006.  Google Scholar

[24]

C. M. Strother, V. B. Graves and A. Rappe, Aneurysm hemodynamics: An experimental study,, AJNR American Journal of Neuroradiology, 13 (1992), 1089.   Google Scholar

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