# American Institute of Mathematical Sciences

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
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