A Abdelsamie

D Thevenin

D Thévenin

G Janiga

H Yu

P Berg

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Copyright © 2013 by ASME 1 
INTRODUCTION 
According to the Dorland Medical Dictionary a cerebral aneurysm is 
an abnormal bulge or ballooning in a blood vessel supplying the brain.  
Aneurysms can rupture and bleed into the area between the brain and 
the surrounding membrane. A noticeable percentage of the human 
population, typically 2 to 5% depending on the country, harbors a 
cerebral aneurysm, but only about 0.1% of those aneurysms rupture 
annually [1]. 
However, the rupture of a cerebral aneurysm leads in 80-90% of all 
cases to a subarachnoid hemorrhage (SAH). More than 50% of the 
patients affected by SAH die within the first 6 months. These facts 
emphasize the importance of a careful investigation of the blood flows 
in cerebral aneurysms in order to understand and prevent rupture using 
appropriate treatments [2, 3]. 
In order to obtain accurate three-dimensional and time-dependent flow 
information in cerebral aneurysms, an enormous computational effort 
is required. Hence, several simplifications are usually employed to 
decrease model complexity and therefore the computational costs. The 
non-Newtonian behavior of blood is often neglected since shear-
thinning effects first appear at small vessel diameters [4]. Almost 
systematically, blood flow is assumed to be laminar with constant flow 
properties, which is up to now commonly accepted for intracranial 
vessels. However, a few groups have recently shown the existence of 
highly fluctuating structures within the human vascular system [5, 6], 
which could be interpreted as a transition to turbulence followed by 
relaminarization after peak systole.  
Especially in the case of diseased arteries (e.g., caused by a stenosis) 
or strong bifurcations non-laminar flow behavior was observed, 
although diameter-based Reynolds numbers Re < 500 were calculated 
[7, 8].  Transitional effects occurring around peak systole might have a 
significant impact on the weakened vessel layers and should be further 
investigated as a possible explanation for rupture.   
Predictive numerical tools are deeply needed to understand the 
hemodynamics in patient-specific geometries and support operation 
planning. Transitional multi-phase flows in very complex geometries 
cannot be solved with a unique method. It is therefore useful to 
identify different levels of modeling, describing their domain of 
application and characteristic features. Direct numerical simulation 
(DNS) is only possible for relatively simple geometrical 
configurations, but can now easily access the low Reynolds numbers 
found in cerebral aneurysms. They can additionally take into account 
the presence of particles in the flow. 
As a complement, Large and Detached Eddy Simulations (LES/DES) 
resolve the large structures of the flow, while the small scales and 
boundary layers are modeled. DES would be in particular much more 
attractive than DNS in terms of computing times, if it can predict with 
a sufficient accuracy transition, relaminarization and the impact of the 
dispersed phase on the flow. Laminar simulations are even more 
attractive for operation planning, since they can be used in a 
systematic manner to investigate the outcome of different treatments. 
All three are considered here. 
 
METHODS 
The interaction mechanisms between a transitional flow and a high 
particle volume fraction of red blood cells (RBC) might be very 
important to understand in a quantitative manner the observed flow 
properties and the resulting loading of the vessel wells. Furthermore, 
hemolysis [9] and thrombosis implying cell-cell and cell-wall 
interactions could be ultimately investigated in this manner. 
Most important for the simulations are the RBC length scale (d) and 
dissipation length scale (η). Antiga and Steinman [5] considered RBC 
 
MULTI-PHASE BLOOD FLOW MODELING IN INTRACRANIAL ANEURYSMS 
CONSIDERING POSSIBLE TRANSITION TO TURBULENCE 
P. Berg, A. Abdelsamie, H. Yu, G. Janiga, D. Thévenin 
Department of Fluid Dynamics and Technical Flows  
University of Magdeburg   
39106 Magdeburg, Germany 
Proceedings of the ASME 2013 Summer Bioengineering Conference 
SBC2013 
June 26-29, 2013, Sunriver, Oregon, USA 
SBC2013-14240
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Copyright © 2013 by ASME 2 
with d similar to η, while Valen-Sendstad et al. [6] considered RBC 
with d eight times smaller than η, explaining discrepancies in the 
statements. These two situations, both physically and computationally, 
are completely different. In [5] (Case I) the motion of the RBC is 
described considering fully resolved bodies, while in [6] (Case II) a 
point-force approach is employed. 
Multiphase DNS relying on point-particles has been considered for 
many years in our group [10], but is obviously a coarse approximation 
when trying to check the possible influence of particles on transition. 
Therefore, we consider at present two different approaches, in which 
solid spherical particles are coupled with an unsteady, incompressible 
and homogeneous Newtonian fluid. In this manner, the interaction 
mechanism can be investigated separately from all other effects. 
Figure 1 exemplifies the obtained instantaneous turbulence structure 
after coupling with resolved particles (like in Case I), using an 
Immersed Boundary Method (IBM), compared to results obtained for 
the same turbulence conditions with a point-force approximation (Case 
II). 
 
 
Figure 1: Turbulence structure modulation by solid particles: (left) 
Enstrophy iso-surface with superimposed particles, fully resolved 
approach (Case I), (right) Vorticity contours with superimposed 
particles, point-force approach (Case II) 
 
First statistics showed that the turbulence kinetic energy and its 
dissipation rate in Case II are noticeably modified as a function of 1) 
the ratio between the characteristic time scale of the particles to the 
Kolmogorov time scale and 2) the volumetric loading of the particles 
[11]. In Case I, similar but weaker modulations also occur but with 
different mechanisms, as will be explained during the conference.     
Finally, the present project involves three levels of flow simulations 
for hemodynamic prediction and for an improved physical 
understanding: 
1) First, the Navier-Stokes equations are solved considering unsteady 
but laminar conditions to analyze the intra-aneurysmal flow in a 
patient-specific aneurysm geometry using the open-source finite 
volume software OpenFOAM. Blood is considered as an 
incompressible isothermal fluid with Newtonian as well as shear-
thinning behavior (see Figure 2). 
2) As a comparison, LES/DES are carried out in the same geometry 
and considering the same fluid models. The occurrence of strongly 
fluctuating structures, possible transition to turbulence and 
relaminarization can be investigated in this manner. 
3) Finally, in order to understand the possible influence of RBC on the 
observations, DNS of a two-phase flow with both resolved and non-
resolved particles is considered. 
Combining these three approaches, relevant parameters that are known 
to play an important role in vessel wall degradation and ultimately in 
rupture can be assessed qualitatively as well as quantitatively. This 
investigation is thus a contribution toward a better understanding of 
this life-threatening vessel disease, in order to support the 
development of improved treatment options. 
 
PRELIMINARILY RESULTS 
Figures 1 and 2 illustrate the preliminarily results generated under 
turbulent as well as laminar flow conditions.  
 
 
 
Figure 2: Massless particles in patient-specific intracranial an 
aneurysm under laminar and pulsatile flow conditions  
 
REFERENCES 
[1] M. Kaminogo, M. Yonekura and S. Shibata. Incidence and 
outcome of multiple intracranial aneurysms in a defined population. 
Stroke, 34(1):16-21, 2003. 
[2] S. Seshadhri, G. Janiga, O. Beuing, M. Skalej and D. Thévenin. 
Impact of stents and flow diverters on hemodynamics in idealized 
aneurysm models. Journal of Biomechanical Engineering, 
133(7):071005, 2011. 
[3] G. Janiga, C. Rössl, M. Skalej and D. Thévenin. Realistic virtual 
intracranial stenting and computational fluid dynamics for treatment 
analysis. Journal of Biomechanics, 46(1):7-12, 2013. 
[4] J.R. Cebral, M.A. Castro, S. Appanaboyina, C.M. Putman, D. 
Millan and A.F. Frangi. E. Efficient pipeline for image-based patient-
specific analysis of cerebral aneurysm hemodynamics: technique and 
sensitivity. IEEE Transactions on Medical Imaging, 24(4):457-467, 
2005. 
[5] L. Antiga and D.A. Steinman. Rethinking turbulence in blood. 
Biorheology, 46(2):77-81, 2009. 
[6] K. Valen-Sendstad, K.A. Mardal, M. Mortensen, B.A.P. Reif and 
H.P. Langtangen. Direct numerical simulation of transitional flow in a 
patient-specific intracranial aneurysm. Journal of Biomechanics, 
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[7] K.M. Khanafer, J.L. Bull, G.R. Upchurch and R. Berguer. 
Turbulence significantly increases pressure and fluid shear stress in an 
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[8] S.E. Lee, S.W. Lee, P.F. Fischer, H.S. Bassiouny and F. Loth. 
Direct numerical simulation of transitional flow in a stenosed carotid 
bifurcation. Journal of Biomechanics, 41(16):2551-2561, 2008. 
[9] H. Yu, G. Janiga and D. Thévenin. Numerical prediction of 
hemolysis based on computational fluid dynamics. In: C. Lacor, editor, 
Simulation and Modeling of Biological Flows (SIMBIO11), pages 
10/1-5, Brussels, Belgium, 2011. 
[10] G. Janiga and D. Thévenin. Direct numerical simulation of 
turbulent reacting flows involving dilute particles. In Direct and 
Large-Eddy Simulation VI, pages 101-108, Springer, 2006. 
[11] A. H. Abdelsamie and C. Lee. Decaying versus stationary 
turbulence in particle-laden isotropic turbulence: Turbulence 
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Multi-Phase Blood Flow Modeling in Intracranial Aneurysms Considering Possible Transition to Turbulence

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Multi-Phase Blood Flow Modeling in Intracranial Aneurysms Considering Possible Transition to Turbulence

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