Mathematics of Computational Science

# Mathematical Analysis and Classification of Flow Topologies in Cerebral Aneurysms

## Mathematical Analysis and Classification of Flow Topologies in Cerebral Aneurysms

### Organization:

Funded by: University of Twente
PhD: Julia Mikhal
Supervisor: Bernard Geurts
Collaboration: Prof. C. H. Slump, System & Signals Group, EWI, UT

### Description:

The prediction of blood flow inside aneurysms that can develop in a human brain is a field of intense research – such aneurysm formation is illustrated in Fig. 1. It is important in relation to the growing medical need for an effective planning and execution of surgical intervention.

Figure 1. Cerebral aneurysm, which can form in a human brain is mostly located in ‘T’ or ‘Y’ – junctions in the vessel system.

We present a computational model for the simulation of blood flow inside the human brain. The main focus is on the analysis of flow behavior especially near vessel walls to better understand factors contributing to formation and rupture of aneurysms. As a main characteristic for the prediction of risks of rupture the shear stress along the walls is computed. Literature indicates that both high as well as low levels of shear stress can be important triggers of slow vessel remodeling processes.

The computational model for the simulation of blood flow through vessels in the human brain is formulated in terms of the incompressible Navier-Stokes equations in three-dimensional domains. We apply the immersed boundary method based on volume penalization to represent the complex shaped and flexible solid vessel walls of the aneurysm. Any such complex geometry is described in terms of a so-called ‘masking function’ that is put to zero inside the flow domain and unity in the solid parts of the domain. This masking function technique allows a fast definition of the geometry, which can be extracted from real patient data, e.g., from 3d rotational angiography images.

The flow inside the vessels is simulated with the use of a finite-volume discretization and explicit time stepping. The reliability of the model was analyzed for canonical geometries such as straight tubes, where it could be compared to Poiseuille flow and smoothly curved cylindrical tubes where it was assessed using grid refinement.

Figure 2. Velocity streamlines (a) and predicted ‘normalized’ shear-stress distribution (b) in realistic cerebral aneurysm

As a key component for the prediction of the risk of aneurysm rupture the shear stress was calculated at the vessel walls. The procedure was tested and reliable results were observed already at modest spatial resolution. A characteristic impression of physiological flow and shear stresses is shown in Fig. 2. This gives confidence in the application of the methodology to realistic aneurysms as developed in a set of human patients.

### Publications:

E-prints overview

### Conference items:

Julia Mikhal, Bernard J. Geurts
Simulation of realistic pulsatile flow in cerebral aneurysms. Euromech 529 – Cardiovascular Fluid Mechanics, Cagliari, Italy, June 2011, accepted.

### Posters:

J. Mikhal, B.J. Geurts
Computational Modeling of Pulsatile Flow in Realistic Cerebral Aneuriysms
-JMBC Burgersdag 2012 – TUE, Eindhoven, NL, 12 January 2012
-TW Alumni Day – UT, Enschede, NL, 26 November 2011
-Woudschoten 2011 Conference of the Dutch-Flemish Numerical Analysis Communities, Zeist, NL, 5-7 October 2011

J. Mikhal, B.J. Geurts
Immersed boundary method for pulsatile flow in cerebral aneurysms
-NMC 2011, Enschede, The Netherlands, April 2011.

J. Mikhal, B.J. Geurts
Shear Stress Predictions for a Model Aneurysm using the Immersed Boundary Method
-Woudschoten 2010 Conference of the Dutch-Flemish Numerical Analysis Communities, Zeist, The Netherlands, October 2010 (awarded 1st prize in the poster presentation competition)
-The 5th International Symposium on Biomechanics in Vascular Biology and Cardiovascular Disease, Rotterdam, The Netherlands,April 2010
-3TU AMI Symposium – Delft, NL, 15 April 2010

B.S. Deb, B.J. Geurts, L. Ghazaryan, D.J. Lopez Penha, J. Mikhal, S. Stolz
Multiscale Modeling and Simulation
-Woudschoten 2009 Conference of the Dutch-Flemish Numerical Analysis Communities, Zeist, NL, 7-9 October 2009

### PHD defence:

19-10-2012:    14:45 Hours Mikhal, J. Modeling and simulation of flow in cerebral aneurysms