### Abstract

Cerebral aneurysms are weak spots in the vessel structure of the brain, which present a serious problem to the patient. Julia Mikhal and Bernard Geurts present the application of an Immersed Boundary (IB) method to the simulation of blood flow through such aneurysms. The goal is to understand the flow in these diseased parts of the human brain system and to assess the risk of rupture. The IB method is applied to a generic model aneurysm for which the authors study the flow and forces on the vessel wall at a variety of physiological conditions. The definition of complex aneurysm geometries is hampered by uncertainties associated with the available spatial resolution of medical images. With the IB method onemay readily approximate flow dynamics for the ‘most likely’ reference vessel shape aswell as for ‘nearby’ bounding geometries. The latter approximations are respectively ‘inner’ or ‘outer’ with respect to the likely reference geometry. Several important characteristics of the flow inside the reference geometry appear to be bounded by the solutions corresponding to the inner and outer geometries. Although no strict mathematical bounding property has been established, numerical experimentation shows the practical bounding property of inner and outer simulations. The authors illustrate their numerical method on the selected ‘model aneurysm’ and show the sensitivity of the solution to inherent variations in the definition of the flow domain and flow conditions. Julia Mikhal was the winner of the Philips Wiskundeprijs voor Promovendi 2011.

Original language | Undefined |
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Pages (from-to) | 163-168 |

Number of pages | 6 |

Journal | Nieuw archief voor wiskunde |

Volume | 12 |

Issue number | 3 |

Publication status | Published - 3 Sep 2011 |

### Keywords

- EWI-21062
- Sensitivity to geometry
- IR-79119
- Immersed boundary method
- METIS-285213
- Cerebral aneurysm

## Cite this

Mikhal, J. O., & Geurts, B. J. (2011). Bounding solutions for cerebral aneurysms.

*Nieuw archief voor wiskunde*,*12*(3), 163-168.