Applied Analysis Seminar  Multi-Scale Modeling and Patient-Specific Simulations for Endovascular Interventions in Cerebral Aneurysms

Cerebral aneurysms are pathological, local deformations of the artery wall within the brain. They are the leading cause of haemorrhagic stroke upon rupture due to their high prevalence (about 3.2% of the population) and high rupture fatality rate (27–44%) [1]. Especially catheter-assisted coil embolization [2] became a standard treatment technique. Nevertheless, the prediction of the treatment outcome, including optimal coiling, the subsequent reduction of blood flow and wall shear stress in the aneurysm, and the risk of relapse, including endemic inflammation processes and thrombus formation, is still an open problem.

In this presentation, I will discuss mathematical models and numerical simulations which can support clinicians to decide for or against certain treatment options. The aim is incorporate the whole treatment process into the simulations, ranging from the mechanical placement of medical embolization devices such as coils, flow diverters, or woven EndoBridge devices within the aneurysm during surgery over short-term thrombus formation up to the long-term perspective assessment for the patient in terms of treatment success vs. the risk of a potential relapse.

Medical imaging techniques provide the basis for patient-specific digital models. First, we resolve the mechanics and contact of coiling devices with an embedded micro-structure [3,4]. The resulting fine-scale geometries can be used either directly for lattice Boltzmann simulations of the pre- and post-surgical blood flow, or volume averaged beforehand, leading to a porous medium model yielding similar results [5]. Incorporating the deformation of the vessel walls and of the endovascular device during the pulsatile blood flow results in complex, coupled systems of PDEs, which need approriate analysis and numerical treatment. Furthermore, the thrombus formation is included using a porous medium model to assess its long-term stability and the overall occlusion quality.

As the long-term goal is the adaptive stochastic optimization of the patient-specific treatment planning, the separation of time scales (heart beat vs. long-scale thrombus formation), as well as inflammatory responses or edema formation due to altered flow conditions will be addressed in the future using multi-physics, multi-scale (in space and time) simulations joining different methodologies, such as lattice Boltzmann and finite element methods, as well as machine learning to significntly reduce the computation time for sensible medical outputs for patient-specific cases.

1. L. Pierot and A. K. Wakhloo. "Endovascular Treatment of Intracranial Aneurysms". Stroke 44 (7, 2013), pp. 2046–2054. 

   https://doi.org/10.1161/STROKEAHA.113.000733

2. J. Zhao, H. Lin, R. Summers, M. Yang, B.G. Cousins, and J. Tsui. "Current treatment strategies for intracranial aneurysms: an overview". Angiology 69.1 (2018), pp. 17–30. 

   https://doi.org/10.1

   177/0003319717700503
3. F. Holzberger, J. Kirschke, M. Muhr, N. Nebulishvili, J. Schwarting, and B. Wohlmuth. "Breaking Blood Flow with Wires in Aneurysm Coiling Treatment Simulations". SIAM News (2023). 

   https://sinews.siam.org/Details-Page/breaking-blood-flow-with-wires-in-aneurysm-coiling-treatment-simulations

4. M. Frank, F. Holzberger, M. Horvat, J. Kirschke, M. Mayr, M. Muhr, N. Nebulishvili, A. Popp, J. Schwarting, and B. Wohlmuth. "Numerical simulation of endovascular treatment options for cerebral aneurysms". GAMM-Mitteilungen 47 (2024), e202370007. 

   https://doi.org/10.1002/gamm.202370007

5. M. Horvat, S. B. Lunowa, D. Sytnyk, and B. Wohlmuth. "A lattice Boltzmann method for non-Newtonian blood flow in coiled intracranial aneurysms". In Numerical Mathematics and Advanced Applications (ENUMATH 2023), Springer, accepted. ArXiv preprint 2402.10809. 

   https://doi.org/10.48550/arXiv.2402.10809