A Comprehensive Numerical Approach to Coil Placement in Cerebral Aneurysms: Mathematical Modeling and In Silico Occlusion Classification

Endovascular coil embolization is one of the primary treatment techniques for cerebral aneurysms. Although it is a well established and minimally invasive method, it bears the risk of sub-optimal coil placement which can lead to incomplete occlusion of the aneurysm possibly causing recurrence. One of the key features of coils is that they have an imprinted natural shape supporting the fixation within the aneurysm. For the spatial discretization our mathematical coil model is based on the Discrete Elastic Rod model which results in a dimension-reduced 1D system of differential equations. We include bending and twisting responses to account for the coils natural curvature. Collisions between coil segments and the aneurysm-wall are handled by an efficient contact algorithm that relies on an octree based collision detection. The numerical solution of the model is obtained by a symplectic semi-implicit Euler time stepping method. Our model can be easily incorporated into blood flow simulations of embolized aneurysms. In order to differentiate optimal from sub-optimal placements, we employ a suitable in silico Raymond-Roy type occlusion classification and measure the local packing density in the aneurysm at its neck, wall-region and core. We investigate the impact of uncertainties in the coil parameters and embolization procedure. To this end, we vary the position and the angle of insertion of the microcatheter, and approximate the local packing density distributions by evaluating sample statistics.