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.

翻译：血管内弹簧圈栓塞术是治疗脑动脉瘤的主要技术之一。尽管这是一种成熟且微创的方法，但仍存在弹簧圈放置欠佳的风险，可能导致动脉瘤不完全闭塞并引发复发。弹簧圈的关键特征在于其具有预成形的自然形态，有助于在动脉瘤内固定。在空间离散化中，我们的数学弹簧圈模型基于离散弹性杆模型，形成降维的一维微分方程组。我们引入弯曲和扭转响应以考虑弹簧圈的自然曲率。弹簧圈节段与动脉瘤壁之间的碰撞通过高效接触算法处理，该算法基于八叉树碰撞检测。模型的数值求解采用辛半隐式欧拉时间步进方法。我们的模型可轻松整合到栓塞动脉瘤的血流模拟中。为区分最优与次优放置，我们采用合适的计算机模拟Raymond-Roy型闭塞分类，并测量动脉瘤颈部、壁区域和核心的局部填充密度。我们研究了弹簧圈参数和栓塞过程中不确定性的影响。为此，我们改变微导管插入的位置和角度，并通过评估样本统计量来近似局部填充密度分布。