The main respiratory muscle, the diaphragm, is an example of a thin structure. We aim to perform detailed numerical simulations of the muscle mechanics based on individual patient data. This requires a representation of the diaphragm geometry extracted from medical image data. We design an adaptive reconstruction method based on a least-squares radial basis function partition of unity method. The method is adapted to thin structures by subdividing the structure rather than the surrounding space, and by introducing an anisotropic scaling of local subproblems. The resulting representation is an infinitely smooth level set function, which is stabilized such that there are no spurious zero level sets. We show reconstruction results for 2D cross sections of the diaphragm geometry as well as for the full 3D geometry. We also show solutions to basic PDE test problems in the reconstructed geometries.

翻译：主要呼吸肌——膈肌，是薄结构的一个典型实例。我们旨在基于个体患者数据对肌肉力学进行精细数值模拟。这要求从医学图像数据中提取膈肌几何表示。本文设计了一种基于最小二乘径向基函数单位分解方法的自适应重构方法。该方法通过细分结构本身而非周围空间，并引入局部子问题的各向异性缩放，从而适用于薄结构。所得到的表示形式为无限光滑的水平集函数，并通过稳定性处理避免产生虚假零水平集。我们展示了膈肌几何二维截面及完整三维几何的重构结果，并给出了在重构几何中求解基础PDE测试问题的结果。