Wong Jonathan, Kuhl Ellen
a Department of Mechanical Engineering , Stanford University , Stanford , CA 94305 , USA.
Comput Methods Biomech Biomed Engin. 2014;17(11):1217-26. doi: 10.1080/10255842.2012.739167. Epub 2012 Dec 5.
Smoothly varying muscle fibre orientations in the heart are critical to its electrical and mechanical function. From detailed histological studies and diffusion tensor imaging, we now know that fibre orientations in humans vary gradually from approximately -70° in the outer wall to +80° in the inner wall. However, the creation of fibre orientation maps for computational analyses remains one of the most challenging problems in cardiac electrophysiology and cardiac mechanics. Here, we show that Poisson interpolation generates smoothly varying vector fields that satisfy a set of user-defined constraints in arbitrary domains. Specifically, we enforce the Poisson interpolation in the weak sense using a standard linear finite element algorithm for scalar-valued second-order boundary value problems and introduce the feature to be interpolated as a global unknown. User-defined constraints are then simply enforced in the strong sense as Dirichlet boundary conditions. We demonstrate that the proposed concept is capable of generating smoothly varying fibre orientations, quickly, efficiently and robustly, both in a generic bi-ventricular model and in a patient-specific human heart. Sensitivity analyses demonstrate that the underlying algorithm is conceptually able to handle both arbitrarily and uniformly distributed user-defined constraints; however, the quality of the interpolation is best for uniformly distributed constraints. We anticipate our algorithm to be immediately transformative to experimental and clinical settings, in which it will allow us to quickly and reliably create smooth interpolations of arbitrary fields from data-sets, which are sparse but uniformly distributed.
心脏中平滑变化的肌纤维方向对其电功能和机械功能至关重要。通过详细的组织学研究和扩散张量成像，我们现在知道人类心脏中的纤维方向从外壁的约-70°逐渐变化到内壁的+80°。然而，创建用于计算分析的纤维方向图仍然是心脏电生理学和心脏力学中最具挑战性的问题之一。在此，我们表明泊松插值可生成在任意域中满足一组用户定义约束的平滑变化向量场。具体而言，我们使用用于标量值二阶边值问题的标准线性有限元算法在弱意义上实施泊松插值，并将待插值的特征作为全局未知数引入。然后，用户定义的约束作为狄利克雷边界条件在强意义上简单地实施。我们证明，所提出的概念能够在通用双心室模型和特定患者的人体心脏中快速、高效且稳健地生成平滑变化的纤维方向。敏感性分析表明，底层算法在概念上能够处理任意分布和均匀分布的用户定义约束；然而，对于均匀分布的约束，插值质量最佳。我们预计我们的算法将立即对实验和临床环境产生变革性影响，在这些环境中，它将使我们能够从稀疏但均匀分布的数据集中快速可靠地创建任意场的平滑插值。
