Cubic Hermite hexahedral finite element meshes have some well-known advantages over linear tetrahedral finite element meshes in biomechanical and anatomic modeling using isogeometric analysis. These include faster convergence rates as well as the ability to easily model rule-based anatomic features such as cardiac fiber directions. However, it is not possible to create closed complex objects with only regular nodes; these objects require the presence of extraordinary nodes (nodes with 3 or $>=5$ adjacent elements in 2D) in the mesh. The presence of extraordinary nodes requires new constraints on the derivatives of adjacent elements to maintain continuity. We have developed a new method that uses an ensemble coordinate frame at the nodes and a local-to-global mapping to maintain continuity. In this paper, we make use of this mapping to create cubic Hermite models of the human ventricles and a four-chamber heart. We also extend the methods to the finite element equations to perform biomechanics simulations using these meshes. The new methods are validated using simple test models and applied to anatomically accurate ventricular meshes with valve annuli to simulate complete cardiac cycle simulations.

在使用等几何分析的生物力学和解剖学建模中，三次Hermite六面体有限元网格比线性四面体有限元网格具有一些众所周知的优势。这些功能包括更快的收敛速度，以及轻松建模基于规则的解剖特征（例如心脏纤维方向）的能力。但是，不可能仅使用常规节点来创建封闭的复杂对象。这些对象需要存在非同寻常的节点（具有3或3个节点的节点）$>=5$网格中2D中的相邻元素）。非凡节点的存在要求对相邻元素的派生有新的约束，以保持连续性。我们开发了一种新方法，该方法在节点上使用整体坐标系并使用局部到全局映射来保持连续性。在本文中，我们利用此映射来创建人类心室和四腔心脏的三次Hermite模型。我们还将这些方法扩展到有限元方程，以使用这些网格进行生物力学模拟。使用简单的测试模型对新方法进行了验证，并将其应用于解剖学上精确的带有瓣膜环的心室网格，以模拟完整的心动周期模拟。