title: Biomechanics Simulations Using Cubic Hermite Meshes with Extraordinary Nodes for Isogeometric Cardiac Modeling.
abstract: 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.
authors.affiliation: Mechanical Engineering, Iowa State University; Bioengineering, University of California, San Diego.
authors.forename: Adarsh
authors.initials: A
authors.lastname: Krishnamurthy
authors.affiliation: Bioengineering, University of California, San Diego.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Gonzales
authors.affiliation: Carl E. Ravin Advanced Imaging Laboratories, Duke University.
authors.forename: Gregory
authors.initials: G
authors.lastname: Sturgeon
authors.affiliation: Carl E. Ravin Advanced Imaging Laboratories, Duke University.
authors.forename: W Paul
authors.initials: WP
authors.lastname: Segars
authors.affiliation: Bioengineering, University of California, San Diego.
authors.forename: Andrew D
authors.initials: AD
authors.lastname: McCulloch
keywords: Cardiac Modeling; Cubic-Hermite Hexahedral Elements; Extraordinary Nodes; Finite Element Analysis; Isogeometric Analysis