title: A three-dimensional finite element model of human atrial anatomy: new methods for cubic Hermite meshes with extraordinary vertices.
abstract: High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 mm, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology.
authors.affiliation: Department of Bioengineering, University of California San Diego, La Jolla, CA, USA.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Gonzales
authors.forename: Gregory
authors.initials: G
authors.lastname: Sturgeon
authors.forename: Adarsh
authors.initials: A
authors.lastname: Krishnamurthy
authors.forename: Johan
authors.initials: J
authors.lastname: Hake
authors.forename: René
authors.initials: R
authors.lastname: Jonas
authors.forename: Paul
authors.initials: P
authors.lastname: Stark
authors.forename: Wouter-Jan
authors.initials: WJ
authors.lastname: Rappel
authors.forename: Sanjiv M
authors.initials: SM
authors.lastname: Narayan
authors.forename: Yongjie
authors.initials: Y
authors.lastname: Zhang
authors.forename: W Paul
authors.initials: WP
authors.lastname: Segars
authors.forename: Andrew D
authors.initials: AD
authors.lastname: McCulloch
mesh_terms: D000368:Aged; D000465:Algorithms; D003198:Computer Simulation; D020342:Finite Element Analysis; D006325:Heart Atria / Q000033:anatomy & histology* / Q000000981:diagnostic imaging*; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008297:Male; D008953:Models, Anatomic; D008955:Models, Cardiovascular; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*