title: Computation of a finite element-conformal tetrahedral mesh approximation for simulated soft tissue deformation using a deformable surface model.
abstract: In this article, we present a new method for the generation of surface meshes of biological soft tissue. The method is based on the deformable surface model technique and is extended to histological data sets. It relies on an iterative adjustment towards polygonal segments describing the histological structures of the soft tissue. The generated surface meshes allow for the construction of volumetric meshes through a standard constrained Delaunay approach and, thus, for the application in finite element methods. The geometric properties of volumetric meshes have an immediate influence on the numerical conditioning and, therewith, on the stability of the finite element method and the convergence of iterative solvers. In this article, the influence of the surface meshes on the quality of the volumetric meshes is analysed in terms of the spectral condition number of the stiffness matrices, which are assembled within Newton's method. The non-linear material behavior of biological soft tissue is modeled by the Mooney-Rivlin material law. The subject is motivated by the requirements of virtual surgery.
authors.affiliation: Department of Computer Science VII, TU Dortmund University, Dortmund, Germany. frank.weichert@tu-dortmund.de
authors.forename: Frank
authors.initials: F
authors.lastname: Weichert
authors.forename: Andreas
authors.initials: A
authors.lastname: Schröder
authors.forename: Constantin
authors.initials: C
authors.lastname: Landes
authors.forename: Ali
authors.initials: A
authors.lastname: Shamaa
authors.forename: Said Kamel
authors.initials: SK
authors.lastname: Awad
authors.forename: Lars
authors.initials: L
authors.lastname: Walczak
authors.forename: Heinrich
authors.initials: H
authors.lastname: Müller
authors.forename: Mathias
authors.initials: M
authors.lastname: Wagner
mesh_terms: D000465:Algorithms; D002971:Cleft Lip / Q000503:physiopathology / Q000601:surgery; D002972:Cleft Palate / Q000503:physiopathology / Q000601:surgery; D003198:Computer Simulation; D003238:Connective Tissue / Q000503:physiopathology*; D004548:Elasticity; D020342:Finite Element Analysis; D006801:Humans; D008954:Models, Biological; D013314:Stress, Mechanical