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Fast intersections on nested tetrahedrons (FINT): An algorithm for adaptive finite element based distributed

Jae Hoon Lee1, Amit Joshi, Eva M Sevick-Muraca

  • 1Department of Radiology, Baylor College of Medicine, Photon Migration Laboratory, One Baylor Plaza, BCM 360, Houston, TX 77030, USA.

Journal of Computational Physics
|August 9, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a novel algorithm for efficiently resolving intersections in dual-adaptive finite element meshes used in biomedical imaging. This method enhances image reconstruction accuracy and computational efficiency for complex geometries.

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Area of Science:

  • Biomedical Imaging
  • Computational Science
  • Finite Element Analysis

Background:

  • Biomedical imaging techniques often involve solving inverse problems to reconstruct images from physical models.
  • Finite element discretization using tetrahedral elements is common for complex geometries in imaging.
  • Dual-adaptive mesh approaches can improve image reconstruction but require handling mesh intersections.

Purpose of the Study:

  • To develop a fast and robust algorithm for identifying and resolving tetrahedron intersections in independently refined dual meshes.
  • To enable fully adaptive tetrahedral finite element methods for improved biomedical image reconstruction.

Main Methods:

  • A novel algorithm utilizing finite element weight functions to identify and resolve intersections between tetrahedrons in nested dual meshes.
  • Employs an 8-similar subtetrahedron subdivision scheme for mesh generation.
  • Supports independent mesh refinement and coarsening.

Main Results:

  • The algorithm efficiently identifies and resolves tetrahedron intersections in dual meshes.
  • Demonstrated computational efficiency using diffuse photon density wave solutions.
  • Successfully reconstructed a fluorescent inclusion in a simulated phantom using boundary frequency domain fluorescence measurements.

Conclusions:

  • The developed algorithm facilitates fully adaptive tetrahedral finite element methods for biomedical imaging.
  • Enables high-resolution image reconstruction with reduced computational effort.
  • Paves the way for more efficient and accurate inverse problem solutions in medical imaging.