Mapped Hexahedral Meshing

Objective:

• Develop a tool for mapped meshing that will warp a template mesh onto a surface for a new subject
• Determine the limits that the warping algorithm will succeed and fail
• Apply these techniques to a sample of data to determine the reliability of the algorithm with respect to mesh quality

Progress:

• Previous work on this project was performed at the 2007 AHM - Mapped Mesh 4 Block
• Warped meshing framework has been developed using VTK and ITK using a finite element approach
  • VTK
    • Support the reading and writing of meshes (vtkUnstructuredGrid) and surfaces (vtkPolyData)
    • Distance measures between the deforming mesh and the subject surface
    • Initial registration - Iterative Closest Point or Procrustes
  • ITK
    • Finite element framework used to warped the template mesh onto the subject surface
• Registration made hierarchical to speed up the registration process
  • Requires multiple template meshes to exist
  • This is readily supported using the interactive meshing tools by changing the average edge length
  • Subsequent meshes are initialized using a thin plate splines
• Parameters allowed to vary at each level of the registration
  • Iterations
  • Young's Modulus
• Convergence based on distance between the warped template and the subject surface
  • User specified convergence threshold in mm
  • Convergence can be based on average or maximum distance
• Boundary conditions can be applied
  • Center of the mesh - Holds the eight nodes closest to the center of the mesh fixed
  • External - Applies boundary conditions to the mesh as they fall within a user specified tolerance of the subject surface
• Initial testing done by warping a cube mesh onto a sphere
  • Evaluation:
    • Distance between warped mesh and subject surface
    • Mesh quality

Publications:

• Grosland NM, Bafna R, Magnotta VA. Automated hexahedral meshing of anatomic structures using deformable registration. Comput Methods Biomech Biomed Engin. 12(1):35-43, 2009.

Key Investigators:

• Iowa: Nicole Grosland, Vincent Magnotta, Ritesh Bafna

Links:

• Musculoskeletal Imaging, Modeling and Experimentation (MIMX)

Figures:

Initial position of the cube template mesh and the sphere surface prior to registration using the itk::FEM mapped meshing algorithm

Mesh quality evaluation of the warped cube

a)Position of the template cube mesh and surface after ICP registration. b) Resulting warped cube after itk::FEM mapped meshing. c) Distance map between the warped cube and the sphere surface

Initial attempt to apply mapped meshing algorithm to the proximal phalanx