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:

• 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

To Do:

• Further evaluation on the phalanx bones of the hand
• Convert the code into a Slicer3 execution model program
• Develop additional Slicer3 execution model programs to support complete workflow
  • Assignment of material properties based in image signal intensity
  • Export to Abaqus format
• Determine if there are ways to improve the speed of the algorithm

Key Investigators:

• Iowa: Nicole Grosland, Vincent Magnotta, Ritesh Bafna

Links:

• Musculoskeletal Imaging, Modelling and Experimentation (MIMX)

Execution Model Program Description:

• To be filled in once developed

This tool was developed as part of an NIH NA-MIC Collaboration Grant EB005973.

Program Usage:

• To be filled in once developed

Figures:

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

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

Mesh quality evaluation of the warped cube

Initial attempt to apply mapped meshing algorithm to the proximal phalanx