View source for 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 -  [http://www.na-mic.org/Wiki/images/3/34/2007_AHM_Programming_Half_Week_MappedMesh.ppt 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 - [http://www.vtk.org/doc/nightly/html/classvtkIterativeClosestPointTransform.html Iterative Closest Point] or [http://www.vtk.org/doc/nightly/html/classvtkProcrustesAlignmentFilter.html 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. [http://www.informaworld.com/smpp/content~db=all?content=10.1080/10255840802136143 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:'''
*[http://www.ccad.uiowa.edu/mimx Musculoskeletal Imaging, Modeling 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:'''

[[Image:MappedHexMeshSquareSphereInit.jpg|left|thumb|300px|Initial position of the cube template mesh and the sphere surface prior to registration using the itk::FEM mapped meshing algorithm]]

[[Image:MappedMeshCubeSphereQuality.jpg|left|thumb|325px|Mesh quality evaluation of the warped cube]]

[[Image:MappedMeshSquareSphere.jpg|left|thumb|300px|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]]

[[Image:MappedMeshProximalPhalanxTrial.jpg|left|thumb|300px|Initial attempt to apply mapped meshing algorithm to the proximal phalanx]]