Medially Based Meshing with Finite Element Analysis of Prostate Deformation

1
Medially Based Meshing with Finite Element
Analysis of Prostate Deformation
Jessica R. Crouch1, Stephen M. Pizer1, Edward L.
Chaney1, and Marco Zaider2
1 Medical Image Display and Analysis Group at
UNC-Chapel Hill 2 Memorial Sloan-Kettering
Cancer Center
Results

• Motivation
• Brachytherapy treatment planning
• Prostate deformed by intra-rectal imaging probe
• Non-rigidly register planning image with
  intra-operative prostate

Left Slice through the deformed prostate
mesh Right The deformation applied to a
regular grid.
Approach
M-rep shape models Hexahedral meshing

• M-reps represent shape based on medial sheets
• Medial atoms are point samples of object
  geometry
• Continuous solid objects are constructed by
• interpolating geometry between medial atoms.

CT slice of phantom prostate with the uninflated
probe
CT slice of phantom prostate with inflated probe
Same as left, with computed deformation applied

• Prostate explicitly modeled
• Surrounding area represented as homogeneous
• Goal register prostate volume
• (no effort made to minimize registration error
  outside the prostate)

• Hexahedral mesh constructed in m-rep
  coordinates
• Subdivision allows control of solution precision

Slice of deformed prostate image overlaid on the
computationally deformed image ?
Boundary Conditions

• Average registration error for 75 brachytherapy
  seeds
• Green bars indicate CT voxel size in a
  direction.
• M-rep predicted category is registration
  using m-rep geometry correspondences without
  using FEM

Conclusion

• Automated process for FEM based registration
  the Deformation Solution applied to Image A
  registers it with Image B

• Point correspondences defined by the m-rep
  object coordinate system that is shared by a
  model and a deformed model.
• u1 and u2 mark corresponding points
• Corresponding points slide along the object
  surface to minimize the solid objects
  deformation energy

• Solution of Finite Element Equations
• Linear elastic equations with the assumption of
  nearly incompressible tissue. Poissons ratio,
  ? .495
• Sparse matrices conjugate gradient iterative
  solver
• Coarse-to-Fine approach

• Seed registration error for phantom prostate
  was approximately the size of an image voxel

Funding provided by NIH grants CA P01 47982 and
EB P01 02779, and a Lucent GRPW fellowship.
November 2003