1. 01/21/2006 SPIE Photonic West 2006 Geometry modeling and nonlinear reconstruction for X-ray guided breast DOT Qianqian Fang +, David Boas +, Greg Boverman*, Quan Zhang +, Tina Kauffman + + Massachusetts General Hospital *Northeastern University NTROI

2. 01/21/2006SPIE Photonic West 2006 Outline  Instrument overview  Binary function based mesh generator  Iterative block solver  Reconstruction results  Summary

3. 01/21/2006SPIE Photonic West 2006 Why combine X-ray with DOT?  Mammography is low-cost and routinely used across the country  X-ray only provide morphological info.  DOT can provide functional measurement but is low-resolution. Combined X-ray/DOT imaging can help doctor’s assessment by overlaying functional image on top of structural image.

4. 01/21/2006SPIE Photonic West 2006 System Picture Tomosynthesis: 3D Mammography TOBI: tomographical optical breast imaging system

5. 01/21/2006SPIE Photonic West 2006 Binary function based mesh generation Why another mesh generator?  Conventional method for mesh generation from medical images  segmentation and boundary extraction  surface smoothing  advance-front method  mesh optimization  What the new generator can offer?  anyone can understand and implement  no need for boundary extraction and smoothing  high quality elements, no need for mesh optimization  in some cases, may faster than conventional method

6. 01/21/2006SPIE Photonic West 2006 Prologue: Distance function based mesh generation  Persson & Strang (MIT), 2004 SIAM Review: Simple mesh generation based on signed- distance functions  Pros:  simple  high quality  Cons:  difficult for compli- cated geometries  slow http://www-math.mit.edu/~persson/mesh/

7. 01/21/2006SPIE Photonic West 2006 Binary Functions  A binary function: inside or out side int binary_shape(double x, double y) { return (x>2. && x 2. && y<-2. && x*x+y*y>1.); } 2 -2 1 For medical images, only memory access is needed, no arithmetic !

8. 01/21/2006SPIE Photonic West 2006 Step 1-3 of 5  Step 1: initial mesh  Truncating isotropic mesh by binary function  Step 2: boundary layer  Use Laplacian operator to find out the boundary layer  Reduce computational complexity from O(N) to O(N 1/2 ) for 2D, O(N) to O(N 2/3 ) for 3D  Step 3: moving mesh  treat mesh as truss system, solve for physical equilibrium

9. 01/21/2006SPIE Photonic West 2006 Step 4 of 5: Boundary Correction  if nodes move outside the geometry 1. bi-sect search between P i and P i+1 2. line search over a circle, find out the closest boundary point  Moving mesh will change mesh topology, without timely updating neighbor list, this may cause method to diverge.  Delaunay based triangulation (for example: QHull) can be used (only apply to the nodes within boundary layer) Step 5 of 5: Re-Triangulation

10. 01/21/2006SPIE Photonic West 2006 More complicated cases  Mesh generation in 3D or in R n space  Step 1: using uniform grid as initial mesh  Step 4: the second line search in boundary correction is performed on a (hyper-)sphere surface  For medical images: segmentations  Anisotropic elements  Non-uniform mesh density  Quadtree or Octree

11. 01/21/2006SPIE Photonic West 2006 Examples

12. 01/21/2006SPIE Photonic West 2006 Iterative Block Solver for FEM forward modeling  Solving FEM forward equation: large scale, sparse, complex (or real) entries  Direct methods: SuperLU, UMFPACK, WSMP …  Iterative methods: CG, BiCG, GMRES, QMR …  QMR multi-RHS solver(Boyes&Seidl,1996): A[x1,x2,x3,..,x N ]=[b1,b2,b3,…,b N ] N: block size

13. 01/21/2006SPIE Photonic West 2006 Solver Performance  mesh: 42122 nodes and 230745 elements  RF diffusion equation optimal block size

14. 01/21/2006SPIE Photonic West 2006 Results: Simulations  TOMO Slices Forward&Recon meshes Slice#35 Slice#50

15. 01/21/2006SPIE Photonic West 2006 Simulation – Cont’d True absorption Recovered absorption w/o geometry modeling A tumor

16. 01/21/2006SPIE Photonic West 2006 Summary  Take home messages:  TOBI: RF+CW+MUX, can co-register with 2D or 3D mammography  Mesh generator is simple and easy to implement, good for mesh generation from medical images  Block solver is efficient in solving forward problems  Problems: mesh generator not entirely stable; some elements close to boundary are not perfect; 3D triangulation produces empty elements.

17. 01/21/2006SPIE Photonic West 2006 Acknowledgements  Funding Agencies  NIH  NTROI  Avon Breast Cancer Center  Daniel Kopans  Richard Moore  Dianne Georgian-Smith  Jennifer Curry  Dianne Scourletis  Donna Burgess  Jayne Cormier  Lockheed Palo Alto Research Laboratories  William Boyse  Photon Migration Lab at MGH  Maria Franceschini  Stefan Carp  Juliette Selb  Elizabeth Hillman  Sol Diamond  Phill Jones  Danny Joseph  Ted Hupper  Anand Kumar  GW Krauss  George Themelis ...

18. 01/21/2006SPIE Photonic West 2006  Questions?