Geometry modeling and nonlinear reconstruction for x ray guided breast dot
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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. Outline. Instrument overview Binary function based mesh generator

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Geometry modeling and nonlinear reconstruction for x ray guided breast dot

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

SPIE Photonic West 2006


Outline
Outline guided breast DOT

  • Instrument overview

  • Binary function based mesh generator

  • Iterative block solver

  • Reconstruction results

  • Summary

SPIE Photonic West 2006


Why combine x ray with dot
Why combine X-ray with DOT? guided breast 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.

SPIE Photonic West 2006


System picture
System Picture guided breast DOT

TOBI: tomographical optical breast

imaging system

Tomosynthesis: 3D Mammography

SPIE Photonic West 2006


Binary function based mesh generation
Binary function based mesh generation guided breast DOT

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

SPIE Photonic West 2006


Prologue distance function based mesh generation
Prologue: Distance function based mesh generation guided breast DOT

  • 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/

SPIE Photonic West 2006


Binary functions
Binary Functions guided breast DOT

  • A binary function: inside or out side

1

-2

2

int binary_shape(double x, double y)

{

return (x>2. && x<-2. && y>2. && y<-2.

&& x*x+y*y>1.);

}

For medical images, only memory access is needed,

no arithmetic !

SPIE Photonic West 2006


Step 1 3 of 5
Step 1-3 of 5 guided breast DOT

  • Step 1: initial mesh

    • Truncating isotropic mesh by binary function

  • Step 2: boundary layer

    • Use Laplacian operator to find out the boundary layer

    • Reduce computationalcomplexity fromO(N) to O(N1/2) for2D, O(N) to O(N2/3)for 3D

  • Step 3: moving mesh

    • treat mesh as truss system, solve for physical equilibrium

SPIE Photonic West 2006


Step 4 of 5 boundary correction
Step 4 of 5: Boundary Correction guided breast DOT

  • if nodes move outside the geometry

  • bi-sect search betweenPi and Pi+1

  • line search over a circle,find out the closest boundary point

Step 5 of 5: Re-Triangulation

  • 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)

SPIE Photonic West 2006


More complicated cases
More complicated cases guided breast DOT

  • Mesh generation in 3D or in Rnspace

    • 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

SPIE Photonic West 2006


Examples
Examples guided breast DOT

SPIE Photonic West 2006


Iterative block solver for fem forward modeling
Iterative Block Solver for FEM forward modeling guided breast DOT

  • 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,..,xN]=[b1,b2,b3,…,bN] N: block size

SPIE Photonic West 2006


Solver performance
Solver Performance guided breast DOT

  • mesh: 42122 nodes and 230745 elements

  • RF diffusion equation

optimal block size

SPIE Photonic West 2006


Results simulations
Results: Simulations guided breast DOT

  • TOMO Slices Forward&Recon meshes

Slice#35

Slice#50

SPIE Photonic West 2006


Simulation cont d
Simulation – Cont’d guided breast DOT

True absorption Recovered absorption w/o geometry modeling

A tumor

SPIE Photonic West 2006


Summary
Summary guided breast DOT

  • 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.

SPIE Photonic West 2006


Acknowledgements
Acknowledgements guided breast DOT

  • 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

    • ...

SPIE Photonic West 2006


Geometry modeling and nonlinear reconstruction for x ray guided breast dot

SPIE Photonic West 2006