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Numerical results - PowerPoint PPT Presentation


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Singular perturbations for an elastic model of the heart . Jérôme Pousin. 24 juin 2008.  Objectives. RV. LV.  Extract the heart anatomy (3-D+t segmentation)  Combine complementary functional data (Multimodal registration).  Difficulties. patient movement

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Presentation Transcript
slide2

 Objectives

RV

LV

  •  Extract the heart anatomy
    • (3-D+t segmentation)
  • Combine complementary functional data
    • (Multimodal registration)

 Difficulties

  • patient movement
  • moving deformable organ
  • acquisition geometry
  • the anatomy cannot be easily determined in all modalities
slide3

Segmentation of the heart using an elastic deformable template

1. Elastic deformable template

2. Boundary regularization

3. Singular perturbation

4. Sketch of the proof

ICJ

slide4

 Theoretical context

t(x)

u(x)

Superficial forces

x

Initial domain

Deformed domain

 Continuum mechanics : equilibrium of an elastic body

slide5

 Theoretical context

Equilibrium

Stress tensor

 Potential energy

Stress vector

Strain vector

External energy

Elastic energy

slide6

 Elastic deformable template

[Vincent, 2001]

Incremental load

Assumption : small displacements

slide7

 Elastic deformable template

Iterative local formulation

Discretized expression

slide8

 Computing a 3-D force field

 Force field deriving from a potential image

- Potential minimum on the object border

 Gradient vector flow [Xu, 1998]

 Imposed condition

Force field null on the border of the object to be segmented

slide9

 Computing a 3-D force field

 Example : cube image

slide10

Part 1.

Segmentation of the heart using an elastic deformable template

1. Elastic deformable template

2. Improving the model’s convergence

3. Boundary regularization

4. Model inititialization

5. Results of segmentation

slide11

 Boundary regularization

 Three-layer model

- Ratio of circumferential fibers to longitudinal fibers 10:1

[Streeter, 1969]

Longitudinal

Circumferential

Longitudinal

Large isotropic

middle layer

Thin peripheral layers

slide12

 Boundary regularization

 Constitutive law for a fiber-collagen model

[Ohayon, 1988]

pression

fibers

Fiber direction

 Asymptotic model (  0)

[Destuynder, 1996]

t1, t2

slide13

 Boundary regularization

Without boundary constraint

With boundary constraint

 Boundary constraint energy

slide14

 Elastic deformable template

Singular perturbation

  • Formaly take Dt=0
  • Vanishing elasticity allows larger motion
slide15

Part 1.

Segmentation of the heart using an elastic deformable template

1. Elastic deformable template

2. Improving the model’s convergence

3. Boundary regularization

4. Model inititialization

5. Results of segmentation

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