Dynamic Modelling of the Whole Heart Based on a Frequency - - PowerPoint PPT Presentation

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Dynamic Modelling of the Whole Heart Based on a Frequency - - PowerPoint PPT Presentation

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D EPARTAMENTO DE C IENCIAS P OLITCNICAS UCAM U NIVERSIDAD C ATLICA DE M URCIA D. T ECNOLOGAS DE LA I NFORMACIN Y LAS C OMUNICACIONES U NIVERSIDAD P OLITCNICA DE C ARTAGENA 6th. International Work-Conference on the Interplay between

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SLIDE 1

DEPARTAMENTO DE CIENCIAS POLITÉCNICAS UCAM UNIVERSIDAD CATÓLICA DE MURCIA

  • D. TECNOLOGÍAS DE LA INFORMACIÓN Y LAS COMUNICACIONES

UNIVERSIDAD POLITÉCNICA DE CARTAGENA

  • 6th. International Work-Conference on the Interplay between Natural and

Artificial Computation - IWINAC 2015

Dynamic Modelling of the Whole Heart Based on a Frequency Formulation and Implementation of Parametric Deformable Models

Rafael Berenguer-Vidal Rafael Verdú-Monedero Álvar Legaz-Aparicio

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SLIDE 2

Outline

Outline

1

Introduction

2

Multidimensional parametric deformable models

3

Practical implementation of the method

4

Results

5

Conclusions

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 2 / 22

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SLIDE 3

Introduction

Outline

1

Introduction Deformable models

2

Multidimensional parametric deformable models

3

Practical implementation of the method

4

Results

5

Conclusions

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 3 / 22

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SLIDE 4

Introduction Deformable models

Deformable models in CVD analysis

Description Analysis of motion and deformation of the heart

Considerable interest in the literature Great impact of cardiovascular disease (CVD) Several approaches proposed

Deformable models Deformable models based on B-splines

Interesting approach for cardiac characterization Use of frequency-based multidimensional parametric deformable models Efficient implementation

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 4 / 22

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SLIDE 5

Introduction Deformable models

Deformable models in CVD analysis

Description Analysis of motion and deformation of the heart

Considerable interest in the literature Great impact of cardiovascular disease (CVD) Several approaches proposed

Deformable models Deformable models based on B-splines

Interesting approach for cardiac characterization Use of frequency-based multidimensional parametric deformable models Efficient implementation

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 4 / 22

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SLIDE 6

Multidimensional parametric deformable models

Outline

1

Introduction

2

Multidimensional parametric deformable models Static model Dynamic model Spatial and temporal discretization Implementation in the frequency domain

3

Practical implementation of the method

4

Results

5

Conclusions

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 5 / 22

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SLIDE 7

Multidimensional parametric deformable models Static model

Parametric deformable model

Time-varying parametric Hypersurface defined in Rd v ≡ v(s, t) = [v1(s, t), v2(s, t), . . . , vd(s, t)]⊤, Parametric variables s ≡ [s1, . . . , se] with sj ∈ [0, Lj] and e d Coordinate functions vi(s, t)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 6 / 22

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SLIDE 8

Multidimensional parametric deformable models Static model

Parametric deformable model

Time-varying parametric Hypersurface defined in Rd v ≡ v(s, t) = [v1(s, t), v2(s, t), . . . , vd(s, t)]⊤, Parametric variables s ≡ [s1, . . . , se] with sj ∈ [0, Lj] and e d Coordinate functions vi(s, t)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 6 / 22

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SLIDE 9

Multidimensional parametric deformable models Static model

Parametric deformable model

Time-varying parametric Hypersurface defined in Rd v ≡ v(s, t) = [v1(s, t), v2(s, t), . . . , vd(s, t)]⊤, Parametric variables s ≡ [s1, . . . , se] with sj ∈ [0, Lj] and e d Coordinate functions vi(s, t)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 6 / 22

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SLIDE 10

Multidimensional parametric deformable models Static model

Parametric deformable model

Time-varying parametric Hypersurface defined in Rd v ≡ v(s, t) = [v1(s, t), v2(s, t), . . . , vd(s, t)]⊤, Parametric variables s ≡ [s1, . . . , se] with sj ∈ [0, Lj] and e d Coordinate functions vi(s, t)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 6 / 22

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SLIDE 11

Multidimensional parametric deformable models Static model

Parametric deformable model

Time-varying parametric Hypersurface defined in Rd v ≡ v(s, t) = [v1(s, t), v2(s, t), . . . , vd(s, t)]⊤, Parametric variables s ≡ [s1, . . . , se] with sj ∈ [0, Lj] and e d Coordinate functions vi(s, t)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 6 / 22

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SLIDE 12

Multidimensional parametric deformable models Static model

Static model

Energy functional The model shape is governed by an energy functional: E(v) = S(v) + P(v)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 7 / 22

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SLIDE 13

Multidimensional parametric deformable models Static model

Static model

Energy functional The model shape is governed by an energy functional: E(v) = S(v) + P(v) Internal and external energies Internal deformation energy, S(v): S(v) = 1 2

d

  • i=1
  • Ω

α(s) ∇vi(s)2 + β(s) |∆vi(s)|2 ds

  • Ω := [0, L1] × [0, L2] × . . . × [0, Le]

α(s) and β(s) represent elasticidad and rigidity Rest of energies, P(v):

External energies, gradient of data, ... Non-lineal restrictions, hard-constraints, ...

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 7 / 22

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SLIDE 14

Multidimensional parametric deformable models Static model

Static model

Energy functional The model shape is governed by an energy functional: E(v) = S(v) + P(v) Euler-Lagrange equation To minimize E(v), model v(s) must satisfy E-L equation. For the multidimensional case, we obtain a system of d PDE’s: −∇ ·

  • α(s)∇v(s)
  • + ∆
  • β(s)∆v(s)
  • = q
  • v(s)
  • where

q

  • v(s)
  • = −∇viP
  • v(s)
  • + f
  • v(s)
  • ∈ Rd

Represents the balance between internal and external energies

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 7 / 22

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SLIDE 15

Multidimensional parametric deformable models Dynamic model

Dynamic model

Temporal evolution Lagrangian mechanics theory Dynamic deformable mechanics Temporal parameters Mass density: µ(s) Dumping density: γ(s)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 8 / 22

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SLIDE 16

Multidimensional parametric deformable models Dynamic model

Dynamic model

Temporal evolution Lagrangian mechanics theory Dynamic deformable mechanics Temporal parameters Mass density: µ(s) Dumping density: γ(s)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 8 / 22

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SLIDE 17

Multidimensional parametric deformable models Dynamic model

Dynamic model

Temporal evolution Lagrangian mechanics theory Dynamic deformable mechanics Temporal parameters Mass density: µ(s) Dumping density: γ(s) Dynamic model d decoupled PDE’s system:

µ(s)∂ttvi(s, t) + γ(s)∂tvi(s, t) − ∂s1

  • α(s)∂s1vi(s, t)
  • − · · · − ∂se
  • α(s)∂sevi(s, t)
  • +
  • ∂s1s1 + · · · + ∂sese
  • β(s)∂s1s1vi(s, t) + · · · + β(s)∂sesev1(s, t)
  • =

q

  • v(s)
  • 1 i d

i ∈ N

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 8 / 22

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SLIDE 18

Multidimensional parametric deformable models Spatial and temporal discretization

Spatial discretization

Finite elements formulation Parametric domain 0 sj Lj partitioned into Nj finite subdomains. Model represented as the union of N = N1N2 · · · Ne elements:

vi(s, t) =

N1−1

  • n1=0

· · ·

Ne−1

  • ne=0

v n

i (s, t),

n = [n1, . . . , ne],

Each vi is represented using shape functions and variable vectors:

v n

i (s, t) = Nn i (s)un i (s, t),

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 9 / 22

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SLIDE 19

Multidimensional parametric deformable models Spatial and temporal discretization

Spatial discretization

Finite elements formulation Parametric domain 0 sj Lj partitioned into Nj finite subdomains. Model represented as the union of N = N1N2 · · · Ne elements:

vi(s, t) =

N1−1

  • n1=0

· · ·

Ne−1

  • ne=0

v n

i (s, t),

n = [n1, . . . , ne],

Each vi is represented using shape functions and variable vectors:

v n

i (s, t) = Nn i (s)un i (s, t),

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 9 / 22

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SLIDE 20

Multidimensional parametric deformable models Spatial and temporal discretization

Spatial discretization

Finite elements formulation Parametric domain 0 sj Lj partitioned into Nj finite subdomains. Model represented as the union of N = N1N2 · · · Ne elements:

vi(s, t) =

N1−1

  • n1=0

· · ·

Ne−1

  • ne=0

v n

i (s, t),

n = [n1, . . . , ne],

Each vi is represented using shape functions and variable vectors:

v n

i (s, t) = Nn i (s)un i (s, t),

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 9 / 22

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SLIDE 21

Multidimensional parametric deformable models Spatial and temporal discretization

Spatial discretization

Finite elements formulation Parametric domain 0 sj Lj partitioned into Nj finite subdomains. Model represented as the union of N = N1N2 · · · Ne elements:

vi(s, t) =

N1−1

  • n1=0

· · ·

Ne−1

  • ne=0

v n

i (s, t),

n = [n1, . . . , ne],

Each vi is represented using shape functions and variable vectors:

v n

i (s, t) = Nn i (s)un i (s, t),

Shape functions B-spline and Finite differences Both shape functions are separable

Allow the decomposition of the multidimensional shape functions in

  • ne-dimensional functions
  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 9 / 22

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SLIDE 22

Multidimensional parametric deformable models Spatial and temporal discretization

Spatial discretization

Finite elements formulation Parametric domain 0 sj Lj partitioned into Nj finite subdomains. Model represented as the union of N = N1N2 · · · Ne elements:

vi(s, t) =

N1−1

  • n1=0

· · ·

Ne−1

  • ne=0

v n

i (s, t),

n = [n1, . . . , ne],

Each vi is represented using shape functions and variable vectors:

v n

i (s, t) = Nn i (s)un i (s, t),

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 9 / 22

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SLIDE 23

Multidimensional parametric deformable models Spatial and temporal discretization

Spatial discretization

Matrix formulation Assuming same shape function for all segments. Applying Galerkin’s method to E-L equation. Mdttui(t) + Cdtui(t) + Kui(t) = qi(t)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 10 / 22

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SLIDE 24

Multidimensional parametric deformable models Spatial and temporal discretization

Spatial discretization

Matrix formulation Assuming same shape function for all segments. Applying Galerkin’s method to E-L equation. Mdttui(t) + Cdtui(t) + Kui(t) = qi(t)

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 10 / 22

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SLIDE 25

Multidimensional parametric deformable models Spatial and temporal discretization

Temporal discretization

Discrete approximations for time derivatives Notation used: u(ξ∆t) = uξ Discrete approximations:

dtui(t) ≈ (ui(t) − ui(t − ∆t)) /(∆t) dttui(t) ≈ (ui(t) − 2ui(t − ∆t) + ui(t − 2∆t)) /(∆t)2

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 11 / 22

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SLIDE 26

Multidimensional parametric deformable models Spatial and temporal discretization

Temporal discretization

Discrete approximations for time derivatives Notation used: u(ξ∆t) = uξ Discrete approximations:

dtui(t) ≈ (ui(t) − ui(t − ∆t)) /(∆t) dttui(t) ≈ (ui(t) − 2ui(t − ∆t) + ui(t − 2∆t)) /(∆t)2

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 11 / 22

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SLIDE 27

Multidimensional parametric deformable models Implementation in the frequency domain

Frequency domain

Discrete domain translated into the frequency domain (eDFT ) Frequency approach reduces computational cost Allows us to isolate the spectral components of the nodes

ˆ uξ = ˆ h

  • a1ˆ

uξ−1 + a2 ˆ uξ−2 + (ηˆ f)−1ˆ qξ−1

  • ,

where ˆ u, ˆ f and ˆ q are the eDFT ’s of their sequences, η = m/∆t2 + c/∆t, γ = ∆t c/m , a1 = 1 + (1 + γ)−1 and a2 = − (1 + γ)−1 Internal forces imposed by e-dimensional filter ˆ h External forces applied by ˆ q The processing of each spectral component is independent of the others

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 12 / 22

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SLIDE 28

Multidimensional parametric deformable models Implementation in the frequency domain

Frequency domain

Discrete domain translated into the frequency domain (eDFT ) Frequency approach reduces computational cost Allows us to isolate the spectral components of the nodes

ˆ uξ = ˆ h

  • a1ˆ

uξ−1 + a2 ˆ uξ−2 + (ηˆ f)−1ˆ qξ−1

  • ,

where ˆ u, ˆ f and ˆ q are the eDFT ’s of their sequences, η = m/∆t2 + c/∆t, γ = ∆t c/m , a1 = 1 + (1 + γ)−1 and a2 = − (1 + γ)−1 Internal forces imposed by e-dimensional filter ˆ h External forces applied by ˆ q The processing of each spectral component is independent of the others

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 12 / 22

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SLIDE 29

Multidimensional parametric deformable models Implementation in the frequency domain

Frequency domain

Discrete domain translated into the frequency domain (eDFT ) Frequency approach reduces computational cost Allows us to isolate the spectral components of the nodes

ˆ uξ = ˆ h

  • a1ˆ

uξ−1 + a2 ˆ uξ−2 + (ηˆ f)−1ˆ qξ−1

  • ,

where ˆ u, ˆ f and ˆ q are the eDFT ’s of their sequences, η = m/∆t2 + c/∆t, γ = ∆t c/m , a1 = 1 + (1 + γ)−1 and a2 = − (1 + γ)−1 Internal forces imposed by e-dimensional filter ˆ h External forces applied by ˆ q The processing of each spectral component is independent of the others

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 12 / 22

slide-30
SLIDE 30

Multidimensional parametric deformable models Implementation in the frequency domain

Frequency domain

Discrete domain translated into the frequency domain (eDFT ) Frequency approach reduces computational cost Allows us to isolate the spectral components of the nodes

ˆ uξ = ˆ h

  • a1ˆ

uξ−1 + a2 ˆ uξ−2 + (ηˆ f)−1ˆ qξ−1

  • ,

where ˆ u, ˆ f and ˆ q are the eDFT ’s of their sequences, η = m/∆t2 + c/∆t, γ = ∆t c/m , a1 = 1 + (1 + γ)−1 and a2 = − (1 + γ)−1 Internal forces imposed by e-dimensional filter ˆ h External forces applied by ˆ q The processing of each spectral component is independent of the others

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 12 / 22

slide-31
SLIDE 31

Multidimensional parametric deformable models Implementation in the frequency domain

Frequency domain

Discrete domain translated into the frequency domain (eDFT ) Frequency approach reduces computational cost Allows us to isolate the spectral components of the nodes

ˆ uξ = ˆ h

  • a1ˆ

uξ−1 + a2 ˆ uξ−2 + (ηˆ f)−1ˆ qξ−1

  • ,

where ˆ u, ˆ f and ˆ q are the eDFT ’s of their sequences, η = m/∆t2 + c/∆t, γ = ∆t c/m , a1 = 1 + (1 + γ)−1 and a2 = − (1 + γ)−1 Internal forces imposed by e-dimensional filter ˆ h External forces applied by ˆ q The processing of each spectral component is independent of the others

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 12 / 22

slide-32
SLIDE 32

Multidimensional parametric deformable models Implementation in the frequency domain

Frequency domain

Discrete domain translated into the frequency domain (eDFT ) Frequency approach reduces computational cost Allows us to isolate the spectral components of the nodes

ˆ uξ = ˆ h

  • a1ˆ

uξ−1 + a2 ˆ uξ−2 + (ηˆ f)−1ˆ qξ−1

  • ,

where ˆ u, ˆ f and ˆ q are the eDFT ’s of their sequences, η = m/∆t2 + c/∆t, γ = ∆t c/m , a1 = 1 + (1 + γ)−1 and a2 = − (1 + γ)−1 Internal forces imposed by e-dimensional filter ˆ h External forces applied by ˆ q The processing of each spectral component is independent of the others

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 12 / 22

slide-33
SLIDE 33

Practical implementation of the method

Outline

1

Introduction

2

Multidimensional parametric deformable models

3

Practical implementation of the method

4

Results

5

Conclusions

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 13 / 22

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SLIDE 34

Practical implementation of the method

Algorithm

Aim of this work To segment and characterize shape and volume of human heart Analyze the evolution over time 4D medical data processed Formulation applied in applied in R3, i.e., d = 3 Dynamic analysis achieved by applying the process through the whole cardiac cycle Algorithm detailed in the paper

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 14 / 22

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SLIDE 35

Practical implementation of the method

Algorithm

Aim of this work To segment and characterize shape and volume of human heart Analyze the evolution over time 4D medical data processed Formulation applied in applied in R3, i.e., d = 3 Dynamic analysis achieved by applying the process through the whole cardiac cycle Algorithm detailed in the paper

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 14 / 22

slide-36
SLIDE 36

Practical implementation of the method

Algorithm

Aim of this work To segment and characterize shape and volume of human heart Analyze the evolution over time 4D medical data processed Formulation applied in applied in R3, i.e., d = 3 Dynamic analysis achieved by applying the process through the whole cardiac cycle Algorithm detailed in the paper

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 14 / 22

slide-37
SLIDE 37

Practical implementation of the method

Algorithm

Aim of this work To segment and characterize shape and volume of human heart Analyze the evolution over time 4D medical data processed Formulation applied in applied in R3, i.e., d = 3 Dynamic analysis achieved by applying the process through the whole cardiac cycle Algorithm detailed in the paper

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 14 / 22

slide-38
SLIDE 38

Practical implementation of the method

Algorithm

Aim of this work To segment and characterize shape and volume of human heart Analyze the evolution over time 4D medical data processed Formulation applied in applied in R3, i.e., d = 3 Dynamic analysis achieved by applying the process through the whole cardiac cycle Algorithm detailed in the paper

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 14 / 22

slide-39
SLIDE 39

Practical implementation of the method

Algorithm

Aim of this work To segment and characterize shape and volume of human heart Analyze the evolution over time 4D medical data processed Formulation applied in applied in R3, i.e., d = 3 Dynamic analysis achieved by applying the process through the whole cardiac cycle Algorithm detailed in the paper

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 14 / 22

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SLIDE 40

Practical implementation of the method

Preprocessing and gradient calculation

Preprocessing Application of a 3D low pass filter Basic operations of mathematical morphology applied 2D B-spline filter applied to each slice Gradient calculation of data External forces for the algorithm

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 15 / 22

slide-41
SLIDE 41

Practical implementation of the method

Preprocessing and gradient calculation

Preprocessing Application of a 3D low pass filter Basic operations of mathematical morphology applied 2D B-spline filter applied to each slice Gradient calculation of data External forces for the algorithm

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 15 / 22

slide-42
SLIDE 42

Practical implementation of the method

Preprocessing and gradient calculation

Preprocessing Application of a 3D low pass filter Basic operations of mathematical morphology applied 2D B-spline filter applied to each slice Gradient calculation of data External forces for the algorithm

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 15 / 22

slide-43
SLIDE 43

Practical implementation of the method

Preprocessing and gradient calculation

Preprocessing Application of a 3D low pass filter Basic operations of mathematical morphology applied 2D B-spline filter applied to each slice Gradient calculation of data External forces for the algorithm

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 15 / 22

slide-44
SLIDE 44

Practical implementation of the method

Preprocessing and gradient calculation

Preprocessing Application of a 3D low pass filter Basic operations of mathematical morphology applied 2D B-spline filter applied to each slice Gradient calculation of data External forces for the algorithm

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 15 / 22

slide-45
SLIDE 45

Practical implementation of the method

Preprocessing and gradient calculation

Preprocessing

x y 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500

(a) z=32 slice

x y 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500

(b) Extended-max tr.

x y 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500

(c) Discon. points joining

x y 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500

(d) Closing

x y 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500

(e) Internal pixels rem.

x y 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500

(f) B-splines filtering

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 16 / 22

slide-46
SLIDE 46

Practical implementation of the method

Preprocessing and gradient calculation

Gradient calculation and external forces

x y 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500 −4 −2 2 4 6

(g) x-axis gradient, FI;x

x y 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500 −5 −4 −3 −2 −1 1 2 3 4 5

(h) y-axis gradient, FI;y

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 16 / 22

slide-47
SLIDE 47

Practical implementation of the method

Filtering process

Parameters Model N1 = 64 and N2 = 45 based on B-splines Motion for coordinate function ux and uy Model initialized as a cylinder in nf = 1 Model initialization from the position of previous frames for nf > 1

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 17 / 22

slide-48
SLIDE 48

Practical implementation of the method

Filtering process

Parameters Model N1 = 64 and N2 = 45 based on B-splines Motion for coordinate function ux and uy Model initialized as a cylinder in nf = 1 Model initialization from the position of previous frames for nf > 1 Temporal evolution ξ = 0, 50, 150 and t = 1

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 17 / 22

slide-49
SLIDE 49

Practical implementation of the method

Filtering process

Parameters Model N1 = 64 and N2 = 45 based on B-splines Motion for coordinate function ux and uy Model initialized as a cylinder in nf = 1 Model initialization from the position of previous frames for nf > 1 Slice z = 14: ξ = 0, 50, 150 and t = 1

x y 100 200 300 400 500 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 x y 100 200 300 400 500 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 x y 100 200 300 400 500 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 17 / 22

slide-50
SLIDE 50

Results

Outline

1

Introduction

2

Multidimensional parametric deformable models

3

Practical implementation of the method

4

Results

5

Conclusions

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 18 / 22

slide-51
SLIDE 51

Results

Estimation of volume of the heart

Deformable model v applied to all data frames Boundaries of the heart defined by a parametric function Deformation and motion can be analyzed Other parameters as velocity or acceleration also calculable

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 19 / 22

slide-52
SLIDE 52

Results

Estimation of volume of the heart

Deformable model v applied to all data frames Boundaries of the heart defined by a parametric function Deformation and motion can be analyzed Other parameters as velocity or acceleration also calculable

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 19 / 22

slide-53
SLIDE 53

Results

Estimation of volume of the heart

Deformable model v applied to all data frames Boundaries of the heart defined by a parametric function Deformation and motion can be analyzed Other parameters as velocity or acceleration also calculable

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 19 / 22

slide-54
SLIDE 54

Results

Estimation of volume of the heart

Deformable model v applied to all data frames Boundaries of the heart defined by a parametric function Deformation and motion can be analyzed Other parameters as velocity or acceleration also calculable Volume of the heart throughout the cardiac cycle

2 4 6 8 10 12 14 16 18 20 5150 5200 5250 5300 5350 5400 5450 5500

nf cm3

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 19 / 22

slide-55
SLIDE 55

Conclusions

Outline

1

Introduction

2

Multidimensional parametric deformable models

3

Practical implementation of the method

4

Results

5

Conclusions

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 20 / 22

slide-56
SLIDE 56

Conclusions

Conclusions

Contributions Parametric deformable model in the frequency domain

Proposed to characterize the shape of a heart over time Iterative process in the Fourier domain provides a high computational efficiency

This work shows the preliminary results

Method applied to a 4D CT Parametric formulation allows us to derive dynamical parameters

Future lines of work Comparative evaluation of existing methods to characterize the shape Use of the model to the segmentation and tracking of the left ventricle

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 21 / 22

slide-57
SLIDE 57

Conclusions

Conclusions

Contributions Parametric deformable model in the frequency domain

Proposed to characterize the shape of a heart over time Iterative process in the Fourier domain provides a high computational efficiency

This work shows the preliminary results

Method applied to a 4D CT Parametric formulation allows us to derive dynamical parameters

Future lines of work Comparative evaluation of existing methods to characterize the shape Use of the model to the segmentation and tracking of the left ventricle

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 21 / 22

slide-58
SLIDE 58

Conclusions

Conclusions

Contributions Parametric deformable model in the frequency domain

Proposed to characterize the shape of a heart over time Iterative process in the Fourier domain provides a high computational efficiency

This work shows the preliminary results

Method applied to a 4D CT Parametric formulation allows us to derive dynamical parameters

Future lines of work Comparative evaluation of existing methods to characterize the shape Use of the model to the segmentation and tracking of the left ventricle

  • R. Berenguer-Vidal (UCAM)

IWINAC 2015, Elche Spain June 3th 2015 21 / 22

slide-59
SLIDE 59

DEPARTAMENTO DE CIENCIAS POLITÉCNICAS UCAM UNIVERSIDAD CATÓLICA DE MURCIA

  • D. TECNOLOGÍAS DE LA INFORMACIÓN Y LAS COMUNICACIONES

UNIVERSIDAD POLITÉCNICA DE CARTAGENA

  • 6th. International Work-Conference on the Interplay between Natural and

Artificial Computation - IWINAC 2015

Dynamic Modelling of the Whole Heart Based on a Frequency Formulation and Implementation of Parametric Deformable Models

Rafael Berenguer-Vidal Rafael Verdú-Monedero Álvar Legaz-Aparicio