Temporal Diffeomorphic Free-Form Deformation: Application to for Motion and Deformation

Estimation from 3D Echocardiography

Mathieu De Craenea,b, Gemma Piellaa,b, Nicolas Duchateaua,b, Etel Silvad, Adelina Doltrad, Jan D'hoogee, Oscar Camaraa,b, Josep Brugadad,

Marta Sitgesd, and Alejandro F. Frangia,b,c

Center for Computational Imaging & Simulation Technologies in Biomedicine (CISTIB), a Information and Communication Technologies Department, Universitat Pompeu Fabra, Barcelona,

Spain and b Networking Center on Biomedical Research - CIBER-BBN, Barcelona, Spain. c Institucio Catalana de Recerca i Estudis Avancats, Barcelona, Spain.

d Hospital Clínic; IDIBAPS; Universitat de Barcelona, Spain. e Department of Cardiovascular Diseases, Cardiovascular Imaging and Dynamics, Katholieke

Universiteit Leuven, Belgium.

Longitudinal strain color plotted over time

Motion and Deformation Indexes

Motion

Quantify the motion field overthe cardiac cycle

Strain

Compute spatial derivatives F of the motion field

Strain tensor

Deformation tensor

Longitudinal strain color plotted over time

Motion and Deformation Indexes

Motion

Quantify the motion field overthe cardiac cycle

Strain

Compute spatial derivatives F of the motion field

Strain tensor

Deformation tensor

Algorithmic framework

! Extend diffeomorphic registration for joint alignment of image sequences! Exploit temporal

consistency in the dataset

! TDFFD Temporal Diffeomorphic registration using Free Form Deformation

Recent advances in diffeomorphism for quantification of longitudinal changes! Durrleman et al. (1)

! Diffeomorphic framework for longitudinal regression and atlas building. Comparing the evolution of two populations

! Possible discontinuity at data time points! Restricted to 2D/3D contours (skulls)

! Khan et al. (2)

! Dense non-rigid registration for diffeomorphic registration of longitudinal datasets

! 2D synthetic images, few time points! Spatial regularization kernel (nothing done in time) ! Possible discontinuity at data time points

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(1) Durrleman et al. Spatiotemporal Atlas Estimation for Developmental Delay Detection in Longitudinal Datasets. MICCAI 09

(2) Khan et al. Representation of time-varying shapes in the large deformation diffeomorphic framework. ISBI 08.

MethodTransformation model! Continuous velocity field in the 3D+t domain! The displacement field is obtained from the

displacement field by solving the following ODE:

TransformationMaterial point in reference frame

Continuous time Velocity = Sum of 3D + t spatiotemporal kernels

MethodTransformation model! Numerical integration: Forward Euler integration

(1)

t = 0

time

Method Parametric Jacobian! Definitions

! Eq. (1) can then be rewritten as

! We want to compute the derivative of the mapped coordinate of a given material point regarding the velocity parameters using (2)

(2)

Method Objective function

! The first frame is taken as reference! Gradient-based optimization (L-BFGS-B method)! Requires de derivative of w.r.t control point

velocities (Parametric Jacobian)

Experiments on synthetic ultrasound images! Synthetic US 3D Sequence as used in [1]! It models the left ventricle a sa thick-walled ellipsoid

with physiologically relevant end-diastolic dimensions! A simplified kinematic model with an ejection fraction

of 60% gives an analytical expression of the displacement field.

[1] A. Elen, H. Choi, D. Loeckx, H. Gao, P. Claus, P. Suetens, F. Maes, and J.

D’hooge, “Three-dimensional cardiac strain estimation using spatio-

temporal elastic registration of ultrasound images: a feasibility study.” IEEE

Transactions on Medical Imaging, vol. 27, no. 11, pp. 1580 – 1591, 2008.

Synthetic displacement field: Habemus ground truth

Experiments on synthetic ultrasound images ( surface propagation )

Experiments on synthetic ultrasound images

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! Comparing error on displacement fields (magnitude of difference between estimated and ground truth motion) for pairwise registration and our algorithm

! 2 Levels of noise: 20% and 70 %

Experiments on synthetic ultrasound images

0 5 10 15 200

1

2

3

4

5

6

7

time frame

Err

or

mag

nitu

de

(m

m)

Median error for w=0.2

TDFFDFFD

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0 5 10 15 200

1

2

3

4

5

6

7

time frame

Err

or

mag

nitu

de

(m

m)

Median error for w=0.7

TDFFDFFD

! Comparing error on displacement fields (magnitude of difference between estimated and ground truth motion) for pairwise registration and our algorithm

! 2 Levels of noise: 20% and 70 %

Motion quantification in healthy volunteers! Database of 8 healthy subjects (aged 31 +/- 6 years)! The average number of images per cardiac cycle was

of 17.8! The pixel spacing was on average of 0.9 x 0.6 x 0.9

mm3 ! Quantification of strain in mid and basal AHA

segments! Segments either not totally included in the field of

view of the 3D-US images or suffering from typical image artifacts were excluded from the analysis.

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Motion quantification in healthy volunteers

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Volunteer 1

0 0.5 1

!0.25

!0.2

!0.15

!0.1

!0.05

0

0.05 Long. strain volunteer 1

Volunteer 2

0 0.5 1

!0.25

!0.2

!0.15

!0.1

!0.05

0

0.05 Long. strain volunteer 2

Volunteer 3

0 0.5 1

!0.25

!0.2

!0.15

!0.1

!0.05

0

0.05 Long. strain volunteer 3

Volunteer 4

0 0.5 1

!0.25

!0.2

!0.15

!0.1

!0.05

0

0.05 Long. strain volunteer 4

Volunteer 5

0 0.5 1

!0.25

!0.2

!0.15

!0.1

!0.05

0

0.05 Long. strain volunteer 5

Volunteer 6

0 0.5 1

!0.25

!0.2

!0.15

!0.1

!0.05

0

0.05 Long. strain volunteer 6

Volunteer 7

0 0.5 1

!0.25

!0.2

!0.15

!0.1

!0.05

0

0.05 Long. strain volunteer 7

Volunteer 8

0 0.5 1

!0.25

!0.2

!0.15

!0.1

!0.05

0

0.05 Long. strain volunteer 8

Quantification of Motion and Deformation before and after CRT

before afterSeptal stretching

De Craene et al, FIMH09 2009 “Large diffeomorphic FFD Registration for motion and strain quantification from 3D US sequences ”

Quantification of Motion and Deformation before and after CRT

Strain curves before and after CRT

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Strain curves before and after CRT

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Conclusions

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! Extension of diffeomorphic framework to handle image sequences

! Continuity of 4D velocity field enforced through radial basis functions

! Coupling between time steps improved robustness to noise

! Further questions! Include incompressibility constraint! Extension to arbitrary reference in the sequence and

sequential metric! Address unbiased sampling schemes. Symmetric registration.

Thanks !

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