1. 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.

2. Motion and Deformation Indexes
Motion
Quantify the motion
field over
the cardiac cycle
Deformation
Strain tensor
tensor
Strain
Compute spatial
derivatives F of the
motion field
Longitudinal strain color plotted over time

3. Motion and Deformation Indexes
Motion
Quantify the motion
field over
the cardiac cycle
Deformation
Strain tensor
tensor
Strain
Compute spatial
derivatives F of the
motion field
Longitudinal strain color plotted over time

4. Algorithmic framework
! Extend diffeomorphic ! TDFFD
registration for joint Temporal Diffeomorphic
alignment of image registration using Free
sequences Form Deformation
! Exploit temporal
consistency in the
dataset

5. 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
(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. 4

6. Method
Transformation model
! Continuous velocity field in the 3D+t domain
! The displacement field is obtained from the
displacement field by solving the following ODE:
Continuous time Velocity = Sum of 3D + t
spatiotemporal kernels
Material point in reference frame
Transformation

7. Method
Transformation model
! Numerical integration: Forward Euler integration
(1)
time
t=0

8. Method
Parametric Jacobian
! Definitions
! Eq. (1) can then be rewritten as
(2)
! We want to compute the derivative of the mapped
coordinate of a given material point regarding the
velocity parameters using (2)

9. 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)

10. 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.

11. Synthetic displacement field:
Habemus ground truth

12. Experiments on synthetic ultrasound
images ( surface propagation )

13. Experiments on synthetic ultrasound
images
! 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 %
12

14. Experiments on synthetic ultrasound
images
! 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 %
Median error for w=0.2 Median error for w=0.7
7 7
TDFFD TDFFD
6 FFD 6 FFD
Error magnitude (mm)
Error magnitude (mm)
5 5
4 4
3 3
2 2
1 1
0 0
0 5 10 15 20 0 5 10 15 20
time frame time frame 12

15. 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.
13

16. Motion quantification in healthy
volunteers
14

17. Volunteer 1
0.05 Long. strain volunteer 1
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 0.5 1

18. Volunteer 2
0.05 Long. strain volunteer 2
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 0.5 1

19. Volunteer 3
0.05 Long. strain volunteer 3
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 0.5 1

20. Volunteer 4
0.05 Long. strain volunteer 4
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 0.5 1

21. Volunteer 5
0.05 Long. strain volunteer 5
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 0.5 1

22. Volunteer 6
0.05 Long. strain volunteer 6
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 0.5 1

23. Volunteer 7
0.05 Long. strain volunteer 7
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 0.5 1

24. Volunteer 8
0.05 Long. strain volunteer 8
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 0.5 1

25. De Craene et al, FIMH09 2009 “Large
Quantification of Motion and diffeomorphic FFD Registration for motion and
strain quantification from 3D US sequences ”
Deformation before and after CRT
before after
Septal
stretching

26. Quantification of Motion and
Deformation before and after CRT

27. Strain curves before and after CRT
25

28. Strain curves before and after CRT
26

29. Conclusions
! 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.
27

30. Thanks !
28