Large Diffeomorphic FFD Registration for
Motion and Strain Quantification from 3D-US
SequencesMathieu De Craene1,2, Oscar Camara2,1, Bart H. Bijnens3,2,1,
and Alejandro F. Frangi2,1,3
Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)
1 Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine,
(CIBER-BBN), Barcelona, Spain
2 Universitat Pompeu Fabra, Barcelona, Spain
3 Institució Catalana de Recerca i Estudis Avançats (ICREA)
Context (1/2)3D Ultrasound challenges
Motion and deformation estimation from Ultra-sound image sequences Patient friendly Low cost Acquisition noise
challenging for image processing (segmentation and registration)
Exploit temporal consistency
Extend diffeomorphic registration sequences for joint alignment of image sequences
Context (2/2) Motion and deformation
% cardiac cycle
Dis
pla
cem
en
t (m
m)
Point 1
Point 2
06.25
12.518.75 25
31.2537.5
43.75 5056.25
62.568.75 75
81.2587.5
93.75
-5
-4
-3
-2
-1
0
1
2
3
4
5
Point 1
Point 2
% cardiac cycle
Long
str
ain
(%
)
06.25
12.518.75 25
31.2537.5
43.75 5056.25
62.568.75 75
81.2587.5
93.75
-35
-30
-25
-20
-15
-10
-5
0
5
Point 1
Point 2
State of the art (1/2) Diffeomorphic pairwise registration: invertible mapping with
smooth inverse Mainly optimize a dense non-parametric velocity field
Þ Higher computational cost, no implicit regularization as offered by FFD (except [3])
Þ Simple optimization scheme based on first derivatives (except [2])Acronym Transform. model Velocity field Joint optimization
LDDMM [1] Dense incr. disp. field
Non-stationary Yes
Stationary LDDMM [2] Dense vel. field Stationary Yes
Diff. FFD [3] FFD Non-stationary No
Diff. Demons [4] Dense incr. disp. field
Non-stationary No
[1] Beg et al. “Computing large deformation metric mappings via geodesic flows of
diffeomorphisms.” Int. J. Comput. Vis. 61 (2) (2005) pp.139–157.
[2] Hernandez et al. “Registration of anatomical images using geodesic paths of diffeomorphisms
parameterized with stationary vector fields”. MMBIA’07 (2007).
[3] Rueckert et al. “Diffeomorphic Registration using B-Splines”. MICCAI’06, LNCS 4191(2006), pp.
702–709.
[4] Vercauteren et al. “Diffeomorphic image registration with the demons algorithm”. MICCAI’07,
LNCS 4792 (2007), pp. 319–326.
State of the art (2/2)
Extension of diffeomorphic registration to handle temporal data Framework for point sets (landmarks, curves and surfaces)
encoding within-subject shape changes in a global template via parallel transport technique [1]
Dense deformation field for measuring longitudinal changes over follow-up (interval of several months) [2]
Advantages Invertible mapping with smooth inverse Use of velocity fields to enforce temporal consistency
[1] Qiu et al. “Time sequence diffeomorphic metric mapping and parallel
transport track time-dependent shape changes”. NeuroImage. 45(1) Supl. 1
(2009), pp. S51-S60
[2] Khan et al. Representation of time-varying shapes in the large deformation
diffeomorphic framework. ISBI 2008, pp.1521-1524
Method (1/4)Transformation model
time
v(x;t
0)v(x;t1
)v(x;t2
)v(x;t3)
u(x;t2)
Concatenation of FFD transformations Strong coupling between phases
The first transformation influences all subsequent time steps
Method (2/4)
Metric Average of the joint histograms between images at t0 and ti
Mutual information computed from the average joint histogram Optimization method: LBFGS
Limited-memory quasi-Newton method for unconstrained optimization
∆ metric ∆ intensity ∆ mapped coordinate ∆ transformation parameter
Parametric Jacobian at time step M regarding a parameter a time step m<M
∆v(x;t0) v(x;t1) v(x;t2)
∆u(x;t2)
duM (x;! jM1 )d! m
=dum (x;! jm1 )
d! m
M ¡ 1Y
l=m+1
µI +
dvM (y;! M )dy
¶ ¯¯¯¯¯y=x+u l (x;! j l1 )
Parametric Jacobian of mth transformation
Jacobian of all transformations posterior to m: Account for volume
changes
Method (3/4)
First image segmented using an ASM segmentation technique [1]
The segmentation is deformed using the result of the registration
[1] Butakoff et al. “Simulated 3D ultrasound LV cardiac images for active shape model training”. Proc SPIE Med Imag (SPIE’07):Image Processing (2007) 6512:U5123.
Non-rigid transformation used to propagate surface mesh in the first frame
On each triangle, strain is computed by using the first derivatives F of the displacement field
Strain computed in the reference space of coordinates of the first frame (end-diastolic)
F is approximated using linear shape functions
Method (4/4)
Deformed mesh
Undeformed mesh
Results. Longitudinal strain in healthy subject 1 as color map
Longitudinal strain color plotted over time
Results. Longitudinal strain curves in healthy subject 2 over 17 1
2
3
4
5
67
8
9
10
11
1213
14
15
1617
0 0.5 1
-0.2
-0.1
0
0.1
time frame
long
. st
rain
Healthy subject 2
1. Basal anterior 2. Basal anteroseptal 3. Basal inferoseptal 4. Basal inferior 5. Basal inferolateral 6. Basal anterolateral 7. Mid anterior 8. Mid anterospetal 9. Mid inferoseptal10. Mid inferior11. Mid inferolateral12. Mid anterolateral
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
time frame
long
. st
rain
Healthy subject 1
1. Basal anterior 2. Basal anteroseptal 3. Basal inferoseptal 4. Basal inferior 5. Basal inferolateral 6. Basal anterolateral 7. Mid anterior 8. Mid anterospetal 9. Mid inferoseptal10. Mid inferior11. Mid inferolateral12. Mid anterolateral
% cardiac cycle
Long
str
ain
(%
)
Results. Longitudinal strain curves in healthy subject 1 over 17 regions 1
2
3
4
5
67
8
9
10
11
1213
14
15
1617
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
time frame
long
. st
rain
Healthy subject 2
1. Basal anterior 2. Basal anteroseptal 3. Basal inferoseptal 4. Basal inferior 5. Basal inferolateral 6. Basal anterolateral 7. Mid anterior 8. Mid anterospetal 9. Mid inferoseptal10. Mid inferior11. Mid inferolateral12. Mid anterolateral0 0.5 1
-0.2
-0.1
0
0.1
time frame
long
. st
rain
Healthy subject 2
1. Basal anterior 2. Basal anteroseptal 3. Basal inferoseptal 4. Basal inferior 5. Basal inferolateral 6. Basal anterolateral 7. Mid anterior 8. Mid anterospetal 9. Mid inferoseptal10. Mid inferior11. Mid inferolateral12. Mid anterolateral
% cardiac cycle
Long
str
ain
(%
)
Results. Application to CRT case
Results. Strain before and after CRT
before afterSeptal
stretching
Results. Strain before and after CRT
before CRT after CRTnormal
0 0.5 1
-0.1
0
0.1 1. Basal anterior
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 2. Basal anteroseptal
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 3. Basal inferoseptal
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 4. Basal inferior
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 5. Basal inferolateral
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 6. Basal anterolateral
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 7. Mid anterior
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 8. Mid anterospetal
% cardiac cyclelo
ng.
stra
in0 0.5 1
-0.1
0
0.1 9. Mid inferoseptal
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.110. Mid inferior
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.111. Mid inferolateral
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.112. Mid anterolateral
% cardiac cycle
long
. st
rain
1
2
3
4
5
67
8
9
10
11
1213
14
15
1617
Septal stretching
Results. Strain before and after CRT
before CRT after CRTnormal
0 0.5 1
-0.1
0
0.1 1. Basal anterior
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 2. Basal anteroseptal
% cardiac cyclelo
ng.
stra
in0 0.5 1
-0.1
0
0.1 3. Basal inferoseptal
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 4. Basal inferior
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 5. Basal inferolateral
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 6. Basal anterolateral
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 7. Mid anterior
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 8. Mid anterospetal
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.1 9. Mid inferoseptal
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.110. Mid inferior
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.111. Mid inferolateral
% cardiac cycle
long
. st
rain
0 0.5 1
-0.1
0
0.112. Mid anterolateral
% cardiac cycle
long
. st
rain
1
2
3
4
5
67
8
9
10
11
1213
14
15
1617
Conclusions Diffeomorphic registration framework suited for handling
motion and deformation estimation problems The technique can be generalized to other cardiac imaging
modalities and to other organs imaged dynamically Include temporal consistency in the representation of the
transformation Strong coupling between time points
Current drawbacks High computation time Parallelize Dimensionality proportional to the number of images in the
sequence temporal windowing
Future work
Deal with basal fibrous valve ring separately More flexible application-
specific regions Confidence based on image
SNR or distance to transducer
Replace FFD chain by continuous velocity field defined over space and time Increases complexity Modeling velocity instead of
incremental displacements
Add physical constraints Incompressibility
Incorporate in the velocity estimate information coming from modalities that directly estimate velocities Tissue Doppler Imaging
Acknowledgments. Funding agencies European Community’s 7th
framework programme (FP7/2007-2013) under grant agreement n. 224495: euHeart project
CENIT-CDTEAM grant funded by the Spanish Ministry of Science and Innovation (MICINN-CDTI)
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