Decraene fimh09

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


% 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


% cardiac cycle

Long

str

ain

(%

)

Results. Application to CRT case

Results. Strain before and after CRT

before afterSeptal

stretching


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


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)

Decraene fimh09

Technology

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