Decraene spie-09

Non-stationary Diffeomorphic

Registration: Application to

Endo-Vascular Treatment Monitoring

M. De Craene2,1,O. Camara1,2, B.H. Bijnens1,2,3, A.F. Frangi1,2,3

Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), Barcelona Spain.

1. Information and Communication Technologies Department, Universitat Pompeu Fabra, Barcelona, Spain

2. Networking Center on Biomedical Research - Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN

3. Catalan Institution for Research and Advanced Studies (ICREA).

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Context.

Aneurysm Recurrence after Coiling

Causes Compaction of the coil mass

Aneurysm growth

Related factors Packing [Johnston,Kai]

Ratio between the volume of inserted coil and the aneurysm volume

Shown to be a strong predictor of aneurysm recurrence

Others [Cottier] Size

Treatment during the acute phase

Rupture status2

Example of “coil compaction” :

DSA image [Steinman]

Cottier et al. Neuroradiology 45, pp. 818–824, 2003.

Johnston et al. Stroke 39(1), pp. 120–125, 2008.

Kai et al. Neurosurgery 56, pp. 785–791, 2005.

Steinman et al. American Journal of Neuroradiology 24, pp. 559–566, 2003.

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Image-based quantification of aneurysm

recurrence and evolution over time

Objectives

Visualize several time points in a common frame of coordinates

Compute coil and aneurysm volume curves over time

Local deformation maps

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t0 pre t0 post t1 pre

t1 post t2 pre t3 post

t4 pre t4 post t5 pre

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Characterize evolution using non-rigid

registration Local deformation

maps

Where is the aneurysm growing?

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Challenges

Accuracy for detecting small volume changes and retreat if necessary

Flexibility for detecting small and large volume changes

Depends on time follow-up interval, aneurysm location, …

Invertibility of the non-rigid mapping to ensure correctness of the volume change estimate

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Patient 1 Patient 2 Patient 3

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Non-rigid registration and

diffeomorphisms Popular pairwise diffeomorphic registration schemes

Mainly optimize a dense velocity field

Higher computational cost, no implicit regularization as offered by FFD (except [Rueckert])

Simple optimization scheme based on first derivatives (except [Hernandez])

)

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Acronym Transform. model Velocity field Joint

optimization

LDMM [Beg] Dense incr. disp.

field

Non-stationary Yes

Stationary LDDMM

[Herandez]

Dense vel. field Stationary Yes

Diff. FFD [Rueckert] FFD Non-stationary No

Diff. Demons

[Vercauteren]

Dense incr. disp.

field

Non-stationary No

Beg et al. Int. J. Comput. Vis. 61 (2), pp. 139–157, 2005.

Hernandez et al. MMBIA’07 , 2007.

Rueckert et al. MICCAI’06, LNCS 4191, pp. 702–709, 2006.

Vercauteren et al. MICCAI’07, LNCS 4792, pp. 319–326, 2007.

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LDFFD diffeomorphic non-rigid

registration Transformation = Concatenation of FFD transformations

Strong coupling between phases: the first transformation influences all subsequent time steps

Mutual information metric: ITK, Mattes´ implementation

LBFGS optimizer: ITK

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time

v(x;t0) v(x;t1) v(x;t2) v(x;t3)

u(x;t2)

For k=1:M (number of time steps)

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registration

∆ metric ∆ intensity ∆ mapped coordinate ∆ transformation parameter

Parametric Jacobian

Similar expression can be found in LDDMM registration [Beg] when computing variational derivative

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∆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

µ

I +dvM (y ; ! M )

dy

¶ ¯¯¯¯¯y = x + u l (x ;! j l

1)

Parametric Jacobian of mth

transformationJacobian of all transformations posterior

to m

Beg et al. Int. J. Comput. Vis. 61 (2), pp. 139–157, 2005.

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registration

Multi-resolution scheme in the temporal dimension

Initiate algorithm with 2 time steps

In the event that any of these parameters reaches a given threshold (0.4 the spacing between control points, as proposed by [Rueckert])

Interrupt optimization

Restore last set of valid parameters

Break the problematic time steps using square root computation [Arsigny]

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with

ToldTnew Tnew

Arsigny et al. MICCAI’ 06, LNCS 4190, pp. 924-931, 2006.


u(x;t2)

v(x;t0)

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LDFFD at work

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Results: aneurysm volume changes

measured by non-rigid registration

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Patient Reg. of t FFD [Rueckert99] Diff. FFD [Rueckert06] LDFFD

follow-u

ps

min max mean min max mean min max mean

1 t0t1 3 0.13 2.08 0.97 0.52 1.46 0.95 0.37 2.19 0.98

t1t2 24 -1.89 7.12 0.66 0.01 22.63 0.73 0.00 6.37 0.88

t2t3 2 0.03 2.15 0.95 0.53 1.64 0.95 0.50 1.70 0.97

t3t4 3 -0.10 2.61 0.98 0.60 1.68 0.96 0.19 4.06 0.97

2 t0t1 4 0.30 2.04 0.91 0.48 2.03 0.89 0.37 2.02 0.91

t1t2 12 -0.28 2.37 0.90 0.26 3.87 0.87 0.11 3.46 0.91

t2t3 12 -0.06 2.14 0.92 0.17 2.78 0.84 0.10 4.35 0.96

3 t0t1 3 0.24 3.37 0.92 0.41 2.99 0.88 0.32 2.91 0.93

t1t2 3 0.39 2.30 1.00 0.45 2.26 0.96 0.48 2.15 0.99

t2t3 2 0.14 2.69 0.97 0.43 2.31 0.90 0.29 3.29 0.97

t3t4 6 0.03 3.37 1.04 0.16 6.27 0.97 0.30 5.56 1.02

t4t5 2 -0.13 4.50 0.97 0.40 2.51 0.91 0.48 2.30 0.97

Rueckert et al. IEEE Transactions on Medical Imaging 18(8), pp. 712-721, 1999.


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Results: patient 1, second time point

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t1 t2 LDFFD

[Rueck99

]

[Rueck06

]

[Verc06]Rueckert et al. IEEE Transactions on Medical Imaging 18(8), pp. 712-721, 1999.



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Results: patient 1, second time point

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t1 t2 LDFFD

[Rueck99

]

[Rueck06

]




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FFD LDFFDResults: Jacobian distributions

Diff

FFD

Diff. Demons

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Results: displacement fields

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[Rueck99] LDFFD

[Rueck06

]




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Conclusions

LDFFD: non-stationary non-rigid registration algorithm

Dynamically finds the optimal number of time steps

Transformation invertibility

Keep the dimension of the optimization problem reasonably low

Applicable to quantify post interventional volume changes over subsequent follow-ups

Future work,

Exploit Jacobian-based local growth maps

Comparison to other coil compaction predictors published in the literature

Extension to motion and deformation estimation from image sequences: FIMH 09, Nice.

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Acknowledgements

This research has been partially funded by the Industrial and Technological Development Centre (CDTI) under the CENIT Programme (CDTEAM Project) and the Integrated Project @neurIST (IST-2005-027703), which is cofinancedby the European Commission.

The authors wish to acknowledge Elio Vivas for the acquisition of the intra-cranial aneurysm imaging data using 3D rotational angiography at Hospital General de Catalunya, San Cugat del Valles, Spain.

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Decraene spie-09

Technology

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