This document presents a non-rigid registration method called Large Deformation Diffeomorphic Metric Mapping (LDFFD) to quantify changes in aneurysm volume over time after endovascular coiling treatment. LDFFD registers multiple time points into a common coordinate frame to compute coil and aneurysm volume curves. It uses a multi-resolution scheme in the temporal dimension to optimize registration accuracy while maintaining diffeomorphic transformations. Results on patient data show LDFFD achieves good registration accuracy compared to other methods, and can detect and quantify small aneurysm volume changes over time which has implications for monitoring treatment effectiveness.

1. Non-stationary Diffeomorphic Registration: Application toEndo-Vascular TreatmentMonitoring 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).

2. 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 status 2 Example of “coil compaction” : DSA image [Steinman] Cottier et al. Neuroradiology45, 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 Neuroradiology24, pp. 559–566, 2003.

3. 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 3 t0 pre t1 post t2 pre t1 pre t0 post t3 post t4 pre t4 post t5 pre

4. Characterize evolution using non-rigid registration Local deformation maps Where is the aneurysm growing? 4

5. 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, … Invertibilityof the non-rigid mapping to ensure correctness of the volume change estimate 5 Patient 1 Patient 2 Patient 3

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

8. )6 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.

9. 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 7 v(x;t0) v(x;t1) v(x;t2) v(x;t3) u(x;t2) time For k=1:M (number of time steps)

10. LDFFD diffeomorphic non-rigid registration 8 ∆u(x;t2) ∆v(x;t0) v(x;t1) v(x;t2) ∆ metric  ∆ intensity  ∆ mapped coordinate  ∆ transformation parameter Parametric Jacobian Similar expression can be found in LDDMM registration [Beg] when computing variational derivative Parametric Jacobian of mth transformation Jacobian of all transformations posterior to m Beg et al. Int. J. Comput. Vis. 61 (2), pp. 139–157, 2005.

11. LDFFD diffeomorphic non-rigid registration 9 u(x;t2) v(x;t0) 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] with Told Tnew Tnew Arsigny et al. MICCAI’ 06, LNCS 4190, pp. 924-931, 2006. Rueckert et al. MICCAI’06, LNCS 4191, pp. 702–709, 2006.

12. LDFFD at work 10

13. Results: aneurysm volume changes measured by non-rigid registration 11 Rueckert et al. IEEE Transactions on Medical Imaging 18(8), pp. 712-721, 1999. Rueckert et al. MICCAI’06, LNCS 4191, pp. 702–709, 2006.

14. Results: patient 1, second time point 12 t1 t2 LDFFD [Verc06] [Rueck99] [Rueck06] Rueckert et al. IEEE Transactions on Medical Imaging 18(8), pp. 712-721, 1999. Rueckert et al. MICCAI’06, LNCS 4191, pp. 702–709, 2006. Vercauteren et al. MICCAI’07, LNCS 4792, pp. 319–326, 2007.

15. Results: patient 1, second time point 13 t1 t2 LDFFD [Verc06] [Rueck99] [Rueck06] Rueckert et al. IEEE Transactions on Medical Imaging 18(8), pp. 712-721, 1999. Rueckert et al. MICCAI’06, LNCS 4191, pp. 702–709, 2006. Vercauteren et al. MICCAI’07, LNCS 4792, pp. 319–326, 2007.

16. 14 Results: Jacobian distributions FFD LDFFD Diff FFD Diff. Demons

17. Results: displacement fields 15 [Rueck99] LDFFD [Rueck06] [Verc06] Rueckert et al. IEEE Transactions on Medical Imaging 18(8), pp. 712-721, 1999. Rueckert et al. MICCAI’06, LNCS 4191, pp. 702–709, 2006. Vercauteren et al. MICCAI’07, LNCS 4792, pp. 319–326, 2007.

18. 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. 16

19. 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 cofinanced by the European Commission. The authors wish to acknowledge ElioVivasfor the acquisition of the intra-cranial aneurysm imaging data using 3D rotational angiography at Hospital General de Catalunya, San Cugat del Valles, Spain. 17