The objective of this study was to introduce and to evaluate our novel non-rigid registration technique, which is based on a mechanical model. For this purpose, the performances of the method were compared to a 3D/3D rigid registration method and a 2D/3D rigid registration method, both state-of-the-art in current fusion imaging registration methods. After prior discussion with expert vascular surgeons, the acceptability value has been set below 5mm on ostia. The overall accuracy of the registration changes from low (x > 5mm) for the 2D rigid method to good (3 mm < x < 5 mm) for the non-rigid method according to the scale of Kauffmann et al. [

5]. A first qualitative visual comparison between the target aortas and the reconstructed aortas (

Figure 5) gave an overview of the results—the registration in the projection plane (front view) is highly accurate. The registration outside the projection plane is globally less precise but remains acceptable (<5 mm), except for the tortuous geometry of patient 5, where accuracy on the renal arteries is acceptable but should be improved for the mesenteric and celiac trunk arteries, outside the projection plane. When comparing the overall accuracy of the different methods in

Figure 3, it appears that the non-rigid method is the most accurate, ahead of 3D rigid registration and 2D rigid registration. The improvement of accuracy between these methods shows the added value of the non-rigid aspect of registration, even for an aorta subjected to low natural deformations. Moreover, the non-rigid method is more robust. The registration errors are contained in a limited range, while the errors approach 10 mm for the 2D rigid registration in some cases. However, for renal arteries, non-rigid registration, although qualified as good according to Kauffmann et al. [

5], remains qualitatively below 2D rigid registration. The non-rigid and 2D rigid methods are rigidly registered in the same way on the renal arteries. Consequently, the ostia position of renal arteries is slightly modified during the deformation of the non-rigid model, mainly along the antero-posterior axis, outside the registration plane. This is one of the limitations of the method, which seeks to achieve an overall mechanical balance. Weighting the important points could solve the problem in future developments. The one view 2D/3D non-rigid method achieves a better accuracy than the rigid registration methods presented in this study. However, this simple method, with a calculation time of less than half a second using Matlab

^{®}, could be perfectly adapted to the surgery workflow. Indeed, after discussions with vascular surgeons, the maximum allowed duration for a simulation during a surgical procedure was set to 1 min. Here, calculation time refers to computing the deformation field and to registration, including the finite element analysis. In addition, it requires only one DSA taken from a single incidence, theoretically reducing the patient’s irradiation rate. The registration accuracy for both renal arteries (2.5 mm) is qualified as high according to the scale of Kauffmann et al. [

5] and is therefore satisfactory for surgical use. The accuracy of the registration obtained is slightly lower than the Zheng method. However, unlike Zheng et al. [

25], we do not directly compare the positions of 2D points with 3D points. We compare the position of two sets of 2D points and we perfectly know the correspondence between the projected 2D initial points and 3D initial points. Therefore, we can minimize the registration error. Moreover, our non-rigid method is based on a FEM rather than Zheng et al. [

25] and Groher et al. [

24]. It integrates the actual mechanical characteristics of the aorta, such as diameter, thickness and Young’s modulus. Indeed, the diameter and thickness of the aorta are integrated into the stiffness matrix

**K** via the cross-sectional area of the beam

**A** and the cross section moments of inertia

**I** as described in

Appendix A in supplemental materials. Simulation results remain stable for Young’s modulus

**E** ranging between 7 and 13 MPa [

27,

28]. It is therefore possible to implement new functions in the code, such as the navigation of guidewires, in a mechanically consistent model and without significant modifications to the existing code. In summary, it is possible to simulate in real time the deformation of the aorta induced by device insertion during the intervention using the same model.

To evaluate the model with large deformations, the method was tested on an artery deformed by a stent-graft launcher. For the sake of verification, the target artery is deformed using a finite element simulation and does not correspond to actual clinical data but the imposed deformations, reviewed and validated by a vascular surgeon, are similar to a real case. As shown in

Figure 6, the method is able to handle large deformations, with a mean accuracy of 6.3 (SD 2.3) mm and an accuracy for the right and left renal arteries of 3.3 and 2.2 mm respectively. Therefore, this recalibration method enables to set up a mechanical model of the aorta, updated according to operating data and suitable for clinical applications. However, more tests with large deformations should be conducted for confirmation.

The aorta model still suffers from several limitations that can reduce, in some cases, the accuracy of the method, especially regarding boundary conditions. For example, the anchorage points of the aorta and the surrounding structures are not considered, in particular the spine, which can significantly change the mechanical behavior of the aorta [

19]. This should be implemented in a future version of the method. The local stiffness of the aorta is also not considered, although it can vary significantly, for example in the case of different thrombus size or calcification, which are not included in the segmentation of the lumen. As a result, the deformations of the artery would be different, which should be taken into account in a finite element analysis. Therefore, future versions of our methodology should consider these parameters and the underlying local modifications of the stiffness applied to the simplified model of the aorta. However, as our simulations are guided by intraoperative imaging, deformations due to the presence of thrombus and calcification are already partially taken into account, which should minimize errors. The method has other limitations. It depends on the projection matrix and assumes it to be known. Its accuracy depends on the reliability of the matrix. To ensure the stability and robustness of the method, it should be tested with more patients, including cases that are more tortuous. Finally, the evaluation of the methodology used fluoroscopy data taken in similar conditions. We are now considering verification with CT scans acquired at a different time and in different conditions, as our methodology was designed to handle such situations.

As current 3D/3D fusion imaging systems are not optimal for EVAR procedures, we proposed a new 2D/3D registration method making a good trade-off between performances, precision and simplicity. After a comprehensive presentation of the method, we showed its performances on clinical datasets for which a reference CT scan was available to evaluate the registration errors and to compare them with other registration methods based on rigid transformations. The study permitted to evaluate the natural deformations of the aorta observed between two consecutive scan and to differentiate the non-rigid deformations from the rigid displacements. It appeared that a non-rigid registration method is essential to register accurately ostia positions. We also proved that the method was able to handle large deformations induced by tool insertions. Therefore, our method can represent a significant improvement for fusion imaging in EVAR procedures as it has also the potential to reduce patient irradiation and, unlike current 3D/3D methods, it does not require hybrid room facilities. Combined with simulations performed at the planning stage of EVAR [

29,

30,

31,

32], this will participate in the uptake of computer simulations for assisting surgical interventions in future medicine.