**Acknowledgments**

22 Will-be-set-by-IN-TECH

We proposed an approach to accurate and real-time simulation of coil deployment, as well as prediction of coil embolization outcome in a patient-specific environment for clinical planning

• The geometry of the aneurysm and its parent vessel has been reconstructed as an implicit surface. The proposed blobby model is particularly adapted to simulation; it enables to model complex shapes, as smooth surfaces, with a relatively small number of primitives. Our model improves upon previous works in two ways. First the constrained parameterization closely relates the implicit function to the distance field to the surface, and stabilizes the blob selection and subdivision process. Second, reconstruction is expressed as an energy minimization problem. The closed-form expression given for the energy enables to leverage efficient minimization algorithms with derivatives for faster

• We have achieved real-time simulation of flexible medical devices, such as the catheter or coil by using a model based on beams that can handle various rest shapes and large geometric deformations. Special care is taken to make this model computationally robust and efficient by using dedicated linear solver and time-integration scheme. Our contributions also include an accurate contact model to handle the collisions between the coil and the vascular surface. This allows computation times of about 2 ms for a coil

• While most previous work on hemodynamic simulation aimed at accurate results and required dozens of hours computational time, we have achieved fast simulation of blood flow using the DEC method, which is initially developed in the field of computer graphics. However, a much deeper analysis and improvement has been made for medical

• Bilateral interaction between coil and blood flow has been first studied in our work for planning two key steps of the procedure. Firstly, prediction of hemodynamic status after deployment is performed by modeling the inserted coils as porous media. Secondly, the reciprocal force, *i.e.*, the impact of the flow onto the coil, is modeled as drag force and applied on the coil during deployment for interactive choice and placement of the first coil. The results show that our approach permit real-time simulation of the interaction

Regarding future work, first of all, we are further improving the computational efficiency, since real-time simulation has not been achieved when performed on a mesh consisting of over 8,000 elements. We still want to more deeply investigate various computational strategies to obtain real-time computation by using more advanced numerical schemes, such as parallel implementation on GPU of the backtracking step, optimization of linear solvers by the preconditioning technique coupled with a GPU-based conjugate gradient implementation [3]. Additionally, more advanced techniques to generate a multi-resolution mesh, such as adaptive refinement [32], could also be a solution, as it maximizes the result accuracy while

**7. Conclusion and perspectives**

and more accurate results.

composed of 100 beam elements.

between coils and blood flow during coil embolization.

application.

**7.2. Perspectives**

minimizing the computational effort.

**7.1. Conclusion**

and rehearsal.

The authors are grateful to Prof. Anxionnat who provided them with the 2D and 3D angiographic patient data used in this paper. Prof. Anxionnat is with the therapeutic and interventional neuroradiology department of the University Hospital of Nancy, France.
