Michel Duprez

Michel Duprez, Vanessa Lleras, Alexei Lozinski

We consider the finite element method on locally damaged meshes allowing for some distorted cells which are isolated from one another. In the case of the Poisson equation and piecewise linear Lagrange finite elements, we show that the usual a priori error estimates remain valid on such meshes. We also propose an alternative finite element scheme which is optimally convergent and, moreover, well conditioned, i.e. its conditioning is of the same order as that of a standard finite element method on a regular mesh of comparable size.

Ilias Nahmed, Francesco Dettori, Juan Verde et al.

Purpose: MicroWave Ablation (MWA) modeling and simulation bear great potential for loco-regional treatment of liver tumors. However, accurately positioning the antenna according to a planned orientation/location is technically challenging. In cases of misplacement, maintaining the original plan may cause incomplete ablation, while repositioning the antenna may induce tumor seeding. In this work, we propose (i) a digital twin of MWA that simulates ablation outcomes, and (ii) an optimizer that suggests corrections to MWA parameters without antenna reinsertion, while ensuring complete tumor ablations. Methods: A finite element scheme was used to solve the coupled microwave propagation and heat transfer equations governing MWA, with personalized dielectric and thermal properties determined from preoperative CT and MRI images. We then proposed an optimization algorithm able to adjust power input, ablation duration, and antenna position to correct for antenna misplacement. Results: The simulator and optimizer were evaluated against in vivo swine experimental data. Three ablations were performed in liver regions with varying vascularization. The simulations accurately predicted the ablation zones despite the presence of large vessels near the antenna, achieving Dice scores of 0.82, 0.81, and 0.79. In the case of replanning scenarios, our optimizer predicted new parameter sets that led to Dice scores of 0.83, 0.83, 0.80, a corresponding improvement of 20.3%, 40.7% and 48.1% in average over the initial ablation result. Conclusion: This paper is the first to address intra-operative replanning of thermal ablation therapy. It demonstrates that optimal ablation results can be achieved without requiring antenna reinsertion by optimizing specific ablation parameters.

Raphaël Bulle, Michel Duprez, Vanessa Lleras et al.

In this work, we present a combination of a multigrid approach and the phi-FEM immersed boundary finite element method to reduce its computational cost while preserving its accuracy. To further reduce the numerical cost of the approach, we also propose the combination of the previous technique with some neural network methods. We illustrate the efficiency of these two approaches with numerical test cases in 2D and 3D.

Valentina Scarponi, Michel Duprez, Florent Nageotte et al.

Purpose: The treatment of cardiovascular diseases requires complex and challenging navigation of a guidewire and catheter. This often leads to lengthy interventions during which the patient and clinician are exposed to X-ray radiation. Deep Reinforcement Learning approaches have shown promise in learning this task and may be the key to automating catheter navigation during robotized interventions. Yet, existing training methods show limited capabilities at generalizing to unseen vascular anatomies, requiring to be retrained each time the geometry changes. Methods: In this paper, we propose a zero-shot learning strategy for three-dimensional autonomous endovascular navigation. Using a very small training set of branching patterns, our reinforcement learning algorithm is able to learn a control that can then be applied to unseen vascular anatomies without retraining. Results: We demonstrate our method on 4 different vascular systems, with an average success rate of 95% at reaching random targets on these anatomies. Our strategy is also computationally efficient, allowing the training of our controller to be performed in only 2 hours. Conclusion: Our training method proved its ability to navigate unseen geometries with different characteristics, thanks to a nearly shape-invariant observation space.