Stéphane Cotin

Huu Phuoc Bui, Satyendra Tomar, Hadrien Courtecuisse et al.

Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations.

Karl-Philippe Beaudet, Yordanka Velikova, Sidaty El Hadramy et al.

Purpose: Laparoscopic ultrasound (LUS) enhances the safety of liver surgery by visualizing intrahepatic vessels in real-time. Still, vessel identification remains difficult due to probe constraints, complex vascular structure, and tissue deformation. This work aims to enable real-time, patient-specific vessel identification that remains robust under deformation through deformable ultrasound augmentation. Methods: Preoperative CT vessel annotations are used to generate synthetic ultrasound data via optimized physics-based rendering, coupled with domain adaptation to intraoperative ultrasound. The rendering is trained end-to-end for vessel identification and patient-specificity, eliminating the need for preoperative ultrasound. A deformation-aware augmentation simulates realistic intraoperative motion and tissue deformation within the rendering pipeline. Results: In abdominal phantom and limited clinical feasibility experiments (single-case clinical evaluation), the framework achieved real-time intrahepatic vessel-branch identification, maintaining performance under new patient poses. Conclusion: The framework enables real-time vessel identification without preoperative ultrasound and supports technical feasibility, but multi-patient validation is still needed for generalizability and clinical feasibility.

Alban Odot, Guillaume Mestdagh, Yannick Privat et al.

Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern structure deformations. In this article, we propose to formulate the registration problem as an optimal control problem using an artificial neural network where the unknown is the surface force distribution that applies to the object and the resulting deformation computed using a hyper-elastic model. The optimization problem is solved using an adjoint method where the hyper-elastic problem is solved using the feed-forward neural network and the adjoint problem is obtained through the backpropagation of the network. Our process improves the computation speed by multiple orders of magnitude while providing acceptable registration errors.

François Lecomte, Jean-Louis Dillenseger, Stéphane Cotin

Purpose: The purpose of this paper is to present a method for real-time 2D-3D non-rigid registration using a single fluoroscopic image. Such a method can find applications in surgery, interventional radiology and radiotherapy. By estimating a three-dimensional displacement field from a 2D X-ray image, anatomical structures segmented in the preoperative scan can be projected onto the 2D image, thus providing a mixed reality view. Methods: A dataset composed of displacement fields and 2D projections of the anatomy is generated from the preoperative scan. From this dataset, a neural network is trained to recover the unknown 3D displacement field from a single projection image. Results: Our method is validated on lung 4D CT data at different stages of the lung deformation. The training is performed on a 3D CT using random (non domain-specific) diffeomorphic deformations, to which perturbations mimicking the pose uncertainty are added. The model achieves a mean TRE over a series of landmarks ranging from 2.3 to 5.5 mm depending on the amplitude of deformation. Conclusion: In this paper, a CNN-based method for real-time 2D-3D non-rigid registration is presented. This method is able to cope with pose estimation uncertainties, making it applicable to actual clinical scenarios, such as lung surgery, where the C-arm pose is planned before the intervention.

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.

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.

Pablo Alvarez, Stéphane Cotin

Numerous regularization methods for deformable image registration aim at enforcing smooth transformations, but are difficult to tune-in a priori and lack a clear physical basis. Physically inspired strategies have emerged, offering a sound theoretical basis, but still necessitating complex discretization and resolution schemes. This study introduces a regularization strategy that does not require discretization, making it compatible with current registration frameworks, while retaining the benefits of physically motivated regularization for medical image registration. The proposed method performs favorably in both synthetic and real datasets, exhibiting an accuracy comparable to current state-of-the-art methods.

Karl-Philippe Beaudet, Sidaty El Hadramy, Philippe C Cattin et al.

Intraoperative ultrasound images are inherently challenging to interpret in liver surgery due to the limited field of view and complex anatomical structures. Bridging the gap between preoperative and intraoperative data is crucial for effective surgical guidance. 3D IntraVascular UltraSound (IVUS) offers a potential solution by enabling the reconstruction of the entire organ, which facilitates registration between preoperative computed tomography (CT) scans and intraoperative IVUS images. In this work, we propose an optimization-based calibration method using a 3D-printed phantom for accurate 3D Intravascular Ultrasound volume reconstruction. Our approach ensures precise alignment of tracked IVUS data with preoperative CT images, improving intraoperative navigation. We validated our method using in vivo swine liver images, achieving a calibration error from 0.88 to 1.80 mm and a registration error from 3.40 to 5.71 mm between the 3D IVUS data and the corresponding CT scan. Our method provides a reliable and accurate means of calibration and volume reconstruction. It can be used to register intraoperative ultrasound images with preoperative CT images in the context of liver surgery, and enhance intraoperative guidance.

Alban Odot, Ryadh Haferssas, Stéphane Cotin

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of reference for solving the partial differential equations associated with these problems. Yet, deep learning methods have recently shown that they could represent an alternative strategy to solve physics-based problems 1,2,3. In this paper, we propose a solution to simulate hyper-elastic materials using a data-driven approach, where a neural network is trained to learn the non-linear relationship between boundary conditions and the resulting displacement field. We also introduce a method to guarantee the validity of the solution. In total, we present three contributions: an optimized data set generation algorithm based on modal analysis, a physics-informed loss function, and a Hybrid Newton-Raphson algorithm. The method is applied to two benchmarks: a cantilever beam and a propeller. The results show that our network architecture trained with a limited amount of data can predict the displacement field in less than a millisecond. The predictions on various geometries, topologies, mesh resolutions, and boundary conditions are accurate to a few micrometers for non-linear deformations of several centimeters of amplitude.

Jaime Garcia Guevara, Igor Peterlik, Marie-Odile Berger et al.

An automatic elastic registration method suited for vascularized organs is proposed. The vasculature in both the preoperative and intra-operative images is represented as a graph. A typical application of this method is the fusion of pre-operative information onto the organ during surgery, to compensate for the limited details provided by the intra-operative imaging modality (e.g. CBCT) and to cope with changes in the shape of the organ. Due to image modalities differences and organ deformation, each graph has a different topology and shape. The Adaptive Compliance Graph Matching (ACGM) method presented does not require any manual initialization, handles intra-operative nonrigid deformations of up to 65 mm and computes a complete displacement field over the organ from only the matched vasculature. ACGM is better than the previous Biomechanical Graph Matching method 3 (BGM) because it uses an efficient biomechanical vascularized liver model to compute the organ's transformation and the vessels bifurcations compliance. This allows to efficiently find the best graph matches with a novel compliance-based adaptive search. These contributions are evaluated on ten realistic synthetic and two real porcine automatically segmented datasets. ACGM obtains better target registration error (TRE) than BGM, with an average TRE in the real datasets of 4.2 mm compared to 6.5 mm, respectively. It also is up to one order of magnitude faster, less dependent on the parameters used and more robust to noise.

Andrea Mendizabal, Pablo Márquez-Neila, Stéphane Cotin

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition, parallel computing, adaptive meshing, and model order reduction. In this paper we present U-Mesh: a data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm. We show that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly non-linear models in a compact form. Our method is applied to two benchmark examples: a cantilever beam and an L-shape subject to moving punctual loads. A comparison between our method and proper orthogonal decomposition (POD) is done through the paper. The results show that U-Mesh can perform very fast simulations on various geometries, mesh resolutions and number of input forces with very small errors.