Real-Time Error Control for Surgical Simulation.

OBJECTIVE: To present the first 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.1 For simulating soft tissue deformation, the refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local -refinement. 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.

Controlling the error on target motion through real-time mesh adaptation: Applications to deep brain stimulation.

An error-controlled mesh refinement procedure for needle insertion simulations is presented. As an example, the procedure is applied for simulations of electrode implantation for deep brain stimulation. We take into account the brain shift phenomena occurring when a craniotomy is performed. We observe that the error in the computation of the displacement and stress fields is localised around the needle tip and the needle shaft during needle insertion simulation. By suitably and adaptively refining the mesh in this region, our approach enables to control, and thus to reduce, the error whilst maintaining a coarser mesh in other parts of the domain. Through academic and practical examples we demonstrate that our adaptive approach, as compared with a uniform coarse mesh, increases the accuracy of the displacement and stress fields around the needle shaft and, while for a given accuracy, saves computational time with respect to a uniform finer mesh. This facilitates real-time simulations. The proposed methodology has direct implications in increasing the accuracy, and controlling the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anaesthesia, or cryotherapy. Moreover, the proposed approach can be helpful in the development of robotic surgeries because the simulation taking place in the control loop of a robot needs to be accurate, and to occur in real time.

Fast elastic registration of soft tissues under large deformations.

A fast and accurate fusion of intra-operative images with a pre-operative data is a key component of computer-aided interventions which aim at improving the outcomes of the intervention while reducing the patient's discomfort. In this paper, we focus on the problematic of the intra-operative navigation during abdominal surgery, which requires an accurate registration of tissues undergoing large deformations. Such a scenario occurs in the case of partial hepatectomy: to facilitate the access to the pathology, e.g. a tumor located in the posterior part of the right lobe, the surgery is performed on a patient in lateral position. Due to the change in patient's position, the resection plan based on the pre-operative CT scan acquired in the supine position must be updated to account for the deformations. We suppose that an imaging modality, such as the cone-beam CT, provides the information about the intra-operative shape of an organ, however, due to the reduced radiation dose and contrast, the actual locations of the internal structures necessary to update the planning are not available. To this end, we propose a method allowing for fast registration of the pre-operative data represented by a detailed 3D model of the liver and its internal structure and the actual configuration given by the organ surface extracted from the intra-operative image. The algorithm behind the method combines the iterative closest point technique with a biomechanical model based on a co-rotational formulation of linear elasticity which accounts for large deformations of the tissue. The performance, robustness and accuracy of the method is quantitatively assessed on a control semi-synthetic dataset with known ground truth and a real dataset composed of nine pairs of abdominal CT scans acquired in supine and flank positions. It is shown that the proposed surface-matching method is capable of reducing the target registration error evaluated of the internal structures of the organ from more than 40 mm to less then 10 mm. Moreover, the control data is used to demonstrate the compatibility of the method with intra-operative clinical scenario, while the real datasets are utilized to study the impact of parametrization on the accuracy of the method. The method is also compared to a state-of-the art intensity-based registration technique in terms of accuracy and performance.

Brain-shift compensation using intraoperative ultrasound and constraint-based biomechanical simulation.

PURPOSE: During brain tumor surgery, planning and guidance are based on preoperative images which do not account for brain-shift. However, this deformation is a major source of error in image-guided neurosurgery and affects the accuracy of the procedure. In this paper, we present a constraint-based biomechanical simulation method to compensate for craniotomy-induced brain-shift that integrates the deformations of the blood vessels and cortical surface, using a single intraoperative ultrasound acquisition. METHODS: Prior to surgery, a patient-specific biomechanical model is built from preoperative images, accounting for the vascular tree in the tumor region and brain soft tissues. Intraoperatively, a navigated ultrasound acquisition is performed directly in contact with the organ. Doppler and B-mode images are recorded simultaneously, enabling the extraction of the blood vessels and probe footprint, respectively. A constraint-based simulation is then executed to register the pre- and intraoperative vascular trees as well as the cortical surface with the probe footprint. Finally, preoperative images are updated to provide the surgeon with images corresponding to the current brain shape for navigation. RESULTS: The robustness of our method is first assessed using sparse and noisy synthetic data. In addition, quantitative results for five clinical cases are provided, first using landmarks set on blood vessels, then based on anatomical structures delineated in medical images. The average distances between paired vessels landmarks ranged from 3.51 to 7.32 (in mm) before compensation. With our method, on average 67% of the brain-shift is corrected (range [1.26; 2.33]) against 57% using one of the closest existing works (range [1.71; 2.84]). Finally, our method is proven to be fully compatible with a surgical workflow in terms of execution times and user interactions. CONCLUSION: In this paper, a new constraint-based biomechanical simulation method is proposed to compensate for craniotomy-induced brain-shift. While being efficient to correct this deformation, the method is fully integrable in a clinical process.

3D Physics-Based Registration of 2D Dynamic MRI Data.

We present a method allowing for intra-operative targeting of a specific anatomical feature. The method is based on a registration of 3D pre-operative data to 2D intra-operative images. Such registration is performed using an elastic model reconstructed from the 3D images, in combination with sliding constraints imposed via Lagrange multipliers. We register the pre-operative data, where the feature is clearly detectable, to intra-operative dynamic images where such feature is no more visible. Despite the lack of visibility on the 2D MRI images, we are able both to determine the location of the target as well as follow its displacement due to respiratory motion.

Constraint-based simulation for non-rigid real-time registration.

In this paper we propose a method to address the problem of non-rigid registration in real-time. We use Lagrange multipliers and soft sliding constraints to combine data acquired from dynamic image sequence and a biomechanical model of the structure of interest. The biomechanical model plays a role of regularization to improve the robustness and the flexibility of the registration. We apply our method to a pre-operative 3D CT scan of a porcine liver that is registered to a sequence of 2D dynamic MRI slices during the respiratory motion. The finite element simulation provides a full 3D representation (including heterogeneities such as vessels, tumor,...) of the anatomical structure in real-time.

Atlas-based transfer of boundary conditions for biomechanical simulation.

An environment composed of different types of living tissues (such as the abdominal cavity) reveals a high complexity of boundary conditions, which are the attachments (e.g. connective tissues, ligaments) connecting different anatomical structures. Together with the material properties, the boundary conditions have a significant influence on the mechanical response of the organs, however corresponding correct mechanical modeling remains a challenging task, as the connective structures are difficult to identify in certain standard imaging modalities. In this paper, we present a method for automatic modeling of boundary conditions in deformable anatomical structures, which is an important step in patient-specific biomechanical simulations. The method is based on a statistical atlas which gathers data defining the connective structures attached to the organ of interest. In order to transfer the information stored in the atlas to a specific patient, the atlas is registered to the patient data using a physics-based technique and the resulting boundary conditions are defined according to the mean position and variance available in the atlas. The method is evaluated using abdominal scans of ten patients. The results show that the atlas provides a sufficient information about the boundary conditions which can be reliably transferred to a specific patient. The boundary conditions obtained by the atlas-based transfer show a good match both with actual segmented boundary conditions and in terms of mechanical response of deformable organs.

Real-time simulation of contact and cutting of heterogeneous soft-tissues.

This paper presents a numerical method for interactive (real-time) simulations, which considerably improves the accuracy of the response of heterogeneous soft-tissue models undergoing contact, cutting and other topological changes. We provide an integrated methodology able to deal both with the ill-conditioning issues associated with material heterogeneities, contact boundary conditions which are one of the main sources of inaccuracies, and cutting which is one of the most challenging issues in interactive simulations. Our approach is based on an implicit time integration of a non-linear finite element model. To enable real-time computations, we propose a new preconditioning technique, based on an asynchronous update at low frequency. The preconditioner is not only used to improve the computation of the deformation of the tissues, but also to simulate the contact response of homogeneous and heterogeneous bodies with the same accuracy. We also address the problem of cutting the heterogeneous structures and propose a method to update the preconditioner according to the topological modifications. Finally, we apply our approach to three challenging demonstrators: (i) a simulation of cataract surgery (ii) a simulation of laparoscopic hepatectomy (iii) a brain tumor surgery.

Preconditioner-based contact response and application to cataract surgery.

In this paper we introduce a new method to compute, in real-time, the physical behavior of several colliding soft-tissues in a surgical simulation. The numerical approach is based on finite element modeling and allows for a fast update of a large number of tetrahedral elements. The speed-up is obtained by the use of a specific preconditioner that is updated at low frequency. The preconditioning enables an optimized computation of both large deformations and precise contact response. Moreover, homogeneous and inhomogeneous tissues are simulated with the same accuracy. Finally, we illustrate our method in a simulation of one step in a cataract surgery procedure, which require to handle contacts with non homogeneous objects precisely.

GPU-based real-time soft tissue deformation with cutting and haptic feedback.

This article describes a series of contributions in the field of real-time simulation of soft tissue biomechanics. These contributions address various requirements for interactive simulation of complex surgical procedures. In particular, this article presents results in the areas of soft tissue deformation, contact modelling, simulation of cutting, and haptic rendering, which are all relevant to a variety of medical interventions. The contributions described in this article share a common underlying model of deformation and rely on GPU implementations to significantly improve computation times. This consistency in the modelling technique and computational approach ensures coherent results as well as efficient, robust and flexible solutions.