Real-time Error Control for Surgical Simulation

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.Comment: 12 pages, 16 figures, change of the title, submitted to IEEE TBM

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance.Comment: 21 pages, 14 figure

Real-time Error Control for Surgical Simulation

Real-time simulations are becoming increasingly common for various applications, from geometric design to medical simulation. Two of the main factors concurrently involved in defining the accuracy of surgical simulations are: the modeling error and the discretization error. Most work in the area has been looking at the above sources of error as a compounded, lumped, overall error. Little or no work has been done to discriminate between modeling error (e.g. needle-tissue interaction, choice of constitutive models) and discretization error (use of approximation methods like FEM). However, it is impossible to validate the complete surgical simulation approach and, more importantly, to understand the sources of error, without evaluating both the discretization error and the modeling error. Our objective is thus to devise a robust and fast approach to measure the discretization error via a posteriori error estimates, which are then used for local remeshing in surgical simulations. To ensure that the approach can be used in clinical practice, the method should be robust enough to deal, as realistically as possible, with the interaction of surgical tools with the organ, and fast enough for real-time simulations. The approach should also lead to an improved convergence so that an economical mesh is obtained at each time step. The final goal is to achieve optimal convergence and the most economical mesh, which will be studied in our future work

The Effectiveness of Applying Realistic Mathematics Education Approach in Teaching Statistics in Grade 7 to Students' Mathematical Skills

The research was carried out to verify the effectiveness of applying Realistic Mathematics Education (RME) on the development of skills required by students in statistical content in grade 7. For achieving research objectives, the pedagogical experiment was conducted in the form of intrinsic legalization for forty-eight 7th-grade students at Tang Phu Nhan B Junior School, District 9, Ho Chi Minh City, Vietnam. Accordingly, data on pre-test results, study sheets, post-test, and student learning performance were collected and analyzed qualitatively. The results were assessed based on the criteria corresponding to the required skills for the statistical content, including the criteria for data collection, classification, and representation according to the given criteria for the skill, data collection, and organization capabilities; simple problem formation and problem-solving criteria arise from the existing statistical figures and charts for data analysis and processing skills. The primary mathematical statistics method was used to evaluate the achievement level of students for each criterion. Thereby, the experimental results showed that applying the RME approach in teaching statistical content positively impacted the development of some skills that students needed to achieve. Also, a number of guidelines were provided to guide the enhancement of RME activities

Real-time Error Control for Surgical Simulation

International audienceReal-time simulations are becoming increasingly common for various applications, from geometric design to medical simulation.Two of the main factors concurrently involved in defining the accuracy of surgical simulations are: the modeling error and the discretization error. Most work in the area has been looking at the above sources of error as a compounded, lumped, overall error. Little or no work has been done to discriminate between modeling error (e.g. needle-tissue interaction, choice of constitutive models) and discretization error (use of approximation methods like FEM). However, it is impossible to validate the complete surgical simulation approach and, more importantly, to understand the sources of error, without evaluating both the discretization error and the modeling error.Our objective is thus to devise a robust and fast approach to measure the discretization error via a posteriori error estimates, which are then used for local remeshing in surgical simulations. To ensure that the approach can be used in clinical practice, the method should be robust enough to deal, as realistically as possible, with the interaction of surgical tools with the organ, and fast enough for real-time simulations. The approach should also lead to an improved convergence so that an economical mesh is obtained at each time step. The final goal is to achieve optimal convergence and the most economical mesh, which will be studied in our future work

Real-time Error Control for Surgical Simulation

International audienceObjective: To present the first real-time a poste-riori 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. 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. Index Terms—Finite element method, real-time error estimate, adaptive refinement, constraint-based interaction

Face-based Smoothed Finite Element Method for Real-time Simulation of soft tissue

International audienceIn soft tissue surgery, a tumor and other anatomical structures are usually located using the preoperative CT or MR images. However, due to the deformation of the concerned tissues, this information suffers from inaccuracy when employed directly during the surgery. In order to account for these deformations in the planning process, the use of a bio-mechanical model of the tissues is needed. Such models are often designed using the finite element method (FEM), which is, however, computationally expensive, in particular when a high accuracy of the simulation is required. In our work, we propose to use a smoothed finite element method (S-FEM) in the context of modeling of the soft tissue deformation. This numerical technique has been introduced recently to overcome the overly stiff behavior of the standard FEM and to improve the solution accuracy and the convergence rate in solid mechanics problems. In this paper, a face-based smoothed finite element method (FS-FEM) using 4-node tetrahedral elements is presented. We show that in some cases, the method allows for reducing the number of degrees of freedom, while preserving the accuracy of the discretization. The method is evaluated on a simulation of a cantilever beam loaded at the free end and on a simulation of a 3D cube under traction and compression forces. Further, it is applied to the simulation of the brain shift and of the kidney's deformation. The results demonstrate that the method outperforms the standard FEM in a bending scenario and that has similar accuracy as the standard FEM in the simulations of brain shift and kidney deformation

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance

Evaluation of mechanical strength and durability characteristics of eco-friendly mortar with cementitious additives

The mechanical strength and durability of eco-friendly mortars used in the repair of marine concrete structures exposed to freshwater and seawater environments were evaluated in this paper. The eco-friendly mortar samples were produced using various ratios of fly ash (FA), ground granulated blast-furnace slag (GGBFS), and silica fume (SF) as cementitious materials. Seven mixtures of eco-friendly mortars, including a control mixture; three mixtures with respective substitutions of GGBFS for Portland cement of 10, 20, and 30% by cement mass; and three mixtures with respective additions of SF of 5, 10, and 15% by total binder mass, were used to produce the samples. Tests, including compressive strength, flexural strength, ultrasonic pulse velocity (UPV), electrical surface resistivity (ESR), rapid chloride ion penetration (RCP), thermal conductivity (TC), and microstructure analysis, were conducted to determine the mechanical strength and durability values of the samples. The experimental results show that replacing Portland cement with GGBFS negatively affected the properties of the mortars by reducing the mechanical strength, UPV, ESR, and TC while increasing the RCP in the samples. Also, adding an appropriate amount of SF could improve the mechanical strength and durability characteristics of the eco-friendly mortars. As a result, the mortar sample containing 30% GGBFS and 10% SF earned compressive and flexural strength values of approximately 49.2 and 13.8 MPa, respectively, at 56 days of curing age. Mortar samples with UPV values >3660 m/s were identified as "high quality". The corrosion resistance of all of the samples was found to be high, particularly in chloride-contaminated environments, due to relatively low (1000 - 2000 Coulombs) RCP values. The best overall performance was recorded for the sample containing 30% GGBFS and 10% SF.Web of Science24455254