Corotational cut finite element method for real-time surgical simulation: Application to needle insertion simulation

in Computer Methods in Applied Mechanics and Engineering (2018), 345

We present the corotational cut Finite Element Method (FEM) for real-time surgical simulation. The only requirement of the proposed method is a background mesh, which is not necessarily conforming to the ... [more ▼]

We present the corotational cut Finite Element Method (FEM) for real-time surgical simulation. The only requirement of the proposed method is a background mesh, which is not necessarily conforming to the boundaries/interfaces of the simulated object. The details of the surface, which can be directly obtained from binary images, are taken into account by a multilevel embedding algorithm which is applied to elements of the background mesh that are cut by the surface. Dirichlet boundary conditions can be implicitly imposed on the surface using Lagrange multipliers, whereas traction or Neumann boundary conditions, which is/are applied on parts of the surface, can be distributed to the background nodes using shape functions. The implementation is verified by convergences studies, of the geometry and of numerical solutions, which exhibit optimal rates. To verify the reliability of the method, it is applied to various needle insertion simulations (e.g. for biopsy or brachytherapy) into brain and liver models. The numerical results show that, while retaining the accuracy of the standard FEM, the proposed method can (1) make the discretisation independent from geometric description, (2) avoid the complexity of mesh generation for complex geometries, and (3) provide computational speed suitable for real-time simulations. Thereby, the proposed method is very suitable for patient-specific simulations as it improves the simulation accuracy by automatically, and properly, taking the simulated geometry into account, while keeping the low computational cost. [less ▲]

Real-time Error Control for Surgical Simulation

E-print/Working paper (2017)

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 ... [more ▼]

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. [less ▲]

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

E-print/Working paper (n.d.)

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 ... [more ▼]

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. [less ▲]