GPU Implementation of extended total Lagrangian explicit (gpuXTLED) for Surgical Incision Application

An extended total Lagrangian explicit dynamic (XTLED) is presented as a potential numerical method for simulating interactive or physics-based surgical incisions of soft tissues. The simulation of surgical incision is vital to the integrity of virtual reality simulators that are used for immersive surgical training. However, most existing numerical methods either compromise on computational speed for accuracy or vice versa. This is due to the challenge of modelling nonlinear behaviour of soft tissues, incorporating incision and subsequently updating topology to account for the incision. To tackle these challenges, XTLED method which combines the extended finite element method (XFEM) using total Lagrangian formulation with explicit time integration method was developed. The algorithm was developed and deformations of 3D geometries under tension, were simulated. An attempt was made to validate the XTLED method using silicon samples with different incision configuration and a comparison was made between XTLED and FEM. Results show that XTLED could potentially be used to simulate interactive soft tissue incision. However, further quantitative verification and validation are required. In addition, numerical analyses conducted show that solutions may not be obtainable due to simulation errors. However, it is unclear whether these errors are inherent in the XTLED method or the algorithm created for the XTLED method in this thesis

Development of Interactive Simulator for Telepresence Robot in Surgical Applications

The purpose of this Diploma thesis is to develop and implement an interactive simulator for a surgical robot in a Telepresence application. The focus is on an incision procedure of a scalpel during an operation. The geometric deformation of the simulation is based on a Finite Element Method (FEM) model which has to cope with discontinuity due to the incision through the body. The FEM modelling can be done using e.g. FEM with remeshing method or XFEM which treats the cut in the body as a type of material discontinuity. A detailed analyse of the eXtended Finite Element Method (XFEM) and a comparison to the FEM with remeshing is made. For the implementation of simulation, a FEM remeshing method is used. A scalpel mounted to the end effector of a robot is controlled by a Haptic device and cuts through a silicone block. The deformation of the real test object are measured by a 2D scanning device and compared to the results of the simulation. The deviation of the reality and simulation were less than 1% based on the dimension of the body

Real-time hybrid cutting with dynamic fluid visualization for virtual surgery

It is widely accepted that a reform in medical teaching must be made to meet today's high volume training requirements. Virtual simulation offers a potential method of providing such trainings and some current medical training simulations integrate haptic and visual feedback to enhance procedure learning. The purpose of this project is to explore the capability of Virtual Reality (VR) technology to develop a training simulator for surgical cutting and bleeding in a general surgery

Interactively Cutting and Constraining Vertices in Meshes Using Augmented Matrices

We present a finite-element solution method that is well suited for interactive simulations of cutting meshes in the regime of linear elastic models. Our approach features fast updates to the solution of the stiffness system of equations to account for real-time changes in mesh connectivity and boundary conditions. Updates are accomplished by augmenting the stiffness matrix to keep it consistent with changes to the underlying model, without refactoring the matrix at each step of cutting. The initial stiffness matrix and its Cholesky factors are used to implicitly form and solve a Schur complement system using an iterative solver. As changes accumulate over many simulation timesteps, the augmented solution method slows down due to the size of the augmented matrix. However, by periodically refactoring the stiffness matrix in a concurrent background process, fresh Cholesky factors that incorporate recent model changes can replace the initial factors. This controls the size of the augmented matrices and provides a way to maintain a fast solution rate as the number of changes to a model grows. We exploit sparsity in the stiffness matrix, the right-hand-side vectors and the solution vectors to compute the solutions fast, and show that the time complexity of the update steps is bounded linearly by the size of the Cholesky factor of the initial matrix. Our complexity analysis and experimental results demonstrate that this approach scales well with problem size. Results for cutting and deformation of 3D linear elastic models are reported for meshes representing the brain, eye, and model problems with element counts up to 167,000; these show the potential of this method for real-time interactivity. An application to limbal incisions for surgical correction of astigmatism, for which linear elastic models and small deformations are sufficient, is included

An interactive meshless cutting model for nonlinear viscoelastic soft tissue in surgical simulators

In this paper, we present a novel interactive cutting simulation model for soft tissue based on the meshless framework. Unlike most existing methods that consider the cutting process of soft tissue in an over simplified manner, the presented model is able to simulate the complete cutting process that includes three stages: deformation before cutting open (DBCO), cutting open (CO), and deformation after cutting open (DACO). To characterize the complicated physical and mechanical properties of soft tissue, both nonlinearity and viscoelasticity were incorporated into the equations governing the motion of soft tissue. A line contact model was used for simulating the cutting process after analyzing the two major types of surgical instruments, i.e., scalpel and electrostick. The cutting speed and angle were taken into account in order to improve haptic rendering. Biomechanical tests and simulation experiments verified the validity of the introduced model. Specifically, the displacement vs. cutting force curves can be divided into three segments corresponding to the three stages of the cutting process. The results were also applied in a liver cutting simulating system and satisfactory visual effect and haptic feedback were achieved

Remote minimally invasive surgery - haptic feedback and selective automation in medical robotics

Abstract. The automation of recurrent tasks and force feedback are complex problems in medical robotics. We present a novel approach that extends human-machine skill-transfer by a scaffolding framework. It assumes a consolidated working environment for both, the trainee and the trainer. The trainer provides hints and cues in a basic structure which is already understood by the learner. In this work, the scaffolding is constituted by abstract patterns, which facilitate the structuring and segmentation of information during "Learning by Demonstration" (LbD). With this concept, the concrete example of knot-tying for suturing is exemplified and evaluated. During the evaluation, most problems and failures arose due to intrinsic system imprecisions of the medical robot system. These inaccuracies were then improved by the visual guidance of the surgical instruments. While the benefits of force feedback in telesurgery has already been demonstrated and measured forces are also used during task learning, the transmission of signals between the operator console and the robot system over long-distances or across-network remote connections is still a challenge due to time-delay. Especially during incision processes with a scalpel into tissue, a delayed force feedback yields to an unpredictable force perception at the operator-side and can harm the tissue which the robot is interacting with. We propose a XFEM-based incision force prediction algorithm that simulates the incision contact-forces in real-time and compensates the delayed force sensor readings. A realistic 4-arm system for minimally invasive robotic heart surgery is used as a platform for the research

Variational methods for modeling and simulation of tool-tissue interaction

Ph.DDOCTOR OF PHILOSOPH

Cutting in deformable objects

Virtual reality simulations of surgical procedures allow such procedures to be practiced on computers instead of patients and test-animals. The core of such a system is a soft tissue simulation, that has to react very quickly but be realistic at the same time. This thesis discusses how deformable models can be simulated for this context, using an existing mathematical technique, the Finite Element Method. This method represents the object with a mesh, the material is subdivided in geometric primitives, such as triangles. Both the number of primitives and their shape influence the speed of a simulation. Hence, when the mesh changes, e.g. when simulating a procedure, this has to be done with care. This thesis shows how the interaction of meshing and simulation can be handled in software

Accurate Real-Time Framework for Complex Pre-defined Cuts in Finite Element Modeling

PhD ThesisAchieving detailed pre-defined cuts on deformable materials is vitally pivotal for many commercial applications, such as cutting scenes in games and vandalism effects in virtual movies. In these types of applications, the majority of resources are allocated to achieve high-fidelity representations of materials and the virtual environments. In the case of limited computing resources, it is challenging to achieve a convincing cutting effect. On the premise of sacrificing realism effects or computational cost, a considerable amount of research work has been carried out, but the best solution that can be compatible with both cases has not yet been identified. This doctoral dissertation is dedicated to developing a unique framework for representing pre-defined cuts of deformable surface models, which can achieve real-time, detailed cutting while maintaining the realistic physical behaviours. In order to achieve this goal, we have made in-depth explorations from geometric and numerical perspectives. From a geometric perspective, we propose a robust subdivision mechanism that allows users to make arbitrary predetermined cuts on elastic surface models based on the finite element method (FEM). Specifically, after the user separates the elements in an arbitrary manner (i.e., linear or non-linear) on the topological mesh, we then optimise the resulting mesh by regenerating the triangulation within the element based on the Delaunay triangulation principle. The optimisation of regenerated triangles, as a process of refining the ill-shaped elements that have small Aspect Ratio, greatly improves the realism of physical behaviours and guarantees that the refinement process is balanced with real-time requirements. The above subdivision mechanism can improve the visual effect of cutting, but it neglects the fact that elements cannot be perfectly cut through any pre-defined trajectories. The number of ill-shaped elements generated yield a significant impact on the optimisation time: a large number of ill-shaped elements will render the cutting slow or even collapse, and vice versa. Our idea is based on the core observation that the producing of ill-shaped elements is largely attributed to the condition number of the global stiffness matrix. Practically, for a stiffness matrix, a large condition number means that it is almost singular, and the calculation of its inverse or the solution of a system of linear equations are prone to large numerical errors and time-consuming. It motivates us to alleviate the impact of condition number of the global stiffness matrix from the numerical aspects. Specifically, we address this issue in a novel manner by converting the global stiffness matrix into the form of a covariance matrix, in which the number of conditions of the matrix can be reduced by exploiting appropriate matrix normalisation to the eigenvalues. Furthermore, we investigated the efficiency of two different scenarios: an exact square-root normalisation and its approximation based on the Newton-Schulz iteration. Experimental tests of the proposed framework demonstrate that it can successfully reproduce competitive visuals of detailed pre-defined cuts compared with the state-of-the-art method (Manteaux et al. 2015) while obtaining a significant improvement on the FPS, increasing up to 46.49 FPS and 21.93 FPS during and after the cuts, respectively. Also, the new refinement method can stably maintain the average Aspect Ratio of the model mesh after the cuts at less than 3 and the average Area Ratio around 3%. Besides, the proposed two matrix normalisation strategies, including ES-CGM and AS-CGM, have shown the superiority of time efficiency compared with the baseline method (Xin et al. 2018). Specifically, the ES-CGM and AS-CGM methods obtained 5 FPS and 10 FPS higher than the baseline method, respectively. These experimental results strongly support our conclusion which is that this new framework would provide significant benefits when implemented for achieving detailed pre-defined cuts at a real-time rate