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

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

PaRSys: Un nuevo modelo deformable interactivo basado en sistemas de partículas

En esta tesis se ha presentado un nuevo modelo deformable (ParSys) que, al igual que otros modelos deformables, permite, de forma simple, la incorporación de elasticidad a los modelos geométricos sintéticos 3D. Este modelo, basado en volúmenes ligados, se ha centrado principalmente en la velocidad por encima de la precisión, aunque no se ha dejado de lado el comportamiento realista basado en parámetros físicos reales. ParSys ha intentado unir las ventajas de cada uno de los modelos deformables existentes, presentando las siguientes características principales: Es un modelo rápido de calcular. Casi tan rápido como los modelos deformables heurísticos más simples basados en el punto muelle. Permite la realización de cambios topológicos de forma sencilla. Los parámetros que gobiernan la deformación pueden estar basados en parámetros físicos reales, en concreto en el módulo de Young, al igual que los modelos basados en mecánica continua. Posee un comportamiento volumétrico, lo que permite un mayor realismo visual ante las deformaciones producidas. Puede obtener el sistema de partículas encargado de la deformación sin necesidad de conocer la estructura interna de los objetos. Estas características invitan a pensar que ParSys es un modelo ideal para su uso en entornos virtuales interactivos y, en particular, en entornos tan complejos como la simulación quirúrgica.López Escobar, Ó. (2008). PaRSys: Un nuevo modelo deformable interactivo basado en sistemas de partículas [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/2007Palanci

Interaktive Echtzeitsimulation deformierbarer Oberflächen für Trainingssysteme in der Augenchirurgie

Die Arbeit befasst sich mit Simulations-Algorithmen für virtuelle Augenoperationen. Sie konzentriert sich auf die Simulation von Membranen, die im Verlauf eines chirurgischen Eingriffs aus dem Auge entfernt werden müssen. Es werden Algorithmen vorgestellt, die eine realistische Interaktion zwischen Membran und chirurgischem Instrument ermöglichen, und die eine physikalisch plausible Riss-Simulation garantieren

Technologies for Biomechanically-Informed Image Guidance of Laparoscopic Liver Surgery

Laparoscopic surgery for liver resection has a number medical advantages over open surgery, but also comes with inherent technical challenges. The surgeon only has a very limited field of view through the imaging modalities routinely employed intra-operatively, laparoscopic video and ultrasound, and the pneumoperitoneum required to create the operating space and gaining access to the organ can significantly deform and displace the liver from its pre-operative configuration. This can make relating what is visible intra-operatively to the pre-operative plan and inferring the location of sub-surface anatomy a very challenging task. Image guidance systems can help overcome these challenges by updating the pre-operative plan to the situation in theatre and visualising it in relation to the position of surgical instruments. In this thesis, I present a series of contributions to a biomechanically-informed image-guidance system made during my PhD. The most recent one is work on a pipeline for the estimation of the post-insufflation configuration of the liver by means of an algorithm that uses a database of segmented training images of patient abdomens where the post-insufflation configuration of the liver is known. The pipeline comprises an algorithm for inter and intra-subject registration of liver meshes by means of non-rigid spectral point-correspondence finding. My other contributions are more fundamental and less application specific, and are all contained and made available to the public in the NiftySim open-source finite element modelling package. Two of my contributions to NiftySim are of particular interest with regards to image guidance of laparoscopic liver surgery: 1) a novel general purpose contact modelling algorithm that can be used to simulate contact interactions between, e.g., the liver and surrounding anatomy; 2) membrane and shell elements that can be used to, e.g., simulate the Glisson capsule that has been shown to significantly influence the organ’s measured stiffness

A New Approach to Cutting into Finite Element Models

Virtual reality based surgical simulators offer a very elegant approach to enhancing traditional training in endoscopic surgery. In this context a realistic soft tissue model is of central importance. The most accurate procedures for modeling elastic deformations of tissue use the Finite Element Method to solve the governing mechanical equations. Therapeuti