Real-time haptic incision simulation using FEM-based discontinuous free-form deformation

Abstract

Computer-aided surgical simulation is a topic of increasingly extensive research. Computer graphics, geometrical modelling and finite-element analysis all play major roles in these simulations. Furthermore, real-time response, interactivity and accuracy are crucial components in any such simulation system. A major effort has been invested in recent years to find ways to improve the performance, accuracy and realism of existing systems.

In this paper, we extend the work of [Sela G, Schein S, Elber G. Real-time incision simulation using discontinuous free form deformation. In: Cotin S, Metaxas DN, editors. Medical simulation: International symposium, 2004. Lecture notes in computer science, vol. 3078. Springer; 2004. p. 114–123], in which we used discontinuous free-form deformations (DFFD) to artificially simulate real-time surgical operations. The presented scheme now uses accurate data from a finite-element model (FEM), which simulates the motion response of the tissue around the scalpel, during incision. The data are then encoded once into the DFFD, representing the simulation over time. In real-time, The DFFD is applied to the vertices of the surface mesh at the actual incision location and time. The presented scheme encapsulates and takes advantage of both the speed of the DFFD application, and the accuracy of a FEM. In addition, the presented system uses a haptic force feedback device in order to improve realism and ease of use.

Introduction

Today, surgical simulators constitute an active research subject. Surgical simulators allow physicians to practice and hone their skills inside a virtual environment before entering the operating room. Such preoperative training procedures have been shown to significantly improve the results of actual procedures [2]. This is especially true with the recent increase in the use of endoscopic and laparoscopic procedures.

In order to maximize the potential gain in such virtual-reality training, a surgical simulation system should replicate the surgical environment as closely as possible in terms of look and feel. Conveying a realistic impression is difficult. Because of the complexity of such a task, it is best grasped when broken into smaller undertakings. One of the most important roles of any surgical simulator is to realistically animate–in real-time–the way tissue (skin and flesh or internal organs, etc.) behaves under cutting operations. A virtual cutting simulator should supply the following basic capabilities. First, it should have some mechanism for real time collision detection. Such a mechanism should control the location, direction and orientation of a virtual scalpel and constantly test for intersections with the model. Second, a cutting module should implement geometrical operations that would progressively cut through the model, modifying its topology and constructing new geometry (the geometry of the cut) as needed and over time. Third, the cut model should reflect the physical behaviour as accurately as possible, mainly presenting tissue behaviour over time. Another important detail not to be overlooked is the user interface. A haptic force feedback device is invaluable in providing realistic interaction behaviour, both from the visual and the palpable point of view.

When dealing with surface meshes, the actual task of cutting the tissue can be divided into two sub-tasks. First, there is the surface modelling task, in which the model surface should be split along the route of the scalpel as it advances. Second, the geometry around the cut should change, reflecting the shape and orientation of the cutting tool and the internal strain and stress properties of the tissue. In this work, we propose a framework that performs these two tasks. The framework is based upon an augmented variant of free- form deformation (FFD) [3], which allows discontinuities and openings to be created in geometrical models. The Discontinuous FFD (DFFD) [4] is continuous everywhere except at the incision, and hence it has the ability to continuously deform the geometry around the cut. Moreover, we incorporate previously simulated results, using a finite-element model, into the deformation function in order to make the behaviour of the cut as realistic as possible.

Because FEM simulations are difficult to compute in real-time, an alternative approach could apply physical simulations to a low resolution representation of the model and encode it into the DFFD during the interaction, only to be immediately applied to the fine resolution representation of the geometry. This alternative approach would, of course, entail a much higher processing overhead, as the FEM simulation will need to be executed during run time, but on the other hand it will allow for more adaptable results than the first approach. In this work, we will concentrate on the first approach, in which the DFFDs are constructed off-line.

The proposed FEM-DFFD synergy is of low real-time computational complexity while retaining reasonable accuracy. Consequently, the algorithm is capable of handling complex geometric models at interactive rates. The FEM calculations are conducted once as a preprocessing stage using a straight-line scalpel path, whereas the deformation is applied to a limited local set of mesh vertices at every time step, mapping the straight path to a deformed path following the virtual scalpel.

The rest of this work is organized as follows. In Section 2, we give an overview of the previous work on the problems of cutting through and deforming geometrical models. In Section 3, we describe the proposed cutting simulation approach; Section 4 presents a few examples and finally, we conclude in Section 5.