Applications such as suturing in medical simulations require the modeling of knot tying in physically realistic rope. The paper describes the design and implementation of such a system. Our model uses a spline of linear springs, adaptive subdivision and a dynamics sim- ulation. Collisions are discrete event simulated and follow the impulse model. Although some care must taken to maintain stable knots, we demonstrate our simple model is sufficient for this task. In particular, we do not use friction or explicit constraints to maintain the knot. As examples, we tie a square knot and a reef knot.

The goal of haptic rendering is to enable a user to touch, feel, and manipulate virtual objects through a haptic interface. With the introduction of high fidelity haptic devices (ref. **Biggs and Srinivasan Chapter**), it is now possible to simulate the feel of even fine surface textures on rigid complex shapes under dynamic conditions. Starting from the early nineties, significant progress has occurred in our ability

Abstract—Minimally invasive surgery (MIS) involves a multidimensional series of tasks requiring a synthesis between visual information and the kinematics and dynamics of the surgical tools. Analysis of these sources of information is a key step in defining objective criteria for characterizing surgical performance. The Blue DRAGON is a new system for acquiring the kinematics and the dynamics of two endoscopic tools synchronized with the endoscopic view of the surgical scene. Modeling the process of MIS using a finite state model [Markov model (MM)] reveals the internal structure of the surgical task and is utilized as one of the key steps in objectively assessing surgical performance. The experimental protocol includes tying an intracorporeal knot in a MIS setup performed on an animal model (pig) by 30 surgeons at different levels of training including expert surgeons. An objective learning curve was defined based on measuring quantitative statistical distance (similarity) between MM of experts and MM of residents at different levels of training. The objective learning curve was similar to that of the subjective performance analysis. The MM proved to be a powerful and compact mathematical model for decomposing a complex task such as laparoscopic suturing. Systems like surgical robots or virtual reality simulators in which the kinematics and the dynamics of the surgical tool are inherently measured may benefit from incorporation of the proposed methodology. Index Terms—Dynamics, haptics, human machine interface, kinematics, manipulation, Markov model, minimally invasive, robotics, simulation, soft tissue, surgery, surgical skill assessment, surgical tool, vector quantization. I.

This paper explores the use of haptic feedback to teach an abstract motor skill that requires recalling a sequence of forces. Participants are guided along a trajectory and are asked to learn a sequence of onedimensional forces via three paradigms: haptic training, visual training, or combined visuohaptic training. The extent of learning is measured by accuracy of force recall. We find that recall following visuohaptic training is significantly more accurate than recall following visual or haptic training alone, although haptic training alone is inferior to visual training alone. This suggests that in conjunction with visual feedback, haptic training may be an effective tool for teaching sensorimotor skills that have a forcesensitive component to them, such as surgery. We also present a dynamic programming paradigm to align and compare spatiotemporal haptic trajectories. 1. Introduction and Related

In surgery simulation, most existing methods assume that the contact between a virtual instrument and a soft tissue model occur at a single point. However, there is a gross approximation when simulating laparoscopic procedures since the instrument shaft is used in several surgical tasks. In this paper, we propose a new algorithm for modeling the collision response of a soft tissue when interacting with a volumetric virtual instrument involving both the shaft and the tip of the instrument. The

Abstract—Contact and deformation modeling for interactive environments has seen many applications, from surgical simulation and training, to virtual prototyping, to teleoperation, etc., where both visual feedback and haptic feedback are needed. High-quality feedback demands a high level of physical realism as well as a high update rate in rendering, which are often conflicting requirements. In this paper, we present a unique approach to modeling force and deformation between a rigid body and an elastic object under complex contacts, which achieves a good compromise of reasonable physical realism and real-time update rate (at least 1 kHz). We simulate contact forces based on a nonlinear physical model. We further introduce a novel approximation of material deformation suitable for interactive environments based on applying Bernoulli–Euler bending beam theory to the simulation of elastic shape deformation. Our approach is able to simulate the contact forces exerted upon the rigid body (that can be virtually held by a user via a haptic device) not only when it forms one or more than one contact with the elastic object, but also when it moves compliantly on the surface of the elastic object, taking friciton into account. Our approach is also able to simulate the global and local shape deformation of the elastic object due to contact. All the simulations can be performed in a combined update rate of over 1 kHz, which we demonstrate in several examples. Index Terms—Bending beam theory, compliant motion, contact modeling, deformable object modeling, haptic rendering, interactive environment, multiple contacts, nonhomogeneous material. I.

We present a fast technique for simulating fluid-filled elastic objects with the Finite Element Method. By simulating the presence of fluid with hydrostatic fluid pressure, a quasi-static simulation of fluid can be achieved by applying a force boundary condition to the nodes on the fluidelastic interface. Using a proportional feedback control algorithm, a relationship between the volume and pressure of the fluid structure can be maintained. Optimal parameters for the control algorithm are found by determining the response of the elastic system to changes in pressure. This approach has been shown to agree with experimental deformation data taken from a fluid-filled gelatin phantom. Combining linear FEM methods with matrix condensation techniques and the tuned proportional feedback control allows for the simulation of a fluid-filled elastic object at real-time haptic update rates. 1

of a training simulator for urological operations, is presented. The graphic environment simulates endoscope insertion in a small diameter deformable tube and is used with a low-force 5-dof force-feedback haptic mechanism. Piecewise Bezier interpolations are used for smooth urethra deformations. A novel particle-based model computes the forces and torques fed to the haptics. Realistic textures from medical databases are employed and a 25 fps refresh rate is achieved using the Rendering Thread method. The overall simulator software is made of three processes running on two distinct platforms, communicating via Ethernet and TCP/IP. Keywords_Graphical training simulator, force model, haptics. I.

Realistic modeling of the interaction between surgical instruments and human organs has been recognized as a key requirement in the development of high-fidelity surgical simulators. Primarily due to computational considerations, most of the past simulation research within the haptics community has assumed linear elastic behavior for modeling tissues, even though human soft tissues generally possess nonlinear viscoelastic properties. Hence, this paper quantitatively compares linear and nonlinear elasticity-based models. It is demonstrated that, for a nonlinear model, the well-known Poynting effect developed during shearing of the tissue results in normal forces not seen in a linear elastic model. The difference in force magnitude and force direction for linear and nonlinear models are larger than the just noticeable difference for contact force and forcedirection discrimination thresholds published in the psychophysics literature, respectively. This work applies a proposed framework for examining the effect of tool-tissue interaction modeling techniques on human perception of surgical simulators with haptic feedback. 1.

We have developed a new numerical scheme for simulating linear viscoelastic tissue behavior modeled by FEM. We have integrated experimentally-measured viscoelastic tissue properties into our model for realistic force feedback to the user. A new precomputation method based on superposition principle was proposed for real-time computation of nodal displacements and interaction forces. We achieved stable haptic interactions by executing the viscoelastic model at 100Hz while the haptic loop was updated at 1KHz. The developed model and the proposed pre-computation approach have been both validated using ANSYS.