Finite-Element Methods for Real-Time Simulation of Surgery

Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces

Simulation System for Training in Laparoscopic Surgery

A computer-based simulation system creates a visual and haptic virtual environment for training a medical practitioner in laparoscopic surgery. Heretofore, it has been common practice to perform training in partial laparoscopic surgical procedures by use of a laparoscopic training box that encloses a pair of laparoscopic tools, objects to be manipulated by the tools, and an endoscopic video camera. However, the surgical procedures simulated by use of a training box are usually poor imitations of the actual ones. The present computer-based system improves training by presenting a more realistic simulated environment to the trainee. The system includes a computer monitor that displays a real-time image of the affected interior region of the patient, showing laparoscopic instruments interacting with organs and tissues, as would be viewed by use of an endoscopic video camera and displayed to a surgeon during a laparoscopic operation. The system also includes laparoscopic tools that the trainee manipulates while observing the image on the computer monitor (see figure). The instrumentation on the tools consists of (1) position and orientation sensors that provide input data for the simulation and (2) actuators that provide force feedback to simulate the contact forces between the tools and tissues. The simulation software includes components that model the geometries of surgical tools, components that model the geometries and physical behaviors of soft tissues, and components that detect collisions between them. Using the measured positions and orientations of the tools, the software detects whether they are in contact with tissues. In the event of contact, the deformations of the tissues and contact forces are computed by use of the geometric and physical models. The image on the computer screen shows tissues deformed accordingly, while the actuators apply the corresponding forces to the distal ends of the tools. For the purpose of demonstration, the system has been set up to simulate the insertion of a flexible catheter in a bile duct. [As thus configured, the system can also be used to simulate other endoscopic procedures (e.g., bronchoscopy and colonoscopy) that include the insertion of flexible tubes into flexible ducts.] A hybrid approach has been followed in developing the software for real-time simulation of the visual and haptic interactions (1) between forceps and the catheter, (2) between the forceps and the duct, and (3) between the catheter and the duct. The deformations of the duct are simulated by finite-element and modalanalysis procedures, using only the most significant vibration modes of the duct for computing deformations and interaction forces. The catheter is modeled as a set of virtual particles uniformly distributed along the center line of the catheter and connected to each other via linear and torsional springs and damping elements. The interactions between the forceps and the duct as well as the catheter are simulated by use of a ray-based haptic-interaction- simulating technique in which the forceps are modeled as connected line segments

Tactile Roughness Perception of Virtual Gratings by Electrovibration

Realistic display of tactile textures on touch screens is a big step forward for haptic technology to reach a wide range of consumers utilizing electronic devices on a daily basis. Since the texture topography cannot be rendered explicitly by electrovibration on touch screens, it is important to understand how we perceive the virtual textures displayed by friction modulation via electrovibration. We investigated the roughness perception of real gratings made of plexiglass and virtual gratings displayed by electrovibration through a touch screen for comparison. In particular, we conducted two psychophysical experiments with 10 participants to investigate the effect of spatial period and the normal force applied by finger on roughness perception of real and virtual gratings in macro size. We also recorded the contact forces acting on the participants' finger during the experiments. The results showed that the roughness perception of real and virtual gratings are different. We argue that this difference can be explained by the amount of fingerpad penetration into the gratings. For real gratings, penetration increased tangential forces acting on the finger, whereas for virtual ones where skin penetration is absent, tangential forces decreased with spatial period. Supporting our claim, we also found that increasing normal force increases the perceived roughness of real gratings while it causes an opposite effect for the virtual gratings. These results are consistent with the tangential force profiles recorded for both real and virtual gratings. In particular, the rate of change in tangential force ($dF_t/dt$) as a function of spatial period and normal force followed trends similar to those obtained for the roughness estimates of real and virtual gratings, suggesting that it is a better indicator of the perceived roughness than the tangential force magnitude.Comment: Manuscript received June 25, 2019; revised November 15, 2019; accepted December 11, 201

Algorithms for Haptic Rendering of 3D Objects

Algorithms have been developed to provide haptic rendering of three-dimensional (3D) objects in virtual (that is, computationally simulated) environments. The goal of haptic rendering is to generate tactual displays of the shapes, hardnesses, surface textures, and frictional properties of 3D objects in real time. Haptic rendering is a major element of the emerging field of computer haptics, which invites comparison with computer graphics. We have already seen various applications of computer haptics in the areas of medicine (surgical simulation, telemedicine, haptic user interfaces for blind people, and rehabilitation of patients with neurological disorders), entertainment (3D painting, character animation, morphing, and sculpting), mechanical design (path planning and assembly sequencing), and scientific visualization (geophysical data analysis and molecular manipulation)