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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.

Walker ML, Ringleb SI, Maihafer GC, Walker R, Crouch JR, Van Lunen B, Morrison S. Virtual reality–enhanced partial body weight–supported treadmill training poststroke: feasibility and effectiveness in 6 subjects. Objective To determine whether the use of a low-cost virtual reality (VR) system used in conjunction with partial body weight–supported treadmill training (BWSTT) was feasible and effective in improving the walking and balance abilities of patients poststroke. Design A before-after comparison of a single group with BWSTT intervention. Setting University research laboratory. Participants A convenience sample of 7 adults who were within 1 year poststroke and who had completed traditional rehabilitation but still exhibited gait deficits. Six participants completed the study. Intervention Twelve treatment sessions of BWSTT with VR. The VR system generated a virtual environment that showed on a television screen in front of the treadmill to give participants the sensation of walking down a city street. A head-mounted position sensor provided postural feedback. Main Outcome Measures Functional Gait Assessment (FGA) score, Berg Balance Scale (BBS) score, and overground walking speed. Results One subject dropped out of the study. All other participants made significant improvements in their ability to walk. FGA scores increased from mean of 13.8 to 18. BBS scores increased from mean of 43.8 to 48.8, although a ceiling effect was seen for this test. Overground walking speed increased from mean of .49m/s to .68m/s. Conclusions A low-cost VR system combined with BWSTT is feasible for improved gait and balance of patients poststroke.

The CALIPSO satellite launched by NASA in 2006 uses an on-board LIDAR instrument to measure the vertical distribution of clouds and aerosols along the orbital path. This satellite's dense vertical sampling of the atmosphere provides previously unavailable information about the altitude and composition of clouds, including the polar stratospheric clouds (PSCs) that play an important role in the annual formation of polar ozone holes. Reconstruction of cloud surfaces through interpolation of CALIPSO data is challenging due to the sparsity of the data in the non-vertical dimensions and the complex sampling pattern created by intersecting non-planar orbital paths. This paper presents a method for computing cloud surfaces by reconstructing a continuous cloud surface distance field. The distance field reconstruction is performed via shape-based interpolation of the cloud contours on each cross section using a medial axis representation of each contour. The interpolation algorithm employs a projection operator that is defined in terms of (latitude, longitude, altitude) coordinates, so that projection between cross sections follows the earth's curved atmosphere and preserves cloud altitude. This process successfully interpolated cloud contours from CALIPSO data acquired during the 2006 polar winter and enabled three-dimensional visualization of the PSCs.

The shape of anatomic objects often depends in complex ways on the shapes and locations of neighboring objects. Shape parameter networks provide an approach for representing shape dependencies and producing multi-object models that share consistent boundary definitions. This paper provides an overview of the modeling framework provided by shape parameter networks, and demonstrates their use through the development of a detailed multi-object eye model. The eye model presented contains analytically defined shape equations that produce models matching user-specified physical measurements such as cornea width, cornea thickness, anterior chamber angle, and eye axial length.

Cornea surgeons have observed that changes in cornea curvature can follow cataract surgery and cause astigmatism. The placement of surgical incisions has been shown to influence these curvature changes. Though empirical data has been collected about this phenomenon, a biomechanical model has not been employed in predicting post-surgical outcomes. This work implemented an incised finite element model of the eye to investigate factors influencing corneal shape after surgery. In particular, the effects of eye muscle forces and intra-ocular pressure were simulated. Cornea shape change was computed via finite element analysis, and the resulting change in cornea curvature was measured by fitting quadratic curves to the horizontal and vertical meridians of the cornea. Results suggest that these two sources of deforming force counteract each other and contribute to astigmatism in perpendicular directions.

Models that predict the soft tissue deformation caused by needle insertion could improve the accuracy of procedures such as brachytherapy and needle biopsy. Prior work on needle insertion modeling has focused on static deformation; the experiments presented here show that dynamic effects such as relaxation are important. An experimental setup is described for recording and measuring the deformation that occurs with needle insertion into a soft tissue phantom. Analysis of the collected data demonstrates the time- and velocity-dependent nature of the deformation. Deformation during insertion is shown to be well represented using a velocity-dependent force function with a linear elastic finite element model. The model's accuracy is limited to the period during needle motion, indicating that a viscoelastic tissue model may be required to capture tissue relaxation after the needle stops.

A simulation-based training system for surgical wound debridement was developed and comprises a multimedia introduction, a surgical simulator (tutorial component), and an assessment component. The simulator includes two PCs, a haptic device, and mirrored display. Debridement is performed on a virtual leg model with a shallow laceration wound superimposed. Trainees are instructed to remove debris with forceps, scrub with a brush, and rinse with saline solution to maintain sterility. Research and development issues currently under investigation include tissue deformation models using mass-spring system and finite element methods; tissue cutting using a high-resolution volumetric mesh and dynamic topology; and accurate collision detection, cutting, and soft-body haptic rendering for two devices within the same haptic space.

Surgical simulators are an integration of many models, capabilities, and functions. Development of a working simulator requires the flexibility to integrate various software models, to support interoperability, and facilitate performance optimizations. An object oriented framework is devised to support multithreaded integration of simulation, deformation, and interaction. A demonstration application has been implemented in Java, leveraging the features that are built into the language including multithreading, synchronization, and serialization. Future work includes expanding the capabilities of the framework with a broader range of model and interactive capabilities.

The finite element method (FEM) is well suited for use in the non-rigid registration of magnetic resonance spectroscopy images (MRSI) with intraoperative ultrasound images of the prostate because FEM provides a principled method for modeling the physical deformation caused when the MRSI intra-rectal imaging probe compresses the prostate. However, FEM requires significant labor and computational time to construct a finite element model and solve the resulting large system of equations. In particular, any finite element based registration method must address the questions of how to generate a mesh from an image and how to solve the system of finite element equations efficiently. This paper focuses on how m-rep image segmentations can be used to generate high quality multi-scale hexahedral meshes for use with FEM. Results from the application of this method to the registration of CT images of a prostate phantom with implanted brachytherapy seeds are presented.