George Turkiyyah

Real-time finite element modeling for surgery simulation: an application to virtual suturing

Real-time finite element (FE) analysis can be used to represent complex deformable geometries in virtual environments. The need for accurate surgical simulation has spurred the development of many of the new real-time FE methodologies that enable haptic support and real-time deformation. These techniques are computationally intensive and it has proved to be a challenge to achieve the high modeling resolutions required to accurately represent complex anatomies. We present a new real-time methodology based on linear FE analysis that is appropriate for a wide range of surgical simulation applications. A methodology is proposed that is characterized by high model resolution, low preprocessing time, unrestricted multipoint surface contact, and adjustable boundary conditions. These features make the method ideal for modeling suturing, which is an element common to almost every surgical procedure. We describe constraints in the context of a Suturing Simulator currently being developed.

Computation of 3D skeletons using a generalized Delaunay triangulation technique

Abstract The skeletal representation of 3D solids based on the medial axis transform has many applications in engineering. However, these applications are seldom realized, owing to the lack of viable computational techniques for generating skeletons. Such a computational technique, based on a notion of the generalized Voronoi diagram of a set of mixed-dimensional entities, is presented. It is shown that the generalized Voronoi diagram of a set of specific mixed dimensional set derived from the set of boundary entities of a polyhedron is, in fact, the exact skeleton of the polyhedron. Rather than the generalized Voronoi diagram being directly computed, its dual, an abstract Delaunay triangulation, is computed, from which the skeleton can be derived. An approach based on the Voronoi diagram of a well chosen representative point set on the boundary is also discussed as a special case; it is shown that the limitations of this approach are overcome by the generalization developed. Overall, it is argued that this generalization of the Voronoi diagram and the notion of the abstract generalized Delaunay triangulation are useful, and that they provide a viable approach to the computation of skeletons. Finally, details of the implementation, results, and an evaluation are presented.

Skeleton-based modeling operations on solids

The skeleton is a lower-dimensional geometric abstraction that is useful for performing a number of important geometric operations on solid models. In this paper we develop skeleton-based algorithms that demonstrat,e the utility of the skeleton in addressing: (1) 1 evel-of-detail control, the generation of hierarchical representations that preserve overall shape but blur local boundary features; (2) hexahedral mesh generation, the decomposit,ion of a 3D shape into a collection of block elements suitable for finite element analysis; (3) shape interpolation and morphing, the generation of an “int>ermediate” shape from two given 3D shapes and the generation of a sequence of shapes that smoothly transform one shape into another; and (4) shape synthesis, the generation of an optimal shape from specifications of functional performance requirements and constraints. Besides our goal of providing novel solutions to these problems of significant, practical importance, we seek to illustrate the general usefulness of the skeleton as an intermediate geometric descrig tion that should be more widely implemented in commercial CAD systems.

An accelerated triangulation method for computing the skeletons of free-form solid models

Abstract Shape skeletons are powerful geometric abstractions that provide useful intermediate representations for a number of geometric operations on solid models including feature recognition, shape decomposition, finite element mesh generation, and shape design. As a result there has been significant interest in the development of effective methods for skeleton generation of general free-form solids. In this paper we describe a method that combines Delaunay triangulation with local numerical optimization schemes for the generation of accurate skeletons of 3D implicit solid models. The proposed method accelerates the slow convergence of Voronoi diagrams to the skeleton, which, without optimization, would require impraelically large sample point sets and resulting meshes to attain acceptable accuracy. The Delaunay triangulation forms the basis for generating the topological structure of the skeleton. The optimization step of the process generates the geometry of the skeleton patches by moving the vertices of Delaunay tetrahedra and relocating their centres to form maximally inscribed spheres. The computational advantage of the optimization scheme is that it involves the solution of one small optimization problem per tetrahedron and its complexity is therefore only linear (O(n)) in the number of points used for the skeleton approximation. We demonstrate the effectiveness of the method on a number of representative solid models.

Implicit reconstruction of solids from cloud point sets

Chek T. Lirnl George M. Turkiyyah2 hark A. G’ante# Duane W. storti~ University of Washington Seattle, WA 98195 {ctlim@u, george@ce,ganter@u, storti@u}.Washington.edu This paper describes a new technique that combines numerical optimization methods with triangulation methods for generating mathematical representations of solids from 3D point data. The solid representation obtained takes the form of an algebraic function whose level surface closely approximates the surface described by the data, The algebraic function is obtained via Implicit Solid Modeling, a constructive scheme for approximating Boolean volume set operations on implicitly defined primitive volumes, and is comprised of a blended union of spherical primitives. The parameters of the algebraic function are the spatial locations and radii of the spheres as well as the parameters that describe the blending of these primitives, Fitting an implicit solid model to a data set is formulated as a sequence of non-linear optimization problems of an increasing number of variables. The cost function we employ in these optimizations is a weighted combination of discrepancies in location (distance from points to boundary of reconstructed object), discrepancies in surface normals, and desired curvature characteristics of the reconstructed solid. Since a set of trivariate data points without any connectivity information is ambiguous, an infinite number of solids, in principle, can be constructed to fit them. Different characteristics of the solid can be specified through the cost function to create the most desirable interpretation of the data. The starting point of the optimization—corresponding to the starting configuration of the primitives—is determined by performing a 3D Delaunay triangulation on the data set, and is based on the locations and sizes of the resulting tetrahedral. The effectiveness of the algorithm is demonstrated through the reconstruction of several sample data sets, including a molar and a femur. Tradeoffs between accuracy and compactness of the representations are also examined. 1Department of Mechanical Engineering, FU-10 ‘Department of Civil Engineering, FX-10. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association of Computing Machinery.To copy otherwise, or to republish, requires a fee andlor specific permission. Solid Modeling ’95, Salt Lake City, Utah USA

Optimization Models and Algorithms for Joint Uplink/Downlink UMTS Radio Network Planning With SIR-Based Power Control

Universal mobile telecommunication system (UMTS) networks should be deployed according to cost-effective strategies that optimize a cost objective and satisfy target quality-of-service (QoS) requirements. In this paper, we propose novel algorithms for joint uplink/downlink UMTS radio planning with the objective of minimizing total power consumption in the network. Specifically, we define two components of the radio planning problem: 1) continuous-based site placement and 2) integer-based site selection. In the site-placement problem, our goal is to find the optimal locations of UMTS base stations (BSs) in a certain geographic area with a given user distribution to minimize the total power expenditure such that a satisfactory level of downlink and uplink signal-to-interference ratio (SIR) is maintained with bounded outage constraints. We model the problem as a constrained optimization problem with SIR-based uplink and downlink power control scheme. An algorithm is proposed and implemented using pattern search techniques for derivative-free optimization with augmented Lagrange multiplier estimates to support general constraints. In the site-selection problem, we aim to select the minimum set of BSs from a fixed set of candidate sites that satisfies quality and outage constraints. We develop an efficient elimination algorithm by proposing a method for classifying BSs that are critical for network coverage and QoS. Finally, the problem is reformulated to take care of location constraints whereby the placement of BSs in a subset of the deployment area is not permitted due to, e.g., private property limitations or electromagnetic radiation constraints. Experimental results and optimal tradeoff curves are presented and analyzed for various scenarios.

Automated hexahedral mesh generation from biomedical image data: applications in limb prosthetics

A general method to generate hexahedral meshes for finite element analysis of residual limbs and similar biomedical geometries is presented. The method utilizes skeleton-based subdivision of cross-sectional domains to produce simple subdomains in which structured meshes are easily generated. Application to a below-knee residual limb and external prosthetic socket is described. The residual limb was modeled as consisting of bones, soft tissue, and skin. The prosthetic socket model comprised a socket wall with an inner liner. The geometries of these structures were defined using axial cross-sectional contour data from X-ray computed tomography, optical scanning, and mechanical surface digitization. A tubular surface representation, using B-splines to define the directrix and generator, is shown to be convenient for definition of the structure geometries. Conversion of cross-sectional data to the compact tubular surface representation is direct, and the analytical representation simplifies geometric querying and numerical optimization within the mesh generation algorithms. The element meshes remain geometrically accurate since boundary nodes are constrained to lie on the tubular surfaces. Several element meshes of increasing mesh density were generated for two residual limbs and prosthetic sockets. Convergence testing demonstrated that approximately 19 elements are required along a circumference of the residual limb surface for a simple linear elastic model. A model with the fibula absent compared with the same geometry with the fibula present showed differences suggesting higher distal stresses in the absence of the fibula. Automated hexahedral mesh generation algorithms for sliced data represent an advancement in prosthetic stress analysis since they allow rapid modeling of any given residual limb and optimization of mesh parameters.

Creating fast finite element models from medical images.

The procedure for creating a patient-specific virtual tissue model with finite element (FE) based haptic (force) feedback varies substantially from that which is required for generating a typical volumetric model. In addition to extracting geometrical and texture map data to provide visual realism, it is necessary to obtain information for supporting a FE model. Among many differences, FE-based VR environments require a FE model with appropriate material properties assigned. The FE equation must also be processed in a manner specific to the surgical task in order to maximize deformation and haptic computation speed. We are currently developing methodologies and support software for creating patient-specific models from medical images. The steps for creating such a model are as follows: 1) obtain medical images and texture maps of tissue structures; 2) extract tissue structure contours; 3) generate a 3D mesh from the tissue structure contours; 4) alter mesh based on simulation objectives; 5) assign material properties, boundary nodes and texture maps; 6) generate a fast (or real-time) FE model; and 7) support the tissue models with task-specific tools and training aids. This paper will elaborate on the above steps with particular reference to the creation of suturing simulation software, which will also be described.

Knowledge-based assistance for finite-element modeling

The authors propose a knowledge-based framework for assisting users in setting up, interpreting, and hierarchically refining finite-element models in a structural engineering domain. The central mechanism for providing modeling assistance is the explicit representation and incremental activation and refraction of modeling assumptions that operate on functional descriptions.

Skeleton-based three-dimensional geometric morphing

Abstract In this paper, we describe a method for generating geometric morphs between general 3D solid models. The method is based on the Euclidean skeleton and is capable of generating morphs between shapes that possess different feature sets and different topology. The essential concept that enables the morphing method is utilization of the trimmed skeleton of the symmetric difference as an intermediate shape. The intermediate shape is a valid solid model whose boundary does not self-intersect and is everywhere equidistant from the boundaries of the source shapes. We apply the skeleton-based intermediate shape generation procedure recursively to produce a sequence of shapes, referred to as a morph history, that gradually transform between the initial and target shapes. The method is sufficiently robust to handle significant changes in geometry and topology, such as the creation and annihilation of protrusions, indentations, internal holes and handles, and produces intuitive morph histories. The skeleton also establishes a correspondence between points on the boundaries of the source and target objects. Interpolation between corresponding points is performed to enable fast generation of a morph history consisting of a sequence of valid solid models. For source and target models that are sufficiently close, this interpolative morphing scheme generates results comparable to those obtained by the recursive skeletonization procedure, but with improved computational efficiency. The boundary point correspondence generated by the skeleton enables morphing with surface attributes (e.g., color, texture, surface roughness, and transparency). The skeleton-based procedure also allows for morphing between open curves or surfaces. A modification of the basic procedure allows the user to control the morph by specifying corresponding feature sets on the initial and final objects. Examples are presented to demonstrate the capabilities of the methods described.