Showing papers on "Displacement field published in 2005"

Spatio-temporal nonrigid registration for ultrasound cardiac motion estimation

Abstract: We propose a new spatio-temporal elastic registration algorithm for motion reconstruction from a series of images. The specific application is to estimate displacement fields from two-dimensional ultrasound sequences of the heart. The basic idea is to find a spatio-temporal deformation field that effectively compensates for the motion by minimizing a difference with respect to a reference frame. The key feature of our method is the use of a semi-local spatio-temporal parametric model for the deformation using splines, and the reformulation of the registration task as a global optimization problem. The scale of the spline model controls the smoothness of the displacement field. Our algorithm uses a multiresolution optimization strategy to obtain a higher speed and robustness. We evaluated the accuracy of our algorithm using a synthetic sequence generated with an ultrasound simulation package, together with a realistic cardiac motion model. We compared our new global multiframe approach with a previous method based on pairwise registration of consecutive frames to demonstrate the benefits of introducing temporal consistency. Finally, we applied the algorithm to the regional analysis of the left ventricle. Displacement and strain parameters were evaluated showing significant differences between the normal and pathological segments, thereby illustrating the clinical applicability of our method.

The effect of long-range forces on the dynamics of a bar

Abstract: The one-dimensional dynamic response of an infinite bar composed of a linear “microelastic material” is examined. The principal physical characteristic of this constitutive model is that it accounts for the effects of long-range forces. The general theory that describes our setting, including the accompanying equation of motion, was developed independently by Kunin (Elastic Media with Microstructure I, 1982), Rogula (Nonlocal Theory of Material Media, 1982) and Silling (J. Mech. Phys. Solids 48 (2000) 175), and is called the peridynamic theory. The general initial-value problem is solved and the motion is found to be dispersive as a consequence of the long-range forces. The result converges, in the limit of short-range forces, to the classical result for a linearly elastic medium. Explicit solutions in elementary form are given in a broad class of special cases. The most striking observations arise in the Riemann-like problem corresponding to a constant initial displacement field and a piecewise constant initial velocity field. Even though, initially, the displacement field is continuous, it involves a jump discontinuity for all later times, the Lagrangian location of which remains stationary. For some materials the magnitude of the discontinuity-jump oscillates about an average value, while for others it grows monotonically, presumably fracturing the material when it exceeds some critical level.

Finite element formulation for a digital image correlation method

Abstract: A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust.

Continuum limit of amorphous elastic bodies. III. Three-dimensional systems

Abstract: Extending recent numerical studies on two-dimensional amorphous bodies, we characterize the approach of the elastic continuum limit in three-dimensional (weakly polydisperse) Lennard-Jones systems. While performing a systematic finite-size analysis (for two different quench protocols), we investigate the nonaffine displacement field under external strain, the linear response to an external $\ensuremath{\delta}$ force, and the low-frequency harmonic eigenmodes and their density distribution. Qualitatively similar behavior is found as in two dimensions: The classical elasticity description breaks down below a surprisingly large length scale $\ensuremath{\xi}$, which in our system is approximately 23 molecular sizes. This length characterizes the correlations of the nonaffine displacement field, the self-averaging of external noise with distance from the source, and gives the lower wavelength bound for the applicability of the classical eigenfrequency calculations. Moreover, we demonstrate that the position of the ``Boson peak'' in the density of vibrational states is related to this self-averaging length $\ensuremath{\xi}$.

Estimation of mixed-mode stress intensity factors using digital image correlation and an interaction integral

Abstract: This paper presents a technique for the experimental measurement of stress intensity factors in cracked specimens under mixed-mode loading. This technique is based on full-field measurement using digital image correlation and an interaction integral. Such domain-independent integrals are often used in the finite element method to calculate stress intensity factors. The main advantage of this technique is that the errors made in the estimation of the measured displacement field near the crack’s tip do not affect the measurement of the stress intensity factors. The capabilities of the method are illustrated through fracture measurements on compact tension specimens made of maraging steel. Another test under mixed-mode loading is presented.

3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization

Abstract: This paper deals with topology preservation in three-dimensional (3-D) deformable image registration. This work is a nontrivial extension of , which addresses the case of two-dimensional (2-D) topology preserving mappings. In both cases, the deformation map is modeled as a hierarchical displacement field, decomposed on a multiresolution B-spline basis. Topology preservation is enforced by controlling the Jacobian of the transformation. Finding the optimal displacement parameters amounts to solving a constrained optimization problem: The residual energy between the target image and the deformed source image is minimized under constraints on the Jacobian. Unlike the 2-D case, in which simple linear constraints are derived, the 3-D B-spline-based deformable mapping yields a difficult (until now, unsolved) optimization problem. In this paper, we tackle the problem by resorting to interval analysis optimization techniques. Care is taken to keep the computational burden as low as possible. Results on multipatient 3-D MRI registration illustrate the ability of the method to preserve topology on the continuous image domain.

Cross-sectional analysis of nonhomogeneous anisotropic active slender structures

Abstract: A general formulation for the reduction of the three-dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented The dimensional reduction is based on a variationalasymptotic formulation, using the slenderness ratio as small parameter In the proposed scheme, the coupled linear electroelastic equations are solved at the cross-sectional level using the finite element method Furthermore, modal components of the displacement field are added to introduce arbitrary deformation shapes into the onedimensional analysis, and arbitrary electric modes are used to define applied electric fields at the cross section This results in a general definition of a coupled electroelastic stiffness, which can be used in virtually all composite and active beam formulations, as well as in the development of new low-order high-accuracy reduced models for active structures Finally, the formulation also yields recovery relations for the elastic and electric fields in the original three-dimensional solid, once the one-dimensional problem is solved The method has been implemented in a computer program (UM/VABS) and numerical results are presented for active anisotropic beam cross sections of simple geometries, which are shown to compare very well with three-dimensional finite element analysis

Feasability study of wall shear stress imaging using microstructured surfaces with flexible micropillars

Abstract: A new optical sensor technique based on a sensor film with arrays of hair-like flexible micropillars on the surface is presented to measure the temporal and spatial wall shear stress field in boundary layer flows. The sensor principle uses the pillar tip deflection in the viscous sublayer as a direct measure of the wall shear stress. The pillar images are recorded simultaneously as a grid of small bright spots by high-speed imaging of the illuminated sensor film. Two different ways of illumination were tested, one of which uses the fact that the transparent pillars act as optical microfibres, which guide the light to the pillar tips. The other method uses pillar tips which were reflective coated. The tip displacement field of the pillars is measured by image processing with subpixel accuracy. With a typical displacement resolution on the order of 0.2 μm, the minimum resolvable wall friction value is τw≈20 mPa. With smaller pillar structures than those used in this study, one can expect even smaller resolution limits.

Proposal of FEM implemented with particle discretization for analysis of failure phenomena

Abstract: A new method for numerical simulation of failure behavior, namely, FEM- β , is proposed. For a continuum model of a deformable body, FEM- β solves a boundary value problem by applying particle discretization to a displacement field; the domain is decomposed into a set of Voronoi blocks and the non-overlapping characteristic functions for the Voronoi blocks are used to discretize the displacement function. By computing average strain and average strain energy, FEM- β obtains a numerical solution of the variational problem that is transformed from the boundary value problem. In a rigorous form, FEM- β is formulated for a variational problem of displacement and stress with different particle discretization, i.e., the non-overlapping characteristic function of the Voronoi blocks and the conjugate Delaunay tessellations, respectively, are used to discretize the displacement and stress functions. While a displacement field is discretized with non-smooth functions, it is shown that a solution of FEM- β has the same accuracy as that of ordinary FEM with triangular elements. The key point of FEM- β is the ease of expressing failure as separation of two adjacent Voronoi blocks owing to the particle discretization that uses non-overlapping characteristic functions. This paper explains these features of FEM- β with results of numerical simulation of several example problems.

Method and Apparatus for Soft Tissue Material Parameter Estimation Using Tissue Tagged Magnetic Resonance Imaging

Abstract: We describe an experimental method and apparatus for the estimation of constitutive parameters of soft tissue using Magnetic Resonance Imaging (MRI), in particular for the estimation of passive myocardial material properties. MRI tissue tagged images were acquired with simultaneous pressure recordings, while the tissue was cyclically deformed using a custom built reciprocating pump actuator. A continuous three-dimensional (3D) displacement field was reconstructed from the imaged tag motion. Cavity volume changes and local tissue microstructure were determined from phase contrast velocity and diffusion tensor MR images, respectively. The Finite Element Method (FEM) was used to solve the finite elasticity problem and obtain the displacement field that satisfied the applied boundary conditions and a given set of material parameters. The material parameters which best fit the FEM predicted displacements to the displacements reconstructed from the tagged images were found by nonlinear optimization. The equipment and method were validated using inflation of a deformable silicon gel phantom in the shape of a cylindrical annulus. The silicon gel was well described by a neo-Hookian material law with a single material parameter C158.7160.06 k Pa, estimated independently using a rotational shear apparatus. The MRI derived parameter was allowed to vary regionally and was estimated as C158.8060.86 k Pa across the model. Preliminary results from the passive inflation of an isolated arrested pig heart are also presented, demonstrating the feasibility of the apparatus and method for isolated heart preparations. FEM based models can therefore estimate constitutive parameters accurately and reliably from MRI tagging data. @DOI: 10.1115/1.1835360#

Analyses of mode coupling in joined parallel phononic crystal waveguides

Abstract: In this paper, we present an analysis of coupling effects in joined parallel phononic crystal waveguides. The finite difference time domain (FDTD) method with periodic boundary condition is adopted to analyze the band gaps and dispersion relation of phononic waveguides. The defect modes of a single phononic waveguide are analyzed and first discussed to serve as a basis for a joined waveguides system. Then, the dispersion relation and displacement field of supermodes of joined waveguides are calculated and discussed. Both displacement pattern and transmission coefficient of the defect modes are calculated. To transfer the power from one waveguide to another, the coupling lengths are evaluated by numerical experiments and can be understood by the concept of beat length. Finally, we analyze an elastic waveguide coupler and demonstrate that the coupler can potentially be employed as a power switch of the acoustic wave.

Non‐local damage model based on displacement averaging

Abstract: Continuum damage models describe the changes of material stiffness and strength, caused by the evolution of defects, in the framework of continuum mechanics. In many materials, a fast evolution of defects leads to stress–strain laws with softening, which creates serious mathematical and numerical problems. To regularize the model behaviour, various generalized continuum theories have been proposed. Integral-type non-local damage models are often based on weighted spatial averaging of a strain-like quantity. This paper explores an alternative formulation with averaging of the displacement field. Damage is assumed to be driven by the symmetric gradient of the non-local displacements. It is demonstrated that an exact equivalence between strain and displacement averaging can be achieved only in an unbounded medium. Around physical boundaries of the analysed body, both formulations differ and the non-local displacement model generates spurious damage in the boundary layers. The paper shows that this undesirable effect can be suppressed by an appropriate adjustment of the non-local weight function. Alternatively, an implicit gradient formulation could be used. Issues of algorithmic implementation, computational efficiency and smoothness of the resolved stress fields are discussed. Copyright © 2005 John Wiley & Sons, Ltd.

Finite elements methods for modeling the guided waves propagation in structures with weak interfaces

Abstract: This paper describes two methods using a finite element (FE) code for modeling the effects of weak interfaces on the propagation of low-order Lamb modes. The variable properties of the interfaces are modeled by either a thin layer or a uniform repartition of compression and shear springs that insure the continuity of the stresses and impose a discontinuity in the displacement field. The method is tested by comparison with measurements that were presented in a previous paper [J. Acoust. Soc. Am. 113(6) 3161–3170 (2003)]. The interface was the contact between a rough elastomer with high internal damping loaded against one surface of a glass plate. Both normal and shear stiffnesses of the interface were quantified from the attenuation of A0 and S0 Lamb waves caused by leakage of energy from the plate into the elastomer and measured at each step of a compressive loading. The FE model is made in the frequency domain, thus allowing the viscoelastic properties of the elastomer to be modeled by using complex modu...

Digital image correlation used for mechanical tests on crimped glass wool samples

Abstract: Mechanical compression and tearing tests are carried out on crimped glass wool samples. The displacement field is determined by using digital image correlation based on images taken at different stages of the mechanical tests. A multiscale algorithm is used to resolve accurately fine details of the displacement field. This technique reveals strain heterogeneities and further localisation in compression tests well below the peak stress. Crack formations are identified in tearing tests. Reliability and resolution of the displacement and strain fields are validated by using different window sizes in the correlation analysis.

Development of the marks tracking technique for strain field and volume variation measurements

Abstract: The mark tracking method is a simple and efficient technique for a local strain measurement. We show the possibilities of the mark tracking for field measurement. We present a procedure which allows us to experimentally characterise this technique depending on the sensor and the marks' dimensions. The method presented is insensitive to illumination variation and to in-plane rotation of the specimen. The strain values are obtained by analysis of four marks. In order to obtain a displacement field, we analyse a series of small groups of spots. With the help of an average of the parameters (using a series of initial images), we suppress the systematic error that we can observe when we use a method comparing an initial state to a deformed one. So the strain uncertainty becomes less that 0.0002 for a local study and 0.002 for a whole field study (measurement base 20×20 pixel2).

A Least-Squares Mixed Finite Element Method for Biot's Consolidation Problem in Porous Media

Abstract: A least-squares mixed finite element method for the coupled problem of flow and deformation is presented and analyzed in this paper. For the analysis, we restrict ourselves to fully saturated conditions for the flow process and to a linearly elastic material law for the deformation process. This is known in the literature as Biot's consolidation problem. For simplicity, the analysis is presented for the problem in two space dimensions. Our least-squares approach is motivated by the fact that all process variables, i.e., fluid pressure and flux as well as displacement field and stress tensor, are approximated directly by suitable finite element spaces. Ellipticity of the corresponding variational formulation is proven for the stationary case as well as for the subproblems arising at each step of an implicit time discretization in the general time-dependent case. Standard H1-conforming piecewise linear and quadratic finite elements are used for the fluid pressure and for (each component of) the displacement, respectively. For the flux and stress components, the H(div)-conforming Raviart--Thomas spaces (of lowest order) are used. Computational results are presented for some two-dimensional test problems.

System and method for GPU-based 3D nonrigid registration

Abstract: A method of registering two images using a graphics processing unit includes providing a pair of images with a first and second image, calculating a gradient of the second image, initializing a displacement field on the grid point domain of the pair of images, generating textures for the first image, the second image, the gradient, and the displacement field, and loading said textures into the graphics processing unit. A pixel buffer is created and initialized with the texture containing the displacement field. The displacement field is updated from the first image, the second image, and the gradient for one or more iterations in one or more rendering passes performed by the graphics processing unit.

A Stabilized Mixed Finite Element Method for Nearly Incompressible Elasticity

Abstract: We present a new multiscale/stabilized finite element method for compressible and incompressible elasticity. The multiscale method arises from a decomposition of the displacement field into coarse (resolved) and fine (unresolved) scales. The resulting stabilized-mixed form consistently represents the fine computational scales in the solution and thus possesses higher coarse mesh accuracy. The ensuing finite element formulation allows arbitrary combinations of interpolation functions for the displacement and stress fields. Specifically, equal order interpolations that are easy to implement but violate the celebrated Babushka-Brezzi inf-sup condition, become stable and convergent. Since the proposed framework is based on sound variational foundations, it provides a basis for a priori error analysis of the system. Numerical simulations pass various element patch tests and confirm optimal convergence in the norms considered.