Evaluation of a patient-specific finite-element model to simulate conservative treatment in adolescent idiopathic scoliosis

Study design Retrospective validation study. Objectives To propose a method to evaluate, from a clinical standpoint, the ability of a finite-element model (FEM) of the trunk to simulate orthotic correction of spinal deformity and to apply it to validate a previously described FEM. Summary of background data Several FEMs of the scoliotic spine have been described in the literature. These models can prove useful in understanding the mechanisms of scoliosis progression and in optimizing its treatment, but their validation has often been lacking or incomplete. Methods Three-dimensional (3D) geometries of 10 patients before and during conservative treatment were reconstructed from biplanar radiographs. The effect of bracing was simulated by modeling displacements induced by the brace pads. Simulated clinical indices (Cobb angle, T1–T12 and T4–T12 kyphosis, L1–L5 lordosis, apical vertebral rotation, torsion, rib hump) and vertebral orientations and positions were compared to those measured in the patients' 3D geometries. Results Errors in clinical indices were of the same order of magnitude as the uncertainties due to 3D reconstruction; for instance, Cobb angle was simulated with a root mean square error of 5.7°, and rib hump error was 5.6°. Vertebral orientation was simulated with a root mean square error of 4.8° and vertebral position with an error of 2.5 mm. Conclusions The methodology proposed here allowed in-depth evaluation of subject-specific simulations, confirming that FEMs of the trunk have the potential to accurately simulate brace action. These promising results provide a basis for ongoing 3D model development, toward the design of more efficient orthoses.

On a finite element model for the analysis of through cracks in laminated anisotropic cylindrical shells

A finite element model for the analysis of laminated composite cylindrical shells with through cracks is presented. The analysis takes into account anisotropic elastic behaviour, bending-extensional coupling and transverse shear deformation effects. The proposed finite element model is based on the approach of dividing a cracked configuration into triangular shaped singular elements around the crack tip with adjoining quadrilateral shaped regular elements. The parabolic isoparametric cylindrical shell elements (both singular and regular) used in this model employ independent displacement and rotation interpolation in the shell middle surface. The numerical comparisons show the evidence to the conclusion that the proposed model will yield accurate stress intensity factors from a relatively coarse mesh. Through the analysis of a pressurised fibre composite cylindrical shell with an axial crack, the effect of material orthotropy on the crack tip stress intensity factors is shown to be quite significant.

Searching the inclusive ℓγE̸T+b-quark signature for radiative top quark decay and non-standard-model processes

In a search for new phenomena in a signature suppressed in the standard model of elementary particles (SM), we compare the inclusive production of events containing a lepton, a photon, significant transverse momentum imbalance (MET), and a jet identified as containing a b-quark, to SM predictions. The search uses data produced in proton-antiproton collisions at 1.96 TeV corresponding to 1.9 fb-1 of integrated luminosity taken with the CDF detector at the Fermilab Tevatron. We find 28 lepton+photon+MET+b events versus an expectation of 31.0+4.1/-3.5 events. If we further require events to contain at least three jets and large total transverse energy, simulations predict that the largest SM source is top-quark pair production with an additional radiated photon, ttbar+photon. In the data we observe 16 ttbar+photon candidate events versus an expectation from SM sources of 11.2+2.3/-2.1. Assuming the difference between the observed number and the predicted non-top-quark total is due to SM top quark production, we estimate the ttg cross section to be 0.15 +- 0.08 pb.

The Line Spectral Frequency Model of a Finite-Length Sequence

The line spectral frequency (LSF) of a causal finite length sequence is a frequency at which the spectrum of the sequence annihilates or the magnitude spectrum has a spectral null. A causal finite-length sequencewith (L + 1) samples having exactly L-LSFs, is referred as an Annihilating (AH) sequence. Using some spectral properties of finite-length sequences, and some model parameters, we develop spectral decomposition structures, which are used to translate any finite-length sequence to an equivalent set of AH-sequences defined by LSFs and some complex constants. This alternate representation format of any finite-length sequence is referred as its LSF-Model. For a finite-length sequence, one can obtain multiple LSF-Models by varying the model parameters. The LSF-Model, in time domain can be used to synthesize any arbitrary causal finite-length sequence in terms of its characteristic AH-sequences. In the frequency domain, the LSF-Model can be used to obtain the spectral samples of the sequence as a linear combination of spectra of its characteristic AH-sequences. We also summarize the utility of the LSF-Model in practical discrete signal processing systems.

Reconstructing Solid Model from 2D Scanned Images of Biological Organs for Finite Element Simulation

This work presents a methodology to reconstruct 3D biological organs from image sequences or other scan data using readily available free softwares with the final goal of using the organs (3D solids) for finite element analysis. The methodology deals with issues such as segmentation, conversion to polygonal surface meshes, and finally conversion of these meshes to 3D solids. The user is able to control the detail or the level of complexity of the solid constructed. The methodology is illustrated using 3D reconstruction of a porcine liver as an example. Finally, the reconstructed liver is imported into the commercial software ANSYS, and together with a cyst inside the liver, a nonlinear analysis performed. The results confirm that the methodology can be used for obtaining 3D geometry of biological organs. The results also demonstrate that the geometry obtained by following this methodology can be used for the nonlinear finite element analysis of organs. The methodology (or the procedure) would be of use in surgery planning and surgery simulation since both of these extensively use finite elements for numerical simulations and it is better if these simulations are carried out on patient specific organ geometries. Instead of following the present methodology, it would cost a lot to buy a commercial software which can reconstruct 3D biological organs from scanned image sequences.

A nonlinear spectral finite element model for analysis of wave propagation in solid with internal friction and dissipation

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

Resource Pricing for Fair and Efficient Link Sharing with a Finite Data Model

The literature on pricing implicitly assumes an "infinite data" model, in which sources can sustain any data rate indefinitely. We assume a more realistic "finite data" model, in which sources occasionally run out of data. Further, we assume that users have contracts with the service provider, specifying the rates at which they can inject traffic into the network. Our objective is to study how prices can be set such that a single link can be shared efficiently and fairly among users in a dynamically changing scenario where a subset of users occasionally has little data to send. We obtain simple necessary and sufficient conditions on prices such that efficient and fair link sharing is possible. We illustrate the ideas using a simple example

A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

A finite-rate-of-innovation signal sampling perspective of the source-filter model of speech production

We consider the speech production mechanism and the asso- ciated linear source-filter model. For voiced speech sounds in particular, the source/glottal excitation is modeled as a stream of impulses and the filter as a cascade of second-order resonators. We show that the process of sampling speech signals can be modeled as filtering a stream of Dirac impulses (a model for the excitation) with a kernel function (the vocal tract response),and then sampling uniformly. We show that the problem of esti- mating the excitation is equivalent to the problem of recovering a stream of Dirac impulses from samples of a filtered version. We present associated algorithms based on the annihilating filter and also make a comparison with the classical linear prediction technique, which is well known in speech analysis. Results on synthesized as well as natural speech data are presented.

An extended finite element model coupled with level set method for stable pitting corrosion

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution), which requires only three inputs, namely the solid metal concentration, saturation concentration of the dissolved metal ions and diffusion coefficient. A combined eXtended Finite Element Model (XFEM) and level set method is developed in this paper. The extended finite element model handles the jump discontinuity in the metal concentrations at the interface, by using discontinuous-derivative enrichment formulation for concentration discontinuity at the interface. This eliminates the requirement of using front conforming mesh and re-meshing after each time step as in conventional finite element method. A numerical technique known as level set method tracks the position of the moving interface and updates it over time. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed method is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions.

An extended finite-element model coupled with level set method for analysis of growth of corrosion pits in metallic structures

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution). The interface experiences a jump discontinuity in metal concentration. The extended finite-element model (XFEM) handles this jump discontinuity by using discontinuous-derivative enrichment formulation, eliminating the requirement of using front conforming mesh and re-meshing after each time step as in the conventional finite-element method. However, prior interface location is required so as to solve the governing equations for concentration field for which a numerical technique, the level set method, is used for tracking the interface explicitly and updating it over time. The level set method is chosen as it is independent of shape and location of the interface. Thus, a combined XFEM and level set method is developed in this paper. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed model is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions. An empirical model for pitting potential is also derived based on the finite-element results. Studies show that pitting profile depends on factors such as ion concentration, solution pH and temperature to a large extent. Studying the individual and combined effects of these factors on pitting potential is worth knowing, as pitting potential directly influences corrosion rate.

A finite variant of the Toom Model

We present results for a finite variant of the one-dimensional Toom model with closed boundaries. We show that the steady state distribution is not of product form, but is nonetheless simple. In particular, we give explicit formulas for the densities and some nearest neighbour correlation functions. We also give exact results for eigenvalues and multiplicities of the transition matrix using the theory of R-trivial monoids in joint work with A. Schilling, B. Steinberg and N. M. Thiery.

Simulation of Free-Surface Flow in a Tank Using the Navier-Stokes Model and Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.