The Kinematic Effects of the Defects in Liquid Crystal Dynamics

Here we investigate the kinematic transports of the defects in the nematic liquid crystal system by numerical experiments. The model is a shear flow case of the viscoelastic continuum model simplified from the Ericksen-Leslie system. The numerical experiments are carried out by using a difference method. Based on these numerical experiments we find some interesting and important relationships between the kinematic transports and the characteristics of the flow. We present the development and interaction of the defects. These results are partly consistent with the observation from the experiments. Thus this scheme illustrates, to some extent, the kinematic effects of the defects.     

Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

We use front tracking data structures and functions to model the dynamic evolution of fabric surface. We represent the fabric surface by a triangulated mesh with preset equilibrium side length. The stretching and wrinkling of the surface are modeled by the mass-spring system. The external driving force is added to the fabric motion through the "Impulse method" which computes the velocity of the point mass by superposition of momentum. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency. This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.     

Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem

We consider a model of coupled free and porous media flow governed by Stokes equation and Darcy's law with the Beavers-Joseph-Saffman interface condition. In this paper, we propose a new numerical approach for the Stokes-Darcy system. The approach employs the classical finite element method for the Darcy region and the weak Galerkin finite element method for the Stokes region. We construct corresponding discrete scheme and prove its well-posedness. The estimates for the corresponding numerical approximation are derived. Finally, we present some numerical experiments to validate the efficiency of the approach for solving this problem.     

Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms. Classic two-mode approximation method and direct numerical minimization are applied to the model. In the latter approach, we apply the projection method to deal with the potentially quasiperiodic ground states. A variable cell method of optimizing the shape and size of higher-dimensional periodic cell is developed to minimize the free energy with respect to the order parameters. Based on the developed numerical methods, we rediscover decagonal and dodecagonal quasicrystalline phases, and find diverse periodic phases and complex modulated phases. Furthermore, phase diagrams are obtained in various phase spaces by comparing the free energies of different candidate structures. It does show not only the important roles of system parameters, but also the effect of optimizing computational domain. In particular, the optimization of computational cell allows us to capture the ground states and phase behavior with higher fidelity. We also make some discussions on our results and show the potential of applying our numerical methods to a larger class of mean-field free energy functionals.     

A Low Frequency Model for Acoustic Propagation in a 2D Flow Duct: Numerical Computation

In this paper we study a low frequency model for acoustic propagation in a 2D flow duct. For some Mach profile flow, we are able to give a well-posedness theorem. Its proof relies on a quasi-explicit expression of the solution which provides us an efficient numerical method. We give and comment numerical results for particular linear, tangent and quadratic profiles. Finally, we give a numerical validation of our asymptotic model.     

Relaxation Schemes for the $M_1$ Model with Space-Dependent Flux: Application to Radiotherapy Dose Calculation

Because of stability constraints, most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar. This problem emerges with the $M_1$ system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities. Additionally, the flux term of the $M_1$ system is non-linear, and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability. In this paper, we propose a numerical method that overcomes the stability constraint and preserves the realizability property. For this purpose, we relax the $M_1$ system to obtain a linear flux term. Then we extend the stencil of the difference quotient to obtain stability. The scheme is applied to a radiotherapy dose calculation example.     

Simulation of normal pelvic mobilities in building an MRI-validated biomechanical model

Introduction and hypothesis

Three-dimensional modeling of feminine pelvic mobility is difficult because the sustaining system is not well understood and ligaments are especially difficult to identify on imaging.

Methods

We built a 3-D numerical model of the pelvic cavity, based on magnetic resonance (MR) images and knowledge about anatomy and validated it systematically.

Results

The quantitative results of this model allow for the non-destructive localization of the structures involved in pelvic statics. With a better configuration of the functional pelvis and topological criteria, we can obtain a coherent anatomical and functional model.

Conclusions

This model is the first step in developing a tool to localize and characterize pelvic imbalance in patients.     

Fluoroscopic comparison of kinematic patterns in massive rotator cuff tears. A suspension bridge model.

Twelve shoulders with known massive rotator cuff tears were imaged fluoroscopically. The observed kinematic patterns were correlated with the known locations of the rotator cuff tears. Three kinematic patterns emerged: Type I, stable fulcrum kinematics associated with tears of the superior rotator cuff (supraspinatus and a portion of the infraspinatus); Type II, unstable fulcrum kinematics associated with tears that involved virtually all of the superior and posterior rotator cuff; and Type III, captured fulcrum kinematics associated with massive tears that involved the supraspinatus, a major portion of the posterior rotator cuff, and a major portion of the subscapularis. In Type III, an "awning effect" of the acromion was observed to influence active motion. Based on the recorded kinematic patterns, a biomechanical model was developed comparing the rotator cuff tear to a suspension bridge (loaded cable). A biomechanical analysis of forces acting on the rotator cuff according to this model yielded data that supported the contention that certain rotator cuff tears in older individuals may be adequately treated with debridement and decompression, without repair.     

A CAD CAM method for custom below-knee sockets.

The purpose of this investigation was to develop a numerical method for fabricating prosthetic sockets for below-knee amputees. An optical/laser digitiser scans an amputee's stump and collects three dimensional numerical data describing the surface of the limb and describing specific modification site locations. The numerical data from the laser camera representing the stump and modification sites are altered by the prosthetist using a custom computer aided design software system running on a personal computer. Using the altered numerical data a programme is created for a high resolution numerically controlled milling machine and a mould is made. The prosthetist then fabricates a socket. While the system has been tested with below-knee amputees it has been designed for application in most areas of prosthetics and orthotics. Utilising this method 15 patients were fitted. All patients subjectively stated that their "computer designed" socket fitted better than their conventionally made socket. As the research progressed and experience was gained with the system patients were normally fitted with the first socket iteration. The system overcomes five limitations existing with some of the other numerical systems: 1) accurate high resolution surface topography, 2) specific identification of subject modification sites, 3) flexible, user friendly software, 4) high resolution numerically controlled milling, and 5) integrated expansion to other prosthetic and orthotic areas.     

Computation of Shock Profiles in Radiative Hydrodynamics

This article is devoted to the construction of a numerical scheme to solve the equations of radiative hydrodynamics. We use this numerical procedure to compute shock profiles and illustrate some earlier theoretical results about their smoothness and monotonicity properties. We first consider a scalar toy model, then we extend our analysis to a more realistic system for the radiative hydrodynamics that couples the Euler equations and an elliptic equation.     

Einsatzgebiete der numerischen Simulation in der muskuloskelettalen Forschung und ihre Bedeutung für die Orthopädische Chirurgie

Finite element analyses (FEA) as well as multibody system dynamics (MSD) are the main tools used for numerical simulation in the field of musculoskeletal research. While FEA is utilized for field problems, such as calculation of stress and strain distribution, MSD is applied for solving kinematic analyses, such as calculation of muscle and joint forces. Depending on the focus of investigation, modelling of biological tissue may vary from simple homogeneous behavior to modelling biochemical processes on the microscale and nanoscale. An important milestone in biomechanical research was the analysis of stress shielding, which led to further research on bone remodelling. Various models of implant-bone fixation used for the prediction of micromotion have been published. New possibilities for biomechanical analyses are achieved by consideration of complex muscle forces which are generated by MSD simulation and imported into FEA models as limiting conditions. A numerical model always requires experimental validation. If the results are confirmed experimentally, various advantages of numerical simulation apply and problems can be analysed isolated from many influencing factors. Therefore, straightforward parameter variation is possible, enabling studies which would be impossible in an experimental or clinical setup.     

The WASP Model: A Micro-Macro System of Wave-Schrödinger-Plasma Equations for Filamentation

In this paper, we model laser-gas interactions and propagation in some extreme regimes. After a mathematical study of a micro-macro Maxwell-Schrödinger model [1] for short, high-frequency and intense laser-gas interactions, we propose to improve this model by adding a plasma equation in order to precisely take into account free electron effects. We examine if such a model can predict and explain complex structures such as filaments, on a physical and numerical basis. In particular, we present in this paper a first numerical observation of nonlinear focusing effects using an ab-initio gas representation and linking our results with existing nonlinear models.     

Robust (Q,S, R)-γ-dissipative control of Takagi–Sugeno fuzzy systems with interval time-varying delay and sampling

The robust (Q, S, R)-γ-dissipative control of Takagi–Sugeno fuzzy time-delay model is considered by the developed robust control with sampling in this article. The proposed Lyapunov–Krasovskii functional and inequality are investigated to improve the main results in this article. Full matrix formulation approach is present to show our proposed results by some linear matrix inequalities. Interval delay and sampling period are contemplated instead of constant delay and fixed sampling in some circulated literatures. The less conservatism of our proposed results is demonstrated by our proposed numerical examples. Finally, we illustrate a mass-spring-damper nonlinear system to show our developed results.     

Stability and Conservation Properties of Collocated Constraints in Immersogeometric Fluid-Thin Structure Interaction Analysis

The purpose of this study is to enhance the stability properties of our recently-developed numerical method [D. Kamensky, M.-C. Hsu, D. Schillinger, J. A. Evans, A. Aggarwal, Y. Bazilevs, M. S. Sacks, T. J. R. Hughes, "An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves", Comput. Methods Appl. Mech. Engrg., 284 (2015) 1005–1053] for immersing spline-based representations of shell structures into unsteady viscous incompressible flows. In the cited work, we formulated the fluid-structure interaction (FSI) problem using an augmented Lagrangian to enforce kinematic constraints. We discretized this Lagrangian as a set of collocated constraints, at quadrature points of the surface integration rule for the immersed interface. Because the density of quadrature points is not controlled relative to the fluid discretization, the resulting semi-discrete problem may be over-constrained. Semi-implicit time integration circumvents this difficulty in the fully-discrete scheme. If this time-stepping algorithm is applied to fluid-structure systems that approach steady solutions, though, we find that spatially-oscillating modes of the Lagrange multiplier field can grow over time. In the present work, we stabilize the semi-implicit integration scheme to prevent potential divergence of the multiplier field as time goes to infinity. This stabilized time integration may also be applied in pseudo-time within each time step, giving rise to a fully implicit solution method. We discuss the theoretical implications of this stabilization scheme for several simplified model problems, then demonstrate its practical efficacy through numerical examples.     

Stability of Projection Methods for Incompressible Flows Using High Order Pressure-Velocity Pairs of Same Degree: Continuous and Discontinuous Galerkin Formulations

This paper presents limits for stability of projection type schemes when using high order pressure-velocity pairs of same degree. Two high order $h/p$ variational methods encompassing continuous and discontinuous Galerkin formulations are used to explain previously observed lower limits on the time step for projection type schemes to be stable [18], when $h$- or$p$-refinement strategies are considered. In addition, the analysis included in this work shows that these stability limits depend not only on the time step but on the product of the latter and the kinematic viscosity, which is of particular importance in the study of high Reynolds number flows. We show that high order methods prove advantageous in stabilising the simulations when small time steps and low kinematic viscosities are used.Drawing upon this analysis, we demonstrate how the effects of this instability can be reduced in the discontinuous scheme by introducing a stabilisation term into the global system. Finally, we show that these lower limits are compatible with Courant-Friedrichs-Lewy (CFL) type restrictions, given that a sufficiently high polynomial order or a mall enough mesh spacing is selected.     

A Strong Stability-Preserving Predictor-Corrector Method for the Simulation of Elastic Wave Propagation in Anisotropic Media

In this paper, we propose a strong stability-preserving predictor-corrector (SSPC) method based on an implicit Runge-Kutta method to solve the acoustic- and elastic-wave equations. We first transform the wave equations into a system of ordinary differential equations (ODEs) and apply the local extrapolation method to discretize the spatial high-order derivatives, resulting in a system of semi-discrete ODEs. Then we use the SSPC method based on an implicit Runge-Kutta method to solve the semi-discrete ODEs and introduce a weighting parameter into the SSPC method. On top of such a structure, we develop a robust numerical algorithm to effectively suppress the numerical dispersion, which is usually caused by the discretization of wave equations when coarse grids are used or geological models have large velocity contrasts between adjacent layers. Meanwhile, we investigate the performance of the SSPC method including numerical errors and convergence rate, numerical dispersion, and stability criteria with different choices of the weighting parameter to solve 1-D and 2-D acoustic- and elastic-wave equations. When the SSPC is applied to seismic simulations, the computational efficiency is also investigated by comparing the SSPC, the fourth-order Lax-Wendroff correction (LWC) method, and the staggered-grid (SG) finite difference method. Comparisons of synthetic waveforms computed by the SSPC and analytic solutions for acoustic and elastic models are given to illustrate the accuracy and the validity of the SSPC method. Furthermore, several numerical experiments are conducted for the geological models including a 2-D homogeneous transversely isotropic (TI) medium, a two-layer elastic model, and the 2-D SEG/EAGE salt model. The results show that the SSPC can be used as a practical tool for large-scale seismic simulation because of its effectiveness in suppressing numerical dispersion even in the situations such as coarse grids, strong interfaces, or high frequencies.     

Segmental transports for posttraumatic lower extremity bone defects: are femoral bone transports safer than tibial?

Background

The long-term outcomes following femoral and tibial segment transports are not well documented. Purpose of the study is to compare the complication rates and life quality scores of femoral and tibial transports in order to find what are the complication rates of femoral and tibial monorail bone transports and if they are different?

Methods

We retrospectively analyzed the medical records of 8 femoral and 14 tibial consecutive segment transports performed with the monorail technique between 2001 and 2008 in our institution. Mean follow-up was 5.1 ± 2.1 years with a minimum follow-up of 2 years. Aetiology of the defects was posttraumatic in all cases. Four femoral (50%) and nine tibial (64%) fractures were open. The Short Form-36 (SF-36) health survey was used to compare the life quality after femoral and tibial bone transports. The Mann–Whiney U test, Fisher exact test, and the Student’s two tailed t-test were used for statistical analysis. P ≤ 0.05 was considered to be statistically significant.

Results

The tibial transport was associated with higher rates of severe complications and additional procedures (1.5 ± 0.9 vs. 3.4 ± 2.7, p = 0.048). Three patients of the tibial group were amputated because of recurrent infections and one developed a complete regenerate insufficiency that was treated with partial diaphyseal tibial replacement. Contrary to that none of patients of the femoral group developed a complete regenerate insufficiency or was amputated.

Conclusions

Tibial bone transports have a higher rate of complete and incomplete regenerate insufficiency and can more often end in an amputation. The authors suggest systematic weekly controls of the CRP value and of the callus formation in patients with posttraumatic tibia bone transports. Further comparative studies comparing the results of bone transports with and without intramedullary implants are necessary.     

Virtual interactive musculoskeletal system (VIMS) in orthopaedic research, education and clinical patient care

The ability to combine physiology and engineering analyses with computer sciences has opened the door to the possibility of creating the "Virtual Human" reality. This paper presents a broad foundation for a full-featured biomechanical simulator for the human musculoskeletal system physiology. This simulation technology unites the expertise in biomechanical analysis and graphic modeling to investigate joint and connective tissue mechanics at the structural level and to visualize the results in both static and animated forms together with the model. Adaptable anatomical models including prosthetic implants and fracture fixation devices and a robust computational infrastructure for static, kinematic, kinetic, and stress analyses under varying boundary and loading conditions are incorporated on a common platform, the VIMS (Virtual Interactive Musculoskeletal System). Within this software system, a manageable database containing long bone dimensions, connective tissue material properties and a library of skeletal joint system functional activities and loading conditions are also available and they can easily be modified, updated and expanded. Application software is also available to allow end-users to perform biomechanical analyses interactively. Examples using these models and the computational algorithms in a virtual laboratory environment are used to demonstrate the utility of these unique database and simulation technology. This integrated system, model library and database will impact on orthopaedic education, basic research, device development and application, and clinical patient care related to musculoskeletal joint system reconstruction, trauma management, and rehabilitation.