Articular Cartilage in the Knee: Current MR Imaging Techniques and Applications in Clinical Practice and Research

Magnetic resonance (MR) imaging is the most important imaging modality for the evaluation of traumatic or degenerative cartilaginous lesions in the knee. It is a powerful noninvasive tool for detecting such lesions and monitoring the effects of pharmacologic and surgical therapy. The specific MR imaging techniques used for these purposes can be divided into two broad categories according to their usefulness for morphologic or compositional evaluation. To assess the structure of knee cartilage, standard spin-echo (SE) and gradient-recalled echo (GRE) sequences, fast SE sequences, and three-dimensional SE and GRE sequences are available. These techniques allow the detection of morphologic defects in the articular cartilage of the knee and are commonly used in research for semiquantitative and quantitative assessments of cartilage. To evaluate the collagen network and proteoglycan content in the knee cartilage matrix, compositional assessment techniques such as T2 mapping, delayed gadolinium-enhanced MR imaging of cartilage (or dGEMRIC), T1 rho imaging, sodium imaging, and diffusion-weighted imaging are available. These techniques may be used in various combinations and at various magnetic field strengths in clinical and research settings to improve the characterization of changes in cartilage. (C)RSNA, 2011 , radiographics.rsna.org

Decay chain differential equations: Solution through matrix algebra

A matricial method to solve the decay chain differential equations system is presented. The quantity of each nuclide in the chain at a time t may be evaluated by analytical expressions obtained in a simple way using recurrence relations. This method may be applied to problems of radioactive buildup and decay and can be easily implemented computationally. (C) 2009 Elsevier B.V. All rights reserved.

Dimensional Accuracy of Computer-Aided Design/Computer-Assisted Manufactured Orbital Prostheses

Purpose: The aim of this research was to assess the dimensional accuracy of orbital prostheses based on reversed images generated by computer-aided design/computer-assisted manufacturing (CAD/CAM) using computed tomography (CT) scans. Materials and Methods: CT scans of the faces of 15 adults, men and women older than 25 years of age not bearing any congenital or acquired craniofacial defects, were processed using CAD software to produce 30 reversed three-dimensional models of the orbital region. These models were then processed using the CAM system by means of selective laser sintering to generate surface prototypes of the volunteers` orbital regions. Two moulage impressions of the faces of each volunteer were taken to manufacture 15 pairs of casts. Orbital defects were created on the right or left side of each cast. The surface prototypes were adapted to the casts and then flasked to fabricate silicone prostheses. The establishment of anthropometric landmarks on the orbital region and facial midline allowed for the data collection of 31 linear measurements, used to assess the dimensional accuracy of the orbital prostheses and their location on the face. Results: The comparative analyses of the linear measurements taken from the orbital prostheses and the opposite sides that originated the surface prototypes demonstrated that the orbital prostheses presented similar vertical, transversal, and oblique dimensions, as well as similar depth. There was no transverse or oblique displacement of the prostheses. Conclusion: From a clinical perspective, the small differences observed after analyzing all 31 linear measurements did not indicate facial asymmetry. The dimensional accuracy of the orbital prostheses suggested that the CAD/CAM system assessed herein may be applicable for clinical purposes. Int J Prosthodont 2010;23:271-276.

Quantitative CT analysis of the glabellar and anterior nasal spine regions for the placement of implants for nasal prosthesis retention

Objectives: The aim of this study was to determine the precision of the measurements of 2 craniometric anatomic points-glabella and anterior nasal spine-in order to verify their possibility as potential locations for placing implants aimed at nasal prostheses retention. Methods: Twenty-six dry human skulls were scanned in a high-resolution spiral tomography with 1-mm axial slice thickness and 1-mm interval reconstruction using a bone tissue filter. Images obtained were stored and transferred to an independent workstation containing e-film imaging software. The measurements (in the glabella and anterior nasal fossa) were made independently by 2 observers twice for each measurement. Data were submitted to statistical analysis (parametric t test). Results: The results demonstrated no statistically significant difference between interobserver and intraobserver measurements (P > .05). The standard error was found to be between 0.49 mm and 0.84 mrn for measurements in bone protocol, indicating a high /eve/ of precision. Conclusions: The measurements obtained in anterior nasal spine and glabella were considered precise and reproducible. Mean values of such measurements pointed to the possibility of implant placement in these regions, particularly in the anterior nasal spine.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Lattice-dome design using a knowledge-based system approach

In the design of lattice domes, design engineers need expertise in areas such as configuration processing, nonlinear analysis, and optimization. These are extensive numerical, iterative, and lime-consuming processes that are prone to error without an integrated design tool. This article presents the application of a knowledge-based system in solving lattice-dome design problems. An operational prototype knowledge-based system, LADOME, has been developed by employing the combined knowledge representation approach, which uses rules, procedural methods, and an object-oriented blackboard concept. The system's objective is to assist engineers in lattice-dome design by integrating all design tasks into a single computer-aided environment with implementation of the knowledge-based system approach. For system verification, results from design examples are presented.

Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.