Confidence Limits for the Ratio of Two Binomial Proportions Based on Likelihood Scores: Non-Iterative Method

The interval estimation of the ratio of two binomial proportions based on the score statistic is superior over other methods. Iterative algorithms for calculating the approximate confidence interval have been provided by, e.g., KOOPMAN (1984, Biometrics 40:513–517) and GART and NAM (1988a, Biometrics 44:323–338). This note presents the analytical solutions for upper and lower confidence limits in a closed form and gives examples for numerical illustration. The non-iterative method is generally more desirable than the iterative method.     

Partitioning of knee joint internal forces in gait is dictated by the knee adduction angle and not by the knee adduction moment

Medial knee osteoarthritis is a debilitating disease. Surgical and conservative interventions are performed to manage its progression via reduction of load on the medial compartment or equivalently its surrogate measure, the external adduction moment. However, some studies have questioned a correlation between the medial load and adduction moment. Using a musculoskeletal model of the lower extremity driven by kinematics–kinetics of asymptomatic subjects at gait midstance, we aim here to quantify the relative effects of changes in the knee adduction angle versus changes in the adduction moment on the joint response and medial/lateral load partitioning. The reference adduction rotation of 1.6° is altered by ±1.5° to 3.1° and 0.1° or the knee reference adduction moment of 17 N m is varied by ±50% to 25.5 N m and 8.5 N m. Quadriceps, hamstrings and tibiofemoral contact forces substantially increased as adduction angle dropped and diminished as it increased. The medial/lateral ratio of contact forces slightly altered by changes in the adduction moment but a larger adduction rotation hugely increased this ratio from 8.8 to a 90 while in contrast a smaller adduction rotation yielded a more uniform distribution. If the aim in an intervention is to diminish the medial contact force and medial/lateral load ratio, a drop of 1.5° in adduction angle is much more effective (causing respectively 12% and 80% decreases) than a reduction of 50% in the adduction moment (causing respectively 4% and 13% decreases). Substantial role of changes in adduction angle is due to the associated alterations in joint nonlinear passive resistance. These findings explain the poor correlation between knee adduction moment and tibiofemoral compartment loading during gait suggesting that the internal load partitioning is dictated by the joint adduction angle.     

Temporal changes of mechanical signals and extracellular composition in human intervertebral disc during degenerative progression

In this study, a three-dimensional finite element model was used to investigate the changes in tissue composition and mechanical signals within human lumbar intervertebral disc during the degenerative progression. This model was developed based on the cell-activity coupled mechano-electrochemical mixture theory. The disc degeneration was simulated by lowering nutrition levels at disc boundaries, and the temporal and spatial distributions of the fixed charge density, water content, fluid pressure, Von Mises stress, and disc deformation were analyzed. Results showed that fixed charge density, fluid pressure, and water content decreased significantly in the nucleus pulposus (NP) and the inner to middle annulus fibrosus (AF) regions of the degenerative disc. It was found that, with degenerative progression, the Von Mises stress (relative to that at healthy state) increased within the disc, with a larger increase in the outer AF region. Both the disc volume and height decreased with the degenerative progression. The predicted results of fluid pressure change in the NP were consistent with experimental findings in the literature. The knowledge of the variations of temporal and spatial distributions of composition and mechanical signals within the human IVDs provide a better understanding of the progression of disc degeneration.     

On partial local smoothing rules for curve estimation

We compare the performances of local and global rules for smoothingparameter choice, in terms of asymptotic mean squared errorsof the resulting estimators. In some instances there is surprisinglylittle to choose between local and global approaches; our analysisidentifies contexts where the differences are small or large.This work motivates development of smoothing rules that forma ‘half-way house’ between local and global smoothing.There, interpolation provides a basis for partial local smoothing.A key result shows that interpolation on even a coarse gridcan produce a very good approximation to full local smoothing.Our theoretical and numerical results lead us to suggest linearinterpolation of a bandwidth obtained by integral approximationson discrete intervals.     

The Relativistic Quantum Defect Orbital Method and some of its Applications

Justification of a simple and reliable relativistic procedure for the prediction of a large body of transition probability data is made. The main features of the Relativistic Quantum Defect Orbital (RQDO) formalism are described, and several examples of the data yielded by this method are presented in tabular and graph forms.     

Differences in 3D vs. 2D analysis in lumbar spinal fusion simulations

Lumbar interbody fusion is currently the gold standard in treating patients with disc degeneration or segmental instability. Despite it having been used for several decades, the non-union rate remains high. A failed fusion is frequently attributed to an inadequate mechanical environment after instrumentation. Finite element (FE) models can provide insights into the mechanics of the fusion process. Previous fusion simulations using FE models showed that the geometries and material of the cage can greatly influence the fusion outcome. However, these studies used axisymmetric models which lacked realistic spinal geometries. Therefore, different modeling approaches were evaluated to understand the bone-formation process.Three FE models of the lumbar motion segment (L4–L5) were developed: 2D, Sym-3D and Nonsym-3D. The fusion process based on existing mechano-regulation algorithms using the FE simulations to evaluate the mechanical environment was then integrated into these models. In addition, the influence of different lordotic angles (5, 10 and 15°) was investigated. The volume of newly formed bone, the axial stiffness of the whole segment and bone distribution inside and surrounding the cage were evaluated.In contrast to the Nonsym-3D, the 2D and Sym-3D models predicted excessive bone formation prior to bridging (peak values with 36 and 9% higher than in equilibrium, respectively). The 3D models predicted a more uniform bone distribution compared to the 2D model.The current results demonstrate the crucial role of the realistic 3D geometry of the lumbar motion segment in predicting bone formation after lumbar spinal fusion.     

Advances in increment coring system for large tropical trees with high wood densities

Incremental coring of trees is the key method used in non-destructive dendrochronological sampling. Despite the advances in developing such methods, the sampling of large, high-density trees still poses a challenge in remote tropical forests. Manually operated incremental drills, while easy to transport across difficult terrain, limit sample size and can often get damaged in the sampling process, especially when trees have wood densities above 0.8 g/cm³. Here, we discuss the existing available alternatives and present an up-to-date incremental coring system composed of a borer coupled to a hand-held drilling machine and a support attached to the tree which can collect incremental cores of 1.5 mm in diameter and over 1.0 m in length. The support ensures stability for the drill throughout the sampling process. This system is relatively lightweight and portable, offering field flexibility and suitability for sampling in remote locations. It provides a core sample of an appropriate diameter and amount for carrying out ring-width measurements, stable isotope and radiocarbon analyses on some of the large, older trees which are now being found in the tropics. We expect that this methodology will broaden the possibilities in the now-blossoming sub-field of tropical dendrochronology.     

Comparison of Different Standard Methods to Evaluate the Total Concentrations of Heavy Metals in Waste Rock

The mining industry is a very rapidly increasing production sector in Finland. Many new mines have been opened recently and others are in the planning phase. Mining legislation has been recently revised and compilation of an ID-directive (Industrial Emission Directive, 2010) required to implement environmental law revision is in progress. The aim of this study was to compare different digestion methods recommended by the Finnish Environmental Administration for threshold and guideline value determinations in the Finnish PIMA Decree (214/2007) and Government Decree (591/2006) concerning recovery of certain wastes in earth construction. Altogether six methods were tested, of which five were microwave-assisted acid digestion methods: ISO 11466, EPA Method 3051A (aqua region), EPA Method 3051A (HNO₃), EPA Method 3051A (HNO₃/HCl), and SFS-EN 13656, while one was a fusion method with lithium tetraborate (ASTM C 1391 - 95). The results showed that concentrations of heavy metals (As, Cd, Co, Cu, Ni, Pb, Sb, V, and Zn) can be determined reproducibly with standard methods, but the chemical method used can have a significant impact on the results. This conclusion is very important, because the measured heavy metal values can affect the classification and processing of waste materials, and thereby can significantly impact the cost of treatment.     

Causing Physical Change to Create Art

The presentation involves students in a hands-on analysis of artifacts to create a time line of their local area's past societies. This exercise is more of a unit rather than a one-time activity. Procedures, ideas, and background for developing your own unit are presented in this article. The purpose of this unit is to engage students in applying the scientific method to archaeological research. Students will gain experience in designing and conducting their own investigations.