Microstructure and Defect-Based Fatigue Mechanism Evaluation of Brazed Coaxial Ti/Al2O3 Joints for Enhanced Endoprosthesis Design

Alumina-based ceramic hip endoprosthesis heads have excellent tribological properties, such as low wear rates. However, stress peaks can occur at the point of contact with the prosthesis stem, increasing the probability of fracture. This risk should be minimized, especially for younger and active patients. Metal elevations at the stem taper after revision surgery without removal of a well-fixed stem are also known to increase the risk of fracture. A solution that also eliminates the need for an adapter sleeve could be a fixed titanium insert in the ceramic ball head, which would be suitable as a damping element to reduce the occurrence of stress peaks. A viable method for producing such a permanent titanium–ceramic joint is brazing. Therefore, a brazing method was developed for coaxial samples, and two modifications were made to the ceramic surface to braze a joint that could withstand high cyclic loading. This cyclic loading was applied in multiple amplitude tests in a self-developed test setup, followed by fractographic studies. Computed tomography and microstructural analyses—such as energy dispersive X-ray spectroscopy—were also used to characterize the process–structure–property relationships. It was found that the cyclic loading capacity can be significantly increased by modification of the surface structure of the ceramic.

Covariance Generalized Linear Models: An Approach for Quantifying Uncertainty in Tree Stem Taper Modeling

A natural dependence among diameters measured within-tree is expected in taper data due to the hierarchical structure. The aim of this paper was to introduce the covariance generalized linear model (CGLM) framework in the context of forest biometrics for Pinus taeda stem form modeling. The CGLMs are based on marginal specification, which requires a definition of the mean and covariance components. The tree stem mean profiles were modeled by a nonlinear segmented model. The covariance matrix was built considering four strategies of linear combinations of known matrices, which expressed the variance or correlations among observations. The first strategy modeled only the variance of the diameters over the stem as a function of covariates, the second modeled correlation among observations, the third was defined based on a random walk model, the fourth was based on a structure similar to a mixed-effect model with a marginal specification, and the fourth was a traditional mixed-effect model. Mean squared error and bias showed that the approaches were similar for describing the mean profile for fitting and validation dataset. However, uncertainties expressed by confidence intervals of the relative diameters were significant and related to the matrix covariance structures of the CGLMs. Study Implications: We proposed stem taper modeling based on a new class of statistical models. Covariance generalized linear models allow quantification of the stem dynamic by using a nonlinear model. Uncertainty estimates are performed on a covariance matrix given by a linear combination of known matrices. The matrices enable modeling of the nonconstant variance as well as the several correlation patterns, resulting in a framework more flexible and robust than traditional approaches usually applied for stem taper modeling. For practical purposes, uncertainty modeling can improve forest management planning, because the production limits by timber assortments are more reliable due to the confidence intervals derived from an appropriate uncertainty analysis.

A new taper index based on form-factor: application to three bamboo species (Phyllostachys spp.)

The form-factor for the stem surface area is directly proportional to the square root of the form-factor for the stem volume, i.e., the square root law of the form-factor. Although the square root law addresses the stems of coniferous trees, the nature of the proportional coefficient of the law has not been discussed. In this study, we demonstrated that the coefficient indicates the stem taper; therefore, it is named “Taper Index based on Form-Factor (TIFF).” We also examined the relationship between the form-factor for the culm surface area and the form-factor for the apparent culm volume of 570 culms across three bamboo species (Phyllostachys pubescens Mazel ex Houz., P. bambusoides Sieb. et Zucc., and P. nigra var. henonis). The square root law held true for all three bamboo species. The species-specific TIFF was determined to be 0.873 for P. pubescens, 0.897 for P. bambusoides, and 0.901 for P. nigra. This result implied that P. pubescens had a more tapering culm form compared to the other two species, while culm taper was similar between P. bambusoides and P. nigra. Our findings align with empirical observations of the culm taper of the bamboo species. Intra-species variation in TIFF was considerably small, allowing us to evaluate the species-specific culm taper from a small number of samples. Therefore, we conclude that TIFF provides a simple and useful method for quantifying species-specific culm or stem taper, and facilitates the estimation of merchantable or total volume.

A Newly Built Model of an Additive Stem Taper System with Total Disaggregation Model Structure for Dahurian Larch in Northeast China

Stem taper function is an important concept in forest growth and yield modeling, and forest management. However, the additivity of the function and the inherent correlations between stem components (diameter outside bark—dob, diameter inside bark—dib, and double-bark thickness—dbt) are seldom considered. In this paper, a total disaggregation model (TDM) structure was developed based on the well-known Kozak (2004) model to ensure the additivity of the stem components. The reconstructed model was fitted with the data of 1281 felled Dahurian larch trees from three regions of Daxing’anling Mountains in Northeast China. The results from TDM were compared with other additive model structures including adjustment in proportion (AP), non-additive taper models (NAM), and three logical structures of NSUR (AMO, SMI, SMB). The results showed that the difference was significant among the three regions. The performance of TDM was slightly better than those of other model structures. Therefore, TDM was considered as another optimal additive system to estimate stem, bark thickness, and volume predicting for Dahurian larch in Northeast China besides NSUR, a method widely used in calculating additive volume or biomass throughout the world. We believe this work is cutting-edge, and that this methodology can be applied to other tree species.

Variability in stem taper surface topography affects the degree of corrosion and fretting in total hip arthroplasty

Degradation at the modular head-neck interface in total hip arthroplasty (THA) is predominately expressed in the form of corrosion and fretting, potentially causing peri-prosthetic failure by adverse reactions to metal debris. This retrieval study aimed to quantify variations in stem taper surface topographies and to assess the influence on the formation of corrosion and/or fretting in titanium alloy stem tapers combined with metal and ceramic heads. Four hip stem designs (Alloclassic, CLS, Bicontact and SL-Plus) were characterized using high-resolution 3D microscopy, and corrosion and fretting were rated using the Goldberg scoring scheme. Quantification of the taper surface topographies revealed a high variability in surface characteristics between threaded stem tapers: Alloclassic and CLS tapers feature deeply threaded trapezoid-shaped profiles with thread heights over 65 µm. The sawtooth-shaped Bicontact and triangular SL-Plus taper are characterized by low thread heights below 14 µm. Significantly lower corrosion and fretting scores were observed in lightly threaded compared to deeply threaded tapers in ceramic head combinations. No significant differences in corrosion or fretting scores with thread height were found in pairings with metal heads. Understanding the relationship between stem taper surface topography and the formation of corrosion and fretting could help to improve the performance of modern THAs and lead to longer-lasting clinical results.

Stem taper functions for white birch (Betula platyphylla) and costata birch (Betula costata) in the Xiaoxing’an Mountains, northeast China

White birch (Betula platyphylla Sukaczev) and costata birch (Betula costata Trautv.) are valuable hardwood tree species growing in northeast China. Several taper studies have analysed birch species in the countries harbouring the boreal forests. However, this study presents an initial attempt to develop stem taper models using the fixed- and mixed-effects modelling for white birch and costata birch in Xiaoxing’an Mountains, northeast China. Ten commonly used taper models were evaluated by using 228 destructively sampled trees of both tree species comprising of 4582 diameter and height measurements. The performance of these models was tested in predicting diameter at any height, total volume and merchantable volume (10 and 20 cm top diameters). We incorporated a second-order continuous-time error structure to adjust the inherent autocorrelation in the data. The segmented model of Clark best predicted the diameter and total or merchantable volume when the upper stem diameter at 5.3 m was available. When diameter measurements at 5.3 m were not available, the models of Kozak and Max and Burkhart were superior to other models for white birch and costata birch, respectively. After model comparison, the best model of Clark was refitted as the NLME model.

Nonlinear parsimonious forest modeling assuming normal distribution of residuals

To avoid the transformation of the dependent variable, which introduces bias when back-transformed, complex nonlinear forest models have the parameters estimated with heuristic techniques, which can supply erroneous values. The solution for accurate nonlinear models provided by Strimbu et al. (Ecosphere 8:e01945, 2017) for 11 functions (i.e., power, trigonometric, and hyperbolic) is not based on heuristics but could contain a Taylor series expansion. Therefore, the objectives of the present study are to present the unbiased estimates for variance following the transformation of the predicted variable and to identify an expansion of the Taylor series that does not induce numerical bias for mean and variance. We proved that the Taylor series expansion present in the unbiased expectation of mean and variance depends on the variance. We illustrated the new modeling approach on two problems, one at the ecosystem level, namely site productivity, and one at individual tree level, namely stem taper. The two models are unbiased, more parsimonious, and more precise than the existing less parsimonious models. This study focuses on research methods, which could be applied in similar studies of other species, ecosystem, as well as in behavioral sciences and econometrics.