Modeling and sensitivity analysis on the transport of aluminum oxide nanoparticles in saturated sand: effects of ionic strength, flow rate, and nanoparticle concentration.

Aluminum oxide nanoparticles have been widely used in various consumer products and there are growing concerns regarding their exposure in the environment. This study deals with the modeling, sensitivity analysis and uncertainty quantification of one-dimensional transport of nano-sized (~82 nm) aluminum oxide particles in saturated sand. The transport of aluminum oxide nanoparticles was modeled using a two-kinetic-site model with a blocking function. The modeling was done at different ionic strengths, flow rates, and nanoparticle concentrations. The two sites representing fast and slow attachments along with a blocking term yielded good agreement with the experimental results from the column studies of aluminum oxide nanoparticles. The same model was used to simulate breakthrough curves under different conditions using experimental data and calculated 95% confidence bounds of the generated breakthroughs. The sensitivity analysis results showed that slow attachment was the most sensitive parameter for high influent concentrations (e.g. 150 mg/L Al2O3) and the maximum solid phase retention capacity (related to blocking function) was the most sensitive parameter for low concentrations (e.g. 50 mg/L Al2O3).

Random field assessment of nanoscopic inhomogeneity of bone.

Bone quality is significantly correlated with the inhomogeneous distribution of material and ultrastructural properties (e.g., modulus and mineralization) of the tissue. Current techniques for quantifying inhomogeneity consist of descriptive statistics such as mean, standard deviation and coefficient of variation. However, these parameters do not describe the spatial variations of bone properties. The objective of this study was to develop a novel statistical method to characterize and quantitatively describe the spatial variation of bone properties at ultrastructural levels. To do so, a random field defined by an exponential covariance function was used to represent the spatial uncertainty of elastic modulus by delineating the correlation of the modulus at different locations in bone lamellae. The correlation length, a characteristic parameter of the covariance function, was employed to estimate the fluctuation of the elastic modulus in the random field. Using this approach, two distribution maps of the elastic modulus within bone lamellae were generated using simulation and compared with those obtained experimentally by a combination of atomic force microscopy and nanoindentation techniques. The simulation-generated maps of elastic modulus were in close agreement with the experimental ones, thus validating the random field approach in defining the inhomogeneity of elastic modulus in lamellae of bone. Indeed, generation of such random fields will facilitate multi-scale modeling of bone in more pragmatic details.

Probabilistic failure analysis of bone using a finite element model of mineral-collagen composites.

Microdamage accumulation is a major pathway for energy dissipation during the post-yield deformation of bone. In this study, a two-dimensional probabilistic finite element model of a mineral-collagen composite was developed to investigate the influence of the tissue and ultrastructural properties of bone on the evolution of microdamage from an initial defect in tension. The probabilistic failure analyses indicated that the microdamage progression would be along the plane of the initial defect when the debonding at mineral-collagen interfaces was either absent or limited in the vicinity of the defect. In this case, the formation of a linear microcrack would be facilitated. However, the microdamage progression would be scattered away from the initial defect plane if interfacial debonding takes place at a large scale. This would suggest the possible formation of diffuse damage. In addition to interfacial debonding, the sensitivity analyses indicated that the microdamage progression was also dependent on the other material and ultrastructural properties of bone. The intensity of stress concentration accompanied with microdamage progression was more sensitive to the elastic modulus of the mineral phase and the nonlinearity of the collagen phase, whereas the scattering of failure location was largely dependent on the mineral to collagen ratio and the nonlinearity of the collagen phase. The findings of this study may help understanding the post-yield behavior of bone at the ultrastructural level and shed light on the underlying mechanism of bone fractures.

Probabilistic analysis of preload in the abutment screw of a dental implant complex.

STATEMENT OF PROBLEM: Screw loosening is a problem for a percentage of implants. A probabilistic analysis to determine the cumulative probability distribution of the preload, the probability of obtaining an optimal preload, and the probabilistic sensitivities identifying important variables is lacking. PURPOSE: The purpose of this study was to examine the inherent variability of material properties, surface interactions, and applied torque in an implant system to determine the probability of obtaining desired preload values and to identify the significant variables that affect the preload. MATERIAL AND METHODS: Using software programs, an abutment screw was subjected to a tightening torque and the preload was determined from finite element (FE) analysis. The FE model was integrated with probabilistic analysis software. Two probabilistic analysis methods (advanced mean value and Monte Carlo sampling) were applied to determine the cumulative distribution function (CDF) of preload. The coefficient of friction, elastic moduli, Poisson's ratios, and applied torque were modeled as random variables and defined by probability distributions. Separate probability distributions were determined for the coefficient of friction in well-lubricated and dry environments. The probabilistic analyses were performed and the cumulative distribution of preload was determined for each environment. RESULTS: A distinct difference was seen between the preload probability distributions generated in a dry environment (normal distribution, mean (SD): 347 (61.9) N) compared to a well-lubricated environment (normal distribution, mean (SD): 616 (92.2) N). The probability of obtaining a preload value within the target range was approximately 54% for the well-lubricated environment and only 0.02% for the dry environment. The preload is predominately affected by the applied torque and coefficient of friction between the screw threads and implant bore at lower and middle values of the preload CDF, and by the applied torque and the elastic modulus of the abutment screw at high values of the preload CDF. CONCLUSIONS: Lubrication at the threaded surfaces between the abutment screw and implant bore affects the preload developed in the implant complex. For the well-lubricated surfaces, only approximately 50% of implants will have preload values within the generally accepted range. This probability can be improved by applying a higher torque than normally recommended or a more closely controlled torque than typically achieved. It is also suggested that materials with higher elastic moduli be used in the manufacture of the abutment screw to achieve a higher preload.