Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond.We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.

The influence of architecture on degradation and tissue ingrowth into three-dimensional poly(lactic-co-glycolic acid) scaffolds in vitro and in vivo

The in vitro and in vivo degradation properties of poly(lactic-co-glycolic acid) (PLGA) scaffolds produced by two different technologies - thermally induced phase separation (TIPS), and solvent casting and particulate leaching (SCPL) were compared. Over 6 weeks, in vitro degradation produced changes in SCPL scaffold dimension, mass, internal architecture and mechanical properties. TIPS scaffolds produced far less changes in these parameters providing significant advantages over SCPL. In vivo results were based on a microsurgically created arteriovenous (AV) loop sandwiched between two TIPS scaffolds placed in a polycarbonate chamber under rat groin skin. Histologically, a predominant foreign body giant cell response and reduced vascularity was evident in tissue ingrowth between 2 and 8 weeks in TIPS scaffolds. Tissue death occurred at 8 weeks in the smallest pores. Morphometric comparison of TIPS and SCPL scaffolds indicated slightly better tissue ingrowth but greater loss of scaffold structure in SCPL scaffolds. Although advantageous in vitro, large surface area:volume ratios and varying pore sizes in PLGA TIPS scaffolds mean that effective in vivo (AV loop) utilization will only be achieved if the foreign body response can be significantly reduced so as to allow successful vascularisation, and hence sustained tissue growth, in pores less than 300 μm. © 2005 Elsevier Ltd. All rights reserved.

Three-dimensional geological modelling and multivariate statistical analysis of water chemistry data to analyse and visualise aquifer structure and groundwater composition in the Wairau Plain, Marlborough District, New Zealand

Concerns regarding groundwater contamination with nitrate and the long-term sustainability of groundwater resources have prompted the development of a multi-layered three dimensional (3D) geological model to characterise the aquifer geometry of the Wairau Plain, Marlborough District, New Zealand. The 3D geological model which consists of eight litho-stratigraphic units has been subsequently used to synthesise hydrogeological and hydrogeochemical data for different aquifers in an approach that aims to demonstrate how integration of water chemistry data within the physical framework of a 3D geological model can help to better understand and conceptualise groundwater systems in complex geological settings. Multivariate statistical techniques(e.g. Principal Component Analysis and Hierarchical Cluster Analysis) were applied to groundwater chemistry data to identify hydrochemical facies which are characteristic of distinct evolutionary pathways and a common hydrologic history of groundwaters. Principal Component Analysis on hydrochemical data demonstrated that natural water-rock interactions, redox potential and human agricultural impact are the key controls of groundwater quality in the Wairau Plain. Hierarchical Cluster Analysis revealed distinct hydrochemical water quality groups in the Wairau Plain groundwater system. Visualisation of the results of the multivariate statistical analyses and distribution of groundwater nitrate concentrations in the context of aquifer lithology highlighted the link between groundwater chemistry and the lithology of host aquifers. The methodology followed in this study can be applied in a variety of hydrogeological settings to synthesise geological, hydrogeological and hydrochemical data and present them in a format readily understood by a wide range of stakeholders. This enables a more efficient communication of the results of scientific studies to the wider community.

Investigating the change in three dimensional deformity for idiopathic scoliosis using axially loaded MRI

Background: Adolescent idiopathic scoliosis is a complex three-dimensional deformity, involving a lateral deformity in the coronal plane and axial rotation of the vertebrae in the transverse plane. Gravitational loading plays an important biomechanical role in governing the coronal deformity, however, less is known about how they influence the axial deformity. This study investigates the change in three-dimensional deformity of a series of scoliosis patients due to compressive axial loading. Methods: Magnetic resonance imaging scans were obtained and coronal deformity (measured using the coronal Cobb angle) and axial rotations measured for a group of 18 scoliosis patients (Mean major Cobb angle was 43.4 o). Each patient was scanned in an unloaded and loaded condition while compressive loads equivalent to 50% body mass were applied using a custom developed compressive device. Findings: The mean increase in major Cobb angle due to compressive loading was 7.4 o (SD 3.5 o). The most axially rotated vertebra was observed at the apex of the structural curve and the largest average intravertebral rotations were observed toward the limits of the coronal deformity. A level-wise comparison showed no significant difference between the average loaded and unloaded vertebral axial rotations (intra-observer error = 2.56 o) or intravertebral rotations at each spinal level. Interpretation: This study suggests that the biomechanical effects of axial loading primarily influence the coronal deformity, with no significant change in vertebral axial rotation or intravertebral rotation observed between the unloaded and loaded condition. However, the magnitude of changes in vertebral rotation with compressive loading may have been too small to detect given the resolution of the current technique.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

IS service quality as a multi-dimensional formative constuct

This study is motivated by, and proceeds from, a central interest in the importance of evaluating IS service quality and adopts the IS ZOT SERVQUAL instrument (Kettinger & Lee, 2005) as its core theory base. This study conceptualises IS service quality as a multidimensional formative construct and seeks to answer the main research questions: “Is the IS service quality construct valid as a 1st-order formative, 2nd-order formative multidimensional construct?” Additionally, with the aim of validating the IS service quality construct within its nomological net, as in prior service marketing work, Satisfaction was hypothesised as its immediate consequence. With the goal of testing the above research question, IS service quality and Satisfaction were operationalised in a quantitative survey instrument. Partial least squares (PLS), employing 219 valid responses, largely evidenced the validity of IS service quality as a multidimensional formative construct. The nomological validity of the IS service quality construct was also evidenced by demonstrating that 55% of Satisfaction was explained by the multidimensional formative IS service quality construct.

Mixed-dimensional consistent coupling by multi-point constraint equations for efficient multi-scale modeling

Finding an appropriate linking method to connect different dimensional element types in a single finite element model is a key issue in the multi-scale modeling. This paper presents a mixed dimensional coupling method using multi-point constraint equations derived by equating the work done on either side of interface connecting beam elements and shell elements for constructing a finite element multiscale model. A typical steel truss frame structure is selected as case example and the reduced scale specimen of this truss section is then studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details while the different analytical models are developed for numerical simulation. Comparison of dynamic and static response of the calculated results among different numerical models as well as the good agreement with those from experimental results indicates that the proposed multi-scale model is efficient and accurate.

Two-dimensional coordination polymers in rubidium and caesium complexes with orthanilic acid

The crystal structures of the rubidium and caesium complexes with 2-aminobenzenesulfonic acid (orthanilic acid), [Rb4(C6H6NO3S)4(H2O)]n (1) and [Cs(C6H6NO3S)]n (2) and have been determined at 200 K. Complex 1 has a repeating unit comprising four independent and different Rb coordination centres, (RbO8), (RbO7), (RbN2O4) and (RbO10), each having irregular stereochemistry and involving a number of bidentate chelate sulfonate-O,O’-metal and bridging interactions, giving a two-dimensional polymeric layered structure. Anhydrous complex 2 is also polymeric with the irregular (CsO7) coordination polyhedron comprising six sulfonate oxygen donors from three separate bidentate chelate sulfonate ligands and one monodentate bridging sulfonate oxygen, giving a two-dimensional layered structure.

Three-dimensional medical ultrasound

A number of groups around the world are working in the field of three dimensional(3D) ultrasound (US) in order to obtain higher quality diagnostic information. 3D US, in general, involves collecting a sequence of conventional 2D US images along with information on the position and orientation of each image plane. A transformation matrix is calculated relating image space to real world space. This allows image pixels and region of interest (ROI) points drawn on the image to be displayed in 3D. The 3D data can be used for the production of volume or surface rendered images, or for the direct calculation of ROI volumes.