An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Hierarchical Bayesian models for estimating the extent of plant pest invasions

Plant biosecurity requires statistical tools to interpret field surveillance data in order to manage pest incursions that threaten crop production and trade. Ultimately, management decisions need to be based on the probability that an area is infested or free of a pest. Current informal approaches to delimiting pest extent rely upon expert ecological interpretation of presence / absence data over space and time. Hierarchical Bayesian models provide a cohesive statistical framework that can formally integrate the available information on both pest ecology and data. The overarching method involves constructing an observation model for the surveillance data, conditional on the hidden extent of the pest and uncertain detection sensitivity. The extent of the pest is then modelled as a dynamic invasion process that includes uncertainty in ecological parameters. Modelling approaches to assimilate this information are explored through case studies on spiralling whitefly, Aleurodicus dispersus and red banded mango caterpillar, Deanolis sublimbalis. Markov chain Monte Carlo simulation is used to estimate the probable extent of pests, given the observation and process model conditioned by surveillance data. Statistical methods, based on time-to-event models, are developed to apply hierarchical Bayesian models to early detection programs and to demonstrate area freedom from pests. The value of early detection surveillance programs is demonstrated through an application to interpret surveillance data for exotic plant pests with uncertain spread rates. The model suggests that typical early detection programs provide a moderate reduction in the probability of an area being infested but a dramatic reduction in the expected area of incursions at a given time. Estimates of spiralling whitefly extent are examined at local, district and state-wide scales. The local model estimates the rate of natural spread and the influence of host architecture, host suitability and inspector efficiency. These parameter estimates can support the development of robust surveillance programs. Hierarchical Bayesian models for the human-mediated spread of spiralling whitefly are developed for the colonisation of discrete cells connected by a modified gravity model. By estimating dispersal parameters, the model can be used to predict the extent of the pest over time. An extended model predicts the climate restricted distribution of the pest in Queensland. These novel human-mediated movement models are well suited to demonstrating area freedom at coarse spatio-temporal scales. At finer scales, and in the presence of ecological complexity, exploratory models are developed to investigate the capacity for surveillance information to estimate the extent of red banded mango caterpillar. It is apparent that excessive uncertainty about observation and ecological parameters can impose limits on inference at the scales required for effective management of response programs. The thesis contributes novel statistical approaches to estimating the extent of pests and develops applications to assist decision-making across a range of plant biosecurity surveillance activities. Hierarchical Bayesian modelling is demonstrated as both a useful analytical tool for estimating pest extent and a natural investigative paradigm for developing and focussing biosecurity programs.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Subchondral bone osteoblasts can induce chondrocyte mineralization during osteoarthritis and this process is relevant to cartilage degradation

Pathological mineralization of articular cartilage is a characteristic feature of osteoarthritis (OA); however, the underlying mechanisms, and their relevance to cartilage degeneration, are not clear. The involvement of subchondral bone changes in OA have been reported previously with the characterization of abnormal subchondral bone mineral density (BMD), osteiod volume, altered bone mechanical parameters and an increase in bone turnover markers. A number of osteoarthritic animal models have demonstrated that subchondral bone changes often precede cartilage degeneration. In this study site specific localization of mineralization markers were detected in the OA cartilage. Chondrocytes and osteoblasts derived from OA cartilage and subchondral bone showed a significant increase in the mRNA expressions of mineralization markers. Interestingly, osteoblasts from OA subchondral bone could significantly decrease cartilage matrix expression; whereas, increase mineralization of chondrocytes (Figure 1). Osteogenic factors, such as CBFA1, ALP, and type X collagen (Col-X), were detected in chondrocytes under mineralization conditions (Figure 2). Furthermore, chondrocyte mineralization was followed by increased mRNA and protein levels of MMP-2, MMP-9 and MMP-13, all of which are detrimental to cartilage integrity in vivo. The data reported here suggests that the upregulation of subchondral bone-mineralization, typical of OA progression, causes cartilage mineralization, and that the mineralization of chondrocytes induce increased MMP levels with a subsequent degradation of the articular cartilage.

Preclinical animal models for segmental bone defect research and tissue engineering

Currently, well-established clinical therapeutic approaches for bone reconstruction are restricted to the transplantation of autografts and allografts, and the implantation of metal devices or ceramic-based implants to assist bone regeneration. Bone grafts possess osteoconductive and osteoinductive properties, however they are limited in access and availability and associated with donor site morbidity, haemorrhage, risk of infection, insufficient transplant integration, graft devitalisation, and subsequent resorption resulting in decreased mechanical stability. As a result, recent research focuses on the development of alternative therapeutic concepts. Analysing the tissue engineering literature it can be concluded that bone regeneration has become a focus area in the field. Hence, a considerable number of research groups and commercial entities work on the development of tissue engineered constructs for bone regeneration. However, bench to bedside translations are still infrequent as the process towards approval by regulatory bodies is protracted and costly, requiring both comprehensive in vitro and in vivo studies. In translational orthopaedic research, the utilisation of large preclinical animal models is a conditio sine qua non. Consequently, to allow comparison between different studies and their outcomes, it is essential that animal models, fixation devices, surgical procedures and methods of taking measurements are well standardized to produce reliable data pools as a base for further research directions. The following chapter reviews animal models of the weight-bearing lower extremity utilized in the field which include representations of fracture-healing, segmental bone defects, and fracture non-unions.

Investigating the process of teaching and learning principles through practice : a case study on collegiate action by media practitioners and teachers, designing a skills-based learning program

This paper in the journalism education field reports on the construction of a new subject as part of a postgraduate coursework degree. The subject, or unit1 will offer both Journalism students and other students an introductory experience of creating media, using common ‘new media’ tools, with exercises that will model the learning of communication principles through practice. It has been named ‘Fundamental Media Skills for the Workplace’. The conceptualisation and teaching of it will be characteristic of the Journalism academic discipline that uses the ‘inside perspective’—understanding mass media by observing from within. Proposers for the unit within the Journalism discipline have sought to extend the common teaching approach, based on training to produce start-ready recruits for media jobs, backed by a study of contexts, e.g. journalistic ethics, or media audiences. In this proposal, students would then examine the process to elicit additional knowledge about their learning. The paper draws on literature of journalism and its pedagogy, and on communication generally. It also documents a ‘community of practice’ exercise conducted among practitioners as teachers for the subject, developing exercises and models of media work. A preliminary conclusion from that exercise is that it has taken a step towards enhancing skills-based learning for media work, as a portal to more generalised knowledge.

Attribute exclusion strategies in airline choice : accounting for exogenous information on decision maker processing strategies in models of discrete choice

We examine the impact of individual-specific information processing strategies (IPSs) on the inclusion/exclusion of attributes on the parameter estimates and behavioural outputs of models of discrete choice. Current practice assumes that individuals employ a homogenous IPS with regards to how they process attributes of stated choice (SC) experiments. We show how information collected exogenous of the SC experiment on whether respondents either ignored or considered each attribute may be used in the estimation process, and how such information provides outputs that are IPS segment specific. We contend that accounting the inclusion/exclusion of attributes will result in behaviourally richer population parameter estimates.

Bond–slip models for double strap joints strengthened by CFRP

This paper presents the results of a series of tension tests on CFRP bonded steel plate double strap joints. The main aim of this research is to provide detailed understanding of bond characteristics using experimental and numerical analysis of strengthened double strap joints under tension. A parametric study has been performed by numerical modelling with the variables of CFRP bond lengths, adhesive maximum strain and adhesive layer thicknesses. Finally, bond-slip models are proposed for three different types of adhesives within the range of the parametric study.

Robust designs for Poisson regression models

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative.

Quantification of the accuracy of MRI generated 3D models of long bones compared to CT generated 3D models

Orthopaedic fracture fixation implants are increasingly being designed using accurate 3D models of long bones based on computer tomography (CT). Unlike CT, magnetic resonance imaging (MRI) does not involve ionising radiation and is therefore a desirable alternative to CT. This study aims to quantify the accuracy of MRI-based 3D models compared to CT-based 3D models of long bones. The femora of five intact cadaver ovine limbs were scanned using a 1.5T MRI and a CT scanner. Image segmentation of CT and MRI data was performed using a multi-threshold segmentation method. Reference models were generated by digitising the bone surfaces free of soft tissue with a mechanical contact scanner. The MRI- and CT-derived models were validated against the reference models. The results demonstrated that the CT-based models contained an average error of 0.15mm while the MRI-based models contained an average error of 0.23mm. Statistical validation shows that there are no significant differences between 3D models based on CT and MRI data. These results indicate that the geometric accuracy of MRI based 3D models was comparable to that of CT-based models and therefore MRI is a potential alternative to CT for generation of 3D models with high geometric accuracy.

Robust designs for Poisson regression models

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

An examination of the applicability of hydrotalcite for removing oxalate anions from Bayer process solutions

Hydrotalcite and thermally activated hydrotalcites were examined for their potential as methods for the removal of oxalate anions from Bayer Process liquors. Hydrotalcite was prepared and characterised by a number of methods, including X-ray diffraction, thermogravimetric analysis, nitrogen adsorption analysis and vibrational spectroscopy. Thermally activated hydrotalcites were prepared by a low temperature method and characterised using X-ray diffraction, nitrogen adsorption analysis and vibrational spectroscopy. Oxalate intercalated hydrotalcite was prepared by two methods and analysed with X-ray diffraction and for the first time thermogravimetric analysis, Raman spectroscopy and infrared emission spectroscopy. The adsorption of oxalate anions by hydrotalcite and thermally activated hydrotalcite was tested in a range of solutions using both batch and kinetic adsorption models.