An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

The development and evaluation of a culturally affirmative counselling model for deaf clients in Australia

In Australia, there is only one, newly established, dedicated mental health service catering specifically for the signing *Deaf community. It is staffed by four part-time hearing professionals and based in Brisbane. There are currently no Deaf psychologists or psychiatrists and there is no valid or reliable empirical evidence on outcomes for Deaf people accessing specialised or mainstream mental health services. Further compounding these issues, is the fact that there are no sign language versions of the most common standardised mental health or psychological instruments available to clinicians in Australia. Contemporary counselling literature is acknowledging the role of the therapeutic alliance and the impact of 'common factors' on therapeutic outcomes. However, these issues are complicated by the relationship between the Deaf client and the hearing therapist being a cross-cultural exchange. The disability model of deafness is contentious and few professionals in Australia have the requisite knowledge and understanding of deafness from a cultural perspective to attend to the therapeutic relationship with this in mind. Consequently, Deaf people are severely disadvantaged by the current lack of services, resources and skilled professionals in the field of deafness and psychology in this country. The primary aim of the following program of research has been to propose a model for culturally affirmative service delivery and to provide clinicians with tools to evaluate the effect of their therapeutic work with Deaf people seeking mental health treatment. The research document is presented as a thesis by publication and comprises four specific objectives formulated in response to the lack of existing services and resources. The first objective was to explore the use of social constructionist counselling techniques and a reflecting team with Deaf clients, hearing therapists and an interpreter. Following the establishment of a pilot counselling clinic, indepth semi-structured interviews were conducted with two long-term clients following the one year pilot of this service. These interviews generated recommendations for the development of a new 'enriched' model of counselling to be implemented and evaluated in later stages of the research program. The second objective was to identify appropriate psychometric measures that could be translated into Australian Sign Language (Auslan) for research into efficacy, effectiveness and counselling outcomes. Two instruments were identified as potentially suitable; the Outcome Rating Scale (ORS), a measure of global functioning, and the Session Rating Scale (SRS), a measure of therapeutic alliance. A specialised team of bi-lingual and bi-cultural interpreters, native signers and the primary researcher for this thesis, produced the ORS-Auslan and the SRS-Auslan in DVD format, using the translation and back-translation process. The third objective was to establish the validity and reliability of these new Auslan measures based on normative data from the Deaf community. Data from the ORS-Auslan was collected from one clinical and one non-clinical sample of Deaf people. Statistical analyses revealed that the ORS-Auslan is reliable, valid and adequately distinguishes between clinical and non-clinical presentations. Furthermore, construct validity has been established using a yet to be validated sign language version of the Depression, Anxiety and Stress Scale-21 items (DASS-21), providing a platform for further research using the DASS-21 with Deaf people. The fourth objective was to evaluate counselling outcomes following the implementation of an enriched counselling service, based on the findings generated by the first objective, and using the newly translated Auslan measures. A second university counselling clinic was established and implemented over the course of one year. Practice-based evidence guided the research and the ORS-Auslan and the SRS-Auslan were administered at every session and provided outcome data on Deaf clients' global functioning. Data from six clients over the course of ten months indicated that this culturally affirmative model was an effective approach for these six clients. This is the first time that outcome data have been collected in Australia using valid and reliable Auslan measures to establish preliminary evidence for the effectiveness of any therapeutic intervention for clinical work with adult, signing Deaf clients. The research generated by this thesis contributes theoretical knowledge, professional development and practical resources that can be used by a variety of mental health clinicians in the context of mental health service delivery to Deaf clients in Australia.

Part-time job design : symptom and solution for a changing work environment

Part-time work presents a conundrum. Across industrialised countries, there has been significant growth in part-time work as a solution to resolving the diverse interests of employers, workers and families in managing time and resources. However, there are intrinsic disadvantages associated with part-time work; notably with pay and career prospects, which impact the same stakeholders it is intended to benefit. These disadvantages are particularly evident in professional services organisations, due to strong cultural norms of long work hours, single-focused commitment to work and 24x7 availability. There are indications, both in research and practice, that the design of part-time work arrangements could be improved to address some of the disadvantages associated with part-time work, and to challenge norms and dated assumptions that influence the structure of professional work. This study explored the changes made when professional service workers move from a full-time to part-time arrangement. The study drew on a recently proposed framework for work design, which extended previous models to reflect substantial changes in the contemporary work environment. The framework proved to be a useful perspective from which to explore the design of part-time work, principally because it integrated previously disconnected areas of literature and practice through a broader focus on the context of work. Exploration of the differences between part-time and full-time roles, and comparisons between part-time roles in similar types of work, provided insights into the design of professional part-time work. Analysis revealed that having a better understanding of design characteristics may help explain disadvantages associated with professional part-time work, and that some full-time roles can be more easily adapted to part-time arrangements than others. Importantly, comparisons revealed that even roles that are considered difficult to undertake on a part-time basis can potentially be re-designed to be more effective. Through empirical testing of the framework, a contextualised work design model is presented that may guide further research and the practice of crafting part-time arrangements. The findings also suggest that poor work design may lead to the symptoms associated with professional part-time work, and that improved work design may be a potential solution to these structural constraints.

A practical approach for identifying expected solution performance and robustness in operations research applications

A practical approach for identifying solution robustness is proposed for situations where parameters are uncertain. The approach is based upon the interpretation of a probability density function (pdf) and the definition of three parameters that describe how significant changes in the performance of a solution are deemed to be. The pdf is constructed by interpreting the results of simulations. A minimum number of simulations are achieved by updating the mean, variance, skewness and kurtosis of the sample using computationally efficient recursive equations. When these criterions have converged then no further simulations are needed. A case study involving several no-intermediate storage flow shop scheduling problems demonstrates the effectiveness of the approach.

A tissue engineering solution for segmental defect regeneration in load-bearing long bones

The reconstruction of large defects (>10 mm) in humans usually relies on bone graft transplantation. Limiting factors include availability of graft material, comorbidity, and insufficient integration into the damaged bone. We compare the gold standard autograft with biodegradable composite scaffolds consisting of medical-grade polycaprolactone and tricalcium phosphate combined with autologous bone marrow-derived mesenchymal stem cells (MSCs) or recombinant human bone morphogenetic protein 7 (rhBMP-7). Critical-sized defects in sheep - a model closely resembling human bone formation and structure - were treated with autograft, rhBMP-7, or MSCs. Bridging was observed within 3 months for both the autograft and the rhBMP-7 treatment. After 12 months, biomechanical analysis and microcomputed tomography imaging showed significantly greater bone formation and superior strength for the biomaterial scaffolds loaded with rhBMP-7 compared to the autograft. Axial bone distribution was greater at the interfaces. With rhBMP-7, at 3 months, the radial bone distribution within the scaffolds was homogeneous. At 12 months, however, significantly more bone was found in the scaffold architecture, indicating bone remodeling. Scaffolds alone or with MSC inclusion did not induce levels of bone formation comparable to those of the autograft and rhBMP-7 groups. Applied clinically, this approach using rhBMP-7 could overcome autograft-associated limitations.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.