Exponential asymptotics with multiple stokes lines

When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.

A new future for growth factor complexes as wound therapies?

Background: Topical administration of growth factors (GFs) has displayed some potential in wound healing, but variable efficacy, high doses and costs have hampered their implementation. Moreover, this approach ignores the fact that wound repair is driven by interactions between multiple GFs and extracellular matrix (ECM) proteins. The Problem: Deep dermal partial thickness burn (DDPTB) injuries are the most common burn presentation to pediatric hospitals and also represent the most difficult burn injury to manage clinically. DDPTB often repair with a hypertrophic scar. Wounds that close rapidly exhibit reduced scarring. Thus treatments that shorten the time taken to close DDTPB’s may coincidently reduce scarring. Basic/Clinical Science Advances: We have observed that multi-protein complexes comprised of IGF and IGF-binding proteins bound to the ECM protein vitronectin (VN) significantly enhance cellular functions relevant to wound repair in human skin keratinocytes. These responses require activation of both the IGF-1R and the VN-binding αv integrins. We have recently evaluated the wound healing potential of these GF:VN complexes in a porcine model of DDTPB injury. Clinical Care Relevance: This pilot study demonstrates that GF:VN complexes hold promise as a wound healing therapy. Enhanced healing responses were observed after treatment with nanogram doses of the GF:VN complexes in vitro and in vivo. Critically healing was achieved using substantially less GF than studies in which GFs alone have been used. Conclusion: These data suggest that coupling GFs to ECM proteins, such as VN, may ultimately prove to be an improved technique for the delivery of novel GF-based wound therapies.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

A novel technique to demonstrate disturbed appetite profiles in haemodialysis patients

Background Malnutrition is common among dialysis patients and is associated with an adverse outcome. One cause of this is a persistent reduction in nutrient intake, suggesting an abnormality of appetite regulation. Methods We used a novel technique to describe the appetite profile in 46 haemodialysis (HD) patients and 40 healthy controls. The Electronic Appetite Rating System (EARS) employs a palmtop computer to collect hourly ratings of motivation to eat and mood. We collected data on hunger, desire to eat, fullness, and tiredness. HD subjects were monitored on the dialysis day and the interdialytic day. Controls were monitored for 1 or 2 days. Results Temporal profiles of motivation to eat for the controls were similar on both days. Temporal profiles of motivation to eat for the HD group were lower on the dialysis day. Mean HD scores were not significantly different from controls. Dietary records indicated that dialysis patients consumed less food than controls. Conclusions Our data indicate that the EARS can be used to monitor subjective appetite states continuously in a group of HD patients. A HD session reduces hunger and desire to eat. Patients feel more tired after dialysis. This does not correlate with their hunger score, but does correlate with their fullness rating. Nutrient intake is reduced, suggesting a resetting of appetite control for the HD group. The EARS may be useful for intervention studies.

Investigation of 'off-line‘ relaxation phenomena in oil filled transformers

Power transformers are one of the most important and costly equipment in power generation, transmission and distribution systems. Current average age of transformers in Australia is around 25 years and there is a strong economical tendency to use them up to 50 years or more. As the transformers operate, they get degraded due to different loading and environmental operating stressed conditions. In today‘s competitive energy market with the penetration of distributed energy sources, the transformers are stressed more with minimum required maintenance. The modern asset management program tries to increase the usage life time of power transformers with prognostic techniques using condition indicators. In the case of oil filled transformers, condition monitoring methods based on dissolved gas analysis, polarization studies, partial discharge studies, frequency response analysis studies to check the mechanical integrity, IR heat monitoring and other vibration monitoring techniques are in use. In the current research program, studies have been initiated to identify the degradation of insulating materials by the electrical relaxation technique known as dielectrometry. Aging leads to main degradation products like moisture and other oxidized products due to fluctuating thermal and electrical loading. By applying repetitive low frequency high voltage sine wave perturbations in the range of 100 to 200 V peak across available terminals of power transformer, the conductive and polarization parameters of insulation aging are identified. An in-house novel digital instrument is developed to record the low leakage response of repetitive polarization currents in three terminals configuration. The technique is tested with known three transformers of rating 5 kVA or more. The effects of stressing polarization voltage level, polarizing wave shapes and various terminal configurations provide characteristic aging relaxation information. By using different analyses, sensitive parameters of aging are identified and it is presented in this thesis.

In vivo evaluation of an ultra-thin polycaprolactone film as a wound dressing

The use of ultra-thin films as dressings for cutaneous wounds could prove advantageous in terms of better conformity to wound topography and improved vapour transmission. For this purpose, ultra-thin poly(epsilon-caprolactone) (PCL) films of 5-15 microm thickness were fabricated via a biaxial stretching technique. To evaluate their in vivo biocompatibility and feasibility as an external wound dressing, PCL films were applied over full and partial-thickness wounds in rat and pig models. Different groups of PCL films were used: untreated, NaOH-treated, untreated with fibrin, NaOH-treated with perforations, and NaOH-treated with fibrin and S-nitrosoglutathione. Wounds with no external dressings were used as controls. Wound contraction rate, histology and biomechanical analyses were carried out. Wounds re-epithelialized completely at a comparable rate. Formation of a neo-dermal layer and re-epithelialization were observed in all the wounds. A lower level of fibrosis was observed when PCL films were used, compared to the control wounds. Ultimate tensile strength of the regenerated tissue in rats reached 50-60% of that in native rat skin. Results indicated that biaxially-stretched PCL films did not induce inflammatory reactions when used in vivo as a wound dressing and supported the normal wound healing process in full and partial-thickness wounds.

Accelerated Partial Breast Irradiation (APBI) : a review of available techniques

Breast conservation therapy (BCT) is the procedure of choice for the management of the early stage breast cancer. However, its utilization has not been maximized because of logistics issues associated with the protracted treatment involved with the radiation treatment. Accelerated Partial Breast Irradiation (APBI) is an approach that treats only the lumpectomy bed plus a 1-2 cm margin, rather than the whole breast. Hence because of the small volume of irradiation a higher dose can be delivered in a shorter period of time. There has been growing interest for APBI and various approaches have been developed under phase I-III clinical studies; these include multicatheter interstitial brachytherapy, balloon catheter brachytherapy, conformal external beam radiation therapy and intra-operative radiation therapy (IORT). Balloon-based brachytherapy approaches include Mammosite, Axxent electronic brachytherapy and Contura, Hybrid brachytherapy devices include SAVI and ClearPath. This paper reviews the different techniques, identifying the weaknesses and strength of each approach and proposes a direction for future research and development. It is evident that APBI will play a role in the management of a selected group of early breast cancer. However, the relative role of the different techniques is yet to be clearly identified.

Structural health monitoring of bridges : source localisation in acoustic emission technique

Managing the sustainability of urban infrastructure requires regular health monitoring of key infrastructure such as bridges. The process of structural health monitoring involves monitoring a structure over a period of time using appropriate sensors, extracting damage sensitive features from the measurements made by the sensors, and analysing these features to determine the current state of the structure. Various techniques are available for structural health monitoring of structures, and acoustic emission is one technique that is finding an increasing use in the monitoring of civil infrastructures such as bridges. Acoustic emission technique is based on the recording of stress waves generated by rapid release of energy inside a material, followed by analysis of recorded signals to locate and identify the source of emission and assess its severity. This chapter first provides a brief background of the acoustic emission technique and the process of source localization. Results from laboratory experiments conducted to explore several aspects of the source localization process are also presented. The findings from the study can be expected to enhance knowledge of the acoustic emission process, and to aid the development of effective bridge structure diagnostics systems.

Fabrication of osteochondral scaffolds with stereolithography

The osteochondral defect is a classical model for a multiple-tissue problem[1]. Tissue engineering of either bone or cartilage imposes different demands on a scaffold concerning porosity, pore size and interconnectivity. Furthermore, local release of tissue-specific growth factors necessitates a tailored architecture. For the fabrication of an osteochondral scaffold with region specific architecture, an advanced technique is required. Stereolithography is a rapid prototyping technique that allows for the creation of such 3D polymer objects with well-defined architecture. Its working principle is the partial irradiation of a resin, causing a liquid-solid transition. By irradiating this resin by a computer-driven light source, a solid 3D object is constructed layer by layer. To make biodegradable polymers applicable in stereolithography, low-molecular weight polymers have to be functionalised with double bonds to enable photo-initiated crosslinking.

The feasibility of vibration analysis as a technique to detect osseointegration of transfemoral implants

One of the main causes of above knee or transfemoral amputation (TFA) in the developed world is trauma to the limb. The number of people undergoing TFA due to limb trauma, particularly due to war injuries, has been increasing. Typically the trauma amputee population, including war-related amputees, are otherwise healthy, active and desire to return to employment and their usual lifestyle. Consequently there is a growing need to restore long-term mobility and limb function to this population. Traditionally transfemoral amputees are provided with an artificial or prosthetic leg that consists of a fabricated socket, knee joint mechanism and a prosthetic foot. Amputees have reported several problems related to the socket of their prosthetic limb. These include pain in the residual limb, poor socket fit, discomfort and poor mobility. Removing the socket from the prosthetic limb could eliminate or reduce these problems. A solution to this is the direct attachment of the prosthesis to the residual bone (femur) inside the residual limb. This technique has been used on a small population of transfemoral amputees since 1990. A threaded titanium implant is screwed in to the shaft of the femur and a second component connects between the implant and the prosthesis. A period of time is required to allow the implant to become fully attached to the bone, called osseointegration (OI), and be able to withstand applied load; then the prosthesis can be attached. The advantages of transfemoral osseointegration (TFOI) over conventional prosthetic sockets include better hip mobility, sitting comfort and prosthetic retention and fewer skin problems on the residual limb. However, due to the length of time required for OI to progress and to complete the rehabilitation exercises, it can take up to twelve months after implant insertion for an amputee to be able to load bear and to walk unaided. The long rehabilitation time is a significant disadvantage of TFOI and may be impeding the wider adoption of the technique. There is a need for a non-invasive method of assessing the degree of osseointegration between the bone and the implant. If such a method was capable of determining the progression of TFOI and assessing when the implant was able to withstand physiological load it could reduce the overall rehabilitation time. Vibration analysis has been suggested as a potential technique: it is a non destructive method of assessing the dynamic properties of a structure. Changes in the physical properties of a structure can be identified from changes in its dynamic properties. Consequently vibration analysis, both experimental and computational, has been used to assess bone fracture healing, prosthetic hip loosening and dental implant OI with varying degrees of success. More recently experimental vibration analysis has been used in TFOI. However further work is needed to assess the potential of the technique and fully characterise the femur-implant system. The overall aim of this study was to develop physical and computational models of the TFOI femur-implant system and use these models to investigate the feasibility of vibration analysis to detect the process of OI. Femur-implant physical models were developed and manufactured using synthetic materials to represent four key stages of OI development (identified from a physiological model), simulated using different interface conditions between the implant and femur. Experimental vibration analysis (modal analysis) was then conducted using the physical models. The femur-implant models, representing stage one to stage four of OI development, were excited and the modal parameters obtained over the range 0-5kHz. The results indicated the technique had limited capability in distinguishing between different interface conditions. The fundamental bending mode did not alter with interfacial changes. However higher modes were able to track chronological changes in interface condition by the change in natural frequency, although no one modal parameter could uniquely distinguish between each interface condition. The importance of the model boundary condition (how the model is constrained) was the key finding; variations in the boundary condition altered the modal parameters obtained. Therefore the boundary conditions need to be held constant between tests in order for the detected modal parameter changes to be attributed to interface condition changes. A three dimensional Finite Element (FE) model of the femur-implant model was then developed and used to explore the sensitivity of the modal parameters to more subtle interfacial and boundary condition changes. The FE model was created using the synthetic femur geometry and an approximation of the implant geometry. The natural frequencies of the FE model were found to match the experimental frequencies within 20% and the FE and experimental mode shapes were similar. Therefore the FE model was shown to successfully capture the dynamic response of the physical system. As was found with the experimental modal analysis, the fundamental bending mode of the FE model did not alter due to changes in interface elastic modulus. Axial and torsional modes were identified by the FE model that were not detected experimentally; the torsional mode exhibited the largest frequency change due to interfacial changes (103% between the lower and upper limits of the interface modulus range). Therefore the FE model provided additional information on the dynamic response of the system and was complementary to the experimental model. The small changes in natural frequency over a large range of interface region elastic moduli indicated the method may only be able to distinguish between early and late OI progression. The boundary conditions applied to the FE model influenced the modal parameters to a far greater extent than the interface condition variations. Therefore the FE model, as well as the experimental modal analysis, indicated that the boundary conditions need to be held constant between tests in order for the detected changes in modal parameters to be attributed to interface condition changes alone. The results of this study suggest that in a clinical setting it is unlikely that the in vivo boundary conditions of the amputated femur could be adequately controlled or replicated over time and consequently it is unlikely that any longitudinal change in frequency detected by the modal analysis technique could be attributed exclusively to changes at the femur-implant interface. Therefore further development of the modal analysis technique would require significant consideration of the clinical boundary conditions and investigation of modes other than the bending modes.