A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Investigating the links between muscle strength, sun exposure, dietary vitamin D intake and the vitamin D status of ambulatory older adults in South East Queensland

Vitamin D deficiency and insufficiency are now seen as a contemporary health problem in Australia with possible widespread health effects not limited to bone health1. Despite this, the Vitamin D status (measured as serum 25-hydroxyvitamin D (25(OH)D)) of ambulatory adults has been overlooked in this country. Serum 25(OH)D status is especially important among this group as studies have shown a link between Vitamin D and fall risk in older adults2. Limited data also exists on the contributions of sun exposure via ultraviolet radiation and dietary intake to serum 25(OH)D status in this population. The aims of this project were to assess the serum 25(OH)D status of a group of older ambulatory adults in South East Queensland, to assess the association between their serum 25(OH)D status and functional measures as possible indicators of fall risk, obtain data on the sources of Vitamin D in this population and assess whether this intake was related to serum 25(OH)D status and describe sun protection and exposure behaviors in this group and investigate whether a relationship existed between these and serum 25(OH)D status. The collection of this data assists in addressing key gaps identified in the literature with regard to this population group and their Vitamin D status in Australia. A representative convenience sample of participants (N=47) over 55 years of age was recruited for this cross-sectional, exploratory study which was undertaken in December 2007 in south-east Queensland (Brisbane and Sunshine coast). Participants were required to complete a sun exposure questionnaire in addition to a Calcium and Vitamin D food frequency questionnaire. Timed up and go and handgrip dynamometry tests were used to examine functional capacity. Serum 25(OH)D status and blood measures of Calcium, Phosphorus and Albumin were determined through blood tests. The Mean and Median serum 25-Hydroxyvitamin D (25(OH)D) for all participants in this study was 85.8nmol/L (Standard Deviation 29.7nmol/L) and 81.0nmol/L (Range 22-158nmol/L), respectively. Analysis at the bivariate level revealed a statistically significant relationship between serum 25(OH)D status and location, with participants living on the Sunshine Coast having a mean serum 25(OH)D status 21.3nmol/L higher than participants living in Brisbane (p=0.014). While at the descriptive level there was an apparent trend towards higher outdoor exposure and increasing levels of serum 25(OH)D, no statistically significant associations between the sun measures of outdoor exposure, sun protection behaviors and phenotypic characteristics and serum 25(OH)D status were observed. Intake of both Calcium and Vitamin D was low in this sample with sixty-eight (68%) of participants not meeting the Estimated Average Requirements (EAR) for Calcium (Median=771.0mg; Range=218.0-2616.0mg), while eighty-seven (87%) did not meet the Adequate Intake for Vitamin D (Median=4.46ug; Range=0.13-30.0ug). This raises the question of how realistic meeting the new Adequate Intakes for Vitamin D is, when there is such a low level of Vitamin D fortification in this country. However, participants meeting the Adequate Intake (AI) for Vitamin D were observed to have a significantly higher serum 25(OH)D status compared to those not meeting the AI for Vitamin D (p=0.036), showing that meeting the AI for Vitamin D may play a significant role in determining Vitamin D status in this population. By stratifying our data by categories of outdoor exposure time, a trend was observed between increased importance of Vitamin D dietary intake as a possible determinant of serum 25(OH)D status in participants with lower outdoor exposures. While a trend towards higher Timed Up and Go scores in participants with higher 25(OH) D status was seen, this was only significant for females (p=0.014). Handgrip strength showed statistically significant association with serum 25(OH)D status. The high serum 25(OH)D status in our sample almost certainly explains the limited relationship between functional measures and serum 25(OH)D. However, the observation of an association between slower Time Up and Go speeds, and lower serum 25(OH)D levels, even with a small sample size, is significant as slower Timed Up and Go speeds have been associated with increased fall risk in older adults3. Multivariable regression analysis revealed Location as the only significant determinant of serum 25(OH)D status at p=0.014, with trends (p=>0.1) for higher serum 25(OH)D being shown for participants that met the AI for Vitamin D and rated themselves as having a higher health status. The results of this exploratory study show that 93.6% of participants had adequate 25(OH)D status-possibly due to measurement being taken in the summer season and the convenience nature of the sample. However, many participants do not meet their dietary Calcium and Vitamin D requirements, which may indicate inadequate intake of these nutrients in older Australians and a higher risk of osteoporosis. The relationship between serum 25(OH)D and functional measures in this population also requires further study, especially in older adults displaying Vitamin D insufficiency or deficiency.

Processing of polycaprolactone and polycaprolactone-based copolymers into 3D scaffolds and their cellular responses

Synthetic polymers have attracted much attention in tissue engineering due to their ability to modulate biomechanical properties. This study investigated the feasibility of processing poly(varepsilon-caprolactone) (PCL) homopolymer, PCL-poly(ethylene glycol) (PEG) diblock, and PCL-PEG-PCL triblock copolymers into three-dimensional porous scaffolds. Properties of the various polymers were investigated by dynamic thermal analysis. The scaffolds were manufactured using the desktop robot-based rapid prototyping technique. Gross morphology and internal three-dimensional structure of scaffolds were identified by scanning electron microscopy and micro-computed tomography, which showed excellent fusion at the filament junctions, high uniformity, and complete interconnectivity of pore networks. The influences of process parameters on scaffolds' morphological and mechanical characteristics were studied. Data confirmed that the process parameters directly influenced the pore size, porosity, and, consequently, the mechanical properties of the scaffolds. The in vitro cell culture study was performed to investigate the influence of polymer nature and scaffold architecture on the adhesion of the cells onto the scaffolds using rabbit smooth muscle cells. Light, scanning electron, and confocal laser microscopy showed cell adhesion, proliferation, and extracellular matrix formation on the surface as well as inside the structure of both scaffold groups. The completely interconnected and highly regular honeycomb-like pore morphology supported bridging of the pores via cell-to-cell contact as well as production of extracellular matrix at later time points. The results indicated that the incorporation of hydrophilic PEG into hydrophobic PCL enhanced the overall hydrophilicity and cell culture performance of PCL-PEG copolymer. However, the scaffold architecture did not significantly influence the cell culture performance in this study.

New insights into appetite, inflammation and the use of fish oil in hemodialysis patients

Protein-energy wasting (PEW) is commonly seen in patients with chronic kidney disease (CKD). The condition is characterised by chronic, systemic low-grade inflammation which affects nutritional status by a variety of mechanisms including reducing appetite and food intake and increasing muscle catabolism. PEW is linked with co-morbidities such as cardiovascular disease, and is associated with lower quality of life, increased hospitalisations and a 6-fold increase in risk of death1. Significant gender differences have been found in the severity and effects of several markers of PEW. There have been limited studies testing the ability of anti-inflammatory agents or nutritional interventions to reduce the effects of PEW in dialysis patients. This thesis makes a significant contribution to the understanding of PEW in dialysis patients. It advances understanding of measurement techniques for two of the key components, appetite and inflammation, and explores the effect of fish oil, an anti-inflammatory agent, on markers of PEW in dialysis patients. The first part of the thesis consists of two methodological studies conducted using baseline data. The first study aims to validate retrospective ratings of hunger, desire to eat and fullness on visual analog scales (VAS) (paper and pen and electronic) as a new method of measuring appetite in dialysis patients. The second methodological study aims to assess the ability of a variety of methods available in routine practice to detect the presence of inflammation. The second part of the thesis aims to explore the effect of 12 weeks supplementation with 2g per day of Eicosapentaenoic Acid (EPA), a longchain fatty acid found in fish oil, on markers of PEW. A combination of biomarkers and psychomarkers of appetite and inflammation are the main outcomes being explored, with nutritional status, dietary intake and quality of life included as secondary outcomes. A lead in phase of 3 months prior to baseline was used so that each person acts as their own historical control. The study also examines whether there are gender differences in response to the treatment. Being an exploratory study, an important part of the work is to test the feasibility of the intervention, thus the level of adherence and factors associated with adherence are also presented. The studies were conducted at the hemodialysis unit of the Wesley Hospital. Participants met the following criteria: adult, stage 5 CKD on hemodialysis for at least 3 months, not expected to receive a transplant or switch to another dialysis modality during the study, absence of intellectual impairment or mental illness impairing ability to follow instructions or complete the intervention. A range of intermediate, clinical and patient-centred outcome measures were collected at baseline and 12 weeks. Inflammation was measured using five biomarkers: c-reactive protein (CRP), interleukin-6 (IL6), intercellular adhesion molecule (sICAM-1), vascular cell adhesion molecule (sVCAM-1) and white cell count (WCC). Subjective appetite was measured using the first question from the Appetite and Dietary Assessment (ADAT) tool and VAS for measurements of hunger, desire to eat and fullness. A novel feature of the study was the assessment of the appetite peptides leptin, ghrelin and peptide YY as biomarkers of appetite. Nutritional status/inflammation was assessed using the Malnutrition-Inflammation Score (MIS) and the Patient-Generated Subjective Global Assessment (PG-SGA). Dietary intake was measured using 3-day records. Quality of life was measured using the Kidney Disease Quality of Life Short Form version 1.3 (KDQOL-SF™ v1.3 © RAND University), which combines the Short-Form 36 (SF36) with a kidney-disease specific module2. A smaller range of these variables was available for analysis during the control phase (CRP, ADAT, dietary intake and nutritional status). Statistical analysis was carried out using SPSS version 14 (SPSS Inc, Chicago IL, USA). Analysis of the first part of the thesis involved descriptive and bivariate statistics, as well as Bland-Altman plots to assess agreement between methods, and sensitivity analysis/ROC curves to test the ability of methods to predict the presence of inflammation. The unadjusted (paired ttests) and adjusted (linear mixed model) change over time is presented for the main outcome variables of inflammation and appetite. Results are shown for the whole group followed by analyses according to gender and adherence to treatment. Due to the exploratory nature of the study, trends and clinical significance were considered as important as statistical significance. Twenty-eight patients (mean age 61±17y, 50% male, dialysis vintage 19.5 (4- 101) months) underwent baseline assessment. Seven out of 28 patients (25%) reported sub-optimal appetite (self-reported as fair, poor or very poor) despite all being well nourished (100% SGA A). Using the VAS, ratings of hunger, but not desire to eat or fullness, were significantly (p<0.05) associated with a range of relevant clinical variables including age (r=-0.376), comorbidities (r=-0.380) nutritional status (PG-SGA score, r=-0.451), inflammatory markers (CRP r=-0.383; sICAM-1 r=-0.387) and seven domains of quality of life. Patients expressed a preference for the paper and pen method of administering VAS. None of the tools (appetite, MIS, PG-SGA, albumin or iron) showed an acceptable ability to detect patients who are inflamed. It is recommended that CRP should be tested more frequently as a matter of course rather than seeking alternative methods of measuring inflammation. 27 patients completed the 12 week intervention. 20 patients were considered adherent based on changes in % plasma EPA, which rose from 1.3 (0.94)% to 5.2 (1.1)%, p<0.001, in this group. The major barriers to adherence were forgetting to take the tablets as well as their size. At 12 weeks, inflammatory markers remained steady apart from the white cell count which decreased (7.6(2.5) vs 7.0(2.2) x109/L, p=0.058) and sVCAM-1 which increased (1685(654) vs 2249(925) ng/mL, p=0.001). Subjective appetite using VAS increased (51mm to 57mm, +12%) and there was a trend towards reduction in peptide YY (660(31) vs 600(30) pg/mL, p=0.078). There were some gender differences apparent, with the following adjusted change between baseline and week 12: CRP (males -3% vs females +17%, p=0.19), IL6 (males +17% vs females +48%, p=0.77), sICAM-1 (males -5% vs females +11%, p=0.07), sVCAM-1 (males +54% vs females +19%, p=0.08) and hunger ratings (males 20% vs females -5%, p=0.18). On balance, males experienced a maintainence or reduction in three inflammatory markers and an improvement in hunger ratings, and therefore appeared to have responded better to the intervention. Compared to those who didn’t adhere, adherent patients maintained weight (mean(SE) change: +0.5(1.6) vs - 0.8(1.2) kg, p=0.052) and fat-free mass (-0.1 (1.6) vs -1.8 (1.8) kg, p=0.045). There was no difference in change between the intervention and control phase for CRP, appetite, nutritional status or dietary intake. The thesis makes a significant contribution to the evidence base for understanding of PEW in dialysis patients. It has advanced knowledge of methods of assessing inflammation and appetite. Retrospective ratings of hunger on a VAS appear to be a valid method of assessing appetite although samples which include patients with very poor appetite are required to confirm this. Supplementation with fish oil appeared to improve subjective appetite and dampen the inflammatory response. The effectiveness of the intervention is influenced by gender and adherence. Males appear to be more responsive to the primary outcome variables than females, and the quality of response is improved with better adherence. These results provide evidence to support future interventions aimed at reducing the effects of PEW in dialysis patients.

In vitro and in vivo analysis of co-electrospun scaffolds made of medical grade poly(epsilon-caprolactone) and porcine collagen

In this study, a nanofiber mesh made by co-electrospinning medical grade poly(epsilon-caprolactone) and collagen (mPCL/Col) was fabricated and studied. Its mechanical properties and characteristics were analyzed and compared to mPCL meshes. mPCL/Col meshes showed a reduction in strength but an increase in ductility when compared to PCL meshes. In vitro assays revealed that mPCL/Col supported the attachment and proliferation of smooth muscle cells on both sides of the mesh. In vivo studies in the corpus cavernosa of rabbits revealed that the mPCL/Col scaffold used in conjunction with autologous smooth muscle cells resulted in better integration with host tissue when compared to cell free scaffolds. On a cellular level preseeded scaffolds showed a minimized foreign body reaction.

Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

Eccentric calf muscle exercise produces a greater acute reduction in Achilles tendon thickness than concentric exercise

Objective: To investigate the acute effects of isolated eccentric and concentric calf muscle exercise on Achilles tendon sagittal thickness. ---------- Design: Within-subject, counterbalanced, mixed design. ---------- Setting: Institutional. ---------- Participants: 11 healthy, recreationally active male adults. ---------- Interventions: Participants performed an exercise protocol, which involved isolated eccentric loading of the Achilles tendon of a single limb and isolated concentric loading of the contralateral, both with the addition of 20% bodyweight. ---------- Main outcome measurements: Sagittal sonograms were acquired prior to, immediately following and 3, 6, 12 and 24 h after exercise. Tendon thickness was measured 2 cm proximal to the superior aspect of the calcaneus. ---------- Results: Both loading conditions resulted in an immediate decrease in normalised Achilles tendon thickness. Eccentric loading induced a significantly greater decrease than concentric loading despite a similar impulse (−0.21 vs −0.05, p<0.05). Post-exercise, eccentrically loaded tendons recovered exponentially, with a recovery time constant of 2.5 h. The same exponential function did not adequately model changes in tendon thickness resulting from concentric loading. Even so, recovery pathways subsequent to the 3 h time point were comparable. Regardless of the exercise protocol, full tendon thickness recovery was not observed until 24 h. ---------- Conclusions: Eccentric loading invokes a greater reduction in Achilles tendon thickness immediately after exercise but appears to recover fully in a similar time frame to concentric loading.

Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH Model

In this paper, we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new double smooth transition conditional correlation (DSTCC) GARCH model extends the smooth transition conditional correlation (STCC) GARCH model of Silvennoinen and Teräsvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. Applying the model to the stock and bond futures data, we discover that the correlation pattern between them has dramatically changed around the turn of the century. The model is also applied to a selection of world stock indices, and we find evidence for an increasing degree of integration in the capital markets.

Improved image contrast of the bone-muscle interface with 3T MRI compared to 1.5T MRI [Abstract]

Virtual 3D models of long bones are increasingly being used for implant design and research applications. The current gold standard for the acquisition of such data is Computed Tomography (CT) scanning. Due to radiation exposure, CT is generally limited to the imaging of clinical cases and cadaver specimens. Magnetic Resonance Imaging (MRI) does not involve ionising radiation and therefore can be used to image selected healthy human volunteers for research purposes. The feasibility of MRI as alternative to CT for the acquisition of morphological bone data of the lower extremity has been demonstrated in recent studies [1, 2]. Some of the current limitations of MRI are long scanning times and difficulties with image segmentation in certain anatomical regions due to poor contrast between bone and surrounding muscle tissues. Higher field strength scanners promise to offer faster imaging times or better image quality. In this study image quality at 1.5T is quantitatively compared to images acquired at 3T. --------- The femora of five human volunteers were scanned using 1.5T and 3T MRI scanners from the same manufacturer (Siemens) with similar imaging protocols. A 3D flash sequence was used with TE = 4.66 ms, flip angle = 15° and voxel size = 0.5 × 0.5 × 1 mm. PA-Matrix and body matrix coils were used to cover the lower limb and pelvis respectively. Signal to noise ratio (SNR) [3] and contrast to noise ratio (CNR) [3] of the axial images from the proximal, shaft and distal regions were used to assess the quality of images from the 1.5T and 3T scanners. The SNR was calculated for the muscle and bone-marrow in the axial images. The CNR was calculated for the muscle to cortex and cortex to bone marrow interfaces, respectively. --------- Preliminary results (one volunteer) show that the SNR of muscle for the shaft and distal regions was higher in 3T images (11.65 and 17.60) than 1.5T images (8.12 and 8.11). For the proximal region the SNR of muscles was higher in 1.5T images (7.52) than 3T images (6.78). The SNR of bone marrow was slightly higher in 1.5T images for both proximal and shaft regions, while it was lower in the distal region compared to 3T images. The CNR between muscle and bone of all three regions was higher in 3T images (4.14, 6.55 and 12.99) than in 1.5T images (2.49, 3.25 and 9.89). The CNR between bone-marrow and bone was slightly higher in 1.5T images (4.87, 12.89 and 10.07) compared to 3T images (3.74, 10.83 and 10.15). These results show that the 3T images generated higher contrast between bone and the muscle tissue than the 1.5T images. It is expected that this improvement of image contrast will significantly reduce the time required for the mainly manual segmentation of the MR images. Future work will focus on optimizing the 3T imaging protocol for reducing chemical shift and susceptibility artifacts.

Oxygen consumption and muscle activation patterns during constant load exercise

The collective purpose of these two studies was to determine a link between the V02 slow component and the muscle activation patterns that occur during cycling. Six, male subjects performed an incremental cycle ergometer exercise test to determine asub-TvENT (i.e. 80% of TvENT) and supra-TvENT (TvENT + 0.75*(V02 max - TvENT) work load. These two constant work loads were subsequently performed on either three or four occasions for 8 mins each, with V02 captured on a breath-by-breath basis for every test, and EMO of eight major leg muscles collected on one occasion. EMG was collected for the first 10 s of every 30 s period, except for the very first 10 s period. The V02 data was interpolated, time aligned, averaged and smoothed for both intensities. Three models were then fitted to the V02 data to determine the kinetics responses. One of these models was mono-exponential, while the other two were biexponential. A second time delay parameter was the only difference between the two bi-exponential models. An F-test was used to determine significance between the biexponential models using the residual sum of squares term for each model. EMO was integrated to obtain one value for each 10 s period, per muscle. The EMG data was analysed by a two-way repeated measures ANOV A. A correlation was also used to determine significance between V02 and IEMG. The V02 data during the sub-TvENT intensity was best described by a mono-exponential response. In contrast, during supra-TvENT exercise the two bi-exponential models best described the V02 data. The resultant F-test revealed no significant difference between the two models and therefore demonstrated that the slow component was not delayed relative to the onset of the primary component. Furthermore, only two parameters were deemed to be significantly different based upon the two models. This is in contrast to other findings. The EMG data, for most muscles, appeared to follow the same pattern as V02 during both intensities of exercise. On most occasions, the correlation coefficient demonstrated significance. Although some muscles demonstrated the same relative increase in IEMO based upon increases in intensity and duration, it cannot be assumed that these muscles increase their contribution to V02 in a similar fashion. Larger muscles with a higher percentage of type II muscle fibres would have a larger increase in V02 over the same increase in intensity.