Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

Cereal products for specific dietary requirements. Evaluation and improvement of technological and nutritional properties of gluten free raw materials and end products

Coeliac disease is one of the most common food intolerances worldwide and at present the gluten free diet remains the only suitable treatment. A market overview conducted as part of this thesis on nutritional and sensory quality of commercially available gluten free breads and pasta showed that improvements are necessary. Many products show strong off-flavors, poor mouthfeel and reduced shelf-life. Since the life-long avoidance of the cereal protein gluten means a major change to the diet, it is important to also consider the nutritional value of products intending to replace staple foods such as bread or pasta. This thesis addresses this issue by characterising available gluten free cereal and pseudocereal flours to facilitate a better raw material choice. It was observed that especially quinoa, buckwheat and teff are high in essential nutrients, such as protein, minerals and folate. In addition the potential of functional ingredients such as inulin, β-glucan, HPMC and xanthan to improve loaf quality were evaluated. Results show that these ingredients can increase loaf volume and reduce crumb hardness as well as rate of staling but that the effect diverges strongly depending on the bread formulation used. Furthermore, fresh egg pasta formulations based on teff and oat flour were developed. The resulting products were characterised regarding sensory and textural properties as well as in vitro digestibility. Scanning electron and confocal laser scanning microscopy was used throughout the thesis to visualise structural changes occurring during baking and pasta making

Vascular calcification and mineral bone disorder in chronic kidney disease

Chronic Kidney Disease (CKD), osteoporosis and mild hyponatremia are all prevalent chronic conditions that may coexist and are often under-recognized. Mineral-Bone Disorder begins early in the natural history of CKD and results in complex abnormalities of bone which ultimately confers a well-established increased risk of fragility fractures in End Stage Kidney Disease. Hyponatremia is a novel, usually renal mediated metabolic perturbation, that most commonly occurs independently of the stage of renal dysfunction but which may also predispose to increased fracture risk. The extent -if any- to which either early stages of renal dysfunction or the presence of hyponatremia contribute to fracture occurrence in the general population, independently of osteoporosis, is unclear. Renal transplantation is the treatment of choice for ESKD and although it restores endogenous renal function it typically fails to normalize either the long term cardiovascular or fracture risk. One potential mechanism contributing to these elevated long-term risks and to diminished Health Related Quality of Life is persistent, post-transplant hyperparathyroidism. In this study we retrospectively examine the association of renal function and serum sodium with Bone Mineral Density and fracture occurrence in a retrospective cohort of 1930 female members of the general population who underwent routine DXA scan. We then prospectively recruited a cohort of 90 renal transplant recipients in order to examine the association of post transplant parathyroid hormone (PTH) level with measures of CKD Mineral Bone Disorder, including, DXA Bone Mineral Density, Vascular Calcification (assessed using both abdominal radiography and CT techniques, as well as indirectly by carotid-femoral Pulse Wave Velocity) and Quality of Life (using the Short Form-12 and a PTH specific symptom score). In the retrospective DXA cohort, moderate CKD (eGFR 30-59ml/min/1.73m2) and hyponatremia (<135mmol/L) were associated with fracture occurrence, independently of BMD, with an adjusted Odds Ratio (95% Confidence Interval), of 1.37 (1.0, 1.89) and 2.25 (1.24, 4.09) respectively. In the renal transplant study, PTH was independently associated with the presence of osteoporosis, adjusted Odds Ratio (95% Confidence Interval), 1.15 (per 10ng/ml increment), (1.04, 1.26). The presence of osteoporosis but not PTH was independently associated with measures of vascular calcification, adjusted ß (95% Confidence Interval), 12.45, (1.16, 23.75). Of the eight quality-of-life domains examined, post-transplant PTH (per 10ng/ml increment), was only significantly and independently associated with reduced Physical Functioning, (95% Confidence Interval), 1.12 (1.01, 1.23). CKD and hyponatremia are both common health problems that may contribute to fracture occurrence in the general population, a major on-going public health concern. PTH and decreased Bone Mineral Density may signal sub-optimal long-term outcomes post renal transplantation, influencing bone and vascular health and to a limited extent long term Health Related Quality of Life

Vitamin D status and requirements during pregnancy and lactation

Vitamin D deficiency during pregnancy, lactation, and early infancy has been widely reported. Current understanding of vitamin D metabolism during pregnancy and lactation is incomplete, and to date, experimental data to support vitamin D requirements for these life stages are scarce. There is a shortage of nationally representative data and appropriate reference ranges for serum 25-hydroxyvitamin D (25OHD) during pregnancy, lactation and infancy, including in umbilical cord blood. This thesis described concentrations of total 25OHD and individual metabolites including 25OHD3, 25OHD2, and 3-epi-25OHD3 at 15 weeks’ gestation in a large seasonally balanced pregnancy cohort study (n 1768), carried out in Cork, Ireland (52oN). The prevalence of low 25OHD concentrations in pregnant women was higher than published reports in other Caucasian women, and was highest among non-users of vitamin D-containing supplements during winter. A longitudinal pregnancy study was included which suggested gestational stages had an impact on the total serum 25OHD concentration. This thesis incorporated a randomized controlled trial carried out among 100 women across 3 intervention groups using 20 μg/day of vitamin D3 with or without 500 mg calcium, or placebo, over 12-weeks of lactation to investigate the vitamin D requirement for lactating mothers and the vitamin D content of human milk. A daily intake of 25 μg/day was suggested to meet the requirement of lactating women to maintain a 25OHD levels above 50 nmol/L in 97.5% of the population at 52oN all year around. However, vitamin D content in human milk did not increase in response to supplementation. Serum 25OHD concentration has been used as a predictor of a number of health outcomes. This thesis reported large differences in serum 25OHD concentrations using different methods in 86 umbilical cord samples. The need for international standardization of serum 25OHD measurements was re-emphasized in this thesis.

Biomethane production from grass silage: laboratory assessment to maximise yields

On-farm biogas production is typically associated with forage maize as the biomass source. Digesters are designed and operated with the focus of optimising the conditions for this feedstock. Thus, such systems may not be ideally suited to the digestion of grass. Ireland has ca. 3.85 million ha of grassland. Annual excess grass, surplus to livestock requirements, could potentially fuel an anaerobic digestion industry. Biomethane associated with biomass from 1.1 % of grassland in Ireland, could potentially generate over 10 % renewable energy supply in transport. This study aims to identify and optimise technologies for the production of biomethane from grass silage. Mono-digestion of grass silage and co-digestion with slurry, as would occur on Irish farms, is investigated in laboratory trials. Grass silage was shown to have 7 times greater methane potential than dairy slurry on a fresh weight basis (107 m3 t-1 v 16 m3 t-1). However, comprehensive trace element profiles indicated that cobalt, iron and nickel are deficient in mono-digestion of grass silage at a high organic loading rate (OLR) of 4.0 kg VS m-3 d-1. The addition of a slurry co-substrate was beneficial due to its wealth of essential trace elements. To stimulate hydrolysis of high lignocellulose grass silage, particle size reduction (physical) and rumen fluid addition (biological) were investigated. In a continuous trial, digestion of grass silage of <1 cm particle size achieved a specific methane yield of 371 L CH4 kg-1 VS when coupled with rumen fluid addition. The concept of demand driven biogas was also examined in a two-phase digestion system (leaching with UASB). When demand for electricity is low it is recommended to disconnect the UASB from the system and recirculate rumen fluid to increase volatile fatty acid (VFA) and soluble chemical oxygen demand (SCOD) production whilst minimising volatile solids (VS) destruction. At times of high demand for electricity, connection of the UASB increases the destruction of volatiles and associated biogas production. The above experiments are intended to assess a range of biogas production options from grass silage with a specific focus on maximising methane yields and provide a guideline for feasible design and operation of on-farm digesters in Ireland.