A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

Effect of poly(acrylic acid) molecular mass and end-group functionality on calcium oxalate crystal morphology and growth

A number of series of poly(acrylic acids) (PAA) of differing end-groups and molecular mass were used to study the inhibition of calcium oxalate crystallization. The effects of the end-group on crystal speciation and morphology were significant and dramatic, with hexyl-isobutyrate end groups giving preferential formation of calcium oxalate dihydrate (COD) rather than the more stable calcium oxalate monohydrate (COM), while both more hydrophobic end-groups and less-hydrophobic end groups led predominantly to formation of the least thermodynamically stable form of calcium oxalate, calcium oxalate trihydrate. Conversely, molecular mass had little impact on calcium oxalate speciation or crystal morphology. It is probable that the observed effects are related to the rate of desorption of the PAA moiety from the crystal (lite) surfaces and that the results point to a major role for end-group as well as molecular mass in controlling desorption rate.

Development of a multi-scale finite element model of the osteoporotic lumbar vertebral body for the investigation of apparent level vertebra mechanics and micro-level trabecular mechanics.

Osteoporotic spinal fractures are a major concern in ageing Western societies. This study develops a multi-scale finite element (FE) model of the osteoporotic lumbar vertebral body to study the mechanics of vertebral compression fracture at both the apparent (whole vertebral body) and micro-structural (internal trabecular bone core)levels. Model predictions were verified against experimental data, and found to provide a reasonably good representation of the mechanics of the osteoporotic vertebral body. This novel modelling methodology will allow detailed investigation of how trabecular bone loss in osteoporosis affects vertebral stiffness and strength in the lumbar spine.

Quantum Mechanics of Semantic Space

Presentation about information modelling and artificial intelligence, semantic structure, cognitive processing and quantum theory.

Molecular markers of obesity and diabetes

Recently it has been shown that the consumption of a diet high in saturated fat is associated with impaired insulin sensitivity and increased incidence of type 2 diabetes. In contrast, diets that are high in monounsaturated fatty acids (MUFAs) or polyunsaturated fatty acids (PUFAs), especially very long chain n-3 fatty acids (FAs), are protective against disease. However, the molecular mechanisms by which saturated FAs induce the insulin resistance and hyperglycaemia associated with metabolic syndrome and type 2 diabetes are not clearly defined. It is possible that saturated FAs may act through alternative mechanisms compared to MUFA and PUFA to regulate of hepatic gene expression and metabolism. It is proposed that, like MUFA and PUFA, saturated FAs regulate the transcription of target genes. To test this hypothesis, hepatic gene expression analysis was undertaken in a human hepatoma cell line, Huh-7, after exposure to the saturated FA, palmitate. These experiments showed that palmitate is an effective regulator of gene expression for a wide variety of genes. A total of 162 genes were differentially expressed in response to palmitate. These changes not only affected the expression of genes related to nutrient transport and metabolism, they also extend to other cellular functions including, cytoskeletal architecture, cell growth, protein synthesis and oxidative stress response. In addition, this thesis has shown that palmitate exposure altered the expression patterns of several genes that have previously been identified in the literature as markers of risk of disease development, including CVD, hypertension, obesity and type 2 diabetes. The altered gene expression patterns associated with an increased risk of disease include apolipoprotein-B100 (apo-B100), apo-CIII, plasminogen activator inhibitor 1, insulin-like growth factor-I and insulin-like growth factor binding protein 3. This thesis reports the first observation that palmitate directly signals in cultured human hepatocytes to regulate expression of genes involved in energy metabolism as well as other important genes. Prolonged exposure to long-chain saturated FAs reduces glucose phosphorylation and glycogen synthesis in the liver. Decreased glucose metabolism leads to elevated rates of lipolysis, resulting in increased release of free FAs. Free FAs have a negative effect on insulin action on the liver, which in turn results in increased gluconeogenesis and systemic dyslipidaemia. It has been postulated that disruption of glucose transport and insulin secretion by prolonged excessive FA availability might be a non-genetic factor that has contributed to the staggering rise in prevalence of type 2 diabetes. As glucokinase (GK) is a key regulatory enzyme of hepatic glucose metabolism, changes in its activity may alter flux through the glycolytic and de novo lipogenic pathways and result in hyperglycaemia and ultimately insulin resistance. This thesis investigated the effects of saturated FA on the promoter activity of the glycolytic enzyme, GK, and various transcription factors that may influence the regulation of GK gene expression. These experiments have shown that the saturated FA, palmitate, is capable of decreasing GK promoter activity. In addition, quantitative real-time PCR has shown that palmitate incubation may also regulate GK gene expression through a known FA sensitive transcription factor, sterol regulatory element binding protein-1c (SREBP-1c), which upregulates GK transcription. To parallel the investigations into the mechanisms of FA molecular signalling, further studies of the effect of FAs on metabolic pathway flux were performed. Although certain FAs reduce SREBP-1c transcription in vitro, it is unclear whether this will result in decreased GK activity in vivo where positive effectors of SREBP-1c such as insulin are also present. Under these conditions, it is uncertain if the inhibitory effects of FAs would be overcome by insulin. The effects of a combination of FAs, insulin and glucose on glucose phosphorylation and metabolism in cultured primary rat hepatocytes at concentrations that mimic those in the portal circulation after a meal was examined. It was found that total GK activity was unaffected by an increased concentration of insulin, but palmitate and eicosapentaenoic acid significantly lowered total GK activity in the presence of insulin. Despite the fact that total GK enzyme activity was reduced in response to FA incubation, GK enzyme translocation from the inactive, nuclear bound, to active, cytoplasmic state was unaffected. Interestingly, none of the FAs tested inhibited glucose phosphorylation or the rate of glycolysis when insulin is present. These results suggest that in the presence of insulin the levels of the active, unbound cytoplasmic GK are sufficient to buffer a slight decrease in GK enzyme activity and decreased promoter activity caused by FA exposure. Although a high fat diet has been associated with impaired hepatic glucose metabolism, there is no evidence from this thesis that FAs themselves directly modulate flux through the glycolytic pathway in isolated primary hepatocytes when insulin is also present. Therefore, although FA affected expression of a wide range of genes, including GK, this did not affect glycolytic flux in the presence of insulin. However, it may be possible that a saturated FA-induced decrease in GK enzyme activity when combined with the onset of insulin resistance may promote the dys-regulation of glucose homeostasis and the subsequent development of hyperglycaemia, metabolic syndrome and type 2 diabetes.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.