A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

A procedure for the reconstruction of a stochastic stationary temperature field

An iterative procedure is proposed for the reconstruction of a temperature field from a linear stationary heat equation with stochastic coefficients, and stochastic Cauchy data given on a part of the boundary of a bounded domain. In each step, a series of mixed well-posed boundary-value problems are solved for the stochastic heat operator and its adjoint. Well-posedness of these problems is shown to hold and convergence in the mean of the procedure is proved. A discretized version of this procedure, based on a Monte Carlo Galerkin finite-element method, suitable for numerical implementation is discussed. It is demonstrated that the solution to the discretized problem converges to the continuous as the mesh size tends to zero.

Size frequency distributions of the florid prion protein aggregates in variant Creutzfeldt-Jakob disease follow a power-law function

The objective was to test the hypothesis that the size frequency distributions of the prion protein (PrP) plaques in cases of variant Creutzfeldt-Jakob disease (vCJD) follow a power-law function. The design was a retrospective neuropathological study. The patients were 11 cases of clinically and neuropathologically verified vCJD. Size distributions of the diffuse and florid-type plaques were measured in several areas of the cerebral cortex and hippocampus from each case and a power-law function fitted to each distribution. The size distributions of the florid and diffuse plaques were fitted successfully by a powerlaw function in 100% and 42% of brain areas investigated respectively. Processes of aggregation/disaggregation may be more important than surface diffusion in the pathogenesis of the florid plaques. By contrast, surface diffusion may be a more significant factor in the development of the diffuse plaques. © Springer-Verlag Italia 2006.

Visual function and subjective quality of life compared in subjects with acquired macular disease

PURPOSE: To determine the objective measures of visual function that are most relevant to subjective quality of vision and perceived reading ability in patients with acquired macular disease. METHODS: Twenty-eight patients with macular disease underwent a comprehensive assessment of visual function. The patients also completed a vision-related quality-of-life questionnaire that included a section of general questions about perceived visual performance and a section with specific questions on reading. RESULTS: Results of all tests of vision correlated highly with reported vision-related quality-of-life impairment. Low-contrast tests explained most of the variance in self-reported problems with reading. Text-reading speed correlated highly with overall concern about vision. CONCLUSIONS: Reading performance is strongly associated with vision-related quality of life. High-contrast distance acuity is not the only relevant measure of visual function in relation to the perceived visual performance of a patient with macular disease. The results suggest the importance of print contrast, even over print size, in reading performance in patients with acquired macular disease.

The Effect of nutritional supplementation on subjective and objective measures of visual and retinal function:a random controlled trial

In industrialised countries age-related macular disease (ARMD) is the leading cause of visual loss in older people. Because oxidative stress is purported to be associated with an increased risk of disease development the role of antioxidant supplementation is of interest. Lutein is a carotenoid antioxidant that accumulates within the retina and is thought to filter blue light. Increased levels of lutein have been associated with reduced risk of developing ARMD and improvements in visual and retinal function in eyes with ARMD. The aim of this randomised controlled trial (RCT) was to investigate the effect of a lutein-based nutritional supplement on subjective and objective measures of visual function in healthy eyes and in eyes with age-related maculopathy (ARM) – an early form of ARMD. Supplement withdrawal effects were also investigated. A sample size of 66 healthy older (HO), healthy younger (HY), and ARM eyes were randomly allocated to receive a lutein-based supplement or no treatment for 40 weeks. The supplemented group then stopped supplementation to look at the effects of withdrawal over a further 20 weeks. The primary outcome measure was multifocal electroretinogram (mfERG) N1P1 amplitude. Secondary outcome measures were mfERG N1, P1 and N2 latency, contrast sensitivity (CS), Visual acuity (VA) and macular pigment optical density (MPOD). Sample sizes were sufficient for the RCT to have an 80% power to detect a significant clinical effect at the 5% significance level for all outcome measures when the healthy eye groups were combined, and CS, VA and mfERG in the ARM group. This RCT demonstrates significant improvements in MPOD in HY and HO supplemented eyes. When HY and HO supplemented groups were combined, MPOD improvements were maintained, and mfERG ring 2 P1 latency became shorter. On withdrawal of the supplement mfERG ring 1 N1P1 amplitude reduced in HO eyes. When HO and HY groups were combined, mfERG ring 1 and ring 2 N1P1 amplitudes were reduced. In ARM eyes, ring 3 N2 latency and ring 4 P1 latency became longer. These statistically significant changes may not be clinically significant. The finding that a lutein-based supplement increases MPOD in healthy eyes, but does not increase mfERG amplitudes contrasts with the CARMIS study and contributes to the debate on the use of nutritional supplementation in ARM.

A three dimensional surface measurement and reconstruction system for respiratory function analysis

Respiration is a complex activity. If the relationship between all neurological and skeletomuscular interactions was perfectly understood, an accurate dynamic model of the respiratory system could be developed and the interaction between different inputs and outputs could be investigated in a straightforward fashion. Unfortunately, this is not the case and does not appear to be viable at this time. In addition, the provision of appropriate sensor signals for such a model would be a considerable invasive task. Useful quantitative information with respect to respiratory performance can be gained from non-invasive monitoring of chest and abdomen motion. Currently available devices are not well suited in application for spirometric measurement for ambulatory monitoring. A sensor matrix measurement technique is investigated to identify suitable sensing elements with which to base an upper body surface measurement device that monitors respiration. This thesis is divided into two main areas of investigation; model based and geometrical based surface plethysmography. In the first instance, chapter 2 deals with an array of tactile sensors that are used as progression of existing and previously investigated volumetric measurement schemes based on models of respiration. Chapter 3 details a non-model based geometrical approach to surface (and hence volumetric) profile measurement. Later sections of the thesis concentrate upon the development of a functioning prototype sensor array. To broaden the application area the study has been conducted as it would be fore a generically configured sensor array. In experimental form the system performance on group estimation compares favourably with existing system on volumetric performance. In addition provides continuous transient measurement of respiratory motion within an acceptable accuracy using approximately 20 sensing elements. Because of the potential size and complexity of the system it is possible to deploy it as a fully mobile ambulatory monitoring device, which may be used outside of the laboratory. It provides a means by which to isolate coupled physiological functions and thus allows individual contributions to be analysed separately. Thus facilitating greater understanding of respiratory physiology and diagnostic capabilities. The outcome of the study is the basis for a three-dimensional surface contour sensing system that is suitable for respiratory function monitoring and has the prospect with future development to be incorporated into a garment based clinical tool.

Size matters, but not for everyone:Individual differences for contrast discrimination

It is very well known that contrast detection thresholds improve with the size of a grating-type stimulus, but it is thought that the benefit of size is abolished for contrast discriminations well above threshold (e.g., Legge, G. E., & Foley, J. M. (1980)]. Here we challenge the generality of this view. We performed contrast detection and contrast discrimination for circular patches of sine wave grating as a function of stimulus size. We confirm that sensitivity improves with approximately the fourth-root of stimulus area at detection threshold (a log-log slope of -0.25) but find individual differences (IDs) for the suprathreshold discrimination task. For several observers, performance was largely unaffected by area, but for others performance first improved (by as much as a log-log slope of -0.5) and then reached a plateau. We replicated these different results several times on the same observers. All of these results were described in the context of a recent gain control model of area summation [Meese, T. S. (2004)], extended to accommodate the multiple stimulus sizes used here. In this model, (i) excitation increased with the fourth-root of stimulus area for all observers, and (ii) IDs in the discrimination data were described by IDs in the relation between suppression and area. This means that empirical summation in the contrast discrimination task can be attributed to growth in suppression with stimulus size that does not keep pace with the growth in excitation. © 2005 ARVO.

Computational modelling of the impact of particle size to the heat transfer coefficient between biomass particles and a fluidised bed

The fluid–particle interaction and the impact of different heat transfer conditions on pyrolysis of biomass inside a 150 g/h fluidised bed reactor are modelled. Two different size biomass particles (350 µm and 550 µm in diameter) are injected into the fluidised bed. The different biomass particle sizes result in different heat transfer conditions. This is due to the fact that the 350 µm diameter particle is smaller than the sand particles of the reactor (440 µm), while the 550 µm one is larger. The bed-to-particle heat transfer for both cases is calculated according to the literature. Conductive heat transfer is assumed for the larger biomass particle (550 µm) inside the bed, while biomass–sand contacts for the smaller biomass particle (350 µm) were considered unimportant. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. Biomass reaction kinetics is modelled according to the literature using a two-stage, semi-global model which takes into account secondary reactions. The particle motion inside the reactor is computed using drag laws, dependent on the local volume fraction of each phase. FLUENT 6.2 has been used as the modelling framework of the simulations with the whole pyrolysis model incorporated in the form of User Defined Function (UDF).

Contrast summation across eyes and space is revealed along the entire dipper function by a "Swiss cheese" stimulus.

Previous contrast discrimination experiments have shown that luminance contrast is summed across ocular (T. S. Meese, M. A. Georgeson, & D. H. Baker, 2006) and spatial (T. S. Meese & R. J. Summers, 2007) dimensions at threshold and above. However, is this process sufficiently general to operate across the conjunction of eyes and space? Here we used a "Swiss cheese" stimulus where the blurred "holes" in sine-wave carriers were of equal area to the blurred target ("cheese") regions. The locations of the target regions in the monocular image pairs were interdigitated across eyes such that their binocular sum was a uniform grating. When pedestal contrasts were above threshold, the monocular neural images contained strong evidence that the high-contrast regions in the two eyes did not overlap. Nevertheless, sensitivity to dual contrast increments (i.e., to contrast increments in different locations in the two eyes) was a factor of ∼1.7 greater than to single increments (i.e., increments in a single eye), comparable with conventional binocular summation. This provides evidence for a contiguous area summation process that operates at all contrasts and is influenced little, if at all, by eye of origin. A three-stage model of contrast gain control fitted the results and possessed the properties of ocularity invariance and area invariance owing to its cascade of normalization stages. The implications for a population code for pattern size are discussed.

An investigation of reading ability and visual function with eccentric visual field

This study investigated the detrimental effect of central field loss (CFL) on reading ability and general visual function. The aim was to improve the understanding of reading with eccentric retina in order that reading performances of individuals with CFL may be maximised. To improve visual ability of individuals with CFL, it is important to be able to accurately measure the outcome of any intervention. Various methods for determining visual function were therefore compared with perceived visual performance (as measured with a quality of life questionnaire) before and after surgical removal of choroidal new vessels (CNV) in macular disease patients. The results highlight the importance of low contrast measures (low contrast visual acuity and contrast sensitivity) when investigating perceived reading performance. Reading speed was found to be important for reflecting changes in general visual quality of life. Potential causes for reduced peripheral reading ability were investigated using both normally sighted and CFL subjects. For normally sighted subjects reading eccentrically with rapid serial visual presentation (RSVP) text, the inferior visual field was a better position (in terms of reading speed) for the presentation of the text. The size of the visual span was found to reduce with increasing eccentricity of fixation, providing a potential reason for reduced peripheral reading performances. The investigation of the ability to use context when reading with peripheral retina resulted in conflicting results. Studies in this thesis found both a reduction and no reduction in the ability of the peripheral retina to utilise context compared to the fovea. Individuals with long-term CFL showed no improvement in peripheral reading ability over that found for normally sighted subjects reading at the same eccentricity.

The effect of intraocular scattered light on the contrast sensitivity function

Intraocular light scatter is high in certain subject groups eg the elderly, due to increased optical media turbidity, which scatters and attenuates light travelling towards the retina. This causes reduced retinal contrast especially in the presence of glare light. Such subjects have depressed Contrast Sensitivity Functions (CSF). Currently available clinical tests do not effectively reflect this visual disability. Intraocular light scatter may be quantified by measuring the CSF with and without glare light and calculating Light Scatter Factors (LSF). To record the CSF on clinically available equipment (Nicolet CS2000), several psychophysical measurement techniques were investigated, and the 60 sec Method of Increasing Contrast was selected as the most appropriate. It was hypothesised that intraocular light scatter due to particles of different dimensions could be identified by glare sources at wide (30°) and narrow (3.5°) angles. CSFs andLSFs were determined for: (i) Subjects in young, intermediate and old age groups. (ii) Subjects during recovery from large amounts of induced corneal oedema. (iii) A clinical sample of contact lens (CL) wearers with a group of matched controls. The CSF was attenuated at all measured spatial frequencies with the intermediate and old group compared to the young group. High LSF values were found only in the old group (over 60 years). It was concluded that CSF attenuation in the intermediate group was due to reduced pupil size, media absorption and/or neural factors. In the old group, the additional factor was high intraocular light scatter levels of lenticular origin. The rate of reduction of the LSF for the 3.5° glare angle was steeper than that for the 30° angle, following induced corneal oedema. This supported the hypothesis, as it was anticipated that epithelial oedema would recover more rapidly than stromal oedema. CSFs and LSFs were markedly abnormal in the CL wearers. The analytical details and the value of these investigative techniques in contact lens research are discussed.

The investigation of the sensitivity gradient of the visual field, as a function of stimulus dynamic range, in the normal and abnormal eye

The study utilized the advanced technology provided by automated perimeters to investigate the hypothesis that patients with retinitis pigmentosa behave atypically over the dynamic range and to concurrently determine the influence of extraneous factors on the format of the normal perimetric sensitivity profile. The perimetric processing of some patients with retinitis pigmentosa was considered to be abnormal in either the temporal and/or the spatial domain. The standard size III stimulus saturated the central regions and was thus ineffective in detecting early depressions in sensitivity in these areas. When stimulus size was scaled in inverse proportion to the square root of ganglion cell receptive field density (M-scaled), isosensitive profiles did not result, although cortical representation was theoretically equivalent across the visual field. It was conjectured that this was due to variations in the ganglion cell characteristics with increasing peripheral angle, most notably spatial summation. It was concluded that the development of perimetric routines incorporating stimulus sizes adjusted in proportion to the coverage factor of retinal ganglion cells would enhance the diagnostic capacity of perimetry. Good general and local correspondence was found between perimetric sensitivity and the available retinal cell counts. Intraocular light scatter arising both from simulations and media opacities depressed perimetric sensitivity. Attenuation was greater centrally for the smaller LED stimuli, whereas the reverse was true for the larger projected stimuli. Prior perimetric experience and pupil size also demonstrated eccentricity-dependent effect on sensitivity. Practice improved perimetric sensitivity for projected stimuli at eccentricities greater than or equal to 30o; particularly in the superior region. Increase in pupil size for LED stimuli enhanced sensitivity at eccentricities greater than 10o. Conversely, microfluctuation in the accommodative response during perimetric examination and the correction of peripheral refractive error had no significant influence on perimetric sensitivity.

The slope of the psychometric function and non-stationarity of thresholds in spatiotemporal contrast vision

The slope of the two-interval, forced-choice psychometric function (e.g. the Weibull parameter, ß) provides valuable information about the relationship between contrast sensitivity and signal strength. However, little is known about how or whether ß varies with stimulus parameters such as spatiotemporal frequency and stimulus size and shape. A second unresolved issue concerns the best way to estimate the slope of the psychometric function. For example, if an observer is non-stationary (e.g. their threshold drifts between experimental sessions), ß will be underestimated if curve fitting is performed after collapsing the data across experimental sessions. We measured psychometric functions for 2 experienced observers for 14 different spatiotemporal configurations of pulsed or flickering grating patches and bars on each of 8 days. We found ß ˜ 3 to be fairly constant across almost all conditions, consistent with a fixed nonlinear contrast transducer and/or a constant level of intrinsic stimulus uncertainty (e.g. a square law transducer and a low level of intrinsic uncertainty). Our analysis showed that estimating a single ß from results averaged over several experimental sessions was slightly more accurate than averaging multiple estimates from several experimental sessions. However, the small levels of non-stationarity (SD ˜ 0.8 dB) meant that the difference between the estimates was, in practice, negligible.

A case-study investigating the physicochemical characteristics that dictate the function of a liposomal adjuvant

A range of particulate delivery systems have been considered as vaccine adjuvants. Of these systems, liposomes offer a range of advantages including versatility and flexibility in design format and their ability to incorporate a range of immunomodulators and antigens. Here we briefly outline research, from within our laboratories, which focused on the systematic evaluation of cationic liposomes as vaccines adjuvants. Our aim was to identify physicochemical characteristics that correlate with vaccine efficacy, with particular consideration of the interlink between depot-forming action and immune responses. A variety of parameters were investigated and over a range of studies we have confirmed that cationic liposomes, based on dimethyldioctadecylammonium bromide and trehalose 6,6'-dibehenate formed a depot at the injection site, which stimulates recruitment of antigen presenting cells to the injection site and promotes strong humoral and cell-mediated immune responses. Physicochemical factors which promote a strong vaccine depot include the combination of a high cationic charge and electrostatic binding of the antigen to the liposome system and the use of lipids with high transition temperatures, which form rigid bilayer vesicles. Reduction in vesicle size of cationic vesicles did not promote enhanced drainage from the injection site. However, reducing the cationic nature through substitution of the cationic lipid for a neutral lipid, or by masking of the charge using PEGylation, resulted in a reduced depot formation and reduced Th1-type immune responses, while Th2-type responses were less influenced. These studies confirm that the physicochemical characteristics of particulate-based adjuvants play a key role in the modulation of immune responses.

Paternal low protein diet affects adult offspring cardiovascular and metabolic function in mice

Although the association between maternal periconceptional diet and adult offspring health is well characterised, our understanding of the impact of paternal nutrition at the time of conception on offspring phenotype remains poorly defined. Therefore, we determined the effect of a paternal preconception low protein diet (LPD on adult offspring cardiovascular and metabolic health in mice. Male C57BL/6 mice were fed either normal protein diet (NPD; 18% casein or LPD (9% casein for 7 wk before mating. At birth, a reduced male-to-female ratio (P = 0.03 and increased male offspring weight (P = 0.009 were observed in litters from LPD compared with NPD stud males with no differences in mean litter size. LPD offspring were heavier than NPD offspring at 2 and 3 wk of age (P <0.02. However, no subsequent differences in body weight were observed. Adult male offspring derived from LPD studs developed relative hypotension (decreased by 9.2 mmHg and elevated heart rate (P <0.05, whereas both male and female offspring displayed vascular dysfunction and impaired glucose tolerance relative to NPD offspring. At cull (24 wk, LPD males had elevated adiposity (P = 0.04, reduced heart-to-body weight ratio (P = 0.04, and elevated circulating TNF-α levels (P = 0.015 compared with NPD males. Transcript expression in offspring heart and liver tissue was reduced for genes involved in calcium signaling (Adcy, Plcb, Prkcb and metabolism (Fto in LPD offspring (P <0.03. These novel data reveal the impact of suboptimal paternal nutrition on adult offspring cardiovascular and metabolic homeostasis, and provide some insight into the underlying regulatory mechanisms.