Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Exploring non-cancer pain conditions in a community sample : critiquing a current conceptual model of the acute to chronic pain transition and examining predictors of chronicity

This program of research examines the experience of chronic pain in a community sample. While, it is clear that like patient samples, chronic pain in non-patient samples is also associated with psychological distress and physical disability, the experience of pain across the total spectrum of pain conditions (including acute and episodic pain conditions) and during the early course of chronic pain is less clear. Information about these aspects of the pain experience is important because effective early intervention for chronic pain relies on identification of people who are likely to progress to chronicity post-injury. A conceptual model of the transition from acute to chronic pain was proposed by Gatchel (1991a). In brief, Gatchel’s model describes three stages that individuals who have a serious pain experience move through, each with worsening psychological dysfunction and physical disability. The aims of this program of research were to describe the experience of pain in a community sample in order to obtain pain-specific data on the problem of pain in Queensland, and to explore the usefulness of Gatchel’s Model in a non-clinical sample. Additionally, five risk factors and six protective factors were proposed as possible extensions to Gatchel’s Model. To address these aims, a prospective longitudinal mixed-method research design was used. Quantitative data was collected in Phase 1 via a comprehensive postal questionnaire. Phase 2 consisted of a follow-up questionnaire 3 months post-baseline. Phase 3 consisted of semi-structured interviews with a subset of the original sample 12 months post follow-up, which used qualitative data to provide a further in-depth examination of the experience and process of chronic pain from respondents’ point of view. The results indicate chronic pain is associated with high levels of anxiety and depressive symptoms. However, the levels of disability reported by this Queensland sample were generally lower than those reported by clinical samples and consistent with disability data reported in a New South Wales population-based study. With regard to the second aim of this program of research, while some elements of the pain experience of this sample were consistent with that described by Gatchel’s Model, overall the model was not a good fit with the experience of this non-clinical sample. The findings indicate that passive coping strategies (minimising activity), catastrophising, self efficacy, optimism, social support, active strategies (use of distraction) and the belief that emotions affect pain may be important to consider in understanding the processes that underlie the transition to and continuation of chronic pain.

Aberrations and pupil location under corneal topography and Hartmann-Shack illumination conditions

PURPOSE. This study was conducted to determine the magnitude of pupil center shift between the illumination conditions provided by corneal topography measurement (photopic illuminance) and by Hartmann-Shack aberrometry (mesopic illuminance) and to investigate the importance of this shift when calculating corneal aberrations and for the success of wavefront-guided surgical procedures. METHODS. Sixty-two subjects with emmetropia underwent corneal topography and Hartmann-Shack aberrometry. Corneal limbus and pupil edges were detected, and the differences between their respective centers were determined for both procedures. Corneal aberrations were calculated using the pupil centers for corneal topography and for Hartmann-Shack aberrometry. Bland-Altmann plots and paired t-tests were used to analyze the differences between corneal aberrations referenced to the two pupil centers. RESULTS. The mean magnitude (modulus) of the displacement of the pupil with the change of the illumination conditions was 0.21 ± 0.11 mm. The effect of this pupillary shift was manifest for coma corneal aberrations for 5-mm pupils, but the two sets of aberrations calculated with the two pupil positions were not significantly different. Sixty-eight percent of the population had differences in coma smaller than 0.05 µm, and only 4% had differences larger than 0.1 µm. Pupil displacement was not large enough to significantly affect other higher-order Zernike modes. CONCLUSIONS. Estimated corneal aberrations changed slightly between photopic and mesopic illumination conditions given by corneal topography and Hartmann-Shack aberrometry. However, this systematic pupil shift, according to the published tolerances ranges, is enough to deteriorate the optical quality below the theoretically predicted diffraction limit of wavefront-guided corneal surgery.

Driving performance in persons with hemianopia and quadrantanopia assessed under in-traffic conditions

Purpose: To evaluate the on-road driving performance of persons with homonymous hemianopia or quadrantanopia in comparison to age-matched controls with normal visual fields. Methods: Participants were 22 hemianopes and eight quadrantanopes (mean age 53 years) and 30 persons with normal visual fields (mean age 52 years) and were either current drivers or aiming to resume driving. All participants completed a battery of tests of vision (ETDRS visual acuity, Pelli-Robson letter contrast sensitivity, Humphrey visual fields), cognitive tests (trials A and B, Mini Mental State Examination, Digit Symbol Substitution) and an on-road driving assessment. Driving performance was assessed in a dual-brake vehicle with safety monitored by a certified driving rehabilitation specialist. Backseat evaluators masked to the clinical characteristics of participants independently rated driving performance along a 22.7 kilometre route involving urban and interstate driving. Results: Seventy-three per cent of the hemianopes, 88 per cent of quadrantanopes and all of the drivers with normal fields received safe driving ratings. Those hemianopic and quadrantanopic drivers rated as unsafe tended to have problems with maintaining appropriate lane position, steering steadiness and gap judgment compared to controls. Unsafe driving was associated with slower visual processing speed and impairments in contrast sensitivity, visual field sensitivity and executive function. Conclusions: Our findings suggest that some drivers with hemianopia or quadrantanopia are capable of safe driving performance, when compared to those of the same age with normal visual fields. This finding has important implications for the assessment of fitness to drive in this population.

Dynamics of in vitro polymer degradation of polycaprolactone-based scaffolds : accelerated versus simulated physiological conditions

The increasing use of biodegradable devices in tissue engineering and regenerative medicine means it is essential to study and understand their degradation behaviour. Accelerated degradation systems aim to achieve similar degradation profiles within a shorter period of time, compared with standard conditions. However, these conditions only partially mimic the actual situation, and subsequent analyses and derived mechanisms must be treated with caution and should always be supported by actual long-term degradation data obtained under physiological conditions. Our studies revealed that polycaprolactone (PCL) and PCL-composite scaffolds degrade very differently under these different degradation conditions, whilst still undergoing hydrolysis. Molecular weight and mass loss results differ due to the different degradation pathways followed (surface degradation pathway for accelerated conditions and bulk degradation pathway for simulated physiological conditions). Crystallinity studies revealed similar patterns of recrystallization dynamics, and mechanical data indicated that the scaffolds retained their functional stability, in both instances, over the course of degradation. Ultimately, polymer degradation was shown to be chiefly governed by molecular weight, crystallinity susceptibility to hydrolysis and device architecture considerations whilst maintaining its thermodynamic equilibrium.