Is length of experience an appropriate criterion to identify level of expertise?

Clinical experience plays an important role in the development of expertise, particularly when coupled with reflection on practice. There is debate, however, regarding the amount of clinical experience that is required to become an expert. Various lengths of practice have been suggested as suitable for determining expertise, ranging from five years to 15 years. This study aimed to investigate the association between length of experience and therapists’ level of expertise in the field of cerebral palsy with upper limb hypertonicity using an empirical procedure named Cochrane–Weiss–Shanteau (CWS). The methodology involved re-analysis of quantitative data collected in two previous studies. In Study 1, 18 experienced occupational therapists made hypothetical clinical decisions related to 110 case vignettes, while in Study 2, 29 therapists considered 60 case vignettes drawn randomly from those used in Study 1. A CWS index was calculated for each participant's case decisions. Then, in each study, Spearman's rho was calculated to identify the correlations between the duration of experience and level of expertise. There was no significant association between these two variables in both studies. These analyses corroborated previous findings of no association between length of experience and judgemental performance. Therefore, length of experience may not be an appropriate criterion for determining level of expertise in relation to cerebral palsy practice.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Pretreatment malnutrition and quality of life - association with prolonged length of hospital stay among patients with gynecological cancer: A cohort study

Background Length of hospital stay (LOS) is a surrogate marker for patients' well-being during hospital treatment and is associated with health care costs. Identifying pretreatment factors associated with LOS in surgical patients may enable early intervention in order to reduce postoperative LOS. Methods This cohort study enrolled 157 patients with suspected or proven gynecological cancer at a tertiary cancer centre (2004-2006). Before commencing treatment, the scored Patient Generated - Subjective Global Assessment (PG-SGA) measuring nutritional status and the Functional Assessment of Cancer Therapy-General (FACT-G) scale measuring quality of life (QOL) were completed. Clinical and demographic patient characteristics were prospectively obtained. Patients were grouped into those with prolonged LOS if their hospital stay was greater than the median LOS and those with average or below average LOS. Results Patients' mean age was 58 years (SD 14 years). Preoperatively, 81 (52%) patients presented with suspected benign disease/pelvic mass, 23 (15%) with suspected advanced ovarian cancer, 36 (23%) patients with suspected endometrial and 17 (11%) with cervical cancer, respectively. In univariate models prolonged LOS was associated with low serum albumin or hemoglobin, malnutrition (PG-SGA score and PG-SGA group B or C), low pretreatment FACT-G score, and suspected diagnosis of cancer. In multivariable models, PG-SGA group B or C, FACT-G score and suspected diagnosis of advanced ovarian cancer independently predicted LOS. Conclusions Malnutrition, low quality of life scores and being diagnosed with advanced ovarian cancer are the major determinants of prolonged LOS amongst gynecological cancer patients. Interventions addressing malnutrition and poor QOL may decrease LOS in gynecological cancer patients.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Axial length charges during accommodation in myopes and emmetropes

Purpose: To investigate the influence of accommodation upon axial length (and a comprehensive range of ocular biometric parameters), in populations of young adult myopic and emmetropic subjects. Methods: Forty young adult subjects had ocular biometry measured utilizing a non-contact optical biometer (Lenstar LS 900) based upon the principle of optical low coherence reflectometry, under three different accommodation demands (0 D, 3 D and 6 D). Subjects were classified as emmetropes (n=19) or myopes (n=21) based upon their spherical equivalent refraction (mean emmetropic refraction -0.05 ± 0.27DS and mean myopic refraction -1.82 ± 0.84 DS). Results: Axial length changed significantly with accommodation, with a mean increase of 11.9 ± 12.3 µm and 24.1 ± 22.7 µm for the 3 D and 6 D accommodation stimuli respectively. A significant axial elongation associated with accommodation was still evident even following correction of the axial length data for potential error due to lens thickness change. The mean ‘corrected’ increase in axial length was 5.2 ± 11.2 µm, and 7.4 ± 18.9 µm for the 3 D and 6 D stimuli respectively. There was no significant difference between the myopic and emmetropic populations in terms of the magnitude of change in axial length with accommodation, regardless of whether the data were corrected or not. A number of other ocular biometric parameters, such as anterior chamber depth, lens thickness and vitreous chamber depth also exhibited significant change with accommodation. The myopic and emmetropic populations also exhibited no significant difference in the magnitude of change in these parameters with accommodation. Conclusions: The eye undergoes a significant axial elongation associated with a brief period of accommodation, and the magnitude of this change in eye length increases for larger accommodation demands, however there is no significant difference in the magnitude of eye elongation in myopic and emmetropic subjects.

Sustained convergence, axial length, and corneal topography

Purpose: To investigate the influence of convergence on axial length and corneal topography in young adult subjects.---------- Methods: Fifteen emmetropic young adult subjects with normal binocular vision had axial length and corneal topography measured immediately before and after a 15-min period of base out (BO) prismatic spectacle lens wear. Two different magnitude prismatic spectacles were worn in turn (8 [DELTA] BO and 16 [DELTA] BO), and for both tasks, distance fixation was maintained for the duration of lens wear. Eight subjects returned on a separate day for further testing and had axial length measured before, during, and immediately after a 15-min convergence task.---------- Results: No significant change was found to occur in axial length either during or after the sustained convergence tasks (p > 0.6). Some small but significant changes in corneal topography were found to occur after sustained convergence. The most significant corneal change was observed after the 16 [DELTA] BO prism wear. The corneal refractive power spherocylinder power vector J0 was found to change by a small (mean change of 0.03 D after the 16 [DELTA] BO task) but statistically significant (p = 0.03) amount as a result of the convergence task (indicative of a reduction in with-the-rule corneal astigmatism after convergence). Corneal axial power was found to exhibit a significant flattening in superior regions. Conclusions: Axial length appears largely unchanged by a period of sustained convergence. However, small but significant changes occur in the topography of the cornea after convergence.

Human optical axial length and defocus

Purpose: To investigate the short term influence of imposed monocular defocus upon human optical axial length (the distance from anterior cornea to retinal pigment epithelium) and ocular biometrics. Methods: Twenty-eight young adult subjects (14 myopes and 14 emmetropes) had eye biometrics measured before and then 30 and 60 minutes after exposure to monocular (right eye) defocus. Four different monocular defocus conditions were tested, each on a separate day: control (no defocus), myopic (+3 D defocus), hyperopic (-3 D defocus) and diffuse (0.2 density Bangerter filter) defocus. The fellow eye was optimally corrected (no defocus). Results: Imposed defocus caused small but significant changes in optical axial length (p<0.0001). A significant increase in optical axial length (mean change +8 ± 14 μm, p=0.03) occurred following hyperopic defocus, and a significant reduction in optical axial length (mean change -13 ± 14 μm, p=0.0001) was found following myopic defocus. A small increase in optical axial length was observed following diffuse defocus (mean change +6 ± 13 μm, p=0.053). Choroidal thickness also exhibited some significant changes with certain defocus conditions. No significant difference was found between myopes and emmetropes in the changes in optical axial length or choroidal thickness with defocus. Conclusions: Significant changes in optical axial length occur in human subjects following 60 minutes of monocular defocus. The bi-directional optical axial length changes observed in response to defocus implies the human visual system is capable of detecting the presence and sign of defocus and altering optical axial length to move the retina towards the image plane.

Water drinking influences eye length and IOP in young healthy subjects

This study aimed to investigate the influence of water loading upon intraocular pressure (IOP), ocular pulse amplitude (OPA) and axial length. Twenty one young adult subjects who were classified based on their spherical equivalent refraction as either myopes (n=11), or emmetropes (n=10) participated. Measures of IOP, OPA and ocular biometrics were collected before, and then 10, 15, 25 and 30 minutes following the ingestion of 1000 ml of water. Significant increases in both IOP and OPA were found to occur following water loading (p<0.0001), with peaks in both parameters occurring at 10 minutes after water loading (mean ± SEM increase of 2.24 ± 0.31 mmHg in IOP and 0.46 ± 0.06 mmHg in OPA). Axial length was found to reduce significantly following water loading (p=0.0005), with the largest reduction in axial length evident 10 minutes after water drinking (mean decrease 12 ± 3 µm). A significant time by refractive error group interaction (p=0.048) was found in axial length, indicative of a different pattern of change in eye length following water loading between the myopic and emmetropic populations. The largest difference in axial length change was evident at 10 minutes after water loading with a 17 ± 5 µm reduction in axial length evident in the myopes and only a 6 ± 2 µm reduction in the emmetropes. These findings illustrate significant changes in ocular parameters in young adult subjects following water loading.