Loading applied on prosthetic knee of transfemoral amputee: comparison of inverse dynamics and direct measurements

Inverse dynamics is the most comprehensive method that gives access to the net joint forces and moments during walking. However it is based on assumptions (i.e., rigid segments linked by ideal joints) and it is known to be sensitive to the input data (e.g., kinematic derivatives, positions of joint centres and centre of pressure, inertial parameters). Alternatively, transducers can be used to measure directly the load applied on the residuum of transfemoral amputees. So, the purpose of this study was to compare the forces and moments applied on a prosthetic knee measured directly with the ones calculated by three inverse dynamics computations - corresponding to 3 and 2 segments, and « ground reaction vector technique » - during the gait of one patient. The maximum RMSEs between the estimated and directly measured forces (i.e., 56 N) and moment (i.e., 5 N.m) were relatively small. However the dynamic outcomes of the prosthetic components (i.e., absorption of the foot, friction and limit stop of the knee) were only partially assessed with inverse dynamic methods.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Velocity and Concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller. Both the mean axial velocity profile and the mean concentration profile showed self-similarity. Further, the stand deviation growth curve was linear. The effects of propeller speed and dye release location were also investigated.

Application of bag sampling technique for particle size distribution measurements

Bag sampling techniques can be used to temporarily store an aerosol and therefore provide sufficient time to utilize sensitive but slow instrumental techniques for recording detailed particle size distributions. Laboratory based assessment of the method were conducted to examine size dependant deposition loss coefficients for aerosols held in VelostatTM bags conforming to a horizontal cylindrical geometry. Deposition losses of NaCl particles in the range of 10 nm to 160 nm were analysed in relation to the bag size, storage time, and sampling flow rate. Results of this study suggest that the bag sampling method is most useful for moderately short sampling periods of about 5 minutes.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Repeatability and validity of lens densitometry measured with Scheimpflug imaging

Purpose To assess the repeatability and validity of lens densitometry derived from the Pentacam Scheimpflug imaging system. Setting Eye Clinic, Queensland University of Technology, Brisbane, Australia. Methods This prospective cross-sectional study evaluated 1 eye of subjects with or without cataract. Scheimpflug measurements and slitlamp and retroillumination photographs were taken through a dilated pupil. Lenses were graded with the Lens Opacities Classification System III. Intraobserver and interobserver reliability of 3 observers performing 3 repeated Scheimpflug lens densitometry measurements each was assessed. Three lens densitometry metrics were evaluated: linear, for which a line was drawn through the visual axis and a mean lens densitometry value given; peak, which is the point at which lens densitometry is greatest on the densitogram; 3-dimensional (3D), in which a fixed, circular 3.0 mm area of the lens is selected and a mean lens densitometry value given. Bland and Altman analysis of repeatability for multiple measures was applied; results were reported as the repeatability coefficient and relative repeatability (RR). Results Twenty eyes were evaluated. Repeatability was high. Overall, interobserver repeatability was marginally lower than intraobserver repeatability. The peak was the least reliable metric (RR 37.31%) and 3D, the most reliable (RR 5.88%). Intraobserver and interobserver lens densitometry values in the cataract group were slightly less repeatable than in the noncataract group. Conclusion The intraobserver and interobserver repeatability of Scheimpflug lens densitometry was high in eyes with cataract and eyes without cataract, which supports the use of automated lens density scoring using the Scheimpflug system evaluated in the study

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

New insights into appetite, inflammation and the use of fish oil in hemodialysis patients

Protein-energy wasting (PEW) is commonly seen in patients with chronic kidney disease (CKD). The condition is characterised by chronic, systemic low-grade inflammation which affects nutritional status by a variety of mechanisms including reducing appetite and food intake and increasing muscle catabolism. PEW is linked with co-morbidities such as cardiovascular disease, and is associated with lower quality of life, increased hospitalisations and a 6-fold increase in risk of death1. Significant gender differences have been found in the severity and effects of several markers of PEW. There have been limited studies testing the ability of anti-inflammatory agents or nutritional interventions to reduce the effects of PEW in dialysis patients. This thesis makes a significant contribution to the understanding of PEW in dialysis patients. It advances understanding of measurement techniques for two of the key components, appetite and inflammation, and explores the effect of fish oil, an anti-inflammatory agent, on markers of PEW in dialysis patients. The first part of the thesis consists of two methodological studies conducted using baseline data. The first study aims to validate retrospective ratings of hunger, desire to eat and fullness on visual analog scales (VAS) (paper and pen and electronic) as a new method of measuring appetite in dialysis patients. The second methodological study aims to assess the ability of a variety of methods available in routine practice to detect the presence of inflammation. The second part of the thesis aims to explore the effect of 12 weeks supplementation with 2g per day of Eicosapentaenoic Acid (EPA), a longchain fatty acid found in fish oil, on markers of PEW. A combination of biomarkers and psychomarkers of appetite and inflammation are the main outcomes being explored, with nutritional status, dietary intake and quality of life included as secondary outcomes. A lead in phase of 3 months prior to baseline was used so that each person acts as their own historical control. The study also examines whether there are gender differences in response to the treatment. Being an exploratory study, an important part of the work is to test the feasibility of the intervention, thus the level of adherence and factors associated with adherence are also presented. The studies were conducted at the hemodialysis unit of the Wesley Hospital. Participants met the following criteria: adult, stage 5 CKD on hemodialysis for at least 3 months, not expected to receive a transplant or switch to another dialysis modality during the study, absence of intellectual impairment or mental illness impairing ability to follow instructions or complete the intervention. A range of intermediate, clinical and patient-centred outcome measures were collected at baseline and 12 weeks. Inflammation was measured using five biomarkers: c-reactive protein (CRP), interleukin-6 (IL6), intercellular adhesion molecule (sICAM-1), vascular cell adhesion molecule (sVCAM-1) and white cell count (WCC). Subjective appetite was measured using the first question from the Appetite and Dietary Assessment (ADAT) tool and VAS for measurements of hunger, desire to eat and fullness. A novel feature of the study was the assessment of the appetite peptides leptin, ghrelin and peptide YY as biomarkers of appetite. Nutritional status/inflammation was assessed using the Malnutrition-Inflammation Score (MIS) and the Patient-Generated Subjective Global Assessment (PG-SGA). Dietary intake was measured using 3-day records. Quality of life was measured using the Kidney Disease Quality of Life Short Form version 1.3 (KDQOL-SF™ v1.3 © RAND University), which combines the Short-Form 36 (SF36) with a kidney-disease specific module2. A smaller range of these variables was available for analysis during the control phase (CRP, ADAT, dietary intake and nutritional status). Statistical analysis was carried out using SPSS version 14 (SPSS Inc, Chicago IL, USA). Analysis of the first part of the thesis involved descriptive and bivariate statistics, as well as Bland-Altman plots to assess agreement between methods, and sensitivity analysis/ROC curves to test the ability of methods to predict the presence of inflammation. The unadjusted (paired ttests) and adjusted (linear mixed model) change over time is presented for the main outcome variables of inflammation and appetite. Results are shown for the whole group followed by analyses according to gender and adherence to treatment. Due to the exploratory nature of the study, trends and clinical significance were considered as important as statistical significance. Twenty-eight patients (mean age 61±17y, 50% male, dialysis vintage 19.5 (4- 101) months) underwent baseline assessment. Seven out of 28 patients (25%) reported sub-optimal appetite (self-reported as fair, poor or very poor) despite all being well nourished (100% SGA A). Using the VAS, ratings of hunger, but not desire to eat or fullness, were significantly (p<0.05) associated with a range of relevant clinical variables including age (r=-0.376), comorbidities (r=-0.380) nutritional status (PG-SGA score, r=-0.451), inflammatory markers (CRP r=-0.383; sICAM-1 r=-0.387) and seven domains of quality of life. Patients expressed a preference for the paper and pen method of administering VAS. None of the tools (appetite, MIS, PG-SGA, albumin or iron) showed an acceptable ability to detect patients who are inflamed. It is recommended that CRP should be tested more frequently as a matter of course rather than seeking alternative methods of measuring inflammation. 27 patients completed the 12 week intervention. 20 patients were considered adherent based on changes in % plasma EPA, which rose from 1.3 (0.94)% to 5.2 (1.1)%, p<0.001, in this group. The major barriers to adherence were forgetting to take the tablets as well as their size. At 12 weeks, inflammatory markers remained steady apart from the white cell count which decreased (7.6(2.5) vs 7.0(2.2) x109/L, p=0.058) and sVCAM-1 which increased (1685(654) vs 2249(925) ng/mL, p=0.001). Subjective appetite using VAS increased (51mm to 57mm, +12%) and there was a trend towards reduction in peptide YY (660(31) vs 600(30) pg/mL, p=0.078). There were some gender differences apparent, with the following adjusted change between baseline and week 12: CRP (males -3% vs females +17%, p=0.19), IL6 (males +17% vs females +48%, p=0.77), sICAM-1 (males -5% vs females +11%, p=0.07), sVCAM-1 (males +54% vs females +19%, p=0.08) and hunger ratings (males 20% vs females -5%, p=0.18). On balance, males experienced a maintainence or reduction in three inflammatory markers and an improvement in hunger ratings, and therefore appeared to have responded better to the intervention. Compared to those who didn’t adhere, adherent patients maintained weight (mean(SE) change: +0.5(1.6) vs - 0.8(1.2) kg, p=0.052) and fat-free mass (-0.1 (1.6) vs -1.8 (1.8) kg, p=0.045). There was no difference in change between the intervention and control phase for CRP, appetite, nutritional status or dietary intake. The thesis makes a significant contribution to the evidence base for understanding of PEW in dialysis patients. It has advanced knowledge of methods of assessing inflammation and appetite. Retrospective ratings of hunger on a VAS appear to be a valid method of assessing appetite although samples which include patients with very poor appetite are required to confirm this. Supplementation with fish oil appeared to improve subjective appetite and dampen the inflammatory response. The effectiveness of the intervention is influenced by gender and adherence. Males appear to be more responsive to the primary outcome variables than females, and the quality of response is improved with better adherence. These results provide evidence to support future interventions aimed at reducing the effects of PEW in dialysis patients.

Determining a set of surrogate parameters to evaluate urban stormwater quality

This thesis details methodology to estimate urban stormwater quality based on a set of easy to measure physico-chemical parameters. These parameters can be used as surrogate parameters to estimate other key water quality parameters. The key pollutants considered in this study are nitrogen compounds, phosphorus compounds and solids. The use of surrogate parameter relationships to evaluate urban stormwater quality will reduce the cost of monitoring and so that scientists will have added capability to generate a large amount of data for more rigorous analysis of key urban stormwater quality processes, namely, pollutant build-up and wash-off. This in turn will assist in the development of more stringent stormwater quality mitigation strategies. The research methodology was based on a series of field investigations, laboratory testing and data analysis. Field investigations were conducted to collect pollutant build-up and wash-off samples from residential roads and roof surfaces. Past research has identified that these impervious surfaces are the primary pollutant sources to urban stormwater runoff. A specially designed vacuum system and rainfall simulator were used in the collection of pollutant build-up and wash-off samples. The collected samples were tested for a range of physico-chemical parameters. Data analysis was conducted using both univariate and multivariate data analysis techniques. Analysis of build-up samples showed that pollutant loads accumulated on road surfaces are higher compared to the pollutant loads on roof surfaces. Furthermore, it was found that the fraction of solids smaller than 150 ìm is the most polluted particle size fraction in solids build-up on both roads and roof surfaces. The analysis of wash-off data confirmed that the simulated wash-off process adopted for this research agrees well with the general understanding of the wash-off process on urban impervious surfaces. The observed pollutant concentrations in wash-off from road surfaces were different to pollutant concentrations in wash-off from roof surfaces. Therefore, firstly, the identification of surrogate parameters was undertaken separately for roads and roof surfaces. Secondly, a common set of surrogate parameter relationships were identified for both surfaces together to evaluate urban stormwater quality. Surrogate parameters were identified for nitrogen, phosphorus and solids separately. Electrical conductivity (EC), total organic carbon (TOC), dissolved organic carbon (DOC), total suspended solids (TSS), total dissolved solids (TDS), total solids (TS) and turbidity (TTU) were selected as the relatively easy to measure parameters. Consequently, surrogate parameters for nitrogen and phosphorus were identified from the set of easy to measure parameters for both road surfaces and roof surfaces. Additionally, surrogate parameters for TSS, TDS and TS which are key indicators of solids were obtained from EC and TTU which can be direct field measurements. The regression relationships which were developed for surrogate parameters and key parameter of interest were of a similar format for road and roof surfaces, namely it was in the form of simple linear regression equations. The identified relationships for road surfaces were DTN-TDS:DOC, TP-TS:TOC, TSS-TTU, TDS-EC and TSTTU: EC. The identified relationships for roof surfaces were DTN-TDS and TSTTU: EC. Some of the relationships developed had a higher confidence interval whilst others had a relatively low confidence interval. The relationships obtained for DTN-TDS, DTN-DOC, TP-TS and TS-EC for road surfaces demonstrated good near site portability potential. Currently, best management practices are focussed on providing treatment measures for stormwater runoff at catchment outlets where separation of road and roof runoff is not found. In this context, it is important to find a common set of surrogate parameter relationships for road surfaces and roof surfaces to evaluate urban stormwater quality. Consequently DTN-TDS, TS-EC and TS-TTU relationships were identified as the common relationships which are capable of providing measurements of DTN and TS irrespective of the surface type.