Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Technical note : a technique for measuring the surface area of articular cartilage in acetabular fractures

The aim of this study was to develop a reliable technique for measuring the area of a curved surface from an axial computed tomography (CT) scan and to apply this clinically in the measurement of articular cartilage surface area in acetabular fractures. The method used was a triangulation algorithm. In order to determine the accuracy of the technique, areas of hemispheres of known size were measured to give the percentage error in area measurement. Seven such hemispheres were machined into a Perspex block and their area measured geometrically, and also from CT scans by means of the triangulation algorithm. Scans of 1, 2 and 4 mm slice thickness and separation were used. The error varied with slice thickness and hemisphere diameter. It was shown that the 2 mm slice thickness provides the most accurate area measurement, while 1 mm cuts overestimate and 4 mm cuts underestimate the area. For a hemisphere diameter of 5 cm, which is of similar size to the acetabulum, the error was -11.2% for 4 mm cuts, +4.2% for 2 mm cuts and + 5.1% for 1 mm cuts. As expected, area measurement was more accurate for larger hemispheres. This method can be applied clinically to quantify acetabular fractures by measuring the percentage area of intact articular cartilage. In the case of both column fractures, the percentage area of secondary congruence can be determined. This technique of quantifying acetabular fractures has a potential clinical application as a prognostic factor and an indication for surgery in the long term.

Defining standards for modelling the biomechanics of the foot and ankle : a systematic review

The complex interaction of the bones of the foot has been explored in detail in recent years, which has led to the acknowledgement in the biomechanics community that the foot can no longer be considered as a single rigid segment. With the advance of motion analysis technology it has become possible to quantify the biomechanics of simplified units or segments that make up the foot. Advances in technology coupled with reducing hardware prices has resulted in the uptake of more advanced tools available for clinical gait analysis. The increased use of these techniques in clinical practice requires defined standards for modelling and reporting of foot and ankle kinematics. This systematic review aims to provide a critical appraisal of commonly used foot and ankle marker sets designed to assess kinematics and thus provide a theoretical background for the development of modelling standards.

A Systematic Review of kinematic models used in foot & ankle biomechanics

Over the past decade our understanding of foot function has increased significantly[1,2]. Our understanding of foot and ankle biomechanics appears to be directly correlated to advances in models used to assess and quantify kinematic parameters in gait. These advances in models in turn lead to greater detail in the data. However, we must consider that the level of complexity is determined by the question or task being analysed. This systematic review aims to provide a critical appraisal of commonly used marker sets and foot models to assess foot and ankle kinematics in a wide variety of clinical and research purposes.

Defining standards for modelling the biomechanics of the foot and ankle: A systematic review

The complex interaction of the bones of the foot has been explored in detail in recent years, which has led to the acknowledgement in the biomechanics community that the foot can no longer be considered as a single rigid segment. With the advance of motion analysis technology it has become possible to quantify the biomechanics of simplified units or segments that make up the foot. Advances in technology coupled with reducing hardware prices has resulted in the uptake of more advanced tools available for clinical gait analysis. The increased use of these techniques in clinical practice requires defined standards for modelling and reporting of foot and ankle kinematics. This systematic review aims to provide a critical appraisal of commonly used foot and ankle marker sets designed to assess kinematics and thus provide a theoretical background for the development of modelling standards.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

Outcomes following operative and non-operative management of humeral midshaft fractures: a prospective, observational cohort study of 47 patients

Background Although the non-operative management of closed humeral midshaft fractures has been advocated for years, the increasing popularity of operative intervention has left the optimal treatment choice unclear. Objective To compare the outcomes of operative and non-operative treatment of traumatic closed humeral midshaft fractures in adult patients. Methods A multicentre prospective comparative cohort study across 20 centres was conducted. Patients with AO type 12 A2, A3 and B2 fractures were treated with a functional brace or a retrograde-inserted unreamed humeral nail. Follow-up measurements were taken at 6, 12 and 52 weeks after the injury. The primary outcome was fracture healing after 1 year. Secondary outcomes included sub-items of the Constant score, general patient satisfaction, complications and cost-effectiveness parameters. Functions of the uninjured extremity were used as reference parameters. Intention-to-treat analysis was applied with the use of t-tests, Fisher’s exact tests, Mann–Whitney U-tests and adjusted analysis of variance (ANOVA). Results Forty-seven patients were included. The patient sample consisted of 23 women and 24 men, with a mean age of 52.7 years (range 17–86 years). Of the 47 cases, 14 were treated non-operatively and 33 operatively. The follow-up rate at 1 year was 81%. After 1 year, 11 fractures (100%) healed in the non-operative group and at least 24 fractures (≥89%) healed in the operative group [1 non-union patient (4%) and no data for 2 patients (7%)]. There were no significant differences in pain, range of motion (ROM) of the shoulder and elbow, and return to work after 6 weeks, 12 weeks and 1 year. Although operatively treated patients showed significantly greater shoulder abduction strength (p = 0.036), elbow flexion strength (p = 0.021), functional hand positioning (p = 0.008) and return to recreational activities (p = 0.043) after 6 weeks, no statistically significant differences existed in any outcome measure at the 1-year follow-up. Conclusions Our findings indicate that the non-operative management of humeral midshaft fractures can be expected to have similar functional outcomes and patient satisfaction at 1 year, despite an early benefit to operative treatment. If no radiological evidence of fracture healing exists in non-operatively treated patients during early follow-up, a switch to surgical treatment results in good functional outcomes and patient satisfaction. Keywords: Humeral shaft fracture, Non-operative treatment, Functional brace, Operative treatment, Unreamed humeral nail (UHN), Prospective, Cohort study

Life impact of ankle fractures : qualitative analysis of patient and clinician experiences

Background: Ankle fractures are one of the more commonly occurring forms of trauma managed by orthopaedic teams worldwide. The impacts of these injuries are not restricted to pain and disability caused at the time of the incident, but may also result in long term physical, psychological, and social consequences. There are currently no ankle fracture specific patient-reported outcome measures with a robust content foundation. This investigation aimed to develop a thematic conceptual framework of life impacts following ankle fracture from the experiences of people who have suffered ankle fractures as well as the health professionals who treat them. Methods: A qualitative investigation was undertaken using in-depth semi-structured interviews with people (n=12) who had previously sustained an ankle fracture (patients) and health professionals (n=6) that treat people with ankle fractures. Interviews were audio-recorded and transcribed. Each phrase was individually coded and grouped in categories and aligned under emerging themes by two independent researchers. Results: Saturation occurred after 10 in-depth patient interviews. Time since injury for patients ranged from 6 weeks to more than 2 years. Experience of health professionals ranged from 1 year to 16 years working with people with ankle fractures. Health professionals included an Orthopaedic surgeon (1), physiotherapists (3), a podiatrist (1) and an occupational therapist (1). The emerging framework derived from patient data included eight themes (Physical, Psychological, Daily Living, Social, Occupational and Domestic, Financial, Aesthetic and Medication Taking). Health professional responses did not reveal any additional themes, but tended to focus on physical and occupational themes. Conclusions: The nature of life impact following ankle fractures can extend beyond short term pain and discomfort into many areas of life. The findings from this research have provided an empirically derived framework from which a condition-specific patient-reported outcome measure can be developed.

Underground power cable environment on-line monitoring and analysis

Knowledge of cable parameters has been well established but a better knowledge of the environment in which the cables are buried lags behind. Research in Queensland University of Technology has been aimed at obtaining and analysing actual daily field values of thermal resistivity and diffusivity of the soil around power cables. On-line monitoring systems have been developed and installed with a data logger system and buried spheres that use an improved technique to measure thermal resistivity and diffusivity over a short period. Results based on long term continuous field data are given. A probabilistic approach is developed to establish the correlation between the measured field thermal resistivity values and rainfall data from weather bureau records. This data from field studies can reduce the risk in cable rating decisions and provide a basis for reliable prediction of “hot spot” of an existing cable circuit

Probabilistic cable rating based on cable thermal environment studying

This paper describes a new approach to establish the probabilistic cable rating based on cable thermal environment studies. Knowledge of cable parameters has been well established. However the environment in which the cables are buried is not so well understood. Research in Queensland University of Technology has been aimed at obtaining and analysing actual daily field values of thermal resistivity and diffusivity of the soil around power cables. On-line monitoring systems have been developed and installed with a data logger system and buried spheres that use an improved technique to measure thermal resistivity and diffusivity over a short period. Based on the long-term continuous field data for more than 4 years, a probabilistic approach is developed to establish the correlation between the measured field thermal resistivity values and rainfall data from weather bureau records. Hence, a probabilistic cable rating can be established based on monthly probabilistic distribution of thermal resistivity