Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

How critical is fibrous cap thickness to carotid plaque stability? A flow-plaque interaction model

Background and Purpose Acute cerebral ischemic events are associated with rupture of vulnerable carotid atheroma and subsequent thrombosis. Factors such as luminal stenosis and fibrous cap thickness have been thought to be important risk factors for plaque rupture. We used a flow-structure interaction model to simulate the interaction between blood flow and atheromatous plaque to evaluate the effect of the degree of luminal stenosis and fibrous cap thickness on plaque vulnerability. Methods A coupled nonlinear time-dependent model with a flow-plaque interaction simulation was used to perform flow and stress/strain analysis in a stenotic carotid artery model. The stress distribution within the plaque and the flow conditions within the vessel were calculated for every case when varying the fibrous cap thickness from 0.1 to 2 mm and the degree of luminal stenosis from 10% to 95%. A rupture stress of 300 kPa was chosen to indicate a high risk of plaque rupture. A 1-sample t test was used to compare plaque stresses with the rupture stress. Results High stress concentrations were found in the plaques in arteries with >70% degree of stenosis. Plaque stresses in arteries with 30% to 70% stenosis increased exponentially as fibrous cap thickness decreased. A decrease of fibrous cap thickness from 0.4 to 0.2 mm resulted in an increase of plaque stress from 141 to 409 kPa in a 40% degree stenotic artery. Conclusions There is an increase in plaque stress in arteries with a thin fibrous cap. The presence of a moderate carotid stenosis (30% to 70%) with a thin fibrous cap indicates a high risk for plaque rupture. Patients in the future may be risk stratified by measuring both fibrous cap thickness and luminal stenosis.

Power system stability implications from electromechanical wave propagation

Electromechanical wave propagation characterizes the first-swing dynamic response in a spatially delayed manner. This paper investigates the characteristics of this phenomenon in two-dimensional and one-dimensional power systems. In 2-D systems, the wave front expands as a ripple in a pond. In 1-D systems, the wave front is more concentrated, retains most of its magnitude, and travels like a pulse on a string. This large wave front is more impactful upon any weak link and easily causes transient instability in 1-D systems. The initial disturbance injects both high and low frequency components, but the lumped nature of realistic systems only permits the lower frequency components to propagate through. The kinetic energy split at a junction is equal to the generator inertia ratio in each branch in an idealized continuum system. This prediction is approximately valid in a realistic power system. These insights can enhance understanding and control of the traveling waves.

HealthMap: A cluster randomised trial of interactive health plans and self-management support to prevent coronary heart disease in people with HIV

Background The leading causes of morbidity and mortality for people in high-income countries living with HIV are now non-AIDS malignancies, cardiovascular disease and other non-communicable diseases associated with ageing. This protocol describes the trial of HealthMap, a model of care for people with HIV (PWHIV) that includes use of an interactive shared health record and self-management support. The aims of the HealthMap trial are to evaluate engagement of PWHIV and healthcare providers with the model, and its effectiveness for reducing coronary heart disease risk, enhancing self-management, and improving mental health and quality of life of PWHIV. Methods/Design The study is a two-arm cluster randomised trial involving HIV clinical sites in several states in Australia. Doctors will be randomised to the HealthMap model (immediate arm) or to proceed with usual care (deferred arm). People with HIV whose doctors are randomised to the immediate arm receive 1) new opportunities to discuss their health status and goals with their HIV doctor using a HealthMap shared health record; 2) access to their own health record from home; 3) access to health coaching delivered by telephone and online; and 4) access to a peer moderated online group chat programme. Data will be collected from participating PWHIV (n = 710) at baseline, 6 months, and 12 months and from participating doctors (n = 60) at baseline and 12 months. The control arm will be offered the HealthMap intervention at the end of the trial. The primary study outcomes, measured at 12 months, are 1) 10-year risk of non-fatal acute myocardial infarction or coronary heart disease death as estimated by a Framingham Heart Study risk equation; and 2) Positive and Active Engagement in Life Scale from the Health Education Impact Questionnaire (heiQ). Discussion The study will determine the viability and utility of a novel technology-supported model of care for maintaining the health and wellbeing of people with HIV. If shown to be effective, the HealthMap model may provide a generalisable, scalable and sustainable system for supporting the care needs of people with HIV, addressing issues of equity of access. Trial registration Universal Trial Number (UTN) U111111506489; ClinicalTrial.gov Id NCT02178930 submitted 29 June 2014

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.