Dramatically decreased high density lipoprotein cholesterol, increased remnant clearance, and insulin hypersensitivity in apolipoprotein A-II knockout mice suggest a complex role for apolipoprotein A-II in atherosclerosis susceptibility

Apolipoprotein (apo) A-II is the second most abundant apolipoprotein in high density lipoprotein (HDL). To study its role in lipoprotein metabolism and atherosclerosis susceptibility, apo A-II knockout mice were created. Homozygous knockout mice had 67% and 52% reductions in HDL cholesterol levels in the fasted and fed states, respectively, and HDL particle size was reduced. Metabolic turnover studies revealed the HDL decrease to be due to both decreased HDL cholesterol ester and apo A-I transport rate and increased HDL cholesterol ester and apo A-I fractional catabolic rate. The apo A-II deficiency trait was bred onto the atherosclerosis-prone apo E-deficient background, which resulted in a surprising 66% decrease in cholesterol levels due primarily to decreased atherogenic lipoprotein remnant particles. Metabolic turnover studies indicated increased remnant clearance in the absence of apo A-II. Finally, apo A-II deficiency was associated with lower free fatty acid, glucose, and insulin levels, suggesting an insulin hypersensitivity state. In summary, apo A-II plays a complex role in lipoprotein metabolism, with some antiatherogenic properties such as the maintenance of a stable HDL pool, and other proatherogenic properties such as decreasing clearance of atherogenic lipoprotein remnants and promotion of insulin resistance.

Exercise Training Reduces Liver Fat and Increases Rates of VLDL Clearance, but not VLDL Production in NAFLD

Context Randomised controlled trials in non-alcoholic fatty liver disease (NAFLD) have shown that regular exercise, even without calorie restriction, reduces liver steatosis. A previous study has shown that 16 weeks supervised exercise training in NAFLD did not affect total VLDL kinetics. Objective To determine the effect of exercise training on intrahepatocellular fat (IHCL) and the kinetics of large triglyceride-(TG)-rich VLDL1 and smaller denser VLDL2 which has a lower TG content. Design A 16 week randomised controlled trial. Patients 27 sedentary patients with NAFLD. Intervention Supervised exercise with moderate-intensity aerobic exercise or conventional lifestyle advice (control). Main outcome Very low density lipoprotein1 (VLDL1) and VLDL2-TG and apolipoproteinB (apoB) kinetics investigated using stable isotopes before and after the intervention. Results In the exercise group VO2max increased by 31±6% (mean±SEM) and IHCL decreased from 19.6% (14.8, 30.0) to 8.9% (5.4, 17.3) (median (IQR)) with no significant change in VO2max or IHCL in the control group (change between groups p<0.001 and p=0.02, respectively). Exercise training increased VLDL1-TG and apoB fractional catabolic rates, a measure of clearance, (change between groups p=0.02 and p=0.01, respectively), and VLDL1-apoB production rate (change between groups p=0.006), with no change in VLDL1 -TG production rate. Plasma TG did not change in either group. Conclusion An increased clearance of VLDL1 may contribute to the significant decrease in liver fat following 16 weeks of exercise in NAFLD. A longer duration or higher intensity exercise interventions may be needed to lower plasma TG and VLDL production rate.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

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.