Non-alcoholic fatty liver disease : can ultrasound assist in early diagnosis of prediabetes and delay progression to type2 diabetes mellitus

Non Alcoholic Fatty Liver Disease (NAFLD) is a condition that is frequently seen but seldom investigated. Until recently, NAFLD was considered benign, self-limiting and unworthy of further investigation. This opinion is based on retrospective studies with relatively small numbers and scant follow-up of histology data. (1) The prevalence for adults, in the USA is, 30%, and NAFLD is recognized as a common and increasing form of liver disease in the paediatric population (1). Australian data, from New South Wales, suggests the prevalence of NAFLD in “healthy” 15 year olds as being 10%.(2) Non-alcoholic fatty liver disease is a condition where fat progressively invades the liver parenchyma. The degree of infiltration ranges from simple steatosis (fat only) to steatohepatitis (fat and inflammation) steatohepatitis plus fibrosis (fat, inflammation and fibrosis) to cirrhosis (replacement of liver texture by scarred, fibrotic and non functioning tissue).Non-alcoholic fatty liver is diagnosed by exclusion rather than inclusion. None of the currently available diagnostic techniques -liver biopsy, liver function tests (LFT) or Imaging; ultrasound, Computerised tomography (CT) or Magnetic Resonance Imaging (MRI) are specific for non-alcoholic fatty liver. An association exists between NAFLD, Non Alcoholic Steatosis Hepatitis (NASH) and irreversible liver damage, cirrhosis and hepatoma. However, a more pervasive aspect of NAFLD is the association with Metabolic Syndrome. This Syndrome is categorised by increased insulin resistance (IR) and NAFLD is thought to be the hepatic representation. Those with NAFLD have an increased risk of death (3) and it is an independent predictor of atherosclerosis and cardiovascular disease (1). Liver biopsy is considered the gold standard for diagnosis, (4), and grading and staging, of non-alcoholic fatty liver disease. Fatty-liver is diagnosed when there is macrovesicular steatosis with displacement of the nucleus to the edge of the cell and at least 5% of the hepatocytes are seen to contain fat (4).Steatosis represents fat accumulation in liver tissue without inflammation. However, it is only called non-alcoholic fatty liver disease when alcohol - >20gms-30gms per day (5), has been excluded from the diet. Both non-alcoholic and alcoholic fatty liver are identical on histology. (4).LFT’s are indicative, not diagnostic. They indicate that a condition may be present but they are unable to diagnosis what the condition is. When a patient presents with raised fasting blood glucose, low HDL (high density lipoprotein), and elevated fasting triacylglycerols they are likely to have NAFLD. (6) Of the imaging techniques MRI is the least variable and the most reproducible. With CT scanning liver fat content can be semi quantitatively estimated. With increasing hepatic steatosis, liver attenuation values decrease by 1.6 Hounsfield units for every milligram of triglyceride deposited per gram of liver tissue (7). Ultrasound permits early detection of fatty liver, often in the preclinical stages before symptoms are present and serum alterations occur. Earlier, accurate reporting of this condition will allow appropriate intervention resulting in better patient health outcomes. References 1. Chalasami N. Does fat alone cause significant liver disease: It remains unclear whether simple steatosis is truly benign. American Gastroenterological Association Perspectives, February/March 2008 www.gastro.org/wmspage.cfm?parm1=5097 Viewed 20th October, 2008 2. Booth, M. George, J.Denney-Wilson, E: The population prevalence of adverse concentrations with adiposity of liver tests among Australian adolescents. Journal of Paediatrics and Child Health.2008 November 3. Catalano, D, Trovato, GM, Martines, GF, Randazzo, M, Tonzuso, A. Bright liver, body composition and insulin resistance changes with nutritional intervention: a follow-up study .Liver Int.2008; February 1280-9 4. Choudhury, J, Sanysl, A. Clinical aspects of Fatty Liver Disease. Semin in Liver Dis. 2004:24 (4):349-62 5. Dionysus Study Group. Drinking factors as cofactors of risk for alcohol induced liver change. Gut. 1997; 41 845-50 6. Preiss, D, Sattar, N. Non-alcoholic fatty liver disease: an overview of prevalence, diagnosis, pathogenesis and treatment considerations. Clin Sci.2008; 115 141-50 7. American Gastroenterological Association. Technical review on nonalcoholic fatty liver disease. Gastroenterology.2002; 123: 1705-25

Delay-dependent robust H-infinity control for uncertain systems with time-varying delay

This paper proposes a new approach for delay-dependent robust H-infinity stability analysis and control synthesis of uncertain systems with time-varying delay. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional, the construction of an augmented matrix with uncorrelated terms, and the employment of a tighter bounding technique. As a result, significant performance improvement is achieved in system analysis and synthesis without using either free weighting matrices or model transformation. Examples are given to demonstrate the effectiveness of the proposed approach.

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.

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

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.

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.