Mesoporous bioactive glass scaffolds for efficient delivery of vascular endothelial growth factor

In this article, we, for the first time, investigated mesoporous bioactive glass scaffolds for the delivery of vascular endothelial growth factor. We have found that mesoporous bioactive glass scaffolds have significantly higher loading efficiency and more sustained release of vascular endothelial growth factor than non-mesoporous bioactive glass scaffolds. In addition, vascular endothelial growth factor delivery from mesoporous bioactive glass scaffolds has improved the viability of endothelial cells. The study has suggested that mesopore structures in mesoporous bioactive glass scaffolds play an important role in improving the loading efficiency, decreasing the burst release, and maintaining the bioactivity of vascular endothelial growth factor, indicating that mesoporous bioactive glass scaffolds are an excellent carrier of vascular endothelial growth factor for potential bone tissue engineering applications.

The relationship between chronic disease self-efficacy and nutritional status, functional ability and quality of life in older adults at risk of hospital readmission

Background and significance: Older adults with chronic diseases are at increasing risk of hospital admission and readmission. Approximately 75% of adults have at least one chronic condition, and the odds of developing a chronic condition increases with age. Chronic diseases consume about 70% of the total Australian health expenditure, and about 59% of hospital events for chronic conditions are potentially preventable. These figures have brought to light the importance of the management of chronic disease among the growing older population. Many studies have endeavoured to develop effective chronic disease management programs by applying social cognitive theory. However, limited studies have focused on chronic disease self-management in older adults at high risk of hospital readmission. Moreover, although the majority of studies have covered wide and valuable outcome measures, there is scant evidence on examining the fundamental health outcomes such as nutritional status, functional status and health-related quality of life. Aim: The aim of this research was to test social cognitive theory in relation to self-efficacy in managing chronic disease and three health outcomes, namely nutritional status, functional status, and health-related quality of life, in older adults at high risk of hospital readmission. Methods: A cross-sectional study design was employed for this research. Three studies were undertaken. Study One examined the nutritional status and validation of a nutritional screening tool; Study Two explored the relationships between participants. characteristics, self-efficacy beliefs, and health outcomes based on the study.s hypothesized model; Study Three tested a theoretical model based on social cognitive theory, which examines potential mechanisms of the mediation effects of social support and self-efficacy beliefs. One hundred and fifty-seven patients aged 65 years and older with a medical admission and at least one risk factor for readmission were recruited. Data were collected from medical records on demographics, medical history, and from self-report questionnaires. The nutrition data were collected by two registered nurses. For Study One, a contingency table and the kappa statistic was used to determine the validity of the Malnutrition Screening Tool. In Study Two, standard multiple regression, hierarchical multiple regression and logistic regression were undertaken to determine the significant influential predictors for the three health outcome measures. For Study Three, a structural equation modelling approach was taken to test the hypothesized self-efficacy model. Results: The findings of Study One suggested that a high prevalence of malnutrition continues to be a concern in older adults as the prevalence of malnutrition was 20.6% according to the Subjective Global Assessment. Additionally, the findings confirmed that the Malnutrition Screening Tool is a valid nutritional screening tool for hospitalized older adults at risk of readmission when compared to the Subjective Global Assessment with high sensitivity (94%), and specificity (89%) and substantial agreement between these two methods (k = .74, p < .001; 95% CI .62-.86). Analysis data for Study Two found that depressive symptoms and perceived social support were the two strongest influential factors for self-efficacy in managing chronic disease in a hierarchical multiple regression. Results of multivariable regression models suggested advancing age, depressive symptoms and less tangible support were three important predictors for malnutrition. In terms of functional status, a standard regression model found that social support was the strongest predictor for the Instrumental Activities of Daily Living, followed by self-efficacy in managing chronic disease. The results of standard multiple regression revealed that the number of hospital readmission risk factors adversely affected the physical component score, while depressive symptoms and self-efficacy beliefs were two significant predictors for the mental component score. In Study Three, the results of the structural equation modelling found that self-efficacy partially mediated the effect of health characteristics and depression on health-related quality of life. The health characteristics had strong direct effects on functional status and body mass index. The results also indicated that social support partially mediated the relationship between health characteristics and functional status. With regard to the joint effects of social support and self-efficacy, social support fully mediated the effect of health characteristics on self-efficacy, and self-efficacy partially mediated the effect of social support on functional status and health-related quality of life. The results also demonstrated that the models fitted the data well with relative high variance explained by the models, implying the hypothesized constructs under discussion were highly relevant, and hence the application for social cognitive theory in this context was supported. Conclusion: This thesis highlights the applicability of social cognitive theory on chronic disease self-management in older adults at risk of hospital readmission. Further studies are recommended to validate and continue to extend the development of social cognitive theory on chronic disease self-management in older adults to improve their nutritional and functional status, and health-related quality of life.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

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.

A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.