Sirtuin (SIRT) pathway has a crucial role in Alzheimer's disease (AD). The present study evaluated the alterations in serum sirtuin1 (SIRT1) concentration in healthy individuals (young and old) and ...patients with AD and mild cognitive impairment (MCI). Blood samples were collected from 40 AD and 9 MCI patients as cases and 22 young healthy adults and 22 healthy elderly individuals as controls. Serum SIRT1 was estimated by Surface Plasmon Resonance (SPR), Western Blot and Enzyme Linked Immunosorbent Assay (ELISA). A significant (p<0.0001) decline in SIRT1 concentration was observed in patients with AD (2.27 ± 0.46 ng/µl) and MCI (3.64 ± 0.15 ng/µl) compared to healthy elderly individuals (4.82 ± 0.4 ng/µl). The serum SIRT1 concentration in healthy elderly was also significantly lower (p<0.0001) compared to young healthy controls (8.16 ± 0.87 ng/µl). This study, first of its kind, has demonstrated, decline in serum concentration of SIRT1 in healthy individuals as they age. In patients with AD and MCI the decline was even more pronounced, which provides an opportunity to develop this protein as a predictive marker of AD in early stages with suitable cut off values.
•New high-order numerical approach for heat and Poisson equations.•Increase in accuracy by four orders for heat equation in 2-D case.•Increase in accuracy by twelve orders for Poisson equation in 2-D ...case.•A stencil equation with optimal order of accuracy.
A new approach for the increase in the order of accuracy of high order elements used for the time dependent heat equation and for the time independent Poisson equation has been suggested on uniform square and rectangular meshes. It is based on the optimization of the coefficients of the corresponding discrete stencil equation with respect to the local truncation error. By a simple modification of the coefficients of 25-point stencils, the new approach exceeds the accuracy of the quadratic isogeometric elements by four orders for the heat equation and by twelve orders for the Poisson equation. Despite the significant increase in accuracy, the computational costs of the new technique are the same as those for the conventional quadratic isogeometric elements on a given mesh. The numerical examples are in a good agreement with the theoretical results for the new approach and also show that the new approach is much more accurate than the conventional isogeometric elements at the same number of degrees of freedom. Hybrid methods that combine the new stencils with the conventional isogeometric and finite elements and can be applied to irregular domains are also presented.
Recently we have developed the optimal local truncation error method (OLTEM) for PDEs with constant coefficients on irregular domains and unfitted Cartesian meshes. However, many important ...engineering applications include domains with different material properties (e.g., different inclusions, multi-material structural components, etc.) for which this technique cannot be directly applied. In the paper OLTEM is extended to a much more general case of PDEs with discontinuous coefficients and can treat the above-mentioned applications. We show the development of OLTEM for the 1-D and 2-D scalar wave equation as well as the heat equation using compact 3-point (in the 1-D case) and 9-point (in the 2-D case) stencils that are similar to those for linear quadrilateral finite elements. Trivial unfitted Cartesian meshes are used for OLTEM with complex interfaces between different materials. The interface conditions on the interfaces where the jumps in material properties occur are added to the expression for the local truncation error and do not change the width of the stencils. The calculation of the unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique at a given width of stencil equations. In contrast to the second order of accuracy for linear finite elements, OLTEM provides the fourth order of accuracy in the 1-D case and in the 2-D case for horizontal interfaces as well as the third order of accuracy for the general geometry of smooth interfaces. The numerical results for the domains with complex smooth interfaces show that at the same number of degrees of freedom, OLTEM is even much more accurate than quadratic finite elements and yields the results close to those for cubic finite elements with much wider stencils. The wave and heat equations are uniformly treated with OLTEM. OLTEM can be directly applied to other partial differential equations.
•New numerical approach with trivial Cartesian meshes for irregular domains.•Wave and heat equations with discontinuous coefficients.•New high-order accurate 3-point uniform and nonuniform stencils in the 1-D case.•New high-order accurate 9-point uniform and nonuniform stencils in the 2-D case.•New approach is much more accurate than linear and high-order (up to third order) FEM.
Recently we have developed a new 3-D numerical approach for the time dependent wave and heat equations as well as for the time independent Poisson equation on irregular domains with the Dirichlet ...boundary conditions. Its extension to the Neumann boundary conditions that was a big issue due to the presence of normal derivatives along irregular boundaries is considered in this paper. Trivial Cartesian meshes and simple 27-point uniform and nonuniform stencil equations are used with the new approach for 3-D irregular domains. The Neumann boundary conditions are introduced as the known right-hand side into the stencil and do not change the width of the stencil. The calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique. Very small distances (0.1h−10−9h where h is the grid size) between the grid points of a Cartesian mesh and the boundary do not worsen the accuracy of the new technique. At similar 27-point stencils, the accuracy of the new approach is much higher than that for the linear finite elements. The numerical results for irregular domains show that at the same number of degrees of freedom, the new approach is even much more accurate than the high-order (up to the fourth order) tetrahedral finite elements with much wider stencils. The wave and heat equations can be uniformly treated with the new approach. The order of the time derivative in these equations does not affect the coefficients of the stencil equations of the semi-discrete systems. The new approach can be directly applied to other partial differential equations.
•A new numerical approach for irregular domains with Neumann boundary conditions and Cartesian meshes.•High-order accuracy with 27-point stencils in the 3-D case.•New approach is much more accurate than conventional FEM.•Uniform application to wave and heat equations.•Numerical results are in agreement with the theory.
A new approach for the increase in the order of accuracy of high-order numerical techniques used for time-independent elasticity is suggested on uniform square and rectangular meshes. It is based on ...the optimization of the coefficients of the corresponding discrete stencil equations with respect to the local truncation error. It is shown that the second order of accuracy of 2-D linear finite elements with 9-point stencils is optimal and cannot be improved. However, the order of accuracy of 25-point stencils (similar to those for quadratic finite and isogeometric elements) can be significantly improved. We have developed new 25-point stencils for 2-D elastic problems with optimal 10th order of accuracy. The numerical results are in good agreement with the theoretical findings as well as they show a big increase in accuracy of the new stencils compared with those for high-order finite elements. At the same number of degrees of freedom, the new approach yields significantly more accurate results than those obtained by high-order (up to the tenth order) finite elements. The numerical experiments also show that the new approach with 25-point stencils yields very accurate results for nearly incompressible materials with Poisson’s ratio 0.4999.
•A new approach for high-order accurate stencils with optimal accuracy.•New 25-point stencils for 2-D elasticity with 10th order of accuracy.•Proof that linear finite elements for elasticity have optimal order of accuracy.•New approach significantly exceeds accuracy of high-order finite elements.•New approach yields accurate results for nearly incompressible materials.
A new 3-D numerical approach for the time dependent wave and heat equations as well as for the time independent Laplace equation on irregular domains with the Dirichlet boundary conditions has been ...developed. Trivial Cartesian meshes and simple 27-point uniform and nonuniform stencil equations are used for 3-D irregular domains. The calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique. Very small distances (0.1h−10−9h where h is the grid size) between the grid points of a Cartesian mesh and the boundary do not worsen the accuracy of the new technique. At similar 27-point stencils, the accuracy of the new approach is two orders higher than that for the linear finite elements. The numerical results for irregular domains show that at the same number of degrees of freedom, the new approach is even much more accurate than the high-order (up to the fifth order) tetrahedral finite elements with much wider stencils. The wave and heat equations can be uniformly treated with the new approach. The order of the time derivative in these equations does not affect the coefficients of the stencil equations of the semi-discrete systems. The new approach can be directly applied to other partial differential equations.
Hematopoietic stem cell transplantation-associated thrombotic microangiopathy (TA-TMA) remains a difficult complication to address due to its high mortality rate, lack of standard diagnostic criteria ...and limited therapeutic options. Underscoring this challenge is the complex pathophysiology involved and multiple contributing factors that converge on a final pathway involving widespread endothelial injury and complement activation. In addressing our current understanding of TA-TMA, we highlight the risk factors leading to endothelial damage and a pathophysiological cascade that ensues. We have also compared the different definition criteria and biomarkers that can enable early intervention in TA-TMA patients. Current first-line management includes discontinuation or alteration of the immunosuppressive regimen, treatment of co-existing infectious and GVHD, aggressive hypertension control and supportive therapy. We discuss current pharmacological therapies, including newer agents that target the complement cascade and nitric oxide pathways.
•A new approach for high-order accurate stencils with optimal accuracy.•New 25-point stencils for 2-D elastodynamics with 6th order of accuracy.•Proof that linear finite elements for elastodynamics ...have optimal order of accuracy.•New approach significantly exceeds accuracy of high-order finite elements.•New approach yields accurate results for nearly incompressible materials.
A new approach for the increase in the order of accuracy of high-order numerical techniques used for 2-D time-dependent elasticity (structural dynamics and wave propagation) has been suggested on uniform square and rectangular meshes. It is based on the optimization of the coefficients of the corresponding semi-discrete stencil equations with respect to the local truncation error. It is shown that the second order of accuracy of the linear finite elements with 9-point stencils is optimal and cannot be improved. However, we have calculated new 9-point stencils with the second order of accuracy that yield more accurate results than those obtained by the linear finite elements. We have also developed new 25-point stencils (similar to those for the quadratic finite and isogeometric elements) with the optimal sixth order of accuracy for the non-diagonal mass matrix and with the optimal fourth order of accuracy for the diagonal mass matrix. The numerical results are in good agreement with the theoretical findings as well as they show a big increase in accuracy of the new stencils compared with those for the high-order finite elements. At the same number of degrees of freedom, the new approach yields significantly more accurate results than those obtained by the high-order (up to the eighth order) finite elements with the non-diagonal mass matrix. The numerical experiments also show that the new approach with 25-point stencils yields very accurate results for nearly incompressible materials with Poisson’s ratio 0.4999.
Based on the optimal coefficients of the stencil equation, a numerical technique for the reduction of the numerical dispersion error has been suggested. New isogeometric elements with the reduced ...numerical dispersion error for wave propagation problems in the 2-D case have been developed with the suggested approach. By the minimization of the order of the dispersion error of the stencil equation, the order of the dispersion error is improved from order 2p (the conventional isogeometric elements) to order 4p (the isogeometric elements with reduced dispersion) where p is the order of the polynomial approximations. Because all coefficients of the stencil equation are obtained from the minimization procedure, the obtained accuracy is maximum possible. The corresponding elemental mass and stiffness matrices of the isogeometric elements with reduced dispersion are calculated with help of the optimal coefficients of the stencil equation. The analysis of the dispersion error of the isogeometric elements with the lumped mass matrix has also shown that independent of the procedures for the calculation of the lumped mass matrix, the second order of the dispersion error cannot be improved with the conventional stiffness matrix. However, the dispersion error with the lumped mass matrix can be improved from the second order to order 2p by the modification of the stiffness matrix. The numerical examples confirm the computational efficiency of the isogeometric elements with reduced dispersion. The numerical results obtained by the new and conventional isogeometric elements may include spurious oscillations due to the dispersion error. These oscillations can be quantified and filtered by the two-stage time-integration technique developed recently. The approach developed in the paper can be directly applied to other space-discretization techniques with similar stencil equations.
Recently we have developed a new numerical approach for PDEs with constant coefficients on irregular domains and Cartesian meshes. In this paper we extend it to a much more general case of PDEs with ...variable coefficients that have a lot of applications; e.g., the modeling of functionally graded materials, the inhomogeneous materials obtained by 3-D printing and many others. Here, we consider the 2-D wave and heat equations for isotropic and anisotropic inhomogeneous materials. The idea of the extension to the case of PDEs with variable coefficients is based on the representation of the stencil coefficients as functions of the mesh size. This leads to the increase in the size of the local system of algebraic equations solved for each grid point of the new approach; however, this does not change the size of the global system of semidiscrete equations and practically does not increase the computational costs of the proposed technique. Similar to our previous technique, the new 2-D approach with compact 9-point stencils uses trivial Cartesian meshes for complex irregular domains and provides the fourth order of accuracy for the wave and heat equations with variable coefficients. The calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique. At similar 9-point stencils, the accuracy of the new approach is much higher than that for the linear finite elements. The numerical results for irregular domains show that at the same number of degrees of freedom, the new approach is even much more accurate than the high-order (up to the third order) finite elements with much wider stencils. The wave and heat equations are uniformly treated with the new approach.
•A new numerical approach with optimal accuracy for PDEs with variable coefficients.•Wave and heat equations for isotropic and anisotropic inhomogeneous materials.•Stencil coefficients depend on the mesh size.•Cartesian meshes for irregular domains.•New approach significantly exceeds accuracy of high-order finite elements.
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