Reducing the Dimensionality of Grid Approximations

Предложен общий подход к развитию методов математического моделирования сложных систем. Центральной проблемой, связанной с использованием вычислительной техники, являются сеточные аппроксимации большой размерности и суперЭВМ высокой производительности с большим числом параллельно работающих микропроцессоров. В качестве возможных альтернатив сеточным аппроксимациям большой размерности разрабатываются кинетические методы решения дифференциальных уравнений и методы «склейки» точных решений на грубых сетках. A general approach to the development of complex systems simulation is proposed. The key computer applications problem is the high-dimensional grid approximations and high-performance supercomputers with a large number of parallel CPUs. Kinetic methods for solving differential equations and methods for ”gluing” exact solutions produced with coarse meshes are developed as possible alternatives to high-dimensional grid approximations.  

Preparation and non-isothermal cure kinetics study of epoxy resin nanocomposites with amine and epoxy functionalized magnetic nanoparticles

Amine-functionalized magnetic nanoparticles NiFe2O4@SiO2@Amine (AMNP), and epoxy functionalized magnetic nanoparticles, CuFe2O4@SiO2@Epoxy (EMNP) were synthesized in three steps. Homogeneous stable dispersion of AMNP and EMNP, at concentrations of 1, 5, 10, 15, 20 wt% in epoxy resin were prepared using stoichiometric amounts of 4,4’-diaminodiphenylsulfone (DDS) as a curing. The optimum ratio of AMNP and EMNP were found to be 5%, and these were investigated by the total enthalpy of the curing reaction using differential scanning calorimetry (DSC) thermograms at 10°C/min. The cure kinetics of epoxy resin-functional magnetic nanoparticles-DDS composites were studied using non-isothermal DSC thermograms at different heating rates (5, 10, 15, 20°C/min). The kinetic parameters of the curing process, such as activation energy ( Ea), pre-exponential factor ( A), and rate constant ( k) were determined using several non-isothermal kinetic methods: Kissinger-Akahira-Sunose (KAS), Kissinger, Straink, Flynn-Wall-Ozawa (OFW), and Bosewell. The kinetic curing values obtained with different kinetic methods are well-matched. The Ea values were calculated in the range of 59.80 to 65.94, 57.69 to 63.92, and 45.38 to 52.45 kJ.mol−1 for the DGEBA/DDS, DGEBA/DDS/AMNP, and DGEBA/DDS/EMNP systems respectively. Also, The A values, using the Kissinger method, were calculated to be in the range of 7.0 × 105, 4.0 × 105, and 0.2 × 105 S−1 for the DGEBA/DDS, DGEBA/DDS/AMNP, and DGEBA/DDS/EMNP systems respectively. The glass transition temperatures of cured resins were determined with DSC, and the surface morphology of the nanocomposites and also the dispersion of the nanoparticles were investigated using scanning electron microscopy (SEM).

Computed Tomography Perfusion Analysis of Pancreatic Adenocarcinoma using Deconvolution, Maximum Slope, and Patlak Methods – Evaluation of Diagnostic Accuracy and Interchangeability of Cut-Off Values

Purpose The goal of this study was to evaluate the diagnostic accuracy of perfusion computed tomography (CT) parameters obtained by different mathematical-kinetic methods for distinguishing pancreatic adenocarcinoma from normal tissue. To determine cut-off values and to assess the interchangeability of cut-off values, which were determined by different methods. Materials and Methods Perfusion CT imaging of the pancreas was prospectively performed in 23 patients. 19 patients with histopathologically confirmed pancreatic adenocarcinoma were included in the study. Blood flow (BF), blood volume (BV) and permeability-surface area product (PS) were measured in pancreatic adenocarcinoma and normal tissue with the deconvolution (BF, BV, PS), maximum slope (BF), and Patlak methods (BV, PS). The interchangeability of cut-off values was examined by assessing agreement between BF, BV, and PS measured with different mathematical-kinetic methods. Results Bland-Altman analysis demonstrated poor agreement between perfusion parameters, measured with different mathematical-kinetic methods. According to receiver operating characteristic (ROC) analysis, PS measured with the Patlak method had the significantly lowest diagnostic accuracy (area under ROC curve = 0.748). All other parameters were of high diagnostic accuracy (area under ROC curve = 0.940–0.997), although differences in diagnostic accuracy were not statistically different. Cut-off values for BF of ≤ 91.83 ml/100 ml/min and for BV of ≤ 5.36 ml/100 ml, both measured with the deconvolution method, appear to be the most appropriate cut-off values to distinguish pancreatic adenocarcinoma from normal tissue. Conclusion Perfusion parameters obtained by different methods are not interchangeable. Therefore, cut-off values, which were determined using different methods, are not interchangeable either. Perfusion parameters can help to distinguish pancreatic adenocarcinoma from normal tissue with high diagnostic accuracy, except for PS measured with the Patlak method. Key Points: Citation Format

Creatinine Assessment in Non–Steady-State Conditions: A Critical Review

Objectives: To discuss methods for the assessment of creatinine clearance (Clcr) when serum creatinine (SCr) is not at steady state in order to estimate kidney function and apply the estimate to kidney function staging for clinical assessment or drug dosing. Data Sources: A PubMed search was conducted from 1976 to mid-January 2021 with other articles identified through review of bibliographies of retrieved articles and citations in Scopus. Study Selection and Data Extraction: Articles assessing Clcr under non–steady-state conditions and studies evaluating predictive equations were selected. Data Synthesis: When SCr is systematically changing (ie, trending up or down), kinetic methods to estimate Clcr are appropriate. Estimates from kinetic methods should be individual based and not indexed to body surface area, and careful monitoring is required to confirm predictions as the situation evolves. Standard methods intended for steady-state conditions should not be used to estimate Clcr in patients with unstable SCr. Relevance to Patient Care and Clinical Practice: Creatinine continues to be a monitoring parameter of choice and is an important variable in all the commonly used equations for estimating Clcr and most important for estimating glomerular filtration rate. However, standard methods of estimating Clcr for medication dosing are not accurate under non–steady-state conditions. Conclusion: The methods for kinetic clearance estimation and standards methods for clearance estimation, such as the Cockcroft-Gault equation, are mutually exclusive. There are no benefits of using the kinetic method in patients with stable SCr concentrations, and standard equations are not appropriate with unstable SCr concentrations.