Russian Journal of Numerical Analysis and Mathematical Modelling最新文献_第3页

Myocardial perfusion segmentation and partitioning methods in personalized models of coronary blood flow 冠状动脉血流个性化模型中的心肌灌注分割方法

4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-10-01 DOI: 10.1515/rnam-2023-0022

Alexander A. Danilov, Timur M. Gamilov, Fuyou Liang, Alina A. Rebrova, Petr Sh. Chomakhidze, Philipp Yu. Kopylov, Yan R. Bravyy, Sergey S. Simakov

{"title":"Myocardial perfusion segmentation and partitioning methods in personalized models of coronary blood flow","authors":"Alexander A. Danilov, Timur M. Gamilov, Fuyou Liang, Alina A. Rebrova, Petr Sh. Chomakhidze, Philipp Yu. Kopylov, Yan R. Bravyy, Sergey S. Simakov","doi":"10.1515/rnam-2023-0022","DOIUrl":"https://doi.org/10.1515/rnam-2023-0022","url":null,"abstract":"Abstract In this work we present methods and algorithms for construction of a personalized model of coronary haemodynamics based on computed tomography images. This model provides estimations of fractional flow reserve, coronary flow reserve, and instantaneous wave-free ratio taking into account transmural perfusion ratio indices obtained from perfusion images. The presented pipeline consists of the following steps: aorta segmentation, left ventricle wall segmentation, coronary arteries segmentation, construction of 1D network of vessels, partitioning of left ventricle wall, and personalization of the model parameters. We focus on a new technique, which generates specific perfusion zones and computes transmural perfusion ratio according to the quality of available medical images with a limited number of visible terminal coronary vessels. Numerical experiments show that accurate evaluation of stenosis before precutaneous coronary intervention should take into account both fractional flow reserve indices and myocardial perfusion, as well as other indices, in order to avoid misdiagnosis. The presented model provides better understanding of the background of clinical recommendations for possible surgical treatment of a stenosed coronary artery.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136198951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Frontmatter 头版头条

4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-10-01 DOI: 10.1515/rnam-2023-frontmatter5

引用次数: 0

Multiphysics modelling of immune processes using distributed parameter systems 使用分布式参数系统的免疫过程多物理场建模

4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-10-01 DOI: 10.1515/rnam-2023-0021

Gennady A. Bocharov, Dmitry S. Grebennikov, Rostislav S. Savinkov

引用次数: 0

One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity 分数阶粘弹性血管网络的一维血流动力学模型

4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-10-01 DOI: 10.1515/rnam-2023-0024

Ruslan Yanbarisov, Timur Gamilov

引用次数: 0

Mathematical modelling for spatial optimization of irradiation during proton radiotherapy with nanosensitizers 纳米致敏剂质子放射治疗中辐照空间优化的数学建模

4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-10-01 DOI: 10.1515/rnam-2023-0023

Maxim Kuznetsov, Andrey Kolobov

{"title":"Mathematical modelling for spatial optimization of irradiation during proton radiotherapy with nanosensitizers","authors":"Maxim Kuznetsov, Andrey Kolobov","doi":"10.1515/rnam-2023-0023","DOIUrl":"https://doi.org/10.1515/rnam-2023-0023","url":null,"abstract":"Abstract A spatially distributed mathematical model is presented that simulates the growth of a non-invasive tumour undergoing treatment by fractionated proton therapy with the use of non-radioactive tumour-specific nanosensitizers. Nanosensitizers are injected intravenously before each irradiation to increase the locally deposited dose via a chain of reactions with therapeutic protons. Modelling simulations show that the use of nanosensitizers allows increasing treatment efficacy. However, their effect is restricted by the necessity of decreasing the energy deposited in tumour in order to comply to the normal damage restrictions. Normalization of tumour microvasculature that accompanies the treatment, also compromises nanosensitizers effect as it impairs their inflow in tumour. It is shown that spatial optimization of irradiation, with conservation of total dose deposited in tumour, can increase tumour cell damage for each single irradiation. However, eventually it may not lead to the overall increase of treatment efficacy, in terms of minimization of the number of remaining viable tumour cells, due to the influence of tumour cell repopulation between irradiations. It is suggested that an efficient way towards minimization of tumour cell repopulation may be the faster suppression of angiogenesis by eradication of metabolically deprived tumour cells. This method can be efficient even despite the fact that it would also cause the decrease of supply of nanosensitizers into the tumour.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136198949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Pressure-correction projection method for modelling the incompressible fluid flow in porous media 多孔介质中不可压缩流体流动模型的压力修正投影法

IF 0.6 4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-08-01 DOI: 10.1515/rnam-2023-0019

K. Terekhov

引用次数: 0

Multicontinuum homogenization for Richards’ equation: The derivation and numerical experiments 理查兹方程的多连续统均匀化:推导与数值实验

IF 0.6 4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-08-01 DOI: 10.1515/rnam-2023-0016

D. Ammosov, S. Stepanov, D. Spiridonov, Wenyuan Li

引用次数: 0

Frontmatter 头版头条

4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-08-01 DOI: 10.1515/rnam-2023-frontmatter4

引用次数: 0

Operator-difference schemes on non-uniform grids for second-order evolutionary equations 二阶演化方程非均匀网格上的算子差分格式

4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-08-01 DOI: 10.1515/rnam-2023-0020

Petr N. Vabishchevich

{"title":"Operator-difference schemes on non-uniform grids for second-order evolutionary equations","authors":"Petr N. Vabishchevich","doi":"10.1515/rnam-2023-0020","DOIUrl":"https://doi.org/10.1515/rnam-2023-0020","url":null,"abstract":"Abstract The approximate solution of the Cauchy problem for second-order evolution equations is performed, first of all, using three-level time approximations. Such approximations are easily constructed and relatively uncomplicated to investigate when using uniform time grids. When solving applied problems numerically, we should focus on approximations with variable time steps. When using multilevel schemes on non-uniform grids, we should maintain accuracy by choosing appropriate approximations and ensuring stability of the approximate solution. In this paper, we construct unconditionally stable schemes of the first- and second-order accuracy on a non-uniform time grid for the approximate solution of the Cauchy problem for a second-order evolutionary equation. The novelty of the paper consists in the fact that these stability estimates are obtained without any restrictions on the magnitude of the step change and on the number of step changes. We use a special transformation of the original second-order differential-operator equation to a system of first-order equations. For the system of first-order equations, we apply standard two-level time approximations. We obtained stability estimates for the initial data and the right-hand side in finite-dimensional Hilbert space. Eliminating auxiliary variables leads to three-level schemes for the initial second-order evolution equation. Numerical experiments were performed for the test problem for a one-dimensional in space bi-parabolic equation. The accuracy and stability properties of the constructed schemes are demonstrated on non-uniform grids with randomly varying grid steps.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136106961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The group behaviour modelling of workers in the labor market 劳动力市场中工人的群体行为模型

IF 0.6 4区数学

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2023-08-01 DOI: 10.1515/rnam-2023-0017

A. Shananin, N. Trusov

引用次数: 0