Alexander A. Danilov, Timur M. Gamilov, Fuyou Liang, Alina A. Rebrova, Petr Sh. Chomakhidze, Philipp Yu. Kopylov, Yan R. Bravyy, Sergey S. Simakov
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.
{"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}
Pub Date : 2023-10-01DOI: 10.1515/rnam-2023-frontmatter5
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2023-frontmatter5","DOIUrl":"https://doi.org/10.1515/rnam-2023-frontmatter5","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"48 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":"136198954","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}
Gennady A. Bocharov, Dmitry S. Grebennikov, Rostislav S. Savinkov
Abstract The immune system is a complex distributed system consisting of cells, which circulate through the body, communicate and turnover in response to antigenic perturbations. We discuss new approaches to modelling the functioning of the immune system of humans and experimental animals with a focus on its ‘complexity’. Emerging mathematical and computer models are reviewed to describe the immune system diversity, the cell/cytokine network communication structures, hierarchical regulation, and evolutionary dynamics of immune repertoires.
{"title":"Multiphysics modelling of immune processes using distributed parameter systems","authors":"Gennady A. Bocharov, Dmitry S. Grebennikov, Rostislav S. Savinkov","doi":"10.1515/rnam-2023-0021","DOIUrl":"https://doi.org/10.1515/rnam-2023-0021","url":null,"abstract":"Abstract The immune system is a complex distributed system consisting of cells, which circulate through the body, communicate and turnover in response to antigenic perturbations. We discuss new approaches to modelling the functioning of the immune system of humans and experimental animals with a focus on its ‘complexity’. Emerging mathematical and computer models are reviewed to describe the immune system diversity, the cell/cytokine network communication structures, hierarchical regulation, and evolutionary dynamics of immune repertoires.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"10 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":"136198952","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}
Abstract We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a 37-segment network of elastic tubes, and flow in anatomically detailed arterial network consisting of 61 arterial segments. All results for elastic model are in a good agreement with analytical solutions, in vitro data and other well-established approaches. Fractional-order model demonstrates noticeable differences in pulse wave propagation speed and minor differences in pressure and flow profiles. Differences in profiles are negligible in major vessels, but more profound in vessels beyond the third or fourth generation.
{"title":"One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity","authors":"Ruslan Yanbarisov, Timur Gamilov","doi":"10.1515/rnam-2023-0024","DOIUrl":"https://doi.org/10.1515/rnam-2023-0024","url":null,"abstract":"Abstract We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a 37-segment network of elastic tubes, and flow in anatomically detailed arterial network consisting of 61 arterial segments. All results for elastic model are in a good agreement with analytical solutions, in vitro data and other well-established approaches. Fractional-order model demonstrates noticeable differences in pulse wave propagation speed and minor differences in pressure and flow profiles. Differences in profiles are negligible in major vessels, but more profound in vessels beyond the third or fourth generation.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"213 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":"136198953","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}
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.
{"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}
Abstract This work is dedicated to the pressure-correction projection method for the volume-averaged Navier–Stokes system for porous media. A set of parameters controlling the presence of inertia and viscosity is introduced into the system. Switching parameters allows us to reduce the system to either the Brinkman system or the Darcy equation. Considering the jump in the parameters between mesh cells allows capturing the contact of media of different types, such as free-flow and porous media flow. We apply Chorin’s projection method to decouple the system. The splitting of the system yields a momentum conservation equation and an anisotropic pressure correction equation. We propose a combination of collocated finite-volume methods to solve the problem.
{"title":"Pressure-correction projection method for modelling the incompressible fluid flow in porous media","authors":"K. Terekhov","doi":"10.1515/rnam-2023-0019","DOIUrl":"https://doi.org/10.1515/rnam-2023-0019","url":null,"abstract":"Abstract This work is dedicated to the pressure-correction projection method for the volume-averaged Navier–Stokes system for porous media. A set of parameters controlling the presence of inertia and viscosity is introduced into the system. Switching parameters allows us to reduce the system to either the Brinkman system or the Darcy equation. Considering the jump in the parameters between mesh cells allows capturing the contact of media of different types, such as free-flow and porous media flow. We apply Chorin’s projection method to decouple the system. The splitting of the system yields a momentum conservation equation and an anisotropic pressure correction equation. We propose a combination of collocated finite-volume methods to solve the problem.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"241 - 265"},"PeriodicalIF":0.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46895771","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}
D. Ammosov, S. Stepanov, D. Spiridonov, Wenyuan Li
Abstract In the present paper, the authors rigorously derive Richards’ multicontinuum model using the multicontinuum homogenization approach. This approach is based on formulating constraint cell problems and a homogenization-like expansion. We present numerical results for the two continua case with separable coefficients. First, we explore the relationships between the effective coefficients and the hydraulic conductivity. Then, we solve test problems with different contrasts to study the developed multicontinuum model.
{"title":"Multicontinuum homogenization for Richards’ equation: The derivation and numerical experiments","authors":"D. Ammosov, S. Stepanov, D. Spiridonov, Wenyuan Li","doi":"10.1515/rnam-2023-0016","DOIUrl":"https://doi.org/10.1515/rnam-2023-0016","url":null,"abstract":"Abstract In the present paper, the authors rigorously derive Richards’ multicontinuum model using the multicontinuum homogenization approach. This approach is based on formulating constraint cell problems and a homogenization-like expansion. We present numerical results for the two continua case with separable coefficients. First, we explore the relationships between the effective coefficients and the hydraulic conductivity. Then, we solve test problems with different contrasts to study the developed multicontinuum model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"207 - 218"},"PeriodicalIF":0.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47603539","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}
Pub Date : 2023-08-01DOI: 10.1515/rnam-2023-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2023-frontmatter4","DOIUrl":"https://doi.org/10.1515/rnam-2023-frontmatter4","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"183 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":"136106839","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}
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.
{"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}
Abstract We describe the mathematical modelling of the group behaviour of workers in the labor market. The worker receives the salary and seeks to improve his qualifications in order to receive higher wages. The worker enlarges his qualification by the investments in human capital. At a random moment of time, a vacancy appears that provides a jump in the worker’s salary. The mathematical model of the worker’s behaviour in the labor market is presented as an optimal control problem on an infinite time horizon. The paper presents the derivation of the Kolmogorov–Fokker–Planck equation for the Lévy process, which describes the behaviour of a large amount of workers within a social layer. The numerical solution of the Kolmogorov–Fokker–Planck equation and the calculation results are presented.
{"title":"The group behaviour modelling of workers in the labor market","authors":"A. Shananin, N. Trusov","doi":"10.1515/rnam-2023-0017","DOIUrl":"https://doi.org/10.1515/rnam-2023-0017","url":null,"abstract":"Abstract We describe the mathematical modelling of the group behaviour of workers in the labor market. The worker receives the salary and seeks to improve his qualifications in order to receive higher wages. The worker enlarges his qualification by the investments in human capital. At a random moment of time, a vacancy appears that provides a jump in the worker’s salary. The mathematical model of the worker’s behaviour in the labor market is presented as an optimal control problem on an infinite time horizon. The paper presents the derivation of the Kolmogorov–Fokker–Planck equation for the Lévy process, which describes the behaviour of a large amount of workers within a social layer. The numerical solution of the Kolmogorov–Fokker–Planck equation and the calculation results are presented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"219 - 229"},"PeriodicalIF":0.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46830594","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：