Abstract Quantitative systems pharmacology (QSP) is a relatively new modelling discipline, formed within the ever-growing domain of model-informed drug development and actively evolving throughout the last decade. This modelling technique is based on the systems analysis and is used to get a quantitative rather than qualitative understanding of systems dynamics and explore the mechanisms of action of a drug. However, there is no well-defined methodology for the QSP model development, which significantly complicates the practical application of these models. In the current work, we overview the existing mathematical models of antidiabetic therapies and propose a modelling method, which overcomes common limitations and is able to produce a physiologically based mechanistic model describing gliflozin action in type 2 diabetes mellitus. From the practical standpoint, sensitivity analysis preformed in this work helped to reveal subpopulation of patients with better response to gliflozin therapy.
{"title":"Algorithms and methodological challenges in the development and application of quantitative systems pharmacology models: a case study in type 2 diabetes","authors":"V. Sokolov","doi":"10.1515/rnam-2022-0025","DOIUrl":"https://doi.org/10.1515/rnam-2022-0025","url":null,"abstract":"Abstract Quantitative systems pharmacology (QSP) is a relatively new modelling discipline, formed within the ever-growing domain of model-informed drug development and actively evolving throughout the last decade. This modelling technique is based on the systems analysis and is used to get a quantitative rather than qualitative understanding of systems dynamics and explore the mechanisms of action of a drug. However, there is no well-defined methodology for the QSP model development, which significantly complicates the practical application of these models. In the current work, we overview the existing mathematical models of antidiabetic therapies and propose a modelling method, which overcomes common limitations and is able to produce a physiologically based mechanistic model describing gliflozin action in type 2 diabetes mellitus. From the practical standpoint, sensitivity analysis preformed in this work helped to reveal subpopulation of patients with better response to gliflozin therapy.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45577366","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 concept of optimal disturbances of periodic solutions for a system of time-delay differential equations is defined. An algorithm for computing the optimal disturbances is proposed and justified. This algorithm is tested on the known system of four nonlinear time-delay differential equations modelling the dynamics of the experimental infection caused by the lymphocytic choriomeningitis virus. The results of numerical experiments are discussed.
{"title":"Optimal disturbances for periodic solutions of time-delay differential equations","authors":"M. Y. Khristichenko, Y. Nechepurenko","doi":"10.1515/rnam-2022-0017","DOIUrl":"https://doi.org/10.1515/rnam-2022-0017","url":null,"abstract":"Abstract A concept of optimal disturbances of periodic solutions for a system of time-delay differential equations is defined. An algorithm for computing the optimal disturbances is proposed and justified. This algorithm is tested on the known system of four nonlinear time-delay differential equations modelling the dynamics of the experimental infection caused by the lymphocytic choriomeningitis virus. The results of numerical experiments are discussed.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42778205","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 homogeneous Dirichlet initial-boundary value problem for a quasilinear parabolic equation with a time-fractional derivative and coefficients at the elliptic part that depend on the gradient of the solution is considered. Conditions on the coefficients ensure the monotonicity and Lipschitz property of the elliptic operator on the set of functions whose gradients in space variables are uniformly bounded. For this problem, a linear regularized mesh scheme is constructed and investigated. A sufficient condition is derived for the regularization parameter that ensures the so-called local correctness of the mesh scheme. On the basis of correctness and approximation estimates for model problems with time-fractional Caputo or Caputo–Fabrizio derivatives, accuracy estimates are given in terms of mesh and regularization parameters under the assumption of the existence of a smooth solution to the differential problem. The presented results of the numerical experiments confirm the obtained asymptotic accuracy estimates.
{"title":"Linear regularized finite difference scheme for the quasilinear subdiffusion equation","authors":"A. Lapin, E. Laitinen","doi":"10.1515/rnam-2022-0019","DOIUrl":"https://doi.org/10.1515/rnam-2022-0019","url":null,"abstract":"Abstract A homogeneous Dirichlet initial-boundary value problem for a quasilinear parabolic equation with a time-fractional derivative and coefficients at the elliptic part that depend on the gradient of the solution is considered. Conditions on the coefficients ensure the monotonicity and Lipschitz property of the elliptic operator on the set of functions whose gradients in space variables are uniformly bounded. For this problem, a linear regularized mesh scheme is constructed and investigated. A sufficient condition is derived for the regularization parameter that ensures the so-called local correctness of the mesh scheme. On the basis of correctness and approximation estimates for model problems with time-fractional Caputo or Caputo–Fabrizio derivatives, accuracy estimates are given in terms of mesh and regularization parameters under the assumption of the existence of a smooth solution to the differential problem. The presented results of the numerical experiments confirm the obtained asymptotic accuracy estimates.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46827088","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 To solve problems of radiation balance, optical sounding, and tomography, it may be necessary to take into account multiple scattering of radiation in a stochastically inhomogeneous medium. In real radiation models, for this purpose, the numerical-statistical ‘majorant cross-section method’ (MCM, delta-Woodcock tracking) is used based on the alignment of the optical density field by adding an artificial ‘delta scattering’ event. However, the computation cost of the corresponding unbiased estimate of the averaged problem solution infinitely increases as the correlation scale (correlation radius L) of standard mosaic models for a random medium density decreases. Previously, we constructed the MCM randomization providing asymptotically (for L → 0) unbiased estimates of the required functionals, in which the value of the physical attenuation coefficient is randomly chosen at the end of the particle free path l under condition l > L. Otherwise the value of the physical attenuation coefficient is the same as at the starting point of the particle (CR algorithm). In a more accurate functional correlative randomized algorithm (FCR algorithm), the coefficient remains the same with a probability determined by the correlation function. These correlative randomized algorithms were implemented for a mixture of homogeneous substance (water) and a Poisson ensemble of ‘empty’ balls. In the present paper, we construct correlative randomized algorithms for problems related to transfer through a ‘thick’ layer containing a water and a Poisson ensemble of ‘empty’ layers. A detailed comparative analysis of the results obtained by exact direct simulation (MCM) and approximate algorithms (CR, FCR) for the problems of gamma radiation transfer through a ‘thick’ water layer containing a Poisson ensemble of ‘empty’ layers or balls is presented.
{"title":"On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium","authors":"I. N. Medvedev","doi":"10.1515/rnam-2022-0020","DOIUrl":"https://doi.org/10.1515/rnam-2022-0020","url":null,"abstract":"Abstract To solve problems of radiation balance, optical sounding, and tomography, it may be necessary to take into account multiple scattering of radiation in a stochastically inhomogeneous medium. In real radiation models, for this purpose, the numerical-statistical ‘majorant cross-section method’ (MCM, delta-Woodcock tracking) is used based on the alignment of the optical density field by adding an artificial ‘delta scattering’ event. However, the computation cost of the corresponding unbiased estimate of the averaged problem solution infinitely increases as the correlation scale (correlation radius L) of standard mosaic models for a random medium density decreases. Previously, we constructed the MCM randomization providing asymptotically (for L → 0) unbiased estimates of the required functionals, in which the value of the physical attenuation coefficient is randomly chosen at the end of the particle free path l under condition l > L. Otherwise the value of the physical attenuation coefficient is the same as at the starting point of the particle (CR algorithm). In a more accurate functional correlative randomized algorithm (FCR algorithm), the coefficient remains the same with a probability determined by the correlation function. These correlative randomized algorithms were implemented for a mixture of homogeneous substance (water) and a Poisson ensemble of ‘empty’ balls. In the present paper, we construct correlative randomized algorithms for problems related to transfer through a ‘thick’ layer containing a water and a Poisson ensemble of ‘empty’ layers. A detailed comparative analysis of the results obtained by exact direct simulation (MCM) and approximate algorithms (CR, FCR) for the problems of gamma radiation transfer through a ‘thick’ water layer containing a Poisson ensemble of ‘empty’ layers or balls is presented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45510400","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}
R. Fadeev, K. Alipova, Anna S. Koshkina, Timofey E. Lapin, N. Ozerova, Alina E. Pereladova, Andrey V. Sakhno, M. Tolstykh
Abstract In the present paper, we describe a one-dimensional glacier parameterization for use in the numerical weather prediction models. The proposed scheme is implemented into the global atmospheric model SLAV. To avoid inconsistency of surface temperature and turbulent heat fluxes in the lower troposphere, glacier parameterization has been iteratively coupled with both planetary boundary layer and land surface schemes. First results from numerical experiments with the SLAV model show that the introduction of a simplified description of the glacier heat capacity can significantly improve the 2-meter temperature long-range weather forecast skill.
{"title":"Glacier parameterization in SLAV numerical weather prediction model","authors":"R. Fadeev, K. Alipova, Anna S. Koshkina, Timofey E. Lapin, N. Ozerova, Alina E. Pereladova, Andrey V. Sakhno, M. Tolstykh","doi":"10.1515/rnam-2022-0016","DOIUrl":"https://doi.org/10.1515/rnam-2022-0016","url":null,"abstract":"Abstract In the present paper, we describe a one-dimensional glacier parameterization for use in the numerical weather prediction models. The proposed scheme is implemented into the global atmospheric model SLAV. To avoid inconsistency of surface temperature and turbulent heat fluxes in the lower troposphere, glacier parameterization has been iteratively coupled with both planetary boundary layer and land surface schemes. First results from numerical experiments with the SLAV model show that the introduction of a simplified description of the glacier heat capacity can significantly improve the 2-meter temperature long-range weather forecast skill.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44943943","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 paper is devoted to a posteriori error identities for the stationary reaction–convection–diffusion problem with mixed Dirichlét–Neumann boundary conditions. They reflect the most general relations between deviations of approximations from the exact solutions and those values that can be observed in a numerical experiment. The identities contain no mesh dependent constants and are valid for any function in the admissible (energy) class. Therefore, the identities and the estimates that follow from them generate universal and fully reliable tools of a posteriori error control.
{"title":"Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control","authors":"S. Repin","doi":"10.1515/rnam-2022-0021","DOIUrl":"https://doi.org/10.1515/rnam-2022-0021","url":null,"abstract":"Abstract The paper is devoted to a posteriori error identities for the stationary reaction–convection–diffusion problem with mixed Dirichlét–Neumann boundary conditions. They reflect the most general relations between deviations of approximations from the exact solutions and those values that can be observed in a numerical experiment. The identities contain no mesh dependent constants and are valid for any function in the admissible (energy) class. Therefore, the identities and the estimates that follow from them generate universal and fully reliable tools of a posteriori error control.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41281430","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 problem of minimizing the root-mean-square error of the numerical-statistical projection estimation of the solution to an integral equation is solved. It is shown that the optimal estimator in this sense can be obtained by equalizing deterministic and stochastic components of the error in the case when the norm of the remainder of the utilized decomposition decreases inversely proportional to its length. As a test, the Milne problem of radiation transfer in a semi-infinite layer of matter is solved using Laguerre polynomials. To solve such a problem in the case of a finite layer, a special regularized projection algorithm is used.
{"title":"Construction and optimization of numerically-statistical projection algorithms for solving integral equations","authors":"A. S. Korda, G. A. Mikhailov, S. V. Rogasinsky","doi":"10.1515/rnam-2022-0018","DOIUrl":"https://doi.org/10.1515/rnam-2022-0018","url":null,"abstract":"Abstract The problem of minimizing the root-mean-square error of the numerical-statistical projection estimation of the solution to an integral equation is solved. It is shown that the optimal estimator in this sense can be obtained by equalizing deterministic and stochastic components of the error in the case when the norm of the remainder of the utilized decomposition decreases inversely proportional to its length. As a test, the Milne problem of radiation transfer in a semi-infinite layer of matter is solved using Laguerre polynomials. To solve such a problem in the case of a finite layer, a special regularized projection algorithm is used.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42598300","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 An iterative method with the number of iterations independent of the coefficient jumps is proposed for the boundary value problem for a diffusion equation with highly varying coefficient. The method applies one solution of the Poisson equation at each step of iteration. In the present paper we extend the class of domains the iterative method is justified for.
{"title":"Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients","authors":"G. Kobelkov, E. Schnack","doi":"10.1515/rnam-2022-0012","DOIUrl":"https://doi.org/10.1515/rnam-2022-0012","url":null,"abstract":"Abstract An iterative method with the number of iterations independent of the coefficient jumps is proposed for the boundary value problem for a diffusion equation with highly varying coefficient. The method applies one solution of the Poisson equation at each step of iteration. In the present paper we extend the class of domains the iterative method is justified for.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44989861","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 technique for constructing a sequence of difference schemes with the properties of a corrector and a predictor for integrating systems of the second-order ordinary differential equations is presented. The sequence of schemes begins with the explicit three-point Störmer method of the second order of approximation. Each subsequent scheme also implements the Störmer method corrected with additional terms calculated through the solution of the previous scheme. The stability of the resulting schemes and the increase in the order of convergence for the first of them are carefully substantiated. The results of calculations of the test problem are presented, confirming the increase in the order of accuracy of the constructed methods.
{"title":"Difference schemes for second-order ordinary differential equations with corrector and predictor properties","authors":"V. Shaidurov, A. Novikov","doi":"10.1515/rnam-2022-0015","DOIUrl":"https://doi.org/10.1515/rnam-2022-0015","url":null,"abstract":"Abstract A technique for constructing a sequence of difference schemes with the properties of a corrector and a predictor for integrating systems of the second-order ordinary differential equations is presented. The sequence of schemes begins with the explicit three-point Störmer method of the second order of approximation. Each subsequent scheme also implements the Störmer method corrected with additional terms calculated through the solution of the previous scheme. The stability of the resulting schemes and the increase in the order of convergence for the first of them are carefully substantiated. The results of calculations of the test problem are presented, confirming the increase in the order of accuracy of the constructed methods.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45625216","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 finite element method for a monolithic quasi-Lagrangian formulation of a fluid–porous structure interaction problem with a corrected balance of stresses on the fluid–structure interface is considered. Deformations of the elastic medium are not necessarily small and are modelled using Saint Venant–Kirchhoff (SVK) constitutive relation. The stability of the method is proved in a form of energy bound for the finite element solution.
{"title":"A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem","authors":"A. Lozovskiy, M. Olshanskii, Y. Vassilevski","doi":"10.1515/rnam-2022-0014","DOIUrl":"https://doi.org/10.1515/rnam-2022-0014","url":null,"abstract":"Abstract A finite element method for a monolithic quasi-Lagrangian formulation of a fluid–porous structure interaction problem with a corrected balance of stresses on the fluid–structure interface is considered. Deformations of the elastic medium are not necessarily small and are modelled using Saint Venant–Kirchhoff (SVK) constitutive relation. The stability of the method is proved in a form of energy bound for the finite element solution.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44609689","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}
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