Abstract This work is devoted to the comparison of one- (1-D) and zero-dimensional (0-D) models of sea ice thermodynamics. 1-D thermodynamics solvers imply the solution of the diffusion equation with penetrating radiation in the moving domain (moving boundary problem), while 0-D implementations neglect the heat capacity of ice and penetrating radiation, that leads to a linear temperature profile by the construction. So far, some climate models use 0-D implementation of thermodynamics in a block of sea ice, while other models use 1-D implementation with a small number of nodes. In this work we present our fully implicit 0-D and 1-D version of snow–ice thermodynamics, which relieves the model of Courant-type time step constraints. Implicitness is achieved by the relaxation method for nonlinear heat capacity and thermal conductivity coefficients with simultaneous search for the temperature that satisfies the boundary conditions. We introduce the experiment with analytical forcing to compare evolution of temperature profiles. This model experiment shows that 0-D model underestimates ice thickness and overestimates the amplitude of temperature profile variation compared to 1-D solution. Despite the large differences in thickness and internal temperatures, the surface temperatures are very close. The models were also validated on the data of the SHEBA field experiment. According to comparison with observation data, the 0-D model predicts ice thickness and spatiotemporal temperature distribution much worse compared to 1-D model, but the amplitude of error in surface temperature is slightly greater for 0-D code. It can be concluded that 0-D model of sea ice thermodynamics is a good tool for predicting surface temperature, but it gives a large error in thickness and temperature distribution.
{"title":"The new sea ice thermodynamics code for the INM RAS Earth System model: The design and comparison of one- and zero-dimensional approaches with the observational data","authors":"Sergey S. Petrov, Vladimir K. Zyuzin, N. Iakovlev","doi":"10.1515/rnam-2023-0005","DOIUrl":"https://doi.org/10.1515/rnam-2023-0005","url":null,"abstract":"Abstract This work is devoted to the comparison of one- (1-D) and zero-dimensional (0-D) models of sea ice thermodynamics. 1-D thermodynamics solvers imply the solution of the diffusion equation with penetrating radiation in the moving domain (moving boundary problem), while 0-D implementations neglect the heat capacity of ice and penetrating radiation, that leads to a linear temperature profile by the construction. So far, some climate models use 0-D implementation of thermodynamics in a block of sea ice, while other models use 1-D implementation with a small number of nodes. In this work we present our fully implicit 0-D and 1-D version of snow–ice thermodynamics, which relieves the model of Courant-type time step constraints. Implicitness is achieved by the relaxation method for nonlinear heat capacity and thermal conductivity coefficients with simultaneous search for the temperature that satisfies the boundary conditions. We introduce the experiment with analytical forcing to compare evolution of temperature profiles. This model experiment shows that 0-D model underestimates ice thickness and overestimates the amplitude of temperature profile variation compared to 1-D solution. Despite the large differences in thickness and internal temperatures, the surface temperatures are very close. The models were also validated on the data of the SHEBA field experiment. According to comparison with observation data, the 0-D model predicts ice thickness and spatiotemporal temperature distribution much worse compared to 1-D model, but the amplitude of error in surface temperature is slightly greater for 0-D code. It can be concluded that 0-D model of sea ice thermodynamics is a good tool for predicting surface temperature, but it gives a large error in thickness and temperature distribution.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44103749","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 Algorithms for stochastic simulation of the signal arriving at the photodetector matrix of the aircraft navigation system are constructed. During the operation of the aircraft landing navigation system, the laser beam of the navigation system coincides in its direction with the glide path determining safe landing. Two photodetector units placed on board of the aircraft determine the glide path position in the coordinate system of the aircraft, which allows one to adjust the position of the touch point on the runway in poor visibility conditions. In this case, the estimation of the power and angular distributions of radiation recorded by the receiver of the navigation system is a relevant problem. In addition, it is interesting to study the effect of scattering of various multiplicities on the recorded signal. The algorithms developed here are based on direct statistical modelling (estimation over collisions) and local estimates of the Monte Carlo method. The calculations show that the proposed methods allow us to evaluate the efficiency of the laser navigation system in various conditions.
{"title":"Stochastic simulation of a signal on a photodetector matrix of a laser navigation system","authors":"E. Kablukova, V. Oshlakov, S. Prigarin","doi":"10.1515/rnam-2023-0002","DOIUrl":"https://doi.org/10.1515/rnam-2023-0002","url":null,"abstract":"Abstract Algorithms for stochastic simulation of the signal arriving at the photodetector matrix of the aircraft navigation system are constructed. During the operation of the aircraft landing navigation system, the laser beam of the navigation system coincides in its direction with the glide path determining safe landing. Two photodetector units placed on board of the aircraft determine the glide path position in the coordinate system of the aircraft, which allows one to adjust the position of the touch point on the runway in poor visibility conditions. In this case, the estimation of the power and angular distributions of radiation recorded by the receiver of the navigation system is a relevant problem. In addition, it is interesting to study the effect of scattering of various multiplicities on the recorded signal. The algorithms developed here are based on direct statistical modelling (estimation over collisions) and local estimates of the Monte Carlo method. The calculations show that the proposed methods allow us to evaluate the efficiency of the laser navigation system in various conditions.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46798847","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 variational observation data assimilation is considered for the mathematical thermodynamics model developed at the Marchuk Institute of Numerical Mathematics of RAS with the aim to reconstruct the sea surface heat flux. The sensitivity of functionals of solutions to observation data is studied for the considered variational assimilation problem and the results of numerical experiments for the Black Sea dynamics problem are presented.
{"title":"Sensitivity of functionals of the solution to a variational data assimilation problem with heat flux reconstruction for the sea thermodynamics model","authors":"V. Shutyaev, E. Parmuzin","doi":"10.1515/rnam-2022-0030","DOIUrl":"https://doi.org/10.1515/rnam-2022-0030","url":null,"abstract":"Abstract The problem of variational observation data assimilation is considered for the mathematical thermodynamics model developed at the Marchuk Institute of Numerical Mathematics of RAS with the aim to reconstruct the sea surface heat flux. The sensitivity of functionals of solutions to observation data is studied for the considered variational assimilation problem and the results of numerical experiments for the Black Sea dynamics problem are presented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48081967","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 focused on the study of the superexponential growth of the average number of particles in a stochastically homogeneous propagating medium. A mosaic Voronoi field (‘mosaic’) is considered as a random density model. The notion of ‘effective’ correlation radius is introduced to compare the results with previously obtained estimates of superexponential parameters for a spherically symmetric layered mosaic. It is shown that transition from the layered random density model to a chaotic one preserving the correlation scale and one-dimensional distribution weakens the ‘superexponential’ property of the particle flux.
{"title":"Estimation of the average particle flux in a stochastically homogeneous medium by Monte Carlo method","authors":"G. Lotova, G. A. Mikhailov","doi":"10.1515/rnam-2022-0029","DOIUrl":"https://doi.org/10.1515/rnam-2022-0029","url":null,"abstract":"Abstract The paper is focused on the study of the superexponential growth of the average number of particles in a stochastically homogeneous propagating medium. A mosaic Voronoi field (‘mosaic’) is considered as a random density model. The notion of ‘effective’ correlation radius is introduced to compare the results with previously obtained estimates of superexponential parameters for a spherically symmetric layered mosaic. It is shown that transition from the layered random density model to a chaotic one preserving the correlation scale and one-dimensional distribution weakens the ‘superexponential’ property of the particle flux.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43159781","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}
K. Alipova, G. Goyman, M. Tolstykh, V. G. Mizyak, V. Rogutov
Abstract Algorithms for stochastic perturbation of parameters and tendencies of physical parameterizations for subgrid-scale processes are implemented into the ensemble prediction system. This system is based on the global semi-Lagrangian atmospheric model SL-AV with the resolution of 0.9 × 0.72 degrees in longitude and latitude, respectively, 96 vertical levels, and our implementation of the Local Ensemble Tranform Kalman Filter (LETKF). The use of stochastically perturbed parameterizations allows to generate ensembles with a significantly larger spread compared to one obtained with the method of static parameter perturbation. An improvement in the probabilistic estimates of the ensemble forecast for different seasons is shown.
{"title":"Stochastic perturbation of tendencies and parameters of parameterizations in the global ensemble prediction system based on the SL-AV model","authors":"K. Alipova, G. Goyman, M. Tolstykh, V. G. Mizyak, V. Rogutov","doi":"10.1515/rnam-2022-0027","DOIUrl":"https://doi.org/10.1515/rnam-2022-0027","url":null,"abstract":"Abstract Algorithms for stochastic perturbation of parameters and tendencies of physical parameterizations for subgrid-scale processes are implemented into the ensemble prediction system. This system is based on the global semi-Lagrangian atmospheric model SL-AV with the resolution of 0.9 × 0.72 degrees in longitude and latitude, respectively, 96 vertical levels, and our implementation of the Local Ensemble Tranform Kalman Filter (LETKF). The use of stochastically perturbed parameterizations allows to generate ensembles with a significantly larger spread compared to one obtained with the method of static parameter perturbation. An improvement in the probabilistic estimates of the ensemble forecast for different seasons is shown.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49323596","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 new INM RAS global dynamical model of Earth’s ionosphere F region (100–500 km), which takes into account plasma-chemical processes, ambipolar diffusion, and advective ion transport due to electromagnetic drifts and neutral wind is presented. The model includes parameterizations of polar electric fields induced by magnetospheric convection and simplified equatorial drifts considerations. The focus of the paper is directed on the description of specific methods developed and utilized in the ionospheric model. Key processes responsible for the formation of global ionospheric features are outlined and their representation in the model is evaluated. The main global ionospheric characteristic features, such as seasonal and diurnal cycles, the equatorial ionization anomaly (EIA), polar ionization caps and the main trough have been adequately reproduced based on this model.
{"title":"INM-IM: INM RAS Earth ionosphere F region dynamical model","authors":"D. Kulyamin, P. A. Ostanin, V. Dymnikov","doi":"10.1515/rnam-2022-0028","DOIUrl":"https://doi.org/10.1515/rnam-2022-0028","url":null,"abstract":"Abstract A new INM RAS global dynamical model of Earth’s ionosphere F region (100–500 km), which takes into account plasma-chemical processes, ambipolar diffusion, and advective ion transport due to electromagnetic drifts and neutral wind is presented. The model includes parameterizations of polar electric fields induced by magnetospheric convection and simplified equatorial drifts considerations. The focus of the paper is directed on the description of specific methods developed and utilized in the ionospheric model. Key processes responsible for the formation of global ionospheric features are outlined and their representation in the model is evaluated. The main global ionospheric characteristic features, such as seasonal and diurnal cycles, the equatorial ionization anomaly (EIA), polar ionization caps and the main trough have been adequately reproduced based on this model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45188900","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 Mathematical models in immunology differ enormously in the dimensionality of the state space, the number of parameters and the parameterizations used to describe the immune processes. The ongoing diversification of the models needs to be complemented by rigorous ways to evaluate their complexity and select the parsimonious ones in relation to the data available/used for their calibration. A broadly applied metrics for ranking the models in mathematical immunology with respect to their complexity/parsimony is provided by the Akaike information criterion. In the present study, a computational framework is elaborated to characterize the complexity of mathematical models in immunology using a more general approach, namely, the Minimum Description Length criterion. It balances the model goodness-of-fit with the dimensionality and geometrical complexity of the model. Four representative models of the immune response to acute viral infection formulated with either ordinary or delay differential equations are studied. Essential numerical details enabling the assessment and ranking of the viral infection models include: (1) the optimization of the likelihood function, (2) the computation of the model sensitivity functions, (3) the evaluation of the Fisher information matrix and (4) the estimation of multidimensional integrals over the model parameter space.
{"title":"Application of minimum description length criterion to assess the complexity of models in mathematical immunology","authors":"D. Grebennikov, V. V. Zheltkova, G. Bocharov","doi":"10.1515/rnam-2022-0022","DOIUrl":"https://doi.org/10.1515/rnam-2022-0022","url":null,"abstract":"Abstract Mathematical models in immunology differ enormously in the dimensionality of the state space, the number of parameters and the parameterizations used to describe the immune processes. The ongoing diversification of the models needs to be complemented by rigorous ways to evaluate their complexity and select the parsimonious ones in relation to the data available/used for their calibration. A broadly applied metrics for ranking the models in mathematical immunology with respect to their complexity/parsimony is provided by the Akaike information criterion. In the present study, a computational framework is elaborated to characterize the complexity of mathematical models in immunology using a more general approach, namely, the Minimum Description Length criterion. It balances the model goodness-of-fit with the dimensionality and geometrical complexity of the model. Four representative models of the immune response to acute viral infection formulated with either ordinary or delay differential equations are studied. Essential numerical details enabling the assessment and ranking of the viral infection models include: (1) the optimization of the likelihood function, (2) the computation of the model sensitivity functions, (3) the evaluation of the Fisher information matrix and (4) the estimation of multidimensional integrals over the model parameter space.","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":"45560982","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}
S. Simakov, T. Gamilov, A. Danilov, F. Liang, P. Chomakhidze, Mariam K. Gappoeva, Alina A. Rebrova, P. Kopylov
Abstract Coronary artery disease is the leading cause of mortality worldwide, accounting for 12.8% of all deaths. Although the clinical benefits of treating stenosis with percutaneous coronary intervention (PCI) have been extensively demonstrated, residual myocardial ischemia remains in about 30–50% of patients even after a formally successful PCI. We apply previously developed and validated 1D model of haemodynamics, which distributes terminal hydraulic resistance based on the diameters of the parent vessels and Murray’s law by a recursive algorithm. In our new model the terminal resistance is decreased according to a transmural perfusion ratio increase. In contrast to our previous work we calculate the transmural perfusion ratio for personally defined zones. Thus, peripheral hydraulic resistance of myocardial perfusion is personalized based on patient data, whichwere extracted from computed tomography perfusion images. The model serves as a computational tool for simulating pre- to post-PCI changes in coronary haemodynamics of four patients. We simulate fractional flow reserve (FFR), coronary flow reserve (CFR), instantaneous wave-free ratio (iFR), average flow in selected arteries in hyperemic and rest conditions before PCI and after PCI immediately after the surgery (in a short-term) and in a long-term (several months) perspectives. We conclude that high FFR and iFR values in short-term and long-term perspectives are not necessary correlate with CFR improvement and long-term blood flow recovery in coronary arteries.
{"title":"Personalized computational estimation of relative change in coronary blood flow after percutaneous coronary intervention in short-term and long-term perspectives","authors":"S. Simakov, T. Gamilov, A. Danilov, F. Liang, P. Chomakhidze, Mariam K. Gappoeva, Alina A. Rebrova, P. Kopylov","doi":"10.1515/rnam-2022-0024","DOIUrl":"https://doi.org/10.1515/rnam-2022-0024","url":null,"abstract":"Abstract Coronary artery disease is the leading cause of mortality worldwide, accounting for 12.8% of all deaths. Although the clinical benefits of treating stenosis with percutaneous coronary intervention (PCI) have been extensively demonstrated, residual myocardial ischemia remains in about 30–50% of patients even after a formally successful PCI. We apply previously developed and validated 1D model of haemodynamics, which distributes terminal hydraulic resistance based on the diameters of the parent vessels and Murray’s law by a recursive algorithm. In our new model the terminal resistance is decreased according to a transmural perfusion ratio increase. In contrast to our previous work we calculate the transmural perfusion ratio for personally defined zones. Thus, peripheral hydraulic resistance of myocardial perfusion is personalized based on patient data, whichwere extracted from computed tomography perfusion images. The model serves as a computational tool for simulating pre- to post-PCI changes in coronary haemodynamics of four patients. We simulate fractional flow reserve (FFR), coronary flow reserve (CFR), instantaneous wave-free ratio (iFR), average flow in selected arteries in hyperemic and rest conditions before PCI and after PCI immediately after the surgery (in a short-term) and in a long-term (several months) perspectives. We conclude that high FFR and iFR values in short-term and long-term perspectives are not necessary correlate with CFR improvement and long-term blood flow recovery in coronary arteries.","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":"46109070","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 aortic valve neocuspidization (AVNeo) procedure requires the design of patient-specific neo-cusps which can be made numerically through the neovalve closure modelling. Prior the simulation, it is required to ‘suture virtually’ the neocusps into the patient’s aortic geometry, i.e., to find such state in which the neocusps are placed in the aortic root lumen without intersections of physical surfaces and neo-valve prolapse, and the position of the suture boundary satisfies the boundary conditions. To solve this problem, we tried to mimic neocusps suturing in Ozaki’s operation. As a result, we propose a new algorithm for ‘virtual suturing’ of given neocusps, considered as thin shells. The approach is able to work with both small and large (compared to an optimal size) neocusps and to handle each cusp independently of the others.
{"title":"Computational mimicking of surgical leaflet suturing for virtual aortic valve neocuspidization","authors":"A. Liogky","doi":"10.1515/rnam-2022-0023","DOIUrl":"https://doi.org/10.1515/rnam-2022-0023","url":null,"abstract":"Abstract The aortic valve neocuspidization (AVNeo) procedure requires the design of patient-specific neo-cusps which can be made numerically through the neovalve closure modelling. Prior the simulation, it is required to ‘suture virtually’ the neocusps into the patient’s aortic geometry, i.e., to find such state in which the neocusps are placed in the aortic root lumen without intersections of physical surfaces and neo-valve prolapse, and the position of the suture boundary satisfies the boundary conditions. To solve this problem, we tried to mimic neocusps suturing in Ozaki’s operation. As a result, we propose a new algorithm for ‘virtual suturing’ of given neocusps, considered as thin shells. The approach is able to work with both small and large (compared to an optimal size) neocusps and to handle each cusp independently of the others.","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":"42460261","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. Tikhvinskii, Lema R. Merzhoeva, A. Chupakhin, A. Karpenko, D. Parshin
Abstract Abdominal aortic aneurysm is a widespread disease of cardiovascular system. Predicting a moment of its rupture is an important task for modern vascular surgery. At the same time, little attention is paid to the comorbidities, which are often the causes of severe postoperative complications or even death. This work is devoted to a numerical study of the haemodynamics of the model geometry for possible localizations of abdominal aortic aneurysm: on the aortic trunk or on its bifurcation. Both rigid and FSI numerical simulations are considered and compared with the model aortic configuration without aneurysm. It is shown that in the case of localization of the aneurysm on the bifurcation, the pressure in aorta increases upstream. Moreover, only in the case of a special geometry,when the radii of the iliac arteries are equal (r1 = r2), and the angle between them is 60 degrees, there is a linear relationship between the pressure in the aorta above the aneurysm and the size of the aneurysm itself: the slope of the straight line is in the interval a ∈ (0.003; 0.857), and the coefficient of determination is R2 ⩾ 0.75. The area bounded by the curve of the ‘pressure–velocity’ diagram for the values of velocity and pressure upstream in the presence of an aneurysm decreases compared to a healthy case (a vessel without an aneurysm). The simulation results in the rigid and FSI formulations agree qualitatively with each other. The obtained results provide a better understanding of the relationship between the geometrical parameters of the aneurysm and the changing of haemodynamics in the aortic bifurcation and its effect on the cardiovascular system upstream of the aneurysm.
{"title":"Computational analysis of the impact of aortic bifurcation geometry to AAA haemodynamics","authors":"D. Tikhvinskii, Lema R. Merzhoeva, A. Chupakhin, A. Karpenko, D. Parshin","doi":"10.1515/rnam-2022-0026","DOIUrl":"https://doi.org/10.1515/rnam-2022-0026","url":null,"abstract":"Abstract Abdominal aortic aneurysm is a widespread disease of cardiovascular system. Predicting a moment of its rupture is an important task for modern vascular surgery. At the same time, little attention is paid to the comorbidities, which are often the causes of severe postoperative complications or even death. This work is devoted to a numerical study of the haemodynamics of the model geometry for possible localizations of abdominal aortic aneurysm: on the aortic trunk or on its bifurcation. Both rigid and FSI numerical simulations are considered and compared with the model aortic configuration without aneurysm. It is shown that in the case of localization of the aneurysm on the bifurcation, the pressure in aorta increases upstream. Moreover, only in the case of a special geometry,when the radii of the iliac arteries are equal (r1 = r2), and the angle between them is 60 degrees, there is a linear relationship between the pressure in the aorta above the aneurysm and the size of the aneurysm itself: the slope of the straight line is in the interval a ∈ (0.003; 0.857), and the coefficient of determination is R2 ⩾ 0.75. The area bounded by the curve of the ‘pressure–velocity’ diagram for the values of velocity and pressure upstream in the presence of an aneurysm decreases compared to a healthy case (a vessel without an aneurysm). The simulation results in the rigid and FSI formulations agree qualitatively with each other. The obtained results provide a better understanding of the relationship between the geometrical parameters of the aneurysm and the changing of haemodynamics in the aortic bifurcation and its effect on the cardiovascular system upstream of the aneurysm.","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":"41901159","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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