Noninvasive Assessment of Fractional Flow Reserve Using Mathematical Modeling of Coronary Flow

Gognieva, Daria; Сыркин, А. Л.; Vassilevski, Yuri; Simakov, Sergey; Melerzanov, Alexander; Liang, Fuyou; Lomonosova, A. A.; Bykova, A. A.; Manaa, H.E. El; Kopylov, Philippe

doi:10.18087/cardio.2018.12.10164

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…Следует отметить высокую специфичность при выявлении индуцированной ишемии. В последнее время применяется неинвазивная оценка фракционного резерва кровотока [44].…”

Section: индекс колебаний касательного напряженияunclassified

Application of mathematical modelling for the evaluation of the results of systemiс-pulmonary shunts formation

Sinelnikov¹,

Arutunyan²,

Porodikov³

et al. 2020

PKiK

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Surgical treatment of congenital heart defects with the obstruction of the outflow tract of the right ventricle can be performed in several stages. The first stage of surgical correction is the creation of a systemic-pulmonary shunt, followed by radical correction. The main complications of systemic-pulmonary shunts are associated with the development of shunt thrombosis and hypervolemia of the pulmonary circulation. Currently, considering the importance of individual selection of a shunt for effective functioning, the main scientific search is aimed at creating optimal methods that consider all the hemodynamic features of a particular patient. Recently, the direction of mathematical modelling and biomechanical analysis in medicine has been actively developing, facilitating the objective evaluation of the accumulated clinical experience and is one of the main tools in evidence-based medicine. The use of computational fluid dynamics methods for modified Blalock–Taussig shunt analysis allows us evaluate the hemodynamic parameters for various configurations of shunts and anastomosis angles and improve the understanding of pathophysiological processes in the cardiovascular system before or after an application of the modified Blalock–Taussig shunt. Here, we provide an overview of the work related to the use of modelling for the calculation of the currents in the aorta–shunt–pulmonary artery system. It is noteworthy that most studies consider the personalised characteristics of the patients and are therefore highly likely to be used in clinical practice. The main hemodynamic parameters that are analysed with the computer calculations are described. Part of the work is devoted to the stages of computer modelling and the limitations in the implementation of these stages. We believe that this manuscript will be of interest to specialists in cardiovascular surgery and to the several scholars working in areas related to the use of digital technologies in medicine, mathematical modelling in medicine and biomechanics.Received 30 January 2020. Revised 25 May 2020. Accepted 9 June 2020.Conflict of interest: Authors declare no conflict of interest.Funding: The work is supported by the program for the development of the Scientific and Educational Mathematical Center of the Volga Federal District (No. 075-02-2020-1478) and a grant for the development of the scientific school of the Perm Region “Computer biomechanics and digital technologies in biomedicine”.Author contributions Conception and design: Yu.S. Sinelnikov, V.B. Arutunyan, A.A. Porodikov, A.N. Biyanov, V.S. Tuktamyshev, M.I. Shmurak, A.R. Khairulin Drafting the article: A.A. Porodikov, A.N. Biyanov, A.G. Kuchumov Critical revision of the article: A.N. Biyanov, A.G. Kuchumov Final approval of the version to be published: Yu.S. Sinelnikov, V.B. Arutunyan, A.A. Porodikov, A.N. Biyanov, V.S. Tuktamyshev, M.I. Shmurak, A.R. Khairulin, A.G. Kuchumov

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Section: индекс колебаний касательного напряженияunclassified

Application of mathematical modelling for the evaluation of the results of systemiс-pulmonary shunts formation

Sinelnikov¹,

Arutunyan²,

Porodikov³

et al. 2020

PKiK

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“…The other parameters are set according to wellknown physiologically correct ranges for selected groups classified by age, body mass index, smoking and alcohol consumption, lifestyle, etc. The 1D models are capable to predict FFR with acceptable accuracy and are suitable for the bedside applications [31,[77][78][79]. Moreover, these models can be used in multistenotic vasculatures where the classical FFR definition is not applicable: even the case of two successive stenoses has another FFR formula [148].…”

Section: Clinical Applicationsmentioning

confidence: 99%

Mathematical modelling of atherosclerosis

Khatib¹,

Kafi²,

Sequeira³

et al. 2019

Math. Model. Nat. Phenom.

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The review presents the state of the art in the atherosclerosis modelling. It begins with the biological introduction describing the mechanisms of chronic inflammation of artery walls characterizing the development of atherosclerosis. In particular, we present in more detail models describing this chronic inflammation as a reaction-diffusion wave with regimes of propagation depending on the level of cholesterol (LDL) and models of rolling monocytes initializing the inflammation. Further development of this disease results in the formation of atherosclerotic plaque, vessel remodelling and possible plaque rupture due its interaction with blood flow. We review plaque-flow interaction models as well as reduced models (0D and 1D) of blood flow in atherosclerotic vasculature.

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“…Ключевые слова: уравнения в частных производных, графы, вычислительные модели, уравнения гиперболического типа, численное моделирование, граничные условия Разработка сетевых вычислительных моделей для исследования… Введение В различных приложениях возникают задачи, моделируемые уравнениями в частных производных на графах (сетях, деревьях). В качестве примера можно указать глобальные модели дыхательной и кровеносной систем человека [Kholodov et al, 2005;Simakov et al, 2005Simakov et al, , 2006aSimakov et al, , 2006bSimakov, 2018;Carson, 2018;Gognieva et al, 2018Gognieva et al, , 2019, интенсивного уличного движения в мегаполисе [Kholodov, Kholodov, 2004;Kholodov et al, 2006;Холодов и др., 2010;Morozov et al, 2011;Kholodov et al, 2014;Alekseenko et al, 2015;Kholodov et al, 2015;Alekseenko et al, 2017;Prokoptsev et al, 2018], динамики стержневых конструкций и каркасных сооружений [Kholodov et al, 2006], переходных процессов в электроэнергетических системах [Морозов, Холодов, 2008;Bordonos et al, 2009; Морозов и др., 2010], интенсивных информационных потоков в компьютерных и телекоммуникационных сетях [Северов и др., 2008;Трифонов и др., 2008;Severov et al, 2012;Trifonov, Kholodov, 2012], распространения мелкодисперсных примесей в вентиляционных сетях [Geller et al, 2010;Kholodov et al, 2017] и др.…”

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Development of network computational models for the study of nonlinear wave processes on graphs

Kholodov¹

2019

CRM

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In various applications arise problems modeled by nonlinear partial differential equations on graphs (networks, trees). In order to study such problems and various extreme situations arose in the problems of designing and optimizing networks developed the computational model based on solving the corresponding boundary problems for partial differential equations of hyperbolic type on graphs (networks, trees). As applications, three different problems were chosen solved in the framework of the general approach of network computational models. The first was modeling of traffic flow. In solving this problem, a macroscopic approach was used in which the transport flow is described by a nonlinear system of second-order hyperbolic equations. The results of numerical simulations showed that the model developed as part of the proposed approach well reproduces the real situation various sections of the Moscow transport network on significant time intervals and can also be used to select the most optimal traffic management strategy in the city. The second was modeling of data flows in computer networks. In this problem data flows of various connections in packet data network were simulated as some continuous medium flows. Conceptual and mathematical network models are proposed. The numerical simulation was carried out in comparison with the NS-2 network simulation system. The results showed that in comparison with the NS-2 packet model the developed streaming model demonstrates significant savings in computing resources while ensuring a good level of similarity and allows us to simulate the behavior of complex globally distributed IP networks. The third was simulation of the distribution of gas impurities in ventilation networks. It was developed the computational mathematical model for the propagation of finely dispersed or gas impurities in ventilation networks using the gas dynamics equations by numerical linking of regions of different sizes. The calculations shown that the model with good accuracy allows to determine the distribution of gas-dynamic parameters in the pipeline network and solve the problems of dynamic ventilation management.

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Noninvasive Assessment of Fractional Flow Reserve Using Mathematical Modeling of Coronary Flow

Cited by 6 publications

References 19 publications

Application of mathematical modelling for the evaluation of the results of systemiс-pulmonary shunts formation

Application of mathematical modelling for the evaluation of the results of systemiс-pulmonary shunts formation

Mathematical modelling of atherosclerosis

Development of network computational models for the study of nonlinear wave processes on graphs

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