Methods of Blood Flow Modelling

Bessonov, Nikolai; Sequeira, Adélia; Simakov, Sergey; Vassilevski, Yuri; Volpert, Vitaly

doi:10.1051/mmnp/201611101

Cited by 151 publications

(91 citation statements)

References 127 publications

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“…Blood flow can be modeled with partial differential equations or with particle methods. Navier‐Stokes equations were used if blood is considered as a Newtonian fluid, and various viscoelastic models were used if non‐Newtonian properties of blood are taken into account …”

Section: Introductionmentioning

confidence: 99%

“…In order to model platelets, particle and continuous methods were used. Among the particle methods, the immersed boundary method was used in a previous study, cellular Potts model in a previous study, dissipative particle dynamics in previous studies . Advection‐diffusion‐reaction were also used to model platelet concentration (in their active and non‐active forms) .…”

Section: Introductionmentioning

confidence: 99%

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Conditions of microvessel occlusion for blood coagulation in flow

Bouchnita

Galochkina

Kurbatova

et al. 2017

Numer Methods Biomed Eng

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Vessel occlusion is a perturbation of blood flow inside a blood vessel because of the fibrin clot formation. As a result, blood circulation in the vessel can be slowed down or even stopped. This can provoke the risk of cardiovascular events. In order to explore this phenomenon, we used a previously developed mathematical model of blood clotting to describe the concentrations of blood factors with a reaction-diffusion system of equations. The Navier-Stokes equations were used to model blood flow, and we treated the clot as a porous medium. We identify the conditions of partial or complete occlusion in a small vessel depending on various physical and physiological parameters. In particular, we were interested in the conditions on blood flow and diameter of the wounded area. The existence of a critical flow velocity separating the regimes of partial and complete occlusion was demonstrated through the mathematical investigation of a simplified model of thrombin wave propagation in Poiseuille flow. We observed different regimes of vessel occlusion depending on the model parameters both for the numerical simulations and in the theoretical study. Then, we compared the rate of clot growth in flow obtained in the simulations with experimental data. Both of them showed the existence of different regimes of clot growth depending on the velocity of blood flow.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Conditions of microvessel occlusion for blood coagulation in flow

Bouchnita

Galochkina

Kurbatova

et al. 2017

Numer Methods Biomed Eng

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“…These, and other single-scale, two-scale, and multi-scale studies were reviewed by Xu et al [49]. A more recent review by Bessonov et al [50] cites the presence of multi-scale methods apart from the CPM-PDE method used by Xu et al [46] to model cellular interactions in blood plasma, and particularly highlights the results obtained using the Dissipative Particle Dynamics-Partial Differential Equation (DPD-PDE) method for flow of plasma with platelets and RBCs.…”

Section: Multi-scale Modelsmentioning

confidence: 99%

A Short Review of Advances in the Modelling of Blood Rheology and Clot Formation

Mohan

Rajagopal

2017

Fluids

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Several advances have taken place since the early 2000s in the field of blood flow modelling. These advances have been driven by the development of assist devices such as Left Ventricular Assist Devices (LVADs), etc., and by the acceptance of in silico tests for the generation of hypotheses concerning clot formation and lysis. We give an overview of the developments in modelling of blood rheology and clot formation/lysis in the last 10 to 15 years. In blood rheology, advances are increasingly supplemented by flow simulation studies. In clot formation (or coagulation), advances have taken place in both single-scale modeling under quiescent conditions as well as in multi-scale modeling in the presence of flow. The future will possibly see more blood flow simulations in complex geometries and, simultaneously, development and simulation of multi-scale models for clot formation and lysis.

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“…В настоящее время интенсивно развиваются мате-матические методы моделирования кровотока [9]. Одним из наиболее эффективных методов, позволя-ющих охватить сосудистые бассейны с количеством сосудов порядка десяти и более, является одномер-ный подход [10].…”

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Mathematical Modelling of Circulation in Extracranial Brachocephalic Arteries at P Re-Operation Stage in Carotid Endarterectomy

Буренчев¹,

Копылов²,

Bykova³

et al. 2017

Russ J Cardiol

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Атеросклероз сонных артерий является одной из наиболее частых причин развития ишемических инсультов и выступает этиологическим фактором в 20-30% случаев [1]. Учитывая достаточно высокий периоперационный риск (смерть, острые нарушения мозгового кровотока (ОНМК)), каротидная реваску-ляризация (эндартерэктомия и стентирование) пока-зана только пациентом с тяжелым атеросклеротиче-ским поражением брахиоцефальных артерий (стеноз более 70% при ультразвуковом исследовании или более 50% при ангиографии) [1,2]. Несмотря на тща-тельный отбор пациентов, частота ОНМК при каро-тидной реваскуляризации составляет от 1,5 до 9,0% [1,3] Aim. Hemodynamic shifts in the brain, developing due to carotid surgery (carotid endarterectomy or stenting) might be the cause of perioperation strokes. Assessment for hemodynamic shifts is important. The aim of current study was to develop methodics of cerebral hemodynamics assessment at pre-operation and post-operation periods of carotid endarterectomy. Material and methods. The authors propose a mathematical model for preoperation analysis of hemodynamics changes in extracranial regions of brachiocephalic arteries after carotid endarterctomy. The development of mathematical model was based upon the data from pre-and postsurgery duplex scan and CT-angiography. Results. The results showed good prediction capacity for the shifts in cerebral hemodynamics, using the developed mathematical model.

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Methods of Blood Flow Modelling

Cited by 151 publications

References 127 publications

Conditions of microvessel occlusion for blood coagulation in flow

Conditions of microvessel occlusion for blood coagulation in flow

A Short Review of Advances in the Modelling of Blood Rheology and Clot Formation

Mathematical Modelling of Circulation in Extracranial Brachocephalic Arteries at P Re-Operation Stage in Carotid Endarterectomy

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