Hydrodynamical activation of blood coagulation in stenosed vessels. Theoretical analysis

Abstract

Получено 30 января 2012 г., после доработки 15 февраля 2012 г.В настоящей работе исследованы гидродинамические механизмы активации плазменного звена системы свертывания крови при числах Рейнольдса в интервале от 10 до 500. Условия активации изучены в рамках модели, предполагающей, что проницаемость сосудистых стенок по отношению к первичным активаторам системы свертывания крови возрастает с увеличением касательного напряжения. Обнаружено несколько характерных сценариев развития процессов тромбообразования. Изучено влияние изменения топологии течения на активацию внутрисосудистого свертывания крови. Установлено, что пороговая активация плазменного звена системы гемостаза в стенозированных сосудах может иметь место не только при ослаблении, но и при интенсификации кровотока. В заключительной части работы обсуждены возможные медицинские приложения полученных результатов.Ключевые слова: математическое моделирование, свертывание крови, стеноз сосуда, процессы структурообразования Abstract. -The mechanisms of hydrodynamical activation of blood coagulation system are investigated in stenosed vessels for a wide range of Reynolds number values (from 10 up to 500). It is assumed that the vessel wall permeability for procoagulant factors rapidly increases when wall shear stress exceeds specific threshold value. A number of patterns of blood coagulation processes development are described. The influence of blood flow topology changes on activation of blood coagulation is explored. It is established that not only blood flow decrease, but also its increase may promote activation of blood coagulation. It was found that dependence of thrombogenic danger of stenosis on vessel lumen blockage ratio is non-monotonic. The relevance of obtained theoretical results for clinical practice is discussed.

Mathematical Modeling of Intravascular Blood Coagulation under Wall Shear Stress

“…Extended mathematical models have been proposed, however criticism for them has been wide-ranging [ 20 , 21 ]. For this reason the model introduced in this paper is built within the framework of a phenomenological approach in which blood coagulation is treated as a phase transition from a liquid to polymerized and gelled state [ 22 – 25 ]. To supplement the approach we introduce a set of closing relations that allow us to formally treat the polymerized and non-polymerized blood states in a unified manner.…”

“…The pro-coagulant factors that enter the lumen from atherosclerotic plaques are mostly products of inflammatory processes that take place inside the plaques [ 27 , 28 ]. In this work we do not focus on their biochemical nature and describe their effect in terms of a phenomenological “primary activator” of blood coagulation [ 22 – 25 ] denoted as u .…”

“…The kinetics of blood coagulation reactions is described in the framework of the phenomenological model introduced in [ 22 – 25 ]: Here θ and φ denote concentrations of the activator and the inhibitor of biochemical network of blood coagulation reactions (see [ 22 , 31 – 33 ]) and F g corresponds to fibrinogen (fibrin precursor) concentration. The components of the coagulation cascade are subject to convection and diffusion as described by the last term in Eqs ( 11 )–( 14 ).…”

“…Numerical simulations were performed assuming L x = 7.5 cm and L y = 1 cm . The values of other parameters used in numerical calculations are listed in Table 1 (see also [ 24 , 25 ]).…”