Mathematical modelling of platelet rich plasma clotting. Pointwise unified model

Abstract

The mechanistic modelling of blood clotting and fibrin-polymer mesh formation is of significant value for medical and biophysics applications. This paper presents a combination of two pointwise kinetic models represented by system of ODEs. One of them represents the reaction dynamics of clotting factors including the role of the platelet membranes. The second one describes the fibrin-polymer formation as a multistage polymerization process with a sol-gel transition at the final stage. Complex-value second order Rosenbrock method (CROS) is employed for the computational experiments. A sensitivity analysis method built into the computational scheme helps clarify non-evident dependencies in the exhaustive system of ODEs. The unified model was primarily verified using conditions of factor VII deficiency. The model, however requires a significant effort to be tested against experimental data available.

Patient-Specific Modelling of Blood Coagulation

“…Models with more complete kinetics contain too many equations and unknown constants, especially for the platelet-rich plasma. Moreover, these constants are patient-specific with possibly large variations (see Andreeva et al 2018;Chelle et al 2018) and the references therein). Models with simpler kinetics impose some assumptions which can be difficult to verify (Tokarev et al 2019).…”

“…These limitations also concern the application of theoretical modelling in clinical practice, mainly because of the large variation of patient-specific parameters and physiological conditions (Andreeva et al 2018;Bouchnita et al 2017b;Chelle et al 2018). In this work, we develop a modelling approach taking into account patient-specific parameters.…”

“…There are numerous chemical kinetic models describing coagulation reactions, from very simple containing several equations to very complex with more than one hundred of equations (see Belyaev et al 2018;Chelle et al 2018;Hemker 1993;Hemker and Beguin 1995;Hockin 2002;Hoffman et al 2005;Mann et al 2003 and the references therein). The main difficulty of complex models is that they contain many reaction rate constants, mainly unknown or with a large discrepancy of their values in the existing literature (Andreeva et al 2018;Chelle et al 2018). Since the experimental and clinical data are often reduced to thrombin generation curves (thrombin concentration in time), the inverse problem for the determination of the parameters of the model becomes highly under-determined.…”

Using extended ODE systems to investigate the mathematical model of the blood coagulation

“…Включение тромбоцитов в математическую модель позволяет аккуратно учитывать процессы на мембранах. Такой подход развит в [Susree, Anand, 2017;Andreeva et al, 2018]. Модель [Susree, Anand, 2017] подробно описывает процесс активации факторов свертывания крови.…”

“…В настоящей работе рассматривается одна из математических моделей свертывания крови [Andreeva et al, 2018]. Проводится уточнение констант реакций по данным лабораторных экспериментов.…”