Mathematical Modeling of Blood Clotting: From Surface-Mediated Coagulation to Fibrin Polymerization

Tuesday, June 15 at 09:30am (PDT)
Tuesday, June 15 at 05:30pm (BST)
Wednesday, June 16 01:30am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS07" time block.
Note: this minisymposia has multiple sessions. The second session is MS01-MMPB (click here).

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Karin Leiderman (Colorado School of Mines, United States), Anna Nelson (University of Utah, USA)


Blood clotting is an intricate and nonlinear process that occurs under flow and on multiple spatial and temporal scales. Clots form normally during hemostasis, where an injured vessel is sealed to stop bleeding. Regulation of hemostasis depends on platelet adhesion, aggregation, and contraction, the cell-surface mediated enzyme reactions of coagulation, and formation of stabilizing fibrin matrix. Defects or perturbations can lead to serious bleeding or pathological clot formation (thrombosis). Due the complex nature of the clotting system as a whole, responses to these perturbations are challenging to predict and underlying mechanisms are difficult to determine. Here, we bring together researchers taking mathematical and computational approaches to gain insight into the complexity of the clotting system. This minisymposium will consist of two sessions: one with a focus on aspects of fibrin, fibrin polymerization, and clot mechanics and one with a focus on coagulation biochemistry, both static and under flow, and the interplay with coronavirus. The mathematical approaches include continuum and particle-based modeling of various spatial-temporal processes under flow, system biology approaches for complex biochemical systems, as well as uncertainty quantification and parameter estimation using experimental data.

Amandeep Kaur

(University of California Merced, USA)
"A new view of an old mechanism: mathematical modeling of TFPI inhibition in coagulation"
Blood coagulation is a complex network of biochemical reactions necessary to form a blood clot. The process occurs in three, overlapping stages: initiation, amplification, and propagation, with inhibitory mechanisms occurring at each stage to help avoid the system over clotting. Initiation in the tissue factor pathway begins when clotting factor VIIa (FVIIa) in the plasma binds its cofactor, tissue factor (TF), in the subendothelium and forms an active enzyme complex. Next, clotting factor X (FX) in the plasma can bind TF:VIIa, form an intermediate complex where it is enzymatically cleaved into activated FX (FXa). FXa is necessary for further events in coagulation. It has long been recognized that tissue factor pathway inhibitor (TFPI) is a strong inhibitor of TF:VIIa activity during initiation, with the primary mechanism of action reportedly being TFPI binding to FXa in the plasma, forming a complex, and then rebinding to TF:VIIa to form the newly inhibited, quaternary complex TF:VIIa:TFPI:Xa. However, previous mathematical models of this type of inhibition, for small injuries under flow, show that flow itself is a more important inhibitor of the system than TFPI. The goal of this study was to revisit previous experimental studies of TFPI where additional inhibitory reactions were suggested to be at play and use mathematical models and constrained optimization to fit these reactions schemes to multiple sets of data simultaneously. Our preliminary results suggest that the alternative reaction scheme for TFPI better describes the experimental data. Next, we highlight the ramifications of using one scheme versus the other when interpreting results from mathematical models of coagulation.

Jamie Madrigal

(Colorado School of Mines, USA)
"Estimating lipid-dependent reaction velocities"
Blood coagulation is a network of biochemical reactions whereby dozens of proteins act collectively to initiate a rapid clotting response. It is known that many of the coagulation reactions require a cellular (lipid) surface on which to occur and, in addition, the enzymatic rates are thought to be enhanced on lipid surfaces; surface diffusion and near-surface concentrations of substrates are thought to play important roles in this enhancement. Experimental data shows that at both low and high lipid concentration, rates of enzymatic reactions are low while there is some optimal intermediate lipid concentration where the rate is the fastest; this is known as the template effect. To our knowledge, this effect has never been accounted for in previous mathematical models of coagulation reactions and thus these models all result in enzyme generation that increases monotonically as lipid concentration increases. We have developed a mathematical model of lipid-mediated enzyme reactions in which the association rates between lipid-bound reactants are modified by an interaction probability. The interaction probability is derived by considering the fraction of the lipid surface that is occupied by any lipid-bound species. Preliminary model results agree with experiment ones and show the template effect. Next, for an enzymatic reaction where the experimentally measured reaction velocities are considerably different for varying lipid concentrations, we used the model with constrained optimization to estimate the intrinsic kinetic rate constants that can be fixed across lipid concentrations.

Anastasiia Mozokhina

(Peoples Friendship University of Russia (RUDN University), Russia)
"The influence of microthrombi in small vessels on the pulmonary blood flow"
Blood coagulation is an important physiological mechanism aimed to stop bleeding if the integrity of blood vessel walls is violated due to an injury. However, if the fragile balance between pro- and anticoagulant factors is not preserved, this can lead to different pathological states including thrombosis, possibly leading to heart attack, stroke, pulmonary embolism, or deep vein thrombosis. On the other side, various bleeding disorders including hemophilia can appear in the case of insufficient blood coagulation. During the ongoing COVID-19 epidemic, multiple microthrombi are observed in small pulmonary vessels leading to reduced pulmonary blood circulation and to decrease of oxygen saturation level, representing the main mortality cause of the coronavirus disease. In the current work, the model of thrombi growth is combined with the quasi-one-dimensional blood flow model of pulmonary circulation. The model is used to estimate the influence of blood vessel obstruction on the total blood flow through the lungs. The modelling results can be used as a first approximation for a non-invasive estimation of oxygen level during the coronavirus disease. The work is supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018)

Dmitry Nechipurenko

(Lomonosov Moscow State University, Russia)
"Initiation and confinement of coagulation reactions under the shear flow"
Under conditions of the high shear rate, formation of the hemostatic plug relies on platelet adhesion, activation and aggregation, and the platelet plug is additionally stabilized by fibrin mesh. It is generally considered, that coagulation reactions are significantly inhibited under flow conditions due to dilutional effects of the blood flow. However, in vitro experiments suggest that fibrin formation in platelet free plasma is possible even under arterial blood flow conditions and critically depends on the tissue factor density, the size of the “damaged” region with tissue factor and the shear rate itself. However, the exact mechanisms, which a) protect initial stages of coagulation reactions from dilution by arterial flow and b) further confine fibrin polymerization in space - are poorly understood. Here we describe both experimental and theoretical framework to address these questions. In vitro experiments were based on perfusion of recalcified platelet free plasma through microfluidic flow chambers combined with fluorescent microscopy and address the dynamics of fibrin propagation in 4D under controlled shear rate. In silico models are focused on the primary stages of coagulation process under defined shear rate and serve as important tool for elucidation and investigation of the possible mechanisms. Using in vitro model we have inferred the critical spatiotemporal parameters of fibrin polymerization process under arterial shear rate. In silico model was further used to study the kinetics of thrombin generation depending on critical internal parameters and correlated with experimental data. Our results suggest a novel mechanism, which might be important for the protection of the primary coagulation reactions from the blood flow. This work was supported by the Russian Foundation for Basic Research grant 19-51-15004 to F.A. and performed within the framework of the Development Program of the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University

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