Threshold of microvascular occlusion: injury size defines the thrombosis scenario

Damage to the blood vessel triggers formation of a hemostatic plug, which is meant to prevent bleeding, yet the same phenomenon may result in a total blockade of a blood vessel by a thrombus, causing severe medical conditions. Here, we show that the physical interplay between platelet adhesion and hemodynamics in a microchannel manifests in a critical threshold behavior of a growing thrombus. Depending on the size of injury, two distinct dynamic pathways of thrombosis were found: the formation of a nonocclusive plug, if injury length does not exceed the critical value, and the total occlusion of the vessel by the thrombus otherwise. We develop a mathematical model that demonstrates that switching between these regimes occurs as a result of a saddle-node bifurcation. Our study reveals the mechanism of self-regulation of thrombosis in blood microvessels and explains experimentally observed distinctions between thrombi of different physical etiology. This also can be useful for the design of platelet-aggregation-inspired engineering solutions.Comment: 7 pages, 5 figures + Supplementary informatio

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral non-covalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physico-chemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force-deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9+/-0.4 kcal/mol) and longitudinal (14.9+/-1.5 kcal/mol) tubulin-tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000-26,000 pN*nm^2), support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblie

Continuous Modeling of Arterial Platelet Thrombus Formation Using a Spatial Adsorption Equation

In this study, we considered a continuous model of platelet thrombus growth in an arteriole. A special model describing the adhesion of platelets in terms of their concentration was derived. The applications of the derived model are not restricted to only describing arterial platelet thrombus formation; the model can also be applied to other similar adhesion processes. The model reproduces an auto-wave solution in the one-dimensional case; in the two-dimensional case, in which the surrounding flow is taken into account, the typical torch- like thrombus is reproduced. The thrombus shape and the growth velocity are determined by the model parameters. We demonstrate that the model captures the main properties of the thrombus growth behavior and provides us a better understanding of which mechanisms are important in the mechanical nature of the arterial thrombus growth

Modelling of platelet–fibrin clot formation in flow with a DPD–PDE method

International audienceThe paper is devoted to mathematical modelling of clot growth in bloodflow. Great complexity of the hemostatic system dictates the need of usage of themathematical models to understand its functioning in the normal and especially inpathological situations. In this work we investigate the interaction of blood flow,platelet aggregation and plasma coagulation. We develop a hybrid DPD–PDE modelwhere dissipative particle dynamics (DPD) is used to model plasma flow and platelets,while the regulatory network of plasma coagulation is described by a system of partialdifferential equations. Modelling results confirm the potency of the scenario of clotgrowth where at the first stage of clot formation platelets form an aggregate due toweak inter-platelet connections and then due to their activation. This enables the formationof the fibrin net in the centre of the platelet aggregate where the flow velocity issignificantly reduced. The fibrin net reinforces the clot and allows its further growth.When the clot becomes sufficiently large, it stops growing due to the narrowed vesseland the increase of flow shear rate at the surface of the clot. Its outer part is detachedby the flow revealing the inner part covered by fibrin. This fibrin cap does not allownew platelets to attach at the high shear rate, and the clot stops growing. Dependenceof the final clot size on wall shear rate and on other parameters is studied

The role of platelets in blood coagulation during thrombus formation in flow

Hemostatic plug covering the injury site (or a thrombus in the pathological case) is formed due to the complex interaction of aggregating platelets with biochemical reactions in plasma that participate in blood coagulation. The mechanisms that control clot growth and which lead to growth arrest are not yet completely understood. We model them with numerical simulations based on a hybrid DPD-PDE model. Dissipative particle dynamics (DPD) is used to model plasma flow with platelets while fibrin concentration is described by a simplified reaction-diffusion-convection equation. The model takes into account consecutive stages of clot growth. First, a platelet is weakly connected to the clot and after some time this connection becomes stronger due to other surface receptors involved in platelet adhesion. At the same time, the fibrin network is formed inside the clot. This becomes possible because flow does not penetrate the clot and cannot wash out the reactants participating in blood coagulation. Platelets covered by the fibrin network cannot attach new platelets. Modelling shows that the growth of a hemostatic plug can stop as a result of its exterior part being removed by the flow thus exposing its non-adhesive core to the flow

Blood flow controls coagulation onset via the positive feedback of factor VII activation by factor Xa

<p>Abstract</p> <p>Background</p> <p>Blood coagulation is a complex network of biochemical reactions, which is peculiar in that it is time- and space-dependent, and has to function in the presence of rapid flow. Recent experimental reports suggest that flow plays a significant role in its regulation. The objective of this study was to use systems biology techniques to investigate this regulation and to identify mechanisms creating a flow-dependent switch in the coagulation onset.</p> <p>Results</p> <p>Using a detailed mechanism-driven model of tissue factor (TF)-initiated thrombus formation in a two-dimensional channel we demonstrate that blood flow can regulate clotting onset in the model in a threshold-like manner, in agreement with existing experimental evidence. Sensitivity analysis reveals that this is achieved due to a combination of the positive feedback of TF-bound factor VII activation by activated factor X (Xa) and effective removal of factor Xa by flow from the activating patch depriving the feedback of "ignition". The level of this trigger (i.e. coagulation sensitivity to flow) is controlled by the activity of tissue factor pathway inhibitor.</p> <p>Conclusions</p> <p>This mechanism explains the difference between red and white thrombi observed <it>in vivo </it>at different shear rates. It can be speculated that this is a special switch protecting vascular system from uncontrolled formation and spreading of active coagulation factors in vessels with rapidly flowing blood.</p

Computational models of hemostasis: Degrees of complexity

The history of studies on blood clotting goes back to the emergence of civilized society itself. The foundations of the modern scientific study of hemostasis are based on the discovery of erythrocytes in blood in 1674 and, later, that of platelets in 1842. The causes of thrombosis are encapsulated in the Virchow Triad (dated to 1856), which refers, in modern terms, to hypercoagulability, alterations of hemodynamics (stasis), and endothelial injury. The understanding of coagulation, the network of reactions that underlies hemostasis and thrombosis, has evolved from a cascade (in 1964) into spatially distinct sets of reactions dependent on co-factors occurring on different cells in different tissues and linked together by diffusion and flow (as of 2015). Correspondingly, mathematical/computational models for hemostasis and thrombosis (which involve coagulation along with platelet aggregation in the presence of flow) have evolved in design complexity from Continuum temporal (or “homogeneous”) models to Continuum spatio-temporal models (with or without the flow) and lately into Discrete-Continuum spatio-temporal models with the flow. After a brief listing of the discoveries and historical personae that contributed to the understanding of hemostasis up to the present, the development of mathematical/computational models is traced from the late 1980s when they started gaining importance. Influential models are then highlighted. The models are reviewed in increasing order of design complexity (one of four possible methods of classification). The physiological significance of each and the insights they offer into hemostasis regulation are explained. © 2022 The Author

Traumatic vessel injuries initiating hemostasis generate high shear conditions

Blood flow is a major regulator of hemostasis and arterial thrombosis. The current view is that low and intermediate flows occur in intact healthy vessels, whereas high shear levels (&gt;2000 s−1) are reached in stenosed arteries, notably during thrombosis. To date, the shear rates occurring at the edge of a lesion in an otherwise healthy vessel are nevertheless unknown. The aim of this work was to measure the shear rates prevailing in wounds in a context relevant to hemostasis. Three models of vessel puncture and transection were developed and characterized for a study that was implemented in mice and humans. Doppler probe measurements supplemented by a computational model revealed that shear rates at the edge of a wound reached high values, with medians of 22 000 s−1, 25 000 s−1, and 7000 s−1 after puncture of the murine carotid artery, aorta, or saphenous vein, respectively. Similar shear levels were observed after transection of the mouse spermatic artery. These results were confirmed in a human venous puncture model, where shear rates in a catheter implanted in the cubital vein reached 2000 to 27 000 s−1. In all models, the high shear conditions were accompanied by elevated levels of elongational flow exceeding 1000 s−1. In the puncture model, the shear rates decreased steeply with increasing injury size. This phenomenon could be explained by the low hydrodynamic resistance of the injuries as compared with that of the downstream vessel network. These findings show that high shear rates (&gt;3000 s−1) are relevant to hemostasis and not exclusive to arterial thrombosis