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 (>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 (>3000 s−1) are relevant to hemostasis and not exclusive to arterial thrombosis

Platelet Adhesion from Shear Blood Flow Is Controlled by Near-Wall Rebounding Collisions with Erythrocytes

The efficacy of platelet adhesion in shear flow is known to be substantially modulated by the physical presence of red blood cells (RBCs). The mechanisms of this regulation remain obscure due to the complicated character of platelet interactions with RBCs and vascular walls. To investigate this problem, we have created a mathematical model that takes into account shear-induced transport of platelets across the flow, platelet expulsion by the RBCs from the near-wall layer of the flow onto the wall, and reversible capture of platelets by the wall and their firm adhesion to it. This model analysis allowed us to obtain, for the first time to our knowledge, an analytical determination of the platelet adhesion rate constant as a function of the wall shear rate, hematocrit, and average sizes of platelets and RBCs. This formula provided a quantitative description of the results of previous in vitro adhesion experiments in perfusion chambers. The results of the simulations suggest that under a wide range of shear rates and hematocrit values, the rate of platelet adhesion from the blood flow is mainly limited by the frequency of their near-wall rebounding collisions with RBCs. This finding reveals the mechanism by which erythrocytes physically control platelet hemostasis

Changes in the parameters of thrombodynamics and blood clot contraction in patients with rheumatoid arthritis

© 2020 Ima-Press Publishing House. All rights reserved. Autoimmune diseases, including rheumatoid arthritis (RA), are risk factors for thrombotic events. Understanding the pathogenetic role of hemostatic changes in RA can assist in developing measures for prevention, prognosis, early diagnosis, and treatment of immune thromboses. Objective: to investigate the state of platelet and plasma hemostasis in patients with RA, as compared to other laboratory parameters and clinical manifestations of the disease. Subjects and methods. Hemostasis was investigated using two relatively new laboratory tests: thrombodynamics and kinetics of blood clot contraction (BCC). Examinations were made in 60 patients with RA and in 50 apparently healthy individuals of the control group. Results and discussion. In patients with RA, the parameters of thrombodynamics and BCC were found to be significantly different from the normal values. According to thrombodynamics, there was an increase in plasma clot growth rate, size, and density, which indicates chronic hypercoagulation. The rate and completeness of BCC were substantially reduced due to platelet dysfunction in patients with RA compared to healthy individuals. The changes in the parameters of thrombodynamics and BCC correlated with the laboratory signs of systemic inflammation and depended on the radiographic stage of the disease. Conclusion. The results of this investigation confirm that hemostatic disorders are present in RA and indicate the informative value of thrombodynamics and BCC tests as indicators of a pre-thrombotic state, including autoimmune pathology

Accelerated spatial fibrin growth and impaired contraction of blood clots in patients with rheumatoid arthritis

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. Rheumatoid arthritis (RA) is an autoimmune disease associated with thrombotic complications. To elucidate pathogenic mechanisms, hemostatic disorders in RA were correlated with other laboratory and clinical manifestations. Hemostasis was assessed using relatively new complementary tests, the spatial growth of a plasma clot (Thrombodynamics assay), and contraction of whole blood clots. Platelet functionality was assessed with flow cytometry that quantified the expression of P-selectin and the fibrinogen-binding capacity of platelets before and after activation with a thrombin receptor-activating peptide. Parameters of fibrin clot growth and the kinetics of contraction of blood clots were significantly altered in patients with RA compared to the control group. In Thrombodynamics measurements, an increase in the clot growth rate, size, and optical density of plasma clots altogether indicated chronic hypercoagulability. The rate and extent of blood clot contraction in patients with RA was significantly reduced and associated with platelet dysfunction revealed by an impaired response to activation. Changes in the parameters of clot growth and contraction correlated with the laboratory signs of systemic inflammation, including hyperfibrinogenemia. These results confirm the pathogenic role of hemostatic disorders in RA and support the validity of fibrin clot growth and the blood clot contraction assay as indicators of a (pro)thrombotic state

Mechanical properties of tubulin intra- And inter-dimer interfaces and their implications for microtubule dynamic instability

Thirteen tubulin protofilaments, made of αβ-tubulin heterodimers, interact laterally to produce cytoskeletal microtubules. Microtubules exhibit the striking property of dynamic instability, manifested in their intermittent growth and shrinkage at both ends. This behavior is key to many cellular processes, such as cell division, migration, maintenance of cell shape, etc. Although assembly and disassembly of microtubules is known to be linked to hydrolysis of a guanosine triphosphate molecule in the pocket of β-tubulin, detailed mechanistic understanding of corresponding conformational changes is still lacking. Here we take advantage of the recent generation of in-microtubule structures of tubulin to examine the properties of protofilaments, which serve as important microtubule assembly and disassembly intermediates. We find that initially straight tubulin protofilaments, relax to similar non-radially curved and slightly twisted conformations. Our analysis further suggests that guanosine triphosphate hydrolysis primarily affects the flexibility and conformation of the inter-dimer interface, without a strong impact on the shape or flexibility of αβ-heterodimer. Inter-dimer interfaces are significantly more flexible compared to intra-dimer interfaces. We argue that such a difference in flexibility could be key for distinct stability of the plus and minus microtubule ends. The higher flexibility of the inter-dimer interface may have implications for development of pulling force by curving tubulin protofilaments during microtubule disassembly, a process of major importance for chromosome motions in mitosis. © 2019 Fedorov et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Hypercoagulation detected by routine and global laboratory hemostasis assays in patients with infective endocarditis

Background Coagulation system is heavily involved into the process of infective endocarditis (IE) vegetation formation and can facilitate further embolization. In this study we aimed to assess the coagulation and platelet state in IE implementing a wide range of standard and global laboratory assays. We also aim to determine whether prothrombotic genetic polymorphisms play any role in embolization and mortality in IE patients. Methods 37 patients with IE were enrolled into the study. Coagulation was assessed using standard coagulation assays (activated partial thromboplastin time (APTT), prothrombin, fibrinogen, D-dimer concentrations) and integral assays (thromboelastography (TEG) and thrombodynamics (TD)). Platelet functional activity was estimated by flow cytometry. Single nuclear polymorphisms of coagulation system genes were studied. Results Fibrinogen concentration and fibrinogen-dependent parameters of TEG and TD were increased in patients indicating systemic inflammation. In majority of patients clot growth rate in thrombodynamics was significantly shifted towards hypercoagulation in consistency with D-dimers elevation. However, in some patients prothrombin, thromboelastography and thrombodynamics were shifted towards hypocoagulation. Resting platelets were characterized by glycoprotein IIb-IIIa activation and degranulation. In patients with fatal IE, we observed a significant decrease in fibrinogen and thrombodynamics. In patients with embolism, we observed a significant decrease in the TEG R parameter. No association of embolism or mortality with genetic polymorphisms was found in our cohort. Conclusions Our findings suggest that coagulation in patients with infective endocarditis is characterized by general hypercoagulability and platelet pre-activation. Some patients, however, have hypocoagulant coagulation profile, which presumably can indicate progressing of hypercoagulation into consumption coagulopathy. © 2021 Koltsova et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Results of multicenter monitoring of hemostasis parameters in patients with covid-19

Materials and methods: a prospective non-randomized pilot multicenter study of the informative-ness and clinical significance of hemostasis laboratory tests in 1210 patients with COVID-19 in disease course, including favorable and unfavorable outcomes, was performed. Hemostasis was assessed using clotting tests and D-dimer concentration, thromboelastography (TEG) and thrombodynamics (TD). Results: comparison of COVID-19 laboratory parameters and clinical picture showed that 75% of patients have pronounced activation of the plasma coagulation system upon admission to the hospital. Hypercoagulation is recorded in all tests, reaching a maximum in patients with subtotal (CT-3) and total (CT-4) lung lesion and/or resuscitation patients with a clinical picture of pulmonary embolism and unfavorable outcome. Low molecular weight heparins (LMWH) in a standard dosage leads to suppression of the initial hypercoagulable syndrome in more than half of the patients (from 75 to 31%). All patients without LMWH laboratory effect developed thrombotic complications. For clotting tests, insufficient sensitivity to changes in hemostasis against the background of LMWH was revealed. The D-dimer test effectively correlates with the severity and outcomes of COVID-19, but is not suitable for the control of heparin therapy, which is associated with the effect of lysis of existing blood clots and the lack of response to a decrease in the coagulation activity of patients. Methods of thromboelastography and thrombodynamics effectively record a decrease in the activity of the coagulation system and can be used to control heparin therapy. The correlation coefficient between the methods was 0,77. The dynamic indices of D-dimers, TEG and TD in severe patients and, especially, in patients with fatal outcomes revealed the greatest sensitivity to the control of heparin therapy in the Thrombodynamics test, which allows, along with thrombosis, to record hypercoagulable states and the risk of bleeding, which are the outcome of thrombohemorrhagic syndrome in patients with COVID-19. © 2020, Pediatria Ltd. All rights reserved

Bone formation: biological aspects and modelling problems

In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological experimentatio