Subscribe to RSS
![](/products/assets/desktop/img/oa-logo.png)
DOI: 10.1055/s-0041-1722861
The Art and Science of Building a Computational Model to Understand Hemostasis
Funding This work was supported in part by the National Institutes of Health (R01HL120728, R01HL151984), the National Science Foundation (CBET-1351672, DMS-1848221), and the Army Research Office (ARO-12369656).![](https://www.thieme-connect.de/media/sth/202102/lookinside/thumbnails/10-1055-s-0041-1722861_02830-1.jpg)
Abstract
Computational models of various facets of hemostasis and thrombosis have increased substantially in the last decade. These models have the potential to make predictions that can uncover new mechanisms within the complex dynamics of thrombus formation. However, these predictions are only as good as the data and assumptions they are built upon, and therefore model building requires intimate coupling with experiments. The objective of this article is to guide the reader through how a computational model is built and how it can inform and be refined by experiments. This is accomplished by answering six questions facing the model builder: (1) Why make a model? (2) What kind of model should be built? (3) How is the model built? (4) Is the model a “good” model? (5) Do we believe the model? (6) Is the model useful? These questions are answered in the context of a model of thrombus formation that has been successfully applied to understanding the interplay between blood flow, platelet deposition, and coagulation and in identifying potential modifiers of thrombin generation in hemophilia A.
Note
[Figure 1] and [Table 1] schematic were created with BioRender.com.
Publication History
Article published online:
26 February 2021
© 2021. The Author(s). This is an open access article published by Thieme under the terms of the Creative Commons Attribution-NonDerivative-NonCommercial License, permitting copying and reproduction so long as the original work is given appropriate credit. Contents may not be used for commercial purposes, or adapted, remixed, transformed or built upon. (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Thieme Medical Publishers, Inc.
333 Seventh Avenue, 18th Floor, New York, NY 10001, USA
-
References
- 1 Winslow RL, Trayanova N, Geman D, Miller MI. Computational medicine: translating models to clinical care. Sci Transl Med 2012; 4 (158) 158rv11
- 2 Wang S, Guo P, Wang X, Zhou Q, Gallo JM. Preclinical pharmacokinetic/pharmacodynamic models of gefitinib and the design of equivalent dosing regimens in EGFR wild-type and mutant tumor models. Mol Cancer Ther 2008; 7 (02) 407-417
- 3 Miller ML, Molinelli EJ, Nair JS. et al. Drug synergy screen and network modeling in dedifferentiated liposarcoma identifies CDK4 and IGF1R as synergistic drug targets. Sci Signal 2013; 6 (294) ra85-ra85
- 4 Trayanova NA. Mathematical approaches to understanding and imaging atrial fibrillation: significance for mechanisms and management. Circ Res 2014; 114 (09) 1516-1531
- 5 Jurgens J. The exponentiator; a nomogram for uniform quick percentile determination of the blood coagulation factors [in German]. Arztl Wochensch 1954; 9 (18) 420-422
- 6 Nesheim ME, Tracy RP, Mann KG. “Clotspeed,” a mathematical simulation of the functional properties of prothrombinase. J Biol Chem 1984; 259 (03) 1447-1453
- 7 Hockin MF, Jones KC, Everse SJ, Mann KG. A model for the stoichiometric regulation of blood coagulation. J Biol Chem 2002; 277 (21) 18322-18333
- 8 Diamond SL, Anand S. Inner clot diffusion and permeation during fibrinolysis. Biophys J 1993; 65 (06) 2622-2643
- 9 Sorensen EN, Burgreen GW, Wagner WR, Antaki JF. Computational simulation of platelet deposition and activation: I. Model development and properties. Ann Biomed Eng 1999; 27 (04) 436-448
- 10 Fogelson AL. A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting. J Comput Phys 1984; 56: 111-134
- 11 Fogelson AL. Continuum models of platelet aggregation: formulation and mechanical properties. SIAM J Appl Math 1992; 52: 1089-1110
- 12 Freund JB. Numerical simulation of flowing blood cells. Annu Rev Fluid Mech 2013; 46: 130812142306005
- 13 Schneider SW, Nuschele S, Wixforth A. et al. Shear-induced unfolding triggers adhesion of von Willebrand factor fibers. Proc Natl Acad Sci U S A 2007; 104 (19) 7899-7903
- 14 Zhao H, Shaqfeh ESG, Narsimhan V. Shear-induced particle migration and margination in a cellular suspension. Phys Fluids 2012; 24: 011902
- 15 Crowl L, Fogelson AL. Analysis of mechanisms for platelet near-wall excess under arterial blood flow conditions. J Fluid Mech 2011; 676: 348-375
- 16 Mody NA, King MR. Platelet adhesive dynamics. Part I: characterization of platelet hydrodynamic collisions and wall effects. Biophys J 2008; 95 (05) 2539-2555
- 17 Mody NA, King MR. Platelet adhesive dynamics. Part II: high shear-induced transient aggregation via GPIbalpha-vWF-GPIbalpha bridging. Biophys J 2008; 95 (05) 2556-2574
- 18 Fedosov DA, Caswell B, Karniadakis GE. A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys J 2010; 98 (10) 2215-2225
- 19 Wang W, King MR. Multiscale modeling of platelet adhesion and thrombus growth. Ann Biomed Eng 2012; 40 (11) 2345-2354
- 20 Flamm MH, Colace TV, Chatterjee MS. et al. Multiscale prediction of patient-specific platelet function under flow. Blood 2012; 120 (01) 190-198
- 21 Belyaev AV, Dunster JL, Gibbins JM, Panteleev MA, Volpert V. Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones. Phys Life Rev 2018; 26-27: 57-95
- 22 Hemker HC, Bloemen S, Hemker PW. Exploring the limits of modelling thrombus formation: comment on “Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones” by A.V. Belyaev et al. Phys Life Rev 2018; 26-27: 100-105
- 23 Fedosov DA. Hemostasis is a highly multiscale process: comment on “Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones” by A. V. Belyaev et al. Phys Life Rev 2018; 26-27: 108-109
- 24 Tomaiuolo M, Brass LF. Joining forces to understand hemostasis and thrombosis: a call to communicate: comment on “Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones” by A.V. Belyaev et al. Phys Life Rev 2018; 26-27: 110-112
- 25 Andrews RK, Gardiner EE. Monitoring the pulse of thrombus formation: comment on “Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones” by A.V. Belyaev et al. Phys Life Rev 2018; 26-27: 113-115
- 26 Yazdani A, Karniadakis G. Moving toward realistic models: comment on “Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones” by A.V. Belyaev et al. Phys Life Rev 2018; 26-27: 96-99
- 27 Leiderman K, Fogelson A. An overview of mathematical modeling of thrombus formation under flow. Thromb Res 2014; 133 (Suppl. 01) S12-S14
- 28 Neeves KB, Leiderman K. Mathematical Models of Hemostasis Trauma Induced Coagulopathy. In: Gonzalez E, Moore HB, Moore EE. eds. Trauma Induced Coagulopathy. Cham, Switzerland: Springer; 2015
- 29 Fogelson AL, Neeves KB. Fluid mechanics of blood clot formation. Annu Rev Fluid Mech 2015; 47: 377-403
- 30 Diamond SL. Systems analysis of thrombus formation. Circ Res 2016; 118 (09) 1348-1362
- 31 Kuharsky AL, Fogelson AL. Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys J 2001; 80 (03) 1050-1074
- 32 Fogelson AL, Tania N. Coagulation under flow: the influence of flow-mediated transport on the initiation and inhibition of coagulation. Pathophysiol Haemost Thromb 2005; 34 (2-3): 91-108
- 33 Fogelson AL, Hussain YH, Leiderman K. Blood clot formation under flow: the importance of factor XI depends strongly on platelet count. Biophys J 2012; 102 (01) 10-18
- 34 Leiderman K, Fogelson AL. Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow. Math Med Biol 2011; 28 (01) 47-84
- 35 Leiderman K, Fogelson AL. The influence of hindered transport on the development of platelet thrombi under flow. Bull Math Biol 2013; 75 (08) 1255-1283
- 36 Onasoga-Jarvis AA, Leiderman K, Fogelson AL. et al. The effect of factor VIII deficiencies and replacement and bypass therapies on thrombus formation under venous flow conditions in microfluidic and computational models. PLoS One 2013; 8 (11) e78732
- 37 Leiderman K, Chang WC, Ovanesov M, Fogelson AL. Synergy between tissue factor and exogenous factor XIa in initiating coagulation. Arterioscler Thromb Vasc Biol 2016; 36 (12) 2334-2345
- 38 Link KG, Stobb MT, Di Paola J. et al. A local and global sensitivity analysis of a mathematical model of coagulation and platelet deposition under flow. PLoS One 2018; 13 (07) e0200917
- 39 Aledort LM, Haschmeyer RH, Pettersson H. The Orthopaedic Outcome Study Group. A longitudinal study of orthopaedic outcomes for severe factor-VIII-deficient haemophiliacs. J Intern Med 1994; 236 (04) 391-399
- 40 Blanchette VS, Key NS, Ljung LR, Manco-Johnson MJ, van den Berg HM, Srivastava A. Subcommittee on Factor VIII, Factor IX and Rare Coagulation Disorders of the Scientific and Standardization Committee of the International Society on Thrombosis and Hemostasis. Definitions in hemophilia: communication from the SSC of the ISTH. J Thromb Haemost 2014; 12 (11) 1935-1939
- 41 Watson HG, Greaves M. Can we predict bleeding?. Semin Thromb Hemost 2008; 34 (01) 97-103
- 42 Butenas S, van't Veer C, Mann KG. “Normal” thrombin generation. Blood 1999; 94 (07) 2169-2178
- 43 Andersen OS. Cellular electrolyte metabolism. Encyclopedia of Metalloproteins. New York: Springer; 2013: 580-587
- 44 Maloney SF, Brass LF, Diamond SL. P2Y12 or P2Y1 inhibitors reduce platelet deposition in a microfluidic model of thrombosis while apyrase lacks efficacy under flow conditions. Integr Biol 2010; 2 (04) 183-192
- 45 Hansen RR, Wufsus AR, Barton ST, Onasoga AA, Johnson-Paben RM, Neeves KB. High content evaluation of shear dependent platelet function in a microfluidic flow assay. Ann Biomed Eng 2013; 41 (02) 250-262
- 46 de Witt SM, Swieringa F, Cavill R. et al. Identification of platelet function defects by multi-parameter assessment of thrombus formation. Nat Commun 2014; 5: 4257
- 47 Mann KG, Nesheim ME, Church WR, Haley P, Krishnaswamy S. Surface-dependent reactions of the vitamin K-dependent enzyme complexes. Blood 1990; 76 (01) 1-16
- 48 Monroe DM, Roberts HR, Hoffman M. Platelet procoagulant complex assembly in a tissue factor-initiated system. Br J Haematol 1994; 88 (02) 364-371
- 49 Hoffman M, Monroe DM, Roberts HR. Cellular interactions in hemostasis. Haemostasis 1996; 26 (Suppl. 01) 12-16
- 50 Ahmad SS, Rawala-Sheikh R, Walsh PN. Comparative interactions of factor IX and factor IXa with human platelets. J Biol Chem 1989; 264 (06) 3244-3251
- 51 Weiss HJ, Baumgartner HR, Turitto VT. Regulation of platelet-fibrin thrombi on subendothelium. Ann N Y Acad Sci 1987; 516: 380-397
- 52 Nemerson Y, Turitto VT. The effect of flow on hemostasis and thrombosis. Thromb Haemost 1991; 66 (03) 272-276
- 53 Okorie UM, Denney WS, Chatterjee MS, Neeves KB, Diamond SL. Determination of surface tissue factor thresholds that trigger coagulation at venous and arterial shear rates: amplification of 100 fM circulating tissue factor requires flow. Blood 2008; 111 (07) 3507-3513
- 54 Rana K, Neeves KB. Blood flow and mass transfer regulation of coagulation. Blood Rev 2016; 30 (05) 357-368
- 55 Leiderman K, Bannish BE, Kelley MA, Palmisano AM. Mathematical models of thrombus formation and fibrinolysis. In: Topaz O, ed. Cardiovascular Thrombus: From Pathology and Clinical Presentations to Imaging, Pharmacotherapy and Interventions. San Diego, United States: Academic Press; 2018: 67-86
- 56 Banwarth-Kuhn M, Sindi S. How and why to build a mathematical model: a case study using prion aggregation. J Biol Chem 2020; 295 (15) 5022-5035
- 57 Reed MC. Why is mathematical biology so hard?. Not Am Math Soc 2004; 51: 338-342
- 58 Welsh JD, Colace TV, Muthard RW, Stalker TJ, Brass LF, Diamond SL. Platelet-targeting sensor reveals thrombin gradients within blood clots forming in microfluidic assays and in mouse. J Thromb Haemost 2012; 10 (11) 2344-2353
- 59 Stalker TJ, Traxler EA, Wu J. et al. Hierarchical organization in the hemostatic response and its relationship to the platelet-signaling network. Blood 2013; 121 (10) 1875-1885
- 60 Welsh JD, Stalker TJ, Voronov R. et al. A systems approach to hemostasis: 1. The interdependence of thrombus architecture and agonist movements in the gaps between platelets. Blood 2014; 124 (11) 1808-1815
- 61 Du J, Fogelson AL. A two-phase mixture model of platelet aggregation. Math Med Biol 2018; 35 (02) 225-256
- 62 Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J. Global Sensitivity Analysis: The Primer. West Sussex, United Kingdom: Wiley; 2008
- 63 Kahn ML, Nakanishi-Matsui M, Shapiro MJ, Ishihara H, Coughlin SR. Protease-activated receptors 1 and 4 mediate activation of human platelets by thrombin. J Clin Invest 1999; 103 (06) 879-887
- 64 Link KG, Stobb MT, Sorrells MG. et al. A mathematical model of coagulation under flow identifies factor V as a modifier of thrombin generation in hemophilia A. J Thromb Haemost 2020; 18 (02) 306-317
- 65 Shen L, Dahlbäck B. Factor V and protein S as synergistic cofactors to activated protein C in degradation of factor VIIIa. J Biol Chem 1994; 269 (29) 18735-18738
- 66 Duckers C, Simioni P, Spiezia L. et al. Low plasma levels of tissue factor pathway inhibitor in patients with congenital factor V deficiency. Blood 2008; 112 (09) 3615-3623
- 67 Peraramelli S, Thomassen S, Heinzmann A. et al. Role of exosite binding modulators in the inhibition of Fxa by TFPI. Thromb Haemost 2016; 115 (03) 580-590