Advertisement

Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 4, pp 1139–1153 | Cite as

Kinetics of the coagulation cascade including the contact activation system: sensitivity analysis and model reduction

  • Rodrigo Méndez Rojano
  • Simon Mendez
  • Didier Lucor
  • Alexandre Ranc
  • Muriel Giansily-Blaizot
  • Jean-François Schved
  • Franck NicoudEmail author
Original Paper
  • 122 Downloads

Abstract

Thrombus formation is one of the main issues in the development of blood-contacting medical devices. This article focuses on the modeling of one aspect of thrombosis, the coagulation cascade, which is initiated by the contact activation at the device surface and forms thrombin. Models exist representing the coagulation cascade by a series of reactions, usually solved in quiescent plasma. However, large parameter uncertainty involved in the kinetic models can affect the predictive capabilities of this approach. In addition, the large number of reactions of the kinetic models prevents their use in the simulation of complex flow configurations encountered in medical devices. In the current work, both issues are addressed to improve the applicability and fidelity of kinetic models. A sensitivity analysis is performed by two different techniques to identify the most sensitive parameters of an existing detailed kinetic model of the coagulation cascade. The results are used to select the form of a novel reduced model of the coagulation cascade which relies on eight chemical reactors only. Then, once its parameters have been calibrated thanks to the Bayesian inference, this model shows good predictive capabilities for different initial conditions.

Keywords

Coagulation cascade modeling Sensitivity analysis Bayesian inference Model reduction 

Notes

Acknowledgements

We are grateful to the CONACyT, Mexico scholarship and the LabEx Numev (convention ANR-10-LABX-20) for their financial support. This work was performed using HPC resources from GENCI-CINES (Grants 2017-A0020307194 and 2018-A0040307194) and with the support of the High-Performance Computing Platform HPC@LR.

Compliances with ethical standard

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Alderazi YJ, Shastri D, Kass-Hout T, Prestigiacomo CJ, Gandhi CD (2014) Flow diverters for intracranial aneurysms. Stroke Res Treat 415653:1–12Google Scholar
  2. Alemu Y, Bluestein D (2007) Flow-induced platelet activation and damage accumulation in a mechanical heart valve: numerical studies. Artif Organs 31(9):677–688.  https://doi.org/10.1111/j.1525-1594.2007.00446.x CrossRefGoogle Scholar
  3. Anand M, Rajagopal K, Rajagopal KR (2008) A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency. J Theor Biol 253:725–738CrossRefzbMATHGoogle Scholar
  4. Andrieu C, De Freitas N, Doucet A, Jordan MI (2003) An introduction to MCMC for machine learning. Mach Learn 50:5–43CrossRefzbMATHGoogle Scholar
  5. Ashyraliyev M, Fomekong-Nanfack Y, Kaandorp JA, Blom JG (2009) Systems biology: parameter estimation for biochemical models. FEBS J 276(4):886–902CrossRefGoogle Scholar
  6. Belyaev AV, Dunster J, Gibbins J, Panteleev M, Volpert V (2018) Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones. Phys Life Rev 26:57–95CrossRefGoogle Scholar
  7. Bhogal P, Martinez Moreno R, Ganslandt O, Bäzner H, Henkes H, Perez MA (2017) Use of flow diverters in the treatment of unruptured saccular aneurysms of the anterior cerebral artery. J Neurointerv Surg 9(3):283–289CrossRefGoogle Scholar
  8. Bijl H et al (eds) (2013) Uncertainty quantification in computational fluid dynamics, Lecture Notes in Computational Science and Engineering, vol 92. Springer, New York  https://doi.org/10.1007/978-3-319-00885-1
  9. Birolleau A, Poëtte G, Lucor D (2014) Adaptive Bayesian inference for discontinuous inverse problems, application to hyperbolic conservation laws. Commun Comput Phys 16(1):1–34MathSciNetCrossRefzbMATHGoogle Scholar
  10. Campolongo F, Cariboni J, Saltelli A (2007) An effective screening design for sensitivity analysis of large models. Environ Mod Softw 22(10):1509–1518.  https://doi.org/10.1016/j.envsoft.2006.10.004 CrossRefGoogle Scholar
  11. Chatterjee MS, Denney WS, Jing H, Diamond SL (2010) Systems biology of coagulation initiation: kinetics of thrombin generation in resting and activated human blood. PLoS Comput Biol 6(9):e1000950CrossRefGoogle Scholar
  12. Chnafa C, Mendez S, Nicoud F (2016) Image-based simulations show important flow fluctuations in a normal left ventricle: what could be the implications? Ann Biomed Eng 44(11):3346–3358CrossRefGoogle Scholar
  13. Danforth CM, Orfeo T, Mann KG, Brummel-Ziedins KE, Everse SJ (2009) The impact of uncertainty in a blood coagulation model. Math Med Biol 26(4):323–336.  https://doi.org/10.1093/imammb/dqp011 MathSciNetCrossRefzbMATHGoogle Scholar
  14. Danforth CM, Orfeo T, Everse SJ, Mann KG, Brummel-Ziedins KE (2012) Defining the boundaries of normal thrombin generation: investigations into hemostasis. PLoS ONE 7:1–12CrossRefGoogle Scholar
  15. De Biasi AR, Manning KB, Salemi A (2015) Science for surgeons: Understanding pump thrombogenesis in continuous-flow left ventricular assist devices. J Thorac Cardiovasc Surg 149(3):667–673.  https://doi.org/10.1016/j.jtcvs.2014.11.041 CrossRefGoogle Scholar
  16. Dumont K, Vierendeels J, Kaminsky R, van Nooten G, Verdonck P, Bluestein Dd (2007) Comparison of the hemodynamic and thrombogenic performance of two bileaflet mechanical heart valves using a CFD/FSI model. J Biomech Eng 129(4):558–565CrossRefGoogle Scholar
  17. Fogelson AL, Neeves KB (2015) Fluid mechanics of blood clot formation. Ann Rev Fluid Mech 47(1):377–403MathSciNetCrossRefGoogle Scholar
  18. Fogelson AL, Hussain YH, Leiderman K (2012) Blood clot formation under flow: the importance of factor XI depends strongly on platelet count. Biophys J 102(1):10–18CrossRefGoogle Scholar
  19. Gailani D, Bronze GJ (1991) Factor XI activation in a revised model of blood coagulation. Science 253(5022):909–912CrossRefGoogle Scholar
  20. Gorbet MB, Sefton MV (2004) Biomaterial-associated thrombosis: roles of coagulation factors, complement, platelets and leukocytes. Biomaterials 25:5681–5703CrossRefGoogle Scholar
  21. Hastings SM, Ku DN, Wagoner S, Maher OK, Deshpande S (2017) Sources of circuit thrombosis in pediatric extracorporeal membrane oxygenation. Am Soc Artif Intern Org 63(1):86–92CrossRefGoogle Scholar
  22. Hemker H, Giesen P, Al Dieri R, Regnault V, De Smedt E, Wagenvoord R, Lecompte T, Bguin S (2003) Calibrated automated thrombin generation measurement in clotting plasma. Pathophysiol Haemost Thromb 33:4–15CrossRefGoogle Scholar
  23. Hemker HC, Kerdelo S, Kremers RMW (2012) Is there value in kinetic modeling of thrombin generation? No (unless...). J Thromb Haemost 10:1470–1477CrossRefGoogle Scholar
  24. Hockin MF, Jones KC, Everse SJ, Mann KG (2002) A model for the stoichiometric regulation of blood coagulation. J Biol Chem 277(21):18322–18333CrossRefGoogle Scholar
  25. Indolfi C, De Rosa S, Colombo A (2016) Bioresorbable vascular scaffolds—basic concepts and clinical outcome. Nat Rev Cardiol 13:719–729CrossRefGoogle Scholar
  26. Iooss B, Lemaître P (2015) Uncertainty management in simulation-optimization of complex systems: algorithms and applications, Springer US, chap A review on global sensitivity analysis methods, pp 101–122Google Scholar
  27. Jaffer IH, Fredenburgh JC, Hirsh J, Weitz JI (2015) Medical device-induced thrombosis: what causes it and how can we prevent it? J Thromb Haemost 13(Suppl. 1):72–81CrossRefGoogle Scholar
  28. Jones KC, Mann KG (1994) A model for the tissue factor pathway to thrombin. II. A mathematical simulation. J Biol Chem 269:23367–23373Google Scholar
  29. Kirklin JK, Pagani FD, Kormos RL, Stevenson LW, Blume ED, Myers SL, Miller MA, Baldwin JT, Young JB, Naftel DC (2017) Eighth annual INTERMACS report: special focus on framing the impact of adverse events. J Heart Long Transpl 36(10):1080–1086CrossRefGoogle Scholar
  30. Komiyama Y, Pedersen AH, Kisiel W (1990) Proteolytic activation of human factors IX and X by recombinant human factor VIIa: effects of calcium, phospholipids, and tissue factor. Biochem US 29:9418–9425CrossRefGoogle Scholar
  31. Lanotte L, Mauer J, Mendez S, Fedosov DA, Fromental JM, Clavería V, Nicoud F, Gompper G, Abkarian M (2016) Red cells’ dynamic morphologies govern blood shear thinning under microcirculatory flow conditions. Proc Natl Acad Sci USA 113(47):13289–13294.  https://doi.org/10.1073/pnas.1608074113 CrossRefGoogle Scholar
  32. Leiderman K, Fogelson AL (2011) Grow with the flow: A spatial-temporal model of platelet deposition and blood coagulation under flow. Math Med Biol 28:47–84MathSciNetCrossRefzbMATHGoogle Scholar
  33. Link KG, Stobb MT, Di Paola J, Neeves KB, Fogelson AL, Sindi SS, Leiderman K (2018) A local and global sensitivity analysis of a mathematical model of coagulation and platelet deposition under flow. PLoS ONE 13(7):1–38CrossRefGoogle Scholar
  34. Lucor D, Le Maître OP (2018) Cardiovascular modeling with adapted parametric inference. ESAIM: Proc 62:91–107MathSciNetCrossRefzbMATHGoogle Scholar
  35. Mehra MR, Stewart GC, Uber PA (2014) The vexing problem of thrombosis in long-term mechanical circulatory support. J Heart Long Transpl 33:1–11CrossRefGoogle Scholar
  36. Méndez Rojano R, Mendez S, Nicoud F (2018) Introducing the pro-coagulant contact system in the numerical assessment of device-related thrombosis. Biomech Model Mechanobiol 17(3):815–826CrossRefGoogle Scholar
  37. Morris M (1991) Factorial sampling plans for preliminary computational experiments. Technometrics 33:161–174CrossRefGoogle Scholar
  38. Naidu P, Anand M (2014) Importance of VIIIa inactivation in a mathematical model for the formation, growth, and lysis of clots. Math Model Nat Phenom 9(6):17–33MathSciNetCrossRefzbMATHGoogle Scholar
  39. Ngoepe MN, Ventikos Y (2016) Computational modelling of clot development in patient-specific cerebral aneurysm cases. J Thromb Haemost 14(2):262–272CrossRefGoogle Scholar
  40. Ngoepe MN, Frangi AF, Byrne JV, Ventikos Y (2018) Thrombosis in cerebral aneurysms and the computational modeling thereof: a review. Front Physiol 9:306CrossRefGoogle Scholar
  41. Papadopoulos KP, Gavaises M, Atkin C (2014) A simplified mathematical model for thrombin generation. Med Eng Phys 36(2):196–204.  https://doi.org/10.1016/j.medengphy.2013.10.012 CrossRefGoogle Scholar
  42. Saltelli A, Ratto M, Tarantola S, Campolongo F (2004) Sensitivity analysis practice: a guide to scientific models. Wiley, New YorkzbMATHGoogle Scholar
  43. Shadden SC, Hendabadi S (2013) Potential fluid mechanic pathways of platelet activation. Biomech Model Mechanobiol 12:467–474CrossRefGoogle Scholar
  44. Sigüenza J, Mendez S, Nicoud F (2017) How should the optical tweezers experiment be used to characterize the red blood cell membrane mechanics? Biomech Model Mechanobiol 16:1645–1657CrossRefGoogle Scholar
  45. Sigüenza J, Pott D, Mendez S, Sonntag S, Kaufmann TAS, Steinseifer U, Nicoud F (2018) Fluid-structure interaction of a pulsatile flow with an aortic valve model: a combined experimental and numerical study. Int J Numer Methods Biomed Eng 34(e2945):1–19MathSciNetGoogle Scholar
  46. Sobol IM (2001) Global sensitivity indices for rather complex mathematical models can be efficiently computed by Monte Carlo (or quasi-Monte Carlo) methods. These indices are used for estimating the influence of individual variables or groups of variables on the model output. Math Comput Simul 55:271–280CrossRefGoogle Scholar
  47. Sun JCJ, Davidson MJ, Lamy A, Eikelboom JW (2009) Antithrombotic management of patients with prosthetic heart valves: current evidence and future. The Lancet 374(9689):565–576CrossRefGoogle Scholar
  48. Taylor JO, Meyer RS, Deutsch S, Manning KB (2016) Development of a computational model for macroscopic predictions of device-induced thrombosis. Biomech Model Mechanobiol 15(6):1713–1731CrossRefGoogle Scholar
  49. Wagenvoord R, Hemker PW, Hemker HC (2006) The limits of simulation of the clotting system. J Thromb Haemost 4:1331–1338CrossRefGoogle Scholar
  50. Wilson WM, Cruden NL (2013) Advances in coronary stent technology: current expectations and new developments. Res Rep Clin Cardiovasc 4:85–96Google Scholar
  51. Wu WT, Yang F, Wu J, Aubry N, Massoudi M, Antaki JF (2016) High fidelity computational simulation of thrombus formation in Thoratec Heart Mate II continuous flow ventricular assist device. Sc Rep 6:38025-1–11.  https://doi.org/10.1038/srep38025 Google Scholar
  52. Xiu D (2010) Numerical methods for stochastic computations. Princeton University Press, PrincetonCrossRefzbMATHGoogle Scholar
  53. Yan Y, Xu LC, Vogler EA, Siedlecki CA (2018) 1 - Contact activation by the intrinsic pathway of blood plasma coagulation. Woodhead Publishing, SawstonCrossRefGoogle Scholar
  54. Yazdani A, Li H, Humphrey JD, Karniadakis GE (2017) A general shear-dependent model for thrombus formation. PLoS Comput Biol 13(1):e1005291CrossRefGoogle Scholar
  55. Yoganathan AP, He Z, Jones SC (2004) Fluid mechanics of heart valves. Ann Rev Biomed Eng 6:331–62CrossRefGoogle Scholar
  56. Zarnitsina VI, Pokhilko AV, Ataullakhanov FI (1996) A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description. Thromb Res 84(4):225–236CrossRefGoogle Scholar
  57. Zhu D (2007) Mathematical modeling of blood coagulation cascade: kinetics of intrinsic and extrinsic pathways in normal and deficient conditions. Blood Coagul Fibrinolysis 18:637–646CrossRefGoogle Scholar
  58. Zmijanovic V, Mendez S, Moureau V, Nicoud F (2017) About the numerical robustness of biomedical benchmark cases: interlaboratory FDA’s idealized medical device. Int J Numer Methods Biomed Eng 33(1):1–17 e02789CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.IMAG, Univ Montpellier, CNRSMontpellierFrance
  2. 2.LIMSI, CNRS, Université Paris-SaclayOrsayFrance
  3. 3.Department of Haematology BiologyCHU, Univ MontpellierMontpellierFrance

Personalised recommendations