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A viscoelastic fluid model for describing the mechanics of a coarse ligated plasma clot

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Abstract

Thrombi are formed at the end of a series of complex biochemical processes. There are various types of thrombi, and their rheological properties change depending on the conditions during clot formation. In this paper, a model for a particular type of clot, formed from human plasma, is proposed within a thermodynamic framework that recognizes that viscoelastic fluids possess multiple natural configurations.

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References

  1. Anand M., Rajagopal K.R. (2004). A shear-thinning viscoelastic fluid model for describing the flow of blood. Int. J. Cardiovasc. Med. Sci. 4(2):59–68

    Google Scholar 

  2. Anand M., Rajagopal K., Rajagopal K.R. (2003). A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood. J. Theor. Med. 5(3-4):183–218

    Article  MATH  MathSciNet  Google Scholar 

  3. Badimon L., Chesebro J.H., Badimon J.J. (1992). Thrombus formation on ruptured atherosclerotic plaques and rethrombosis on evolving thrombi. Circulation 86(6, Suppl. S):74–85

    Google Scholar 

  4. Bale M.D., Ferry J.D. (1988). Shear enhancement of elastic modulus in fine fibrin clots. Thromb. Res. 52(6):565–572

    Article  Google Scholar 

  5. Blömback B., Okada M. (1982). Fibrin gel structure and clotting time. Thromb. Res. 25(1–2):51–70

    Article  Google Scholar 

  6. Bluestein D., Niu L., Schoephoerster R.T., Dewanjee M.K. (1997). Fluid mechanics of arterial stenosis: relationship to the development of mural thrombus. Ann. Biomed. Eng. 25(2):344–356

    Google Scholar 

  7. Cammerer U., Dietrich W., Rampf T., Braun S.L., Richter J.A. (2003). The predictive value of modified computerized thromboelastography and platelet function analysis for postoperative blood loss in routine cardiac surgery. Anesthetics Analgesics 96(1):51–57

    Article  Google Scholar 

  8. Caro C.G., Pedley T.J., Schroter R.C., Seed W.A. (1978). The Mechanics of the Circulation. Oxford University Press, Oxford

    Google Scholar 

  9. Carr M.E., Hermans J. (1978). Size and density of fibrin fibers from turbidity. Macromolecules 11(1):46–50

    Article  Google Scholar 

  10. Dascombe W.H., Dumanian G., Hong C., Heil B.V., Labadie K., Hessel B., Blömback B., Johnson P.C. (1997). Application of thrombin based fibrin glue and non-thrombin based batroxobin glue on intact human blood vessels: evidence for transmural thrombin activity. Thromb. Haemost. 78(2):947–951

    Google Scholar 

  11. Diamond S.L. (1999). Engineering design of optimal strategies for blood clot dissolution. Annu. Rev. Biomed. Eng. 1, 427–461

    Article  Google Scholar 

  12. Ferry J.D., Morrison P.R. (1947). Preparation and properties of serum and plasma proteins. viii. The conversion of human fibrinogen to fibrin under various conditions. J. Am. Chem. Soc. 69, 388–400

    Article  Google Scholar 

  13. Fogelson A.L. (1992). Continuum models of platelet aggregation: formulation and mechanical properties. SIAM J. Appl. Math. 52(4):1089–1110

    Article  MATH  MathSciNet  Google Scholar 

  14. Fogelson A.L., Guy R.D. (2004). Platelet-wall interactions in continuum models of platelet thrombosis: formulation and numerical solution. Math. Med. Biol. 21(4):293–334

    MATH  Google Scholar 

  15. Fukada E., Kaibara M. (1976). Rheological measurements of fibrin gels during clotting. Thromb. Res. 8(Suppl. II):49–58

    Article  Google Scholar 

  16. Gerth C., Roberts W.W., Ferry J.D. (1974). Rheology of fibrin clots. II. Linear viscoelastic behavior in shear creep. Biophys. Chem. 2(3):208–217

    Article  Google Scholar 

  17. Glover C.J., McIntire L.V., Brown C.H., Natelson E.A. (1975a). Dynamic coagulation studies: influence of normal and abnormal platelets on clot structure formation. Thromb. Res. 7(1):185–198

    Article  Google Scholar 

  18. Glover C.J., McIntire L.V., Brown C.H., Natelson E.A. (1975b). Rheological properties of fibrin clots. Effects of fibrinogen concentration, factor XIII deficiency, and factor XIII inhibition. J. Lab. Clin. Med. 86(4):644–656

    Google Scholar 

  19. Hartert H.H. (1982). The proper phase of coagulation. Its physical differentiation by resonance-thrombography and thromboelastography. Clin. Hemorheol. 2(1-2):51–69

    Google Scholar 

  20. Jackson M.R., Alving B.M. (1999). Fibrin sealant in preclinical and clinical studies. Curr. Opin. Hematol. 6(6):415–419

    Article  Google Scholar 

  21. Jacobs M.L., Pourmoghadam K.K., Geary E.M., Reyes A.T., Madan N., McGrath L.B., Moore J.W. (2002). Fontan’s operation: is aspirin enough? Is coumadin too much? Ann. Thorac. Surg. 73(1):64–68

    Article  Google Scholar 

  22. Janmey P.A., Amis E.J., Ferry J.D. (1983). Rheology of fibrin clots. VI. Stress relaxation, creep, and differential dynamic modulus of fine clots in large shearing deformations. J. Rheol. 27(2):135–153

    Article  ADS  Google Scholar 

  23. Kaibara M. (1994). Rheological studies on blood coagulation and network formation of fibrin. Polym. Gels. Netw. 2(1):1–28

    Article  Google Scholar 

  24. Kaibara M. (1996). Rheology of blood coagulation. Biorheology 33(2):101–117

    Article  Google Scholar 

  25. Kaibara M., Fukada E., Sakaoku K. (1981). Rheological studies on network structure of fibrin clots under various conditions. Biorheology 18(1):23–35

    Google Scholar 

  26. de Korte C.L., Schaar J.A., Mastik F., Serruys P.W., van der Steen A.F. (2003). Intravascular elastography: from bench to bedside. J. Intervent. Cardiol. 16(3):253–259

    Article  Google Scholar 

  27. Krishnan J.M., Rajagopal K.R. (2004). Thermodynamic framework for the constitutive modeling of asphalt concrete: theory and applications. J. Mater. Civ. Eng. 16(2):155–166

    Article  Google Scholar 

  28. Kuharsky A.L., Fogelson A.L. (2001). Surface mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys. J. 80(3):1050–1074

    Article  Google Scholar 

  29. Lowe G.D.O. (1999). Rheological influences on thrombosis. Baillières Clin. Haematol. 12(3):435–449

    Google Scholar 

  30. MacFarlane R.G. (1964). The cascade model of blood coagulation and its role as an amplifier. Nature 202, 498–499

    ADS  Google Scholar 

  31. Morris R.J., Woodcock J.P. (2004). Evidence-based compression: prevention of stasis and deep vein thrombosis. Ann. Surg. 239(2):162–171

    Article  Google Scholar 

  32. Nelb G.W., Gerth C., Ferry J.D., Lorand L. (1976). Rheology of fibrin clots. III. Shear creep and creep recovery of fine ligated and coarse unligated clots. Biophys. Chem. 5(3):377–387

    Article  Google Scholar 

  33. Nelb G.W., Kamykowski G.W., Ferry J.D. (1981). Rheology of fibrin clots. V. Shear modulus, creep, and creep recovery of fine unligated clots. Biophys. Chem. 13(1):15–23

    Article  Google Scholar 

  34. Pifarre R. (1998). Thrombosis and cardiovascular disease. Med. Clin. North. Am. 82(3):511–522

    Article  Google Scholar 

  35. Pipkin A.C. (1972). Lectures on Viscoelasticity Theory. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  36. Prasad S.C., Rao I.J., Rajagopal K.R. (2005). A continuum model for the creep of single crystal nickel-base super alloys. Acta. Materialia 53(3):669–679

    Article  Google Scholar 

  37. Rajagopal, K.R.: Multiple natural configurations in continuum mechanics. In: Reports of the Institute for Computational and Applied Mechanics. University of Pittsburgh, Pittsburgh (1995)

  38. Rajagopal K.R., Srinivasa A.R. (2000). A thermodynamic framework for rate type fluid models. J. Non-Newtonian Fluid Mech. 88(3):207–227

    Article  MATH  Google Scholar 

  39. Rajagopal K.R., Tao L. (2002). Modeling of the microwave drying process of aqueous dielectrics. ZAMP 53(6):923–948

    Article  MATH  MathSciNet  ADS  Google Scholar 

  40. Riha P., Liao F., Stoltz J.F. (1997). Effect of fibrin polymerization on flow properties of coagulating blood. J. Biol. Phys. 23(2):121–128

    Article  Google Scholar 

  41. Riha P., Wang X., Liao R., Stoltz J.F. (1999). Elasticity and fracture strain of whole blood clots. Clin. Hemorheol. Microcirc. 21(1):45–49

    Google Scholar 

  42. Roberts W.W., Lorand L., Mockros L.F. (1973). Viscoelastic properties of fibrin clots. Biorheology 10(1):29–42

    Google Scholar 

  43. Sakharov D.V., Rijken D.C. (2000). The effect of flow on lysis of plasma clots in a plasma environment. Thromb. Haemost. 83(3):469–474

    Google Scholar 

  44. Schaar J.A., de Korte C.L., Mastik F., Baldewsing R., Regar E., de Feyter P., Slager C.J., van der Steen A.F., Serruys P.W. (2003). Intravascular palpography for high-risk vulnerable plaque assessment. Herz 28(6):488–495

    Article  Google Scholar 

  45. Shortland A.P., Jarvis J.C., Salmons S. (2003). Haemodynamic considerations in the design of a skeletal muscle ventricle. Med. Biol. Eng. Comput. 41(5):529–535

    Article  Google Scholar 

  46. Spiess B.D. (1995). Thromboelastography and cardiopulmonary bypass. Semin. Thromb. Haemost. 21(Suppl. 4):27–33

    Google Scholar 

  47. Strony, J., Beaudoin, A., Brands, D., Adelman, B.: Analysis of shear stress and hemodynamic factors in a model of coronary artery stenosis and thrombosis. Am. J. Physiol. 265(5, Pt. 2), H1787–H1796 (1993)s

    Google Scholar 

  48. Sukavaneshvar S., Rosa G.M., Solen K.A. (2000). Enhancement of stent-induced thromboembolism by residual stenoses: contribution of hemodynamics. Ann. Biomed. Eng. 28(2):182–193

    Article  Google Scholar 

  49. Tang D., Yang C., Kobayashi S., Ku D.N. (2001). Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid–wall interactions. J. Biomech. Eng. 123(6):548–557

    Article  Google Scholar 

  50. Thubrikar M.J., Robicsek F., Labrosse M., Chervenkoff V., Fowler B.L. (2003). Effect of thrombus on abdominal aortic aneurysm wall dilation and stress. J. Cardiovasc. Surg. (Torino) 44(1):67–77

    Google Scholar 

  51. Thurston G.B., Henderson N.M. (1993a). The kinetics of viscoelastic changes due to blood clot formation. In: Moldenaers P., Keunings R. (eds) Theoretical and Applied Rheology, Vol. 2. Elsevier, Amsterdam, pp. 741–743

    Google Scholar 

  52. Thurston G.B., Henderson N.M. (1993b). A new method for the analysis of blood and plasma coagulation. Biomed. Sci. Instrum. 29, 95–102

    Google Scholar 

  53. Thurston G.B., Henderson N.M. (1995). Impedance of a fibrin clot in a cylindrical tube – relation to clot permeability and viscoelasticity. Biorheology 32(5):503–520

    Article  Google Scholar 

  54. Velada J.L., Hollingsbee D.A., Menzies A.R., Cornwell R., Dodd R.A. (2002). Reproducibility of the mechanical properties of vivostat system patient-derived fibrin sealant. Biomaterials 23(10):2249–2254

    Article  Google Scholar 

  55. Wang D.H., Makaroun M.S., Webster M.W., Vorp D.A. (2001). Mechanical properties and microstructure of intraluminal thrombus from abdominal aortic aneurysm. J. Biomech. Eng. 123(6):536–539

    Article  Google Scholar 

  56. Wang D.H., Makaroun M.S., Webster M.W., Vorp D.A. (2002). Effect of intraluminal thrombus on wall stress in patient-specific models of abdominal aortic aneurysm. J. Vasc. Surg. 36(3):598–604

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Texas A&M University, College Station, TX, 77843, USA

    M. Anand

  2. Department of Surgery, Duke University Medical Center, Durham, NC, 27710, USA

    K. Rajagopal

  3. Department of Mechanical Engineering, Texas A&M University, College Station, TX, 77843, USA

    K. R. Rajagopal

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  1. M. Anand
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Correspondence to K. R. Rajagopal.

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Communicated by O.E. Jensen and J. Malek

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Anand, M., Rajagopal, K. & Rajagopal, K.R. A viscoelastic fluid model for describing the mechanics of a coarse ligated plasma clot. Theor. Comput. Fluid Dyn. 20, 239–250 (2006). https://doi.org/10.1007/s00162-006-0019-9

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