Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T06:38:09.645Z Has data issue: false hasContentIssue false
  • English
  • Français

Importance of VIIIa Inactivation in a Mathematical Model forthe Formation, Growth, and Lysis of Clots

Published online by Cambridge University Press:  31 July 2014

P. P. Naidu  and
M. Anand
Get access

Abstract

We perform a sensitivity analysis for a thus far unstudied mathematical model for theformation, growth and lysis of clots in vitro. The sensitivity analysis procedure uses anensemble standard deviation for species concentrations, and is equivalent to a variancedecomposition procedure also available in the literature. Our analysis shows that fibrinproduction is most sensitive to the rate constant governing activation of prothrombin tothrombin. Further, the time-averaged sum of all species’ concentrations is most sensitiveto the rate constants governing the inactivation of VIIIa (intrinsic as well as by APC).We therefore conclude that the rate constants for VIIIa inactivation affect the model thegreatest: this conclusion must be experimentally verified to determine if such is indeedthe case for hemostasis.

Keywords

VIIIa inactivationmathematical modelsensitivity analysishemostasisrate constant
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 6: Blood flows , 2014 , pp. 17 - 33
Copyright
© EDP Sciences, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anand, M., Rajagopal, K., Rajagopal, K.R.. A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood. J. Theor. Med., 5 (2003), no. 3-4, 183-218. CrossRefGoogle Scholar
Anand, M., Rajagopal, K., Rajagopal, K.R.. 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 (2008), no. 4, 725-738. CrossRefGoogle ScholarPubMed
Ataullakhanov, F.I., Zarnitsina, V.I., Pokhilko, A.V., Lobanov, A.I., Morozova, O.L.. Spatio-temporal dynamics of blood coagulation and pattern formation. A theoretical approach, Int. J. Bifurcat. Chaos., 12 (2002), no. 9, 1985-2002. CrossRefGoogle Scholar
Booth, N.A.. Fibrinolysis and thrombosis. Baillière Clin. Haem., 12 (1999), no. 3, 423-433. Google ScholarPubMed
Bungay, S.D., Gentry, P.A., Gentry, R.D.. A mathematical model of lipid-mediated thrombin generation. Math. Med. Biol., 20 (2003), no. 1, 105-129. CrossRefGoogle Scholar
Butenas, S., Mann, K.G.. Blood coagulation. Biochemistry-Moscow, 67 (2002), no. 1, 3-12. CrossRefGoogle ScholarPubMed
R.W. Colman, A.W. Clowes, J.N. George, J. Hirsh, V.J. Marder. Overview of Hemostasis, in Hemostasis and Thrombosis. 4th Edition, pp. 1-16, Editors: Colman R. W., Hirsh J., Marder V. J., Clowes A. W., and George J. N., Lippincott, Williams and Wilkins, 2001.
Danforth, C.M., Orfeo, T., Mann, K.G., Brummel-Ziedins, K.E., Everse, S.J.. The impact of uncertainty in a blood coagulation model. Math. Med. Biol., 26 (2009), no. 4, 323-336. CrossRefGoogle Scholar
B. Furie, B.C. Furie. Molecular basis of blood coagulation, in Hematology : Basic principles and practice. 3rd Edition, 1783-1804, Editors: Hoffman R., Benz E. J., Shattil S. J., Furie B., Cohen H. J., Silberstein L. E., and McGlave P., Churchill Livingstone, 2000.
Hockin, M.F., Jones, K.C., Everse, S.J., Mann, K.G.. A model for the stoichiometric regulation of blood coagulation. J. Biol. Chem., 277 (2002), no. 21, 18322-18333. CrossRefGoogle ScholarPubMed
Kalafatis, M., Egan, J.O., vant Veer, C., Cawthern, K.M., Mann, K.G.. The regulation of clotting factors. Crit. Rev. Eukar. Gene, 7 (1997), no. 3, 241-280. CrossRefGoogle ScholarPubMed
A.L. Karsan, J.M. Harlan. The blood vessel wall, in Hematology : Basic principles and practice. 3rd Edition, 1770-1782, Editors: Hoffman R., Benz E. J., Shattil S. J., Furie B., Cohen H. J., Silberstein L. E., and McGlave P., Churchill Livingstone, 2000.
Kuharsky, A.L., Fogelson, A.F.. Surface mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys. J., 80 (2001), no. 3, 1050-1094. CrossRefGoogle ScholarPubMed
Lacroix, D.E., Anand, M.. A model for the formation, growth, and dissolution of clots in vitro. Effect of the intrinsic pathway on antithrombin III deficiency and protein C deficiency. Int. J. Adv. Eng. Sci. Appl. Math., 3 (2012), no. 1-4, 93-105. CrossRefGoogle Scholar
Levine, S.N.. Enzyme amplifier kinetics. Science, 152 (1966), no. 3722, 651-653. CrossRefGoogle Scholar
H.R. Lijnen, D. Collen. Molecular and cellular basis of fibrinolysis, in Hematology : Basic principles and practice , 3rd Edition, 1804-1814, Editors: Hoffman R., Benz E. J., Shattil S. J., Furie B., Cohen H. J., Silberstein L. E., and McGlave P., Churchill Livingstone, 2000.
Luan, D., Zai, M., Varner, J.D.. Computationally derived points of fragility of a human cascase are consistent with current therapeutic strategies. PLOS Comput. Biol., 3 (2007), no. 7, e142. CrossRefGoogle Scholar
K.G. Mann, D. Gaffney, E.G. Bovill. Molecular biology, biochemistry, and lifespan of plasma coagulation factors. in Williams Hematology , 5th Edition, 1205-1226, Editors: Beutler E., Lichtman M., Coller B. S., and Kipps T. J., McGraw Hill Inc., 1995.
Mann, K.G., Brummel-Ziedins, K., Orfeo, T., Butenas, S.. Models of blood coagulation. Blood Cell. Mol. Dis., 36 (2006), 108-117. CrossRefGoogle ScholarPubMed
Orfeo, T., Butenas, S., Brummel-Ziedins, K.E., Mann, K.G.. The tissue factor requirement in blood coagulation. J. Biol. Chem., 280 (2005), no. 52, 42887-42896. CrossRefGoogle ScholarPubMed
P.N. Paluri. Sensitivity analysis of a mathematical model for blood coagulation and fibrinolysis. Master’s thesis, Indian Institute of Technology Hyderabad , Yeddumailaram, AP, INDIA, 2012.
Panteleev, M.A., Ovanesov, M.V., Kireev, D.A., Shibeko, A.M., Sinauridze, E.I., Ananyeva, N.M., Butylin, A.A., Saenko, E.L., Ataullakhanov, F.I.. Spatial propagation and localization of blood coagulation are regulated by intrinsic and protein C pathways, respectively. Biophys. J., 90 (2006), no. 5, 1489-1500. CrossRefGoogle ScholarPubMed
Sequeira, A., Santos, R.F., Bodnar, T.. Blood Coagulation Dynamics: Mathematical modeling and stability results. Math. Biosci. Eng., 8 (2011), no. 2, 425-443. CrossRefGoogle ScholarPubMed
Wells K. R., Blood Coagulation, http://health.yahoo.net/galecontent/blood-coagulation/2 Accessed May 10th 2012.