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Mathematical Models of Blood Coagulation Kinetics

  • David L. Elliott
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 162)

Abstract

If a mammalian blood vessel is severed, it immediately contracts to limit the flow of blood. Within a few seconds cell-like blood platelets (about 1/8 the diameter of a red cell) touch the cut edges, break down, and aggregate into a plug-like mass. Then, in the stagnant blood near the injury, a complex cascade of proteolytic reactions takes place, resulting in the production of the enzyme thrombin, which changes fibrinogen into fibrin monomer; this polymerizes into fibrin strands which reinforce the platelet plug and form a blood clot. Later the clot contracts and is dissolved, while new cellular growth repairs the wound.

Keywords

Bilinear System Fibrin Monomer Stagnant Blood Variable Structure System Platelet Plug 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. W. Suttie and C. M. Jackson, “Prothrombin Structure, Activation and Snythesis,” Physiological Reviews, Vol. 57, 1-70 (Jan. 1977).Google Scholar
  2. 2.
    E. W. Davie, K. Fujikawa, M. E. Legaz and H. Kato, “Role of Proteases in Blood Coagulation,” in Proteases and Biological Control, ed. by E. Reich et al, Vol. 2 of Cold Spring Harbor Conference on Cell Proliferation, 1975.Google Scholar
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    H. C. Hemker and P. W. Hemker, “General Kinetics of Enzyme Cascades,” Proc. Roy. Soc. B Vol. 173, 411–420 (1969).CrossRefGoogle Scholar
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    H. T. Banks, R. P. Miech and D. J. Zinberg, “Nonlinear Systems in Models for Enzyme Cascades,” in Variable Structure Systems with Application to Economics and Biology, ed. by A. Ruberti and R. R. Mohler, Springer LN in Economics and Mathematical Systems Vol. III, New York, 1975.Google Scholar
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    Barbara Abraham-Shrauner, “Generalized Gouy-Chapman Potential of Charged Phospholipid Membranes with Divalent Cations,” J. of Math. Biol. Vol. 2, 333–334 (1975).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • David L. Elliott
    • 1
  1. 1.Department of Systems Science and MathematicsWashington UniversitySt. LouisUSA

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