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A numerical study of oxygen diffusion in a spherical cell with the Michaelis-Menten oxygen uptake kinetics

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Abstract

A numerical method is presented for the solution of reaction diffusion systems in biology. The method is used to re-examine the oxygen diffusion in a spherical cell with the Michaelis-Menten oxygen uptake kinetics.

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References

  1. Anderson, N., Arthurs, A. M.; Complementary variational principles for diffusion problems with Michaelis-Menten kinetics. Bull. Math. Biol. 42, 131 (1980)

    Google Scholar 

  2. Chorin, A. J.: Random choice solution of hyperbolic systems. J. Comp. Phys. 22, 517 (1976)

    Google Scholar 

  3. Chorin, A. J.: Random choice methods with applications to reacting gas flows. J. Comp. Phys. 25, 253 (1977)

    Google Scholar 

  4. Colella, P.: Glimm's method for gas dynamics. SIAM J. Sci. Stat. Comp. 3, 76 (1982)

    Google Scholar 

  5. Glaz, H. M., Liu, T.-P.: The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow. Adv. Appl. Math. 5, 111 (1984)

    Google Scholar 

  6. Glimm, J.: Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18, 697 (1965)

    Google Scholar 

  7. Hiltmann, P., Lory, P.: On oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics. Bull. Math. Biol. 45, 661 (1983)

    Google Scholar 

  8. Lin, S. H.: Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. J. Theor. Biol. 60, 449 (1976)

    Google Scholar 

  9. McElwain, D. L. S.: A re-examination of oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics. J. Theor. Biol. 71, 255 (1978)

    Google Scholar 

  10. Michaelis, L., Menten, M. L.: Die Kinetik der Invertinwirkung, Biochemz. 49, 333 (1913)

    Google Scholar 

  11. Prosser, C. L., Brown, F. A.: Comparative animal physiology. Saunders, Philadelphia, 1962

    Google Scholar 

  12. Sod, G. A.: A numerical study of converging cylindrical shock. J. Fluid Mech. 83, 78 (1977)

    Google Scholar 

  13. Sod, G. A.: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comp. Phys. 27, 1 (1978)

    Google Scholar 

  14. auSod, G. A.: A random choice method with application to reaction-diffusion systems in combustion. Int. J. Comp. Math, with Appl. 11 (1985); and Advances hyperbolic partial differential equations, vol. II. Witten, M. (ed.), Pergamon Press, New York (1985)

  15. Sod, G. A.: Numerical methods in fluid dynamics. Cambridge University Press, New York (1985)

    Google Scholar 

  16. Sod, G. A.: A flame dictionary approach to unsteady combustion phenomena. Matem. Applic, Comp. 3, 157 (1984)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Tulane University, 70118, New Orleans, LA, USA

    Gary A. Sod

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  1. Gary A. Sod
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Sod, G.A. A numerical study of oxygen diffusion in a spherical cell with the Michaelis-Menten oxygen uptake kinetics. J. Math. Biol. 24, 279–289 (1986). https://doi.org/10.1007/BF00275638

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  • DOI: https://doi.org/10.1007/BF00275638

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