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A suggested chain process for radiation damage

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Abstract

It has been suggested that when an organism is exposed to ionizing radiation the initial damage results from the occurrence of ionization in a so-called sensitive volume due to absorption of radiation quanta. The initial radiation damage is then transmitted or amplified to a level of macroscopic perception. In this paper a mechanism by which this transmission may take place and a finite Markov chain model applicable to this transmission are postulated and discussed.

This mechanism is assumed to be the depolymerization of essential chain molecules which are connected to some “central group” associated with the seensitive volume. The depolymerization of the macromolecules following a hit in the sensitive volume is postulated to be determined by a chain mechanism, which acts in a manner inverse to the mechanism controlling the polymerization process. A mathematical study of this problem is made using the theory of Markov chains. The probability of complete degradation of the chain macromolecule, and the probability of recombination of the units to give the intact chain were determined, assuming that the probabilty of successive steps in the degradation increase linearly from the intact state to that of complete breakdown.

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Literature

  • Blau, M. and K. Altenburger. 1923. “Über einige Wirkungen von Strahlen.”Zeit. f. Physik,12, 315–29.

    Article  Google Scholar 

  • Chalmers, W. 1934. “The Mechanism of Macropolymerization Reactions.”Jour. Amer. Chem. Soc.,56, 912–22.

    Article  Google Scholar 

  • Dessauer, F. 1923. “Über einige Wirkungen von Strahlen.”Zeit. f. Physik,12. 38–47.

    Article  Google Scholar 

  • Ehrenfest, P. and T. Ehrenfest. 1907. “Uber zwei bekannte Einwände gegen das Boltzmannsche H-theorem.”Phys. Zeits.,8, 311–14.

    MATH  Google Scholar 

  • Feller, W. 1950.An Introduction to Probability Theory and its Applications. New York: John Wiley and Sons, Inc.

    Google Scholar 

  • Kac, M. 1947. “Random Walk and the Theory of Brownian Motion.”Amer. Math. Month.,54, 369–91.

    Article  MATH  MathSciNet  Google Scholar 

  • Mark, H. and A. V. Tobolsky. 1950.Physical Chemistry of High Polymeric Systems. New York: Interscience Publishers, Inc.

    Google Scholar 

  • Opatowski, I. 1945. “Chain Processes and Their Biophysical Applications: I. General Theory.”Bull. Math. Biophysics,7, 161–80.

    Article  MathSciNet  Google Scholar 

  • — 1946a. “Chain Processes and their Biophysical Applications: II. The Effect of Recovery.” —Ibid.,8, 7–15.

    Article  MATH  MathSciNet  Google Scholar 

  • — 1946b. “The Probabilistic Approach to the Effects of Radiation and Variability and Sensitivity.” —Ibid.,,8, 101–19.

    Article  MathSciNet  Google Scholar 

  • Reboul, J. 1942.Les Bases Physiques et Biologiques de la Roentgentherapie. (Ed. P. Lamarque.) Paris: Masson et Cie.

    Google Scholar 

  • Sax, K, and C. P. Swanson. 1941. “Differential Sensitivity of Cells to X-rays.”Amer. Jour. Botany,28, 52–9.

    Article  Google Scholar 

  • Wang, M. C. and G. E. Uhlenbeck. 1945. “On the Theory of the Brownian Motion. II.”Revs. Mod. Physics,17, 323–42.

    Article  MATH  MathSciNet  Google Scholar 

  • van der Werff, J. Th. 1948.Biological Reactions Caused by Electric Currents and by X-rays. New York: Elsevier Publishing Co., Inc.

    Google Scholar 

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Authors and Affiliations

  1. Committee on Mathematical Biology, The University of Chicago, Chicago, USA

    A. T. Reid & H. G. Landau

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  1. A. T. Reid
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  2. H. G. Landau
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Reid, A.T., Landau, H.G. A suggested chain process for radiation damage. Bulletin of Mathematical Biophysics 13, 153–163 (1951). https://doi.org/10.1007/BF02478224

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