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Randomized multihit models and their identification

Part of: Applications Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

L. G. Hanin ,
L. B. Klebanov  and
A. Yu. Yakovlev
L. G. Hanin*
Affiliation:
Wayne State University
L. B. Klebanov*
Affiliation:
St. Petersburg Technical University
A. Yu. Yakovlev*
Affiliation:
Kernforschungszentrum Karlsruhe
*
∗Postal address: Department of Mathematics, Wayne State University, Detroit, MI 48202, USA.
∗∗Postal address: Department of Applied Mathematics, St. Petersburg Technical University, 29 Polytechnicheskaya, St. Petersburg 195251, Russia.
∗∗∗Postal address: Kernforschungszentrum Karlsruhe, Hauptabteilung Sicherheit/Dosimetrie, Postfach 3640, 76021 Karlsruhe, Germany.
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Abstract

The multihit–one target model induces a stochastic ordering of cell survival with respect to the cell sensitivity characteristics. This property can be used for a description of cell killing effects in heterogeneous populations of cells on the basis of randomized versions of the model. In such versions, either the critical number of lesions or the mean number of hits per unit dose (sensitivity), or both, are assumed to be random. We give some new results specifying conditions under which the randomized multihit models are identifiable, with a focus on the following cases: (1) the critical number of radiation-induced lesions, m, is random; (2) the sensitivity parameter, x, is random given m is known or otherwise; (3) x and m form a pair of independent random variables.

Keywords

MULTIHIT MODELSRANDOMIZED VERSIONSIDENTIFICATIONRADIATION CELL SURVIVAL

MSC classification

Primary: 60E05: Distributions
Secondary: 62P10: Applications to biology and medical sciences
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 458 - 471
Copyright
Copyright © Applied Probability Trust 1996 

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References

[1] Clifford, P. (1972) Nonthreshold models of the survival of bacteria after irradiation. In Proc. 6th Berkeley Symp. on Mathematical Statistics and Probability. Vol. 4: Biology and Health. pp. 265–286. University of California Press, Berkeley.Google Scholar
[2] Danzer, H. (1934) über einige Wirkungen von Strahlen VII. Z. Phys. 89, 421–434.Google Scholar
[3] Garrett, W. R. and Payne, M. G. (1978) Applications of models for cell survival: the fixation time picture. Radiat. Res. 73, 201–211.Google Scholar
[4] Goodhead, D. T. (1980) Models of radiation inactivation and mutagenesis. In Radiation Biology in Cancer Research , pp. 231–247. Raven Press, New York.Google Scholar
[5] Hanin, L. G. (1993) Optimization of radiation cancer treatment: looking for general regularities. Comm. Theor. Biol. 3, 43–74.Google Scholar
[6] Hanin, L. G., Pavlova, L. V. and Yakovlev, A. Yu. (1993) Biomathematical Problems in Optimization of Cancer Radiotherapy. CRC Press, Boca Raton.Google Scholar
[7] Hanin, L. G., Rachev, S. T. and Yakovlev, A. Yu. (1993) On the optimal control of cancer radiotherapy for non-homogeneous cell populations. Adv. Appl. Prob. 25, 1–23.Google Scholar
[8] Rachev, S. T. and Yakovlev, A. Yu. (1988) Theoretical bounds for the tumor treatment efficacy. Syst. Anal. Model. Simul. 5, 37–42.Google Scholar
[9] Turner, M. M. (1975) Some classes of hit-target models. Math. Biosci. 23, 219–235.Google Scholar
[10] Zinninger, G. F. and Little, J. B. (1973) Fractionated radiation response of human cells in stationary and exponential phases of growth. Radiology 108, 423–428.Google Scholar