Study of effect correlated noise in tumor growth using extensive and non-extensive entropy

Document Type : Full length research Paper

Abstract

It is to be noted that tumor growth has been studied by additive and multiplicative noise. These methods can be often employed as discrete procedures or they can be depended. In this paper, the tumor growth has been investigated using three different entropy models. We have calculated the steady state probability distribution function using Plank-Fokker equation. The obtained results show that the variations of intensity of the multiplicative and additive noises lead to the tumor cells growth. Also, the tumor cells growth can be controlled by changing the non-extensive degree. The growth of tumor cells increase with enhancing the correlated noises.

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References

 
[1] A. Bialek, I. Cavagna, T. Giardina, E. Mora, E. Silvestri, M. Viale, and A.M. Walczak, Statistical mechanics for natural flocks of birds,  Proceeding of the National Academy of  Sciences 109 (2012) 4786-4791.
[2] S. Lawrence, C.L. Giles, Accessibility of information on the web, Nature 400 (1999) 107-109.
[3] S.P. Strong, R. Koberle, D.R. Van, R.R. Steveninck, W. Bialek, Entropy and information in neural spike trains, Physical Review Letters 80 (1998) 197-200.
[4] C. Beck, Generalized information and entropy measures in physics, Contemporary Physics 50 (2009) 495-510.
[5] G. Kaniadakis, Statistical mechanics in the contex of special relativity, Physical Review E 66 (2002) 056125-056130.
[6] C. Tsallis, Introduction to Non-extensive Statistical Mechanics, Springer (2009).
[7] T. Byrnes, S. Koyama, K. Yan, Y. Yamamoto, Neural networks using two-component Bose-Einstein condensates, Scientific Reports 3 (2013) 2531-2537.
[8] C. Tsallis, Pssible generalization of Boltzmann-Gibbs statistics, Journal of Statistical Physics 52 (1988) 479-487.
[9] S. Abe, A note on the q-deformation-theoretic aspect of the generalized entropies in nonextensive physics, Physics Letters A 224 (1997) 326-330.
[10] J.J. Hopeld, Neural networks and physical systems with emergent collective computational abilities, Proceeding of the National Academy Sciences 79 (1982) 2554-2558.
[11] D.J. Amit, Modeling Brain Function: The World of Attractor Neural Networks, Cambridge University Press, Cambridge (1989).
[12] R.S. Johal, q calculus and entropy in nonextensive statistical physics, Physical Review E 58 (1998) 4147-4151.
[13] P.T. Landsberg, V. Vedral, Distributions and channel capacities in generalized statistical mechanics, Physics Letters A 247 (1998) 211-217.
[14] G.B. Bagci, T. Oikonomou, Comment on "Third law of thermodynamics as a key test of generalized entropies" Physical Review E 92 (2015) 016103-016108.
[15] E.P. Bento, G.M. Viswanathan, M.G. E. da Luz, R. Silva, Third law of thermodynamics as a key test of generalized entropies, Physical Review E 91 (2015) 022105-022110.
[16] R. Khordad, H.R. Rastegar Sedehi, Application of different entropy formalism in a neural network for novel word learning, The European Physical Journal Plus 130 (2015) 246-255.
[17] R. Khordad, H.R. Rastegar Sedehi, Modeling cancer growth and its treatment by means of statistical mechanics entropy, The European Physical Journal Plus 131 (2016) 291-302.
[18] J.A. Gonzalez, I. Rondon, Cancer and nonextensive statistics, Cancer and nonextensive statistics, Physica A 369 (2006) 645-654.
[19] C. Beck, Non-extensive statistical mechanics and particle spectra in elementary interactions, Physica A 286 (2000) 164-180.
[20] A. Behera, S.F.C. O’Rourke, Comment on "Correlated noise in a logistic growth model, Physical Review E 77 (2008) 013901-013905.
[21] F. Kozusko, Z. Bajzer, Combining Gompertzian growth and cell population dynamics, Mathematical Biosciences 185 (2003) 153-167.
[22] A. Behera, S. F.C. O’Rourke, The effect of correlated noise in a Gompertz tumor growth model, Brazilian Journal Physics 38 (2008) 272-278.
[23] B. Gompertz, On the nature of the function expressive of the law of human mortility, and on a new mode of determining the value of life contingencies, Philosophical Transactions of the Royal Society B 115 (1825) 513-583.
[24] C. Winsor, The Gompertz curve as a growth curve, Proceeding National Academy Sciences USA 18 (1932) 1-8.
[25] B.Q. Ai, X.J. Wang, G.T. Liu, L.G. Liu, Correlated noise in a logistic growth model, Physical Review E 67 (2003) 022903-022909.
[26] D.C. Mei, C.W. Xei, L. Zhang, The stationary properties and the state transition of the tumor cell growth mode, European Physical Journal B 41 (2004) 107-112.
[27] H. Risken, The Fokker-Planck Equation, Springer, Berlin (1996).
[28] C.W. Gardiner, Handbook of Stochastic Methods, Third Edition Springer, Verlag Berlin Heidelberg New York (2004).
[29] D. Hart, E. Schochat, Z. Agur, The growth law of primary breast cancer as inferred from mammography screening trials data, British Journal of Cancer 78 (1998) 382-387.
[30] C.P. Calderon, T.A. Kwenbe, Modeling tumor growth, Mathematical Biosciences 103 (1991) 97-114.
Journal of Research on Many-body Systems
Volume 8, Issue 17
September 2018
Pages 19-29

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History

  • Receive Date: 08 February 2017
  • Revise Date: 12 March 2018
  • Accept Date: 23 April 2018

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