Effect of tumor microenvironmental factors on tumor growth dynamics modeled by correlated colored noises with colored cross-correlation. (English) Zbl 1400.92493
Summary: The effect of non-immunogenic tumor microenvironmental factors on tumor growth dynamics modeled by correlated additive and multiplicative colored noises is investigated. Using the Novikov theorem, Fox approach and Ansatz of Hanggi, an approximate Fokker-Planck equation for the system is obtained and analytic expression for the steady state distribution \(P_{s t}(x)\) is derived. Based on the numerical results, we find that fluctuations of microenvironmental factors within the tumor site with parameter \(\theta\) have a diffusive effect on the tumor growth dynamics, and the tumor response to the microenvironmental factors with parameter \(\alpha\) inhibits growth at weak correlation time \(\tau\). Moreover, at increasing correlation time \(\tau\) the inhibitive effect of tumor response \(\alpha\) is suppressed and instead a systematic growth promotion is noticed. The result also reveals that the strength of the correlation time \(\tau\) has a strong influence on the growth effects exerted by the non-immunogenic component of tumor microenvironment on tumor growth.
MSC:
| 92D30 | Epidemiology |
References:
| [1] | Ai, B.-q.; Shao, Z.-g.; Zhong, W.-r., J. Chem. Phys., 137, Article 174101 pp. (2012) |
| [2] | Lutz, E., Phys. Rev. E, 64, Article 051106 pp. (2001) |
| [3] | Uhlenbeck, G. E.; Ornstein, L. S., Phys. Rev., 36, 823 (1930) · JFM 56.1277.03 |
| [4] | Jia, Y.; Li, J.-r., Phys. Rev. E, 53, 5786 (1996) |
| [5] | Mei, D.; Xie, C.; Zhang, L., Phys. Rev. E, 68, Article 051102 pp. (2003) |
| [6] | Mei, D.-C.; Xie, C.-W.; Xiang, Y.-L., Physica A, 343, 167-174 (2004) |
| [7] | Wang, B.; Wu, X., Chinese Optics Letters, 5, 288-291 (2007) |
| [8] | Bing, W.; Xiu-Qing, W., Chin. Phys. B, 20, Article 114207 pp. (2011) |
| [9] | Zhang, X.-M.; Ai, B.-Q., Eur. Phys. J. B, 73, 433-437 (2010) |
| [10] | Liu, X.-M.; Xie, H.-Z.; Liu, L.-G.; Li, Z.-B., Physica A, 388, 392-398 (2009) |
| [11] | Behera, A.; O’Rourke, S. F.C., Braz. J. Phys., 38, 272-278 (2008) |
| [12] | Bose, T.; Trimper, S., Phys. Rev. E, 84, Article 021927 pp. (2011) |
| [13] | Yang, T.; Han, Q.; Zeng, C.; Wang, H.; Liu, Z.; Zhang, C.; Tian, D., Indian J. Phys., 88, 1211-1219 (2014) |
| [14] | Wang, C.; Mei, D., Phys. Scr., 76, 131 (2007) · Zbl 1121.82350 |
| [15] | Jin, S.; Shi-Qun, Z., Commun. Theor. Phys., 46, 175 (2006) |
| [16] | Wang, C.-J.; Wei, Q.; Mei, D.-C., Modern Phys. Lett. B, 21, 789-797 (2007) · Zbl 1113.92041 |
| [17] | Can-Jun, W.; Di, L.; Dong-Cheng, M., Commun. Theor. Phys., 52, 463 (2009) · Zbl 1179.92032 |
| [18] | Li-Bo, H.; Xiao-Long, G.; Li, C.; Da-Jin, W., Chin. Phys. Lett., 24, 632 (2007) |
| [19] | Zhang, X.; Xu, W.; Zhou, B., Commun. Nonlinear Sci. Numer. Simul., 14, 4220-4225 (2009) |
| [20] | Novikov, E., Sov. Phys.—JETP, 20, 1290-1294 (1965) |
| [21] | Fox, R. F., Phys. Rev. A, 33, 467 (1986) |
| [22] | Ai, B.-Q.; Wang, X.-J.; Liu, G.-T.; Liu, L.-G., Phys. Rev. E, 67, Article 022903 pp. (2003) |
| [23] | Mei, D.; Xie, C.; Zhang, L., Eur. Phys. J. B, 41, 107-112 (2004) |
| [24] | Bose, T.; Trimper, S., Phys. Rev. E, 79, Article 051903 pp. (2009) |
| [25] | Zhang, X.; Nie, D.; Chakrabarty, S., Front. Biosci., 15, 151 (2010), a journal and virtual library |
| [26] | Strell, C.; Rundqvist, H.; Östman, A., Upsala J. Med. Sci., 117, 187-195 (2012) |
| [27] | Witz, I. P., Canc. Microenviron., 2, 9-17 (2009) |
| [28] | Witz, I. P., Canc. Res., 68, 9-13 (2008) |
| [29] | Brú, A.; Albertos, S.; Subiza, J. L.; García-Asenjo, J. L.; Brú, I., Biophys. J., 85, 2948-2961 (2003) |
| [30] | Fuliński, A.; Telejko, T., Phys. Lett. A, 152, 11-14 (1991) |
| [31] | Van Kampen, N. G., Phys. Rep., 24, 171-228 (1976) |
| [32] | Moss, F.; McClintock, P. V., Noise in Nonlinear Dynamical Systems: Theory of Noise Induced Processes in Special Applications, Vol. 2 (1989), Cambridge University Press |
| [33] | Hanggi, P.; Mroczkowski, T. J.; Moss, F.; McClintock, P. V., Phys. Rev. A, 32, 695 (1985) |
| [34] | Gardiner, C. W., Handbook of Stochastic Methods, Vol. 4 (1985), Springer: Springer Berlin |
| [35] | Risken, H., Springer Series in Synergetics (1989) · Zbl 0665.60084 |
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