Entropy Production Rate for Avascular Tumor Growth

Elena Izquierdo-Kulich, Esther Alonso-Becerra, José M Nieto-Villar

.

DOI: 10.4236/jmp.2011.226071                

Abstract

The entropy production rate was determined for avascular tumor growth. The proposed formula relates the fractal dimension of the tumor contour with the quotient between mitosis and apoptosis rate, which can be used to characterize the degree of proliferation of tumor cells. The entropy production rate was determined for fourteen tumor cell lines as a physical function of cancer robustness. The entropy production rate is a hallmark that allows us the possibility of prognosis of tumor proliferation and invasion capacities, key fac-tors to improve cancer therapy.

Keywords

Entropy Production Rate, Cancer Robustness, Cancer Evolution

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. S. Deisboeck, M. E. Berens, A. R. Kansal, S. Torquato, A. O. Stemmer-Rachamimov and E. A. Chiocca, “Pattern of Self-Organization in Tumour Systems: Complex Growth Dynamics In A Novel Brain Tumour Spheroid Model,” Cell Proliferation, Vol. 34, 2001, pp. 115-134. doi:10.1046/j.1365-2184.2001.00202.x
[2]	H. Kitano, “Towards a Theory of Biological Robustness,” Molecular Systems Biology, Vol. 3, 2007, p. 137. doi:10.1038/msb4100179
[3]	D. Rockmore, “Cancer Complex Nature,” Santa Fe Institute Bulletin, Vol. 20, 2005, pp. 18-21.
[4]	H. Kitano, “Cancer Robustness: Tumour Tactics,” Nature, Vol. 426, 2003, p. 125. doi:10.1038/426125a
[5]	H. Kitano, “Cancer as a Robust System: Implications For Anticancer Therapy,” Nature Reviews Cancer, Vol. 4, 2004, pp. 227-235. doi:10.1038/nrc1300
[6]	S. Hauptmann, “A Thermodynamic Interpretation of Malignancy: Do Genes Come Later?,” Medical Hypotheses, Vol. 58, 2002, pp. 144-147. doi:10.1054/mehy.2001.1477
[7]	L. F. Luo, “Entropy Production in a Cell and Reversal of Entropy Flow as an Anticancer Therapy,” Frontiers of Physics in China, Vol. 4, 2009, pp. 122-136. doi:10.1007/s11467-009-0007-9
[8]	J. M. Nieto-Villar, R. Quintana and J. Rieumont, “Entropy Production Rate as a Lyapunov Function in Chemical Systems: Proof,” Physica Scripta, Vol. 68, 2003, pp. 163-165. doi:10.1238/Physica.Regular.068a00163
[9]	A. Brú, S. Albertos, J. L. Subiza, J. L. García-Asenjo and I. Brú, “The Universal Dynamics of Tumour Growth,” Biophysical Journal, Vol. 85, 2003, pp. 2948-2961. doi:10.1016/S0006-3495(03)74715-8
[10]	I. Prigogine, “Introduction to Thermodynamics of Irreversible Processes,” Wiley, New York, 1961.
[11]	Th. De Donder and P. Van Rysselberghe, “Thermodynamic Theory of Affinity, H. Milford,” Oxford University Press, London, 1936.
[12]	N. G. Van Kampen, “Stochastic Processes in Physics and Chemistry,” 3rd Edition, Elsevier, Amsterdam, 2007.
[13]	C. W. Gardiner, “Handbook Oof Stochastic Methods: For Physics, Chemistry And The Natural Sciences, 3rd Edition,” Springer-Verlag, Heidelberg, 2004.
[14]	V. Anishchenko, V. Astakhov, A. Neiman, T. Vadisova and L. Schimansky-Geir, “Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial And Modern Developments,” 2nd Edition, Springerr-Verlag, Heidelberg, 2007.
[15]	V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson, “Nonlinear Dynamics of Immunogenic Tumours: Parameter Estimation and Global Bifurcation Analysis,” Bulletin of Mathematical Biology, Vol. 56, 1994, pp. 295-231.
[16]	A. L. Barabasi and H. E. Stanley, “Fractal Concepts in Surface Growh,” Cambridge University Press, Cambridge, 1995. doi:10.1017/CBO9780511599798
[17]	E. Izquierdo and J. M. Nieto-Villar, “Morphogenesis of the Tumour Patterns,” Mathematical Biosciences and Engineering, Vol. 5, 2008, pp. 299-313.
[18]	L. Norton, “Conceptual and Practical Implications of Breast Tissue Geometry: Toward A More Effective, Less Toxic Therapy,” Oncologist, Vol. 10, 2005, pp. 370-381. doi:10.1634/theoncologist.10-6-370