Phase transition in tumor growth VIII: The spatiotemporal of avascular evolution

P. J. Betancourt-Padron, K. García-Medina, R. Mansilla, José Nieto Villar

Abstract


A 2D cellular automata model, which allows a better understanding of the morphogenesis of the avascular tumor pattern formation, is presented. Using thermodynamics formalism of irreversible processes and results of complex systems theory, we propose markers to able to establish, in a quantitative way, the degree of aggressiveness and the malignancy of tumor patterns, such as a fractal dimension and the entropy production rate.

Keywords


Biological phase transition, Cellular automata, Avascular tumor growth, Entropy production rate, Fractal dimension

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References


https://www.who.int/health-topics/cancer.

Gottesman, M. M., Lavi, O., Hall, M. D., & Gillet, J. P. (2016). Toward a better understanding of the complexity of cancer drug resistance. Annual review of pharmacology and toxicology, 56, 85-102.

Bizzarri, M., et al. (2011). Fractal analysis in a systems biology approach to cancer. In Seminars in cancer biology (Vol. 21, No. 3, pp. 175-182). Academic Press.

Montero, S., Martin, R., Mansilla, R., Cocho, G., & Nieto-Villar JM (2018). Parameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate: A Systems Biology Approach. In Systems Biology (pp. 125-170). Humana Press, New York, NY.

A. Guerra, et al. (2018). Phase transitions in tumor growth VI: Epithelial-Mesenchymal transition, Physica A, DOI: 10.1016/j.physa.2018.01.040.

R.R. Martin, S. Montero, M. Bizzarri, G. Cocho, R. Mansilla & J. M. Nieto-Villar (2017). Phase transitions in tumor growth: V what can be expected from cancer glycolytic oscillations?. Physica A: Statistical Mechanics and its Applications, DOI: 10.1016/j.physa.2017.06.001.

J.A. Betancourt-Mar, et al. (2017). Phase transitions in tumor growth: IV relationship between metabolic rate and fractal dimension of human tumor cells. Physica A: Statistical Mechanics and its Applications 05/2017; 473, DOI:10.1016/j.physa.2016.12.089.

Llanos-Pérez, J. A., Betancourt-Mar, J. A., Cocho, G., Mansilla, R., & Nieto-Villar, J. M. (2016). Phase transitions in tumor growth: III vascular and metastasis behavior. Physica A: Statistical Mechanics and its Applications, 462, 560-568.

Llanos-Pérez, J. A., et al. (2015). Phase transitions in tumor growth: II prostate cancer cell lines. Physica A: Statistical Mechanics and its Applications, 426, 88-92.

Izquierdo-Kulich, E., Rebelo, I., Tejera, E., & Nieto-Villar, J. M. (2013). Phase transition in tumor growth: I avascular development. Physica A: Statistical Mechanics and its Applications, 392(24), 6616-6623.

Roose T., S. Jonathan Chapman, Philip K. Maini, Mathematical Models of Avascular Tumor Growth, SIAM REVIEW, Vol. 49, No. 2,(2007)179-208.

E Izquierdo & JM Nieto-Villar, (2013). Chapter 49 Morphogenesis and Complexity of the Tumor Patterns, R.G. Rubio et al. (eds.), Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics, Understanding Complex Systems, Springer- Verlag Berlin Heidelberg.

Enderling H, Almog N, Hlatky L (2012) Systems biology of tumor dormancy, vol 734 Springer Science & Business Media, New York.

Stott, E. L., Britton, N. F., Glazier, J. A., & Zajac, M. (1999). Stochastic simulation of benign avascular tumour growth using the Potts model. Mathematical and Computer Modelling, 30(5-6), 183-198.

Freyer, J. P., & Sutherland, R. M. (1986). Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply. Cancer research, 46(7), 3504-3512.

A. Brú, S. Albertos, J. L. Subiza, J. L. García-Asenjo, and I. Brú, THE UNIVERSAL DYNAMICS OF TUMOR GROWTH, Biophysical Journal, 85 (2003), 2948-2961.

McElwain DL., Pettet G. Cell Migration In Multicell Spheroids: Swimming Against the Tide. Bull Math Biol. 1993;55(3):655–74.

Cohen IR, Lajtha A, Lambris JD, Paoletti R. Systems Biology of Tumor Dormancy. 2013.

D. Murray Mathematical Biology: I. An Introduction,Third Edition, Springer-Verlag New York Berlin Heidelberg, (2002).

Kitano H (2002) Systems biology: a brief overview. Science 295:1662–1664.

Dinicola S (2011) A systems biology approach to cancer: fractals, attractors, and nonlinear dynamics. OMICS 15(3):93–104.

Mariano Bizzarri (ed.), Systems Biology, Methods in Molecular Biology, vol. 1702, doi.org/10.1007/978-1-4939-7456-6_8.

Preziosi, L. (Ed.). (2003). Cancer modelling and simulation. CRC Press.

G. P. Karev, A. S. Novozhilov and E. V. Koonin, Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics. Biology Direct (2006) 1:30.

L. de Pillis and A. Radunskaya. A mathematical tumor model with immune resistance and drug therapy: An optimal control approach. Journal of Theoretical Medicine. 3, 79-100, 2001.

G. Albano and V. Giorno, ”A stochastic model in tumor growth. J. Theoretical Biol. 242 (2006) 329-336.

C. Escudero, Stochastic models for tumoral growth. arXiv:q-bio.QM/0603009 1 7 Mar (2006).

Izquierdo-Kulich E, Nieto-Villar JM (2008). Morphogenesis of the tumor patterns. Math Biosci Eng 5(2):299–313.

Izquierdo-Kulich E, Nieto-Villar JM (2007). Mesoscopic model for tumor growth. Math Biosci Eng 4(4):687–698.

D. Wodarz and N. Komarova. Computational Biology of Cancer. Lecture Notes and Mathematical Modeling. World Scientific, 2005.

Sabzpoushan SH, Pourhasanzade F. A new method for shrinking tumor based on microenvironmental factors: Introducing a stochastic agent-based model of avascular tumor growth. Physica A [Internet]. 2018; Available from: https://doi.org/10.1016/j.physa.2018.05.131.

Pourhasanzade F, Sabzpoushan SH. A cellular automata model of chemotherapy effects on tumour growth : targeting cancer and immune cells. Math Comput Model Dyn Syst [Internet]. 2019; 00(00):1–27. https://doi.org/10.1080/13873954.2019.1571515.

A. Ilachinski. Cellular Automata. A Discrete Universe. World Scientific, 2001.

Mallet DG and De Pillis LG. A cellular automata model of tumor–immune system interactions. J Theor Biol 2006; 239: 334–350.

Álvaro G. López, Jesús M. Seoane, and Miguel A. F. Sanjuán, Modelling Cancer Dynamics Using Cellular Automata, 2019, F. Berezovskaya, B. Toni (eds.), Advanced Mathematical Methods in Biosciences and Applications, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, Springer Nature Switzerland AG 2019, https://doi.org/10.1007/978-3-030-15715-9_8.

B. Ribba, T. Alarcon, K. Marron, P.K. Maini, and Z. Agur. The use of hybrid cellular automaton models for improving cancer therapy. Proceedings, Cellular Automata: 6th International Conference on Cellular Automata for Research and Industry, ACRI 2004, Amsterdam, The Netherlands, P.M.A. Sloot, B. Chopard, A.G. Hoekstra (Eds.), Lecture Notes in Computer Science, 3305:444–453, 2004.

Deisboeck TS, Wang Z, Macklin P, et al. Multiscale cancer modeling. Ann Rev Biomed Eng 2011; 13: 127–155.

D. Basanta, B. Ribba, E. Watkin, B. You, and A. Deutsch. Computational analysis of the influence of the microenvironment on carcinogenesis. Mathematical Biosiciences, 229:22–20, 2011.

D. Hanahan and R.A. Weinberg. Hallmarks of cancer: The next generation. Cell, 144(5):646–674, 2011.

Pourhasanzade F, Sabzpoushan SH, Alizadeh AM, Esmati E. An agent-based model of avascular tumor growth: Immune response tendency to prevent cancer development. Simulation. 2017; 93(8):641–57.

Python Software Foundation, Python 3 version 3.7.3, March 25, 2019, Available from: http://www.python.org.

S. Wolfram, Cellular automata and complexity. Collected papers. Addinson Wesley, 1994.

Izquierdo-kulich E, Alonso-becerra E, Nieto-villar JM. Entropy Production Rate for Avascular Tumor Growth. Journal of Modern Physics, 2011, 2, 615-620. https://doi:10.4236/jmp.2011.226071.

Cohen IR, Lajtha A, Lambris JD, Paoletti R. Systems Biology of Tumor Dormancy. 2013.

Barabasi, A. L., and H. E. Stanley. 1995. Fractal Concepts in Surface Growth. Cambridge University Press, Cambridge.

Mandelbrot, M. 1982. Fractal Geometry of Nature. Freeman, San Francisco.

Lucia, U., Ponzetto, A., & Deisboeck, T. S. (2015). A thermodynamic approach to the „mitosis/apoptosis‟ ratio in cancer. Physica A: Statistical Mechanics and its Applications, 436, 246-255.

L. Norton, Conceptual and Practical Implications of Breast Tissue Geometry: Toward a More Effective, Less Toxic Therapy, Oncologist 10 (2005) 370-381.




DOI: https://doi.org/10.31349/RevMexFis.66.856

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