The Application of Chaos Theory and Fractal Mathematics to the Study of Cancer Evolution: Placing Metabolism and Immunity Centre Stage

Main Article Content

Vijay Sharma

Abstract

Despite the undoubted triumphs that have occurred in the treatment of some cancers, overall, the outcomes for disseminated disease remain poor. A change in perspective is therefore required to develop more effective treatment strategies. This review provides an overview of the potential contribution of chaos theory and fractal mathematics to the study of cancer evolution. The atavistic model of cancer proposes that cancer represents a reversion to an evolutionarily ancient proliferative phenotype, and suggests that cellular metabolism and the immune system are targets to which cancer may be susceptible. The approaches of chaos theory and fractal mathematics point to the same targets, and the synergy of these two perspectives will be explored. The emerging unifying concept which emerges is that the cellular machinery of the differentiated cell resists entropy in favour of stable structure. Each evolutionary development from multicellular organisms upwards, diverts more energy away from entropy. When malignant transformation occurs, the cell succumbs to the draw of the thermodynamic laws, maximizing fractal entropy, reverting to its ancient proliferative phenotype and moving, in its increased dynamic state, into greater chaos. Changes in the chaotic dynamics of cellular function evolve in parallel with changes in the fractal geometry of cellular structure. If the dynamics of the cancer cell can be worked out mathematically, it may be possible to use these dynamics to plan treatment strategies in the way that chaos theory is currently used to, for example, guide satellites. Although the responses of the tumour to the suggested targets may be weaker, they may also be more sustainable, and produce fewer side effects, than the current modalities and the emerging molecularly targeted therapies. 

Article Details

How to Cite
SHARMA, Vijay. The Application of Chaos Theory and Fractal Mathematics to the Study of Cancer Evolution: Placing Metabolism and Immunity Centre Stage. Medical Research Archives, [S.l.], v. 4, n. 6, oct. 2016. ISSN 2375-1924. Available at: <https://esmed.org/MRA/mra/article/view/717>. Date accessed: 09 dec. 2024.
Keywords
Fractal; chaos theory; evolution; Atavistic model; cancer; metabolism; immunity; immune system; self-organisation; entropy; cancer therapy; epigenetics; mutation; anaplasia
Section
Review Articles

References

Al-Hajj, M., Wicha, M. S., Benito-Hernandez, A., Morrison, S. J., & Clarke, M. F. (2003). Prospective identification of tumorigenic breast cancer cells. Proc Natl Acad Sci U S A, 100(7), 3983-3988, 10.1073/pnas.0530291100
0530291100 [pii]

Barabasi, A. L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509-512,
Bassingthwaighte, J. B., Liebovitch, L. S., & West, B. J. (1994). Fractal Physiology. New York: Oxford University Press.

Bhalla, U. S., & Iyengar, R. (1999). Emergent properties of networks of biological signaling pathways. Science, 283(5400), 381-387,

Bray, D. (1995). Protein molecules as computational elements in living cells. Nature, 376(6538), 307-312,

Caserta, F., Stanley, H. E., Eldred, W. D., Daccord, G., Hausman, R. E., & Nittmann, J. (1990). Physical mechanisms underlying neurite outgrowth: A quantitative analysis of neuronal shape. Phys Rev Lett, 64(1), 95-98,

Cohen, I. R., & Young, D. B. (1991). Autoimmunity, microbial immunity and the immunological homunculus. Immunol Today, 12(4), 105-110, 0167-5699(91)90093-9 [pii]
10.1016/0167-5699(91)90093-9

Dalgleish, A. (1999). The relevance of non-linear mathematics (chaos theory) to the treatment of cancer, the role of the immune response and the potential for vaccines. QJM, 92(6), 347-359,

Deb, D. (2016). Understanding the unpredictability of cancer using chaos theory and modern art techniques. Leonardo, 48(2), 66-67, 10.1162/LEON_a_01099

Garland, J. (2013). Energy management - a critical role in cancer induction? Crit Rev Oncol Hematol, 88(1), 198-217, S1040-8428(13)00081-4 [pii]
10.1016/j.critrevonc.2013.04.001

Goldberger, A. L., Amaral, L. A., Hausdorff, J. M., Ivanov, P., Peng, C. K., & Stanley, H. E. (2002). Fractal dynamics in physiology: alterations with disease and aging. Proc Natl Acad Sci U S A, 99 Suppl 1, 2466-2472,

Goldberger, A. L., Rigney, D. R., & West, B. J. (1990). Chaos and fractals in human physiology. Sci Am, 262(2), 42-49,

Hart, J. R., Zhang, Y., Liao, L., Ueno, L., Du, L., Jonkers, M., et al. (2015). The butterfly effect in cancer: a single base mutation can remodel the cell. Proc Natl Acad Sci U S A, 112(4), 1131-1136, 1424012112 [pii]
10.1073/pnas.1424012112

Hartwell, L. H., Hopfield, J. J., Leibler, S., & Murray, A. W. (1999). From molecular to modular cell biology. Nature, 402(6761 Suppl), C47-52,

Janecka, I. P. (2007). Cancer control through principles of systems science, complexity, and chaos theory: a model. Int J Med Sci, 4(3), 164-173,

Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N., & Barabasi, A. L. (2000). The large-scale organization of metabolic networks. Nature, 407(6804), 651-654,

Kassab, G. S., Rider, C. A., Tang, N. J., & Fung, Y. C. (1993). Morphometry of pig coronary arterial trees. Am J Physiol, 265(1 Pt 2), H350-365,

Kauffman, S. A. (1993). The Origin of Order: Self Organization and Selection in Evolution. Oxford: Oxford University Press.

Langton, G. C., Taylor, C., Fanner, D., & Rassmussen, S. (1992). Artificial Life II (Vol. 10). Redwood City, California: Addison-Wesley.

Lee, L. H., Tambasco, M., Otsuka, S., Wright, A., Klimowicz, A., Petrillo, S., et al. (2014). Digital differentiation of non-small cell carcinomas of the lung by the fractal dimension of their epithelial architecture. Micron, 67, 125-131, S0968-4328(14)00149-8 [pii]
10.1016/j.micron.2014.07.005

Lineweaver, C. H., Davies, P. C., & Vincent, M. D. (2014). Targeting cancer's weaknesses (not its strengths): Therapeutic strategies suggested by the atavistic model. Bioessays, 36(9), 827-835, 10.1002/bies.201400070

Lorenz, E. N. (1963). Deterministic nonperiodic flow. American Meteorological Society Journal, 20, 130-141,

Mandelbrot, B. (1982). The Fractal Geometry of Nature. New York: W.H. Freeman and Company.

Markus, M., & Hess, B. (1985). Input-response relationships in the dynamics of glycolysis. Arch Biol Med Exp (Santiago), 18(3-4), 261-271,

Markus, M., Kuschmitz, D., & Hess, B. (1984). Chaotic dynamics in yeast glycolysis under periodic substrate input flux. FEBS Lett, 172(2), 235-238,

Oestreicher, C. (2007). A history of chaos theory. Dialogues Clin Neurosci, 9(3), 279-289,

Oltvai, Z. N., & Barabasi, A. L. (2002). Systems biology. Life's complexity pyramid. Science, 298(5594), 763-764,

Ruelle, D., & Takens, F. (1978). Thermodynamic formalism: The mathematical structures of classical equilibrium statistical mechanics. In G. C. Rota (Ed.), Encyclopedia of Mathematics and its Applications (Vol. 5). Menlo Park, California: Addison-Wesley.

Schneider, B. L., & Kulesz-Martin, M. (2004). Destructive cycles: the role of genomic instability and adaptation in carcinogenesis. Carcinogenesis, 25(11), 2033-2044, 10.1093/carcin/bgh204
bgh204 [pii]

Smith, T. G., Jr., Marks, W. B., Lange, G. D., Sheriff, W. H., Jr., & Neale, E. A. (1989). A fractal analysis of cell images. J Neurosci Methods, 27(2), 173-180,

Trzeciakowski, J., & Chilian, W. M. (2008). Chaotic behavior of the coronary circulation. Med Biol Eng Comput, 46(5), 433-442,

Turing, A. M. (1990). The chemical basis of morphogenesis. 1953. Bull Math Biol, 52(1-2), 153-197; discussion 119-152,

Vasiljevic, J., Reljin, B., Sopta, J., Mijucic, V., Tulic, G., & Reljin, I. (2012). Application of multifractal analysis on microscopic images in the classification of metastatic bone disease. Biomed Microdevices, 14(3), 541-548, 10.1007/s10544-012-9631-1

West, B. J., Bhargava, V., & Goldberger, A. L. (1986). Beyond the principle of similitude: renormalization in the bronchial tree. J Appl Physiol, 60(3), 1089-1097,

Winfree, A. T. (1972). Spiral Waves of Chemical Activity. Science, 175(4022), 634-636,