Background: Allometric scaling is a well-known research tool used for the metabolic rates of organisms. It measures the living systems with fractal physiology. The metabolic rate versus the mass of the living species has a definite scaling and behaves like a four-dimensional phenomenon. The extended investigations focus on the mass-dependence of the various physiological parameters. Objective: Proving the length of vascularization is the scaling parameter instead of mass in allometric relation. Method: The description of the energy balance of the ontogenic growth of the tumor is an extended cell-death parameter for studying the mass balance at the cellular level. Results: It is shown that when a malignant cellular cluster tries to maximize its metabolic rate, it changes its allometric scaling exponent. A growth description could follow the heterogenic development of the tumor. The mass in the allometric scaling could be replaced by the average length of the circulatory system in each case. Conclusion: According to this concept, the dependence of the mass in allometric scaling is replaced with a more fundamental parameter, the length character of the circulatory system. The introduced scaling parameter has primary importance in cancer development, where the elongation of the circulatory length by angiogenesis is in significant demand.
References
[1]
Sornette, D. (2000) Chaos, Fractals, Self-Organization and Disorder: Concepts and Tools. Springer Verlag, Berlin.
[2]
Walleczek, J. (2000) Self-Organized Biological Dynamics & Nonlinear Control. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511535338
[3]
Kauffman, S.A. (1993) The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, New York. https://doi.org/10.1007/978-94-015-8054-0_8
[4]
West, B.J. (1990) Fractal Physiology and Chaos in Medicine. World Scientific, Singapore.
[5]
Bassingthwaighte, J.B., Leibovitch, L.S. and West, B.J. (1994) Fractal Physiology. Oxford University Press, New York. https://doi.org/10.1007/978-1-4614-7572-9
[6]
Brown, J.H. and West, G.B. (2000) Scaling in Biology. Oxford University Press, Oxford.
[7]
Brown, J.H., West, G.B. and Enquis, B.J. (2005) Yes, West, Brown and Enquist’s Model of Allometric Scaling Is Both Mathematically Correct and Biologically Relevant. Functional Ecology, 19, 735-738. https://doi.org/10.1111/j.1365-2435.2005.01022.x
[8]
West, B.J. (2006) Where Medicine Went Wrong: Rediscovering the Path to Complexity. World Scientific, London. https://doi.org/10.1142/6175
[9]
West, D. and West, B.J. (2012) On Allometry Relations. International Journal of Modern Physics B, 26, 116-171. https://doi.org/10.1142/S0217979212300101
[10]
Deering, W. and West, B.J. (1992) Fractal Physiology. IEEE Engineering in Medicine and Biology, 11, 40-46. https://doi.org/10.1109/51.139035
[11]
Kleiber, M. (1961) The Fire of Life: An Introduction to Animal Energetics. Wiley, Hoboken.
[12]
Tannock, I.F. (1968) The Relation Between Cell Proliferation and the Vascular System in a Transplanted Mouse Mammary Tumour. British Journal of Cancer, 22, 258-273. https://doi.org/10.1038/bjc.1968.34
[13]
Milotti, E., Vyshemirsky, V., Sega, M. and Chignola, R. (2012) Interplay between Distribution of Live Cells and Growth Dynamics of Solid Tumours. Scientific Reports, 2, Article No. 990. https://doi.org/10.1038/srep00990
[14]
Guiot, C., Delsanto, P.P.P., Carpinteri, A., et al. (2006) The Dynamic Evolution of the Power Exponent in a Universal Growth Model of Tumors. Journal of Theoretical Biology, 240, 459-463. https://doi.org/10.1016/j.jtbi.2005.10.006
[15]
West, G.B., Brown, J.H. and Enquist, B.J. (1990) The Four Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms. Science, 284, 1677-1679. https://doi.org/10.1126/science.284.5420.1677
[16]
Labra, F.A., Marquet, P.A. and Bozinovic, F. (2007) Scaling Metabolic Rate Fluctuations. Proceedings of the National Academy of Sciences of the United States of America, 104, 10900-10903. https://doi.org/10.1073/pnas.0704108104
[17]
West, G.B. and Brown, J.H. (2000) Scaling in Biology. Oxford University Press, Oxford.
[18]
Calder, W.A. III (1996) Size, Function and Life History. Dover Publications Inc., Mineola.
[19]
Schlesinger, M.S. (1987) Fractal Time and 1/f Noise in Complex Systems. Annals of the New York Academy of Sciences, 504, 214-228. https://doi.org/10.1111/j.1749-6632.1987.tb48734.x
[20]
Bak, P., Tang, C. and Wieserfeld, K. (1988) Self-Organized Criticality. Physical Review A, 38, 364-373. https://doi.org/10.1103/PhysRevA.38.364
[21]
Musha, T. and Sawada, Y. (1994) Physics of the Living State. IOS Press, Amsterdam.
[22]
Berryman, M.J., Spencer, S.L., Allison, A. and Abbott, D. (2004) Fluctuations and Noise in Cancer Development. Proceedings of SPIE—The International Society for Optical Engineering, 5471. https://doi.org/10.1117/12.546641
[23]
Qui, B., Zhou, T. and Zhang, J. (2020) Stochastic Fluctuations in Apoptotic Threshold of Tumor Cells Can Enhance Apoptosis and Combat Fractional Killing. Royal Society Open Science, 7, Article ID: 190462. https://doi.org/10.1098/rsos.190462
[24]
Fiasconaro, A., Ochab-Marcinek, A., Spagnolo, B. and Gudowska-Nowak, E. (2008) Monitoring Noise-Resonant Effects in Cancer Growth Influenced by External Fluctuations and Periodic Treatment. Physics of Condensed Matter, 65, 435-442. https://doi.org/10.1140/epjb/e2008-00246-2
[25]
Chan, A. and Tuszynski, J.A. (2016) Automatic Prediction of Tumour Malignancy in Breast Cancer with Fractal Dimension. Royal Society Open Science, 3, Article ID: 160558. https://doi.org/10.1098/rsos.160558
[26]
Tambasco, M. and Magliocco, A.M. (2008) Relation between Tumor-Grade and Computed Architectural Complexity in Breast Cancer Specimens. Human Pathology, 39, 740-746. https://doi.org/10.1016/j.humpath.2007.10.001
[27]
Pamatmat, M.M. (1983) Measuring Aerobic and Anaerobic Metabolism of Benthic Infauna under Natural Conditions. Journal of Experimental Zoology, 228, 405-413. https://doi.org/10.1002/jez.1402280303
[28]
Moses, M.E., Hou, C., Woodruff, W.H., et al. (2008) Revisiting a Model of Ontogenic Growth: Estimating Model Parameters from Theory and Data. The American Naturalist, 171, 632-645. https://doi.org/10.1086/587073
[29]
Voet, D., Voet, J.G. and Pratt, C.W. (2006) Fundamentals of Biochemistry. 2nd Edition, John Wiley and Sons, Inc., Hoboken.
[30]
West, G.B. and Brown, J.H. (2005) The Origin of Allometric Scaling Laws in Biology from Genomes to Ecosystems: Towards a Quantitative Unifying Theory of Biological Structure and Organization. Journal of Experimental Biology, 208, 1575-1592. https://doi.org/10.1242/jeb.01589
[31]
West, G.B., Woodruf, W.H. and Born, J.H. (2002) Allometric Scaling of Metabolic Rate from Molecules and Mitochondria to Cells and Mammals. Proceedings of the National Academy of Sciences of the United States of America, 99, 2473-2478. https://doi.org/10.1073/pnas.012579799
[32]
West, G.B., Brown, J.H. and Enquist, B.J. (2004) Growth Models Based on First Principles or Phenomenology? Functional Ecology, 18, 188-196. https://doi.org/10.1111/j.0269-8463.2004.00857.x
[33]
Banavar, J.R., Damuth, J., Maritan, A., et al. (2002) Modelling Universality and Scaling. Nature, 420, 626. https://doi.org/10.1038/420626a
[34]
West, G.B., Enquist, B.J. and Brown, J.H. (2002) Modelling Universality and Scaling—REPLY. Nature, 420, 626-627. https://doi.org/10.1038/420626b
[35]
Stevens, C.F. (2009) Darwin and Huxley Revisited: The Origin of Allometry. Journal of Biology, 8, Article No. 14. https://doi.org/10.1186/jbiol119
[36]
Delides, A., Panayiotides, I., Alegakis, A., et al. (2005) Fractal Dimension as a Prognostic Factor for Laryngeal Carcinoma. Anticancer Research, 25, 2141-2144.
[37]
Guiot, C., Degiorgis, P.G., Delsanto, P.P., et al. (2003) Does Tumor Growth Follow a “Universal Law”? Journal of Theoretical Biology, 225, 147-151. https://doi.org/10.1016/S0022-5193(03)00221-2
[38]
Deisboeck, T.S., Guiot, C., Delsanto, P.P., et al. (2006) Does Cancer Growth Depend on Surface Extension? Medical Hypotheses, 67, 1338-1341. https://doi.org/10.1016/j.mehy.2006.05.029
[39]
Nagy, J.A., Chang, S.-H., Shih, S.-C., Dvorak, A.M. and Dvorak, H.F. (2010) Heterogeneity of the Tumor Vasculature. Seminars in Thrombosis and Hemostasis, 36, 321-331. https://doi.org/10.1055/s-0030-1253454
[40]
Herman, A.B., van Savage, M. and West, G.B. (2011) A Quantitative Theory of Solid Tumor Growth, Metabolic Rate and Vascularization. PLoS ONE, 6, e22973. https://doi.org/10.1371/journal.pone.0022973
[41]
Haanen, C. and Vermes, I. (1996) Apoptosis: Programmed Cell Death in Fetal Development. European Journal of Obstetrics & Gynecology and Reproductive Biology, 64, 129-133. https://doi.org/10.1016/0301-2115(95)02261-9
[42]
Kerr, J.F.R., Wyllie, A.H. and Currie, A.R. (1972) Apoptosis: A Basic Biological Phenomenon with Wide-Ranging Implications in Tissue Kinetics. British Journal of Cancer, 26, 239-257. https://doi.org/10.1038/bjc.1972.33
[43]
Lowe, S.W. and Lin, A.W. (2000) Apoptosis in Cancer. Carcinogenesis, 21, 485-495. https://doi.org/10.1093/carcin/21.3.485
[44]
Karsch-Bluman, A., Feiglin, A., Arbib, E., Stern, T., Shoval, H., Schwob, O., Berger, M. and Benny, O. (2018) Tissue Necrosis and Its Role in Cancer Progression. Oncogene, 38, 1920-1935. https://doi.org/10.1038/s41388-018-0555-y
[45]
West, G.B., Brown, J.H. and Enquist, B.J. (2001) A General Model for Ontogenetic Growth. Nature, 413, 628-631. https://doi.org/10.1038/35098076
[46]
von Bertalanffy, L. (1957) Quantitative Laws of Metabolism and Growth. The Quarterly Review of Biology, 32, 217-231. https://doi.org/10.1086/401873
[47]
Bru, A., Albertos, S., Subiza, J.L., Asenjo, J.L.G. and Bru, I. (2003) The Universal Dynamics of Tumor Growth. Biophysical Journal, 85, 2948-2961. https://doi.org/10.1016/S0006-3495(03)74715-8
[48]
Szasz, A. (2021) Vascular Fractality and Alimentation of Cancer. International Journal of Clinical Medicine, 12, 279-296.
[49]
di Leva, A., Bruner, E., Widhalm, G., Michev, G., Tschabitscher, M. and Grizzi, F. (2012) Computer-Assisted and Fractal-Based Morphometric Assessment of Microvascularity in Histological Specimens of Gliomas. Scientific Reports, 2, Article No. 429. https://doi.org/10.1038/srep00429
[50]
Grizzi, F., Russo, C., Colombo, P., Franceschini, B., Frezza, E.E., et al. (2005) Quantitative Evaluation and Modeling of Two-Dimensional Neovascular Network Complexity: The Surface Fractal Dimension. BMC Cancer, 5, 14. https://doi.org/10.1186/1471-2407-5-14
[51]
Ceelen, W., Boterberg, T., Smeets, P., Van Damme, N., et al. (2007) Recombinant Human Erythropoietin α Modulates the Effects of Radiotherapy on Colorectal Cancer Microvessels. British Journal of Cancer, 96, 692-700. https://doi.org/10.1038/sj.bjc.6603568
[52]
Deisboeck, T.S. and Wang, Z. (2008) A New Concept for Cancer Therapy: Out-Competing the Aggressor. Cancer Cell International, 8, 19. https://doi.org/10.1186/1475-2867-8-19
