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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

has been cited by the following article:

• TITLE: Allometric Scaling by the Length of the Circulatory Network

  AUTHORS: Andras Szasz

  KEYWORDS: Allometry, Metabolism, Four-Dimension, Optimization, Cancer, Circulatory System, Characteristic Length

  JOURNAL NAME: Open Journal of Biophysics, Vol.11 No.4, August 9, 2021

  ABSTRACT: 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.