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.
Highlights
The spatiotemporal organization of biosystems is complex
The concept of cell-death is crucial in cancer development, considering one of the hallmarks of the malignancy is its escape from apoptosis [43], and is instead more susceptible to a more drastic kind of death: necrosis [44]
A death parameter of the single-cell characteristically appears in the energy-balance of the ontogenic growth of the tumor
Summary
The spatiotemporal organization of biosystems is complex. The complexity is driven by self-organization ([1] [2] [3]), and validated by new science: fractal physiology ([4] [5]), including the bioscaling processes ([6] [7]). The Basal Metabolic Rate (BMR) shows allometric scaling of the mass of the organism [9], describes as the power function of the mass ( ) [10]: BMR ∝ α (1). 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. Objective: Proving the length of vascularization is the scaling parameter instead of mass in allometric relation. 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
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