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Why Growth of Cancerous Tumors Is Gompertzian: A Symmetry-Based Explanation

It is known that the growth of a cancerous tumor is well described by the Gompertz’s equation. The existing explanations for this equation rely on specifics of cell dynamics. However, the fact that for many different types of tumors, with different cell dynamics, we observe the same growth pattern, make us believe that there should be a more fundamental explanation for this equation. In this paper, we show that a symmetry-based approach indeed leads to such an explanation: indeed, out of all scaleinvariant growth dynamics, the Gompertzian growth is the closest to the linear-approximation exponential growth model.