ArticlePloS one2019
New formulation of the Gompertz equation to describe the kinetics of untreated tumors.
Article in PloS one, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed, 20 citations in OpenAlex.
- Proper likelihood functions for parameter estimation in S-shaped models of unperturbed tumor growth.Scientific reports · 2025Article
- Article
- Advancing cancer drug development with mechanistic mathematical modeling: bridging the gap between theory and practice.Journal of pharmacokinetics and pharmacodynamics · 2024Review
- Simulations of surface charge density changes during the untreated solid tumour growth.Royal Society open science · 2022Article
- A quantitative systems pharmacology model of hyporesponsiveness to erythropoietin in rats.Journal of pharmacokinetics and pharmacodynamics · 2021Article
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Authors and funding
9 authors at 5 institutions in 5 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
backgroundDifferent equations have been used to describe and understand the growth kinetics of undisturbed malignant solid tumors. The aim of this paper is to propose a new formulation of the Gompertz equation in terms of different parameters of a malignant tumor: the intrinsic growth rate, the deceleration factor, the apoptosis rate, the number of cells corresponding to the tumor latency time, and the fractal dimensions of the tumor and its contour.
methodsFurthermore, different formulations of the Gompertz equation are used to fit experimental data of the Ehrlich and fibrosarcoma Sa-37 tumors that grow in male BALB/c/Cenp mice. The parameters of each equation are obtained from these fittings.
resultsThe new formulation of the Gompertz equation reveals that the initial number of cancerous cells in the conventional Gompertz equation is not a constant but a variable that depends nonlinearly on time and the tumor deceleration factor. In turn, this deceleration factor depends on the apoptosis rate of tumor cells and the fractal dimensions of the tumor and its irregular contour.
conclusionsIt is concluded that this new formulation has two parameters that are directly estimated from the experiment, describes well the growth kinetics of unperturbed Ehrlich and fibrosarcoma Sa-37 tumors, and confirms the fractal origin of the Gompertz formulation and the fractal property of tumors.
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