A viscous modified Gompertz model for the analysis of the kinetics of tumors under electrochemical therapy

Knowledge of tumor growth kinetics constitutes a challenge for researchers. Different models have been used to describe data of unperturbed and perturbed tumors. The modified Gompertz equation had been proposed to describe diverse responses of direct current treated tumors (disease progression, stab...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2018-09, Vol.151, p.96-110
Main Authors: Cabrales, Luis Enrique Bergues, Montijano, Juan I., Schonbek, Maria, Castañeda, Antonio Rafael Selva
Format: Article
Language:English
Subjects:
Diffusion process
Electrochemical therapy
Modified Gompertz equation
Tumor
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Summary:Knowledge of tumor growth kinetics constitutes a challenge for researchers. Different models have been used to describe data of unperturbed and perturbed tumors. The modified Gompertz equation had been proposed to describe diverse responses of direct current treated tumors (disease progression, stable disease, partial response and complete response). Nevertheless, diffusion processes involved in the tumor growth are not integrated in this equation. This paper analyzes the viscous modified Gompertz equation. It is shown that for certain input parameters the corresponding solutions decrease exponentially in appropriate time intervals. •New model that includes a diffusion term in the modified Gompertz equation.•New model that allows us to simulate the tumor growth kinetics (mass, volume and density) under electrochemical treatment.•New model that allows us to study the tumor responses after direct current application.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2018.03.005