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

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  • Cabrales, Luis Enrique Bergues
  • Montijano, Juan I.
  • Schonbek, Maria
  • Castañeda, Antonio Rafael Selva

Abstract

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.

Suggested Citation

  • Cabrales, Luis Enrique Bergues & Montijano, Juan I. & Schonbek, Maria & Castañeda, Antonio Rafael Selva, 2018. "A viscous modified Gompertz model for the analysis of the kinetics of tumors under electrochemical therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 96-110.
    • Handle: RePEc:eee:matcom:v:151:y:2018:i:c:p:96-110
    DOI: 10.1016/j.matcom.2018.03.005
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    References listed on IDEAS

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    1. L. Ferrante & S. Bompadre & L. Possati & L. Leone, 2000. "Parameter Estimation in a Gompertzian Stochastic Model for Tumor Growth," Biometrics, The International Biometric Society, vol. 56(4), pages 1076-1081, December.
    2. Sébastien Benzekry & Clare Lamont & Afshin Beheshti & Amanda Tracz & John M L Ebos & Lynn Hlatky & Philip Hahnfeldt, 2014. "Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth," PLOS Computational Biology, Public Library of Science, vol. 10(8), pages 1-19, August.
    3. Cabrales, Luis Enrique Bergues & Aguilera, Andrés Ramírez & Jiménez, Rolando Placeres & Jarque, Manuel Verdecia & Ciria, Héctor Manuel Camué & Reyes, Juan Bory & Mateus, Miguel Angel O’Farril & Palenc, 2008. "Mathematical modeling of tumor growth in mice following low-level direct electric current," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(1), pages 112-120.
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    Cited by:

    1. Estrada, Ernesto & Bartesaghi, Paolo, 2022. "From networked SIS model to the Gompertz function," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    2. Castañeda, Antonio Rafael Selva & Pozo, Josue Mariño del & Ramirez-Torres, Erick Eduardo & Oria, Eduardo José Roca & Vaillant, Sorangel Bolaños & Montijano, Juan I. & Cabrales, Luis Enrique Bergues, 2023. "Spatio temporal dynamics of direct current in treated anisotropic tumors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 609-632.

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