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Mathematical modeling of tumor growth in mice following low-level direct electric current

Author

Listed:
  • 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
  • Palencia, Fabiola Suárez
  • Ávila, Marisela González

Abstract

A modification to the conventional Gompertz equation (named modified Gompertz equation) is introduced to describe the solid tumor growth perturbed with direct electric current. Simulations of this equation are made. Quantitative fitting criteria as goodness-of-fit, handling missing data and prediction capability are considered. Also, parameter estimation accuracy is calculated. A fit of the experimental data of Ehrlich and fibrosarcoma Sa-37 tumor growths treated with different intensities of direct electric current are also made to validate this modified Gompertz equation. The results obtained in this study corroborate that the direct electric current effectiveness depends on (i/i0) ratio, and also on the duration of the effects of it into the tumor, and of the tumor type. It was concluded that the modified Gompertz equation has a good prediction capability to describe both unperturbed and perturbed tumor growths and it could be used to help physicians choose the most appropriate treatment for patients and animals with malignant solid tumors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:78:y:2008:i:1:p:112-120
    DOI: 10.1016/j.matcom.2007.06.004
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    References listed on IDEAS

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    1. Miklavčič, Damijan & Jarm, Tomaž & Karba, Rihard & Serša, Gregor, 1995. "Mathematical modelling of tumor growth in mice following electrotherapy and bleomycin treatment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(5), pages 597-602.
    2. 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.
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    Cited by:

    1. Aguilera, Andrés Ramírez & Cabrales, Luis Enrique Bergues & Ciria, Héctor Manuel Camué & Pérez, Yudelmis Soler & Oria, Eduardo Roca & Brooks, Soraida Acosta & González, Tamara Rubio, 2009. "Distributions of the potential and electric field of an electrode elliptic array used in tumor electrotherapy: Analytical and numerical solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2091-2105.
    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.
    3. Pupo, Ana Elisa Bergues & González, Maraelys Morales & Cabrales, Luis Enrique Bergues & Reyes, Juan Bory & Oria, Eduardo José Roca & Nava, Juan José Godina & Jiménez, Rolando Placeres & Sánchez, Franc, 2017. "3d current density in tumors and surrounding healthy tissues generated by a system of straight electrode arrays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 138(C), pages 49-64.
    4. 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.
    5. Aguilera, Andrés Ramírez & Cabrales, Luis Enrique Bergues & Ciria, Héctor Manuel Camué & Pérez, Yudelmis Soler & González, Fidel Gilart & González, Maraelys Morales & Zamora, Lisset Ortíz & Palencia, , 2010. "Electric current density distribution in planar solid tumor and its surrounding healthy tissue generated by an electrode elliptic array used in electrotherapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1886-1902.
    6. Ciria, Héctor Manuel Camué & Cabrales, Luis Enrique Bergues & Aguilera, Andrés Ramírez & Nava, Juan José Godina & Joa, Javier Antonio González & García, Raudel Peña & González, Gustavo Sierra & Gonzál, 2012. "Influence of electrode array parameters used in electrotherapy on tumor growth kinetics: A mathematical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1396-1406.

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