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Spatio temporal dynamics of direct current in treated anisotropic tumors

Author

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  • 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

Abstract

The inclusion of a diffusion term in the modified Gompertz equation (Cabrales et al., 2018) allows to describe the spatiotemporal growth of direct current treated tumors. The aim of this study is to extend the previous model to the case of anisotropic tumors, simulating the spatiotemporal behavior of direct current treated anisotropic tumors, also carrying out a theoretical analysis of the proposed model. Growths in the mass, volume and density of the solid tumors are shown for each response type after direct current application (disease progression, partial response, stationary partial response and complete remission). For this purpose, the Method of Lines and different diffusion tensors are used. The results show that the growth of the tumor treated with direct current is faster for the shorter duration of the net antitumor effect and the higher diffusion coefficient and anisotropy degree of the solid tumor. It is concluded that the greatest direct current antitumor effectiveness occurs for the highly heterogeneous, anisotropic, aggressive and hypodense malignant solid tumors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:609-632
    DOI: 10.1016/j.matcom.2022.07.004
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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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