期刊
MATHEMATICS AND COMPUTERS IN SIMULATION
卷 203, 期 -, 页码 609-632出版社
ELSEVIER
DOI: 10.1016/j.matcom.2022.07.004
关键词
Modified Gompertz equation; Anisotropic and heterogeneous malignant solid tumors; Electrochemical therapy; Diffusion tensor
By extending the Gompertz equation, this study simulated the spatiotemporal behavior of anisotropic tumors and conducted a theoretical analysis. The results showed that direct current treatment is most effective for highly heterogeneous, anisotropic, aggressive, and hypodense malignant solid tumors.
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. (c) 2022 The Author(s). Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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