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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. [ABSTRACT FROM AUTHOR]

The knowledge of the adequate current density distribution to apply when using different electrode arrays in tumor tissue and the healthy surrounding tissue is one of the most significant challenges to improve the effectiveness of electrochemical treatment. This paper proposes a mathematical approach to obtain a three-dimensional analytical expression for the current density generated by multi-needle electrodes. Such array of electrodes can be allocated in an arbitrary shape and inserted anywhere in the tumor. Calculations of the electrical potential and electric current density distributions based on a three-dimensional model for different straight multi-needle electrode configurations are carried out by solving the Laplace equation. The results show that appropriate positioning, insertion depth and electrodes polarity are essential for tumor treatment with direct current and multiple needle electrodes, arranged in concentric circumferences, concentrate a higher electric current density in the tumor. This configuration of multiple straight needle electrodes inserted along the tumor improves the effectiveness of electrochemical treatment because the current density covers the entire volume of the tumor, unlike those configurations that are inserted in the tumor base and only partially cover its volume. [ABSTRACT FROM AUTHOR]