Mathematical modeling of physicochemical processes in tumors perturbed and unperturbed with electrochemical ablation therapy
Keywords:
physical-mathematical models, electrochemical ablation, electropermeabilization, growth kinetics of unperturbed solid tumors, electrode arraysAbstract
Introduction: Understanding unperturbed tumor kinetics and the optimization of electrolyte ablation therapy parameters are of vital importance for the cure of cancer.
Objective: To show different physical-mathematical models aimed at understanding processes inherent in the growth of unperturbed tumors and to search for the electrode arrays that maximize tumor destruction with minimal damage to the organism.
Methods: The Avrami, conventional Gompertz, and Montijano-Bergues-Bory-Gompertz equations are used to reveal different findings of unperturbed tumor kinetics. The Poisson, Laplace, Pennes, and Nernst-Planck equations allow calculating the electrical potential in the tumor and in the surrounding healthy tissue, the temperature and mobility of ions generated by multiple electrode geometries, respectively.
Results: The kinetics of unperturbed tumors growth is dominated by nucleation processes, transition between avascular and vascular phases, activation energy much lower than the body thermal energy, vacancies that provide instability to the cancer, fractal dimension of the contour less than 1 and existence of electrical current density at the tumor interface with the surrounding healthy tissue related to the bioelectricity and electronegativity of the tumor. Furthermore, the space-time distributions of electric potential, electric field intensity, temperature, pH fronts, tissue damage and electropermeabilization generated by multiple geometries of individual electrodes and electrode pairs adopt the geometry of the electrode array, and depend on the polarity mode of the electrodes and electrical-thermal properties of both tissues. The antitumor mechanism that prevails in tumor ablation is the electrochemical.
Conclusions: Physical-chemical-mathematical models allow revealing new mechano-electrical findings inherent in the growth kinetics of unperturbed tumors and proposing suitable electrode arrangements that maximize tumor destruction with minimal surrounding damage.
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Copyright (c) 2025 Luis Enrique Bergues Cabrales
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