Ion transport in tumors under electrochemical treatment: in vivo, in vitro and in silico modeling.

The electrochemical treatment of cancer (EChT) consists in the passage of a direct electric current through two or more electrodes inserted locally in the tumor tissue. The extreme pH changes induced have been proposed as the main tumor destruction mechanism. Here, we study ion transport during EChT through a combined modeling methodology: in vivo modeling with BALB/c mice bearing a subcutaneous tumor, in vitro modeling with agar and collagen gels, and in silico modeling using the one-dimensional Nernst-Planck and Poisson equations for ion transport in a four-ion electrolyte. This combined modeling approach reveals that, under EChT modeling, an initial condition with almost neutral pH evolves between electrodes into extreme cathodic alkaline and anodic acidic fronts moving towards each other, leaving the possible existence of a biological pH region between them; towards the periphery, the pH decays to its neutral values. pH front tracking unveils a time scaling close to t(1/2), signature of a diffusion-controlled process. These results could have significant implications in EChT optimal operative conditions and dose planning, in particular, in the way in which the evolving EChT pH region covers the active cancer cells spherical casket.

Three-dimensional nature of ion transport in thin-layer electrodeposition.

A generalized three-dimensional model for ion transport in electrodeposition is introduced. Ion transport is mainly governed by diffusion, migration, and convection. When convection prevails, in particular, in the limiting case of gravity-driven convection, the model predicts concentration shells and convection rolls and their interaction mode with a deposit tip: shell and roll bend and surround the tip forming a three-dimensional envelope tube squeezed at the deposit tip. In the limiting case of electrically driven convection, a vortex ring and an electric spherical drop crowning the deposit tip are predicted. When gravity and electric convection are both relevant, the interaction of ramified deposits, vortex tubes and rings, and electric spherical drops, leading to complex helicoidal flow, is predicted. Many of these predictions are experimentally observed, suggesting that ion transport underlying dendrite growth is remarkably well captured by our model.