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Electropermeabilization (EP) based protocols such as those applied in medicine, food processing or environmental management, are well established and widely used. The applied voltage, as well as tissue electric conductivity, are of utmost importance for assessing final electropermeabilized area and thus EP effectiveness. Experimental results from literature report that, under certain EP protocols, consecutive pulses increase tissue electric conductivity and even the permeabilization amount. Here we introduce a theoretical model that takes into account this effect in the application of an EP-based protocol, and its validation with experimental measurements. The theoretical model describes the electric field distribution by a nonlinear Laplace equation with a variable conductivity coefficient depending on the electric field, the temperature and the quantity of pulses, and the Penne's Bioheat equation for temperature variations. In the experiments, a vegetable tissue model (potato slice) is used for measuring electric currents and tissue electropermeabilized area in different EP protocols. Experimental measurements show that, during sequential pulses and keeping constant the applied voltage, the electric current density and the blackened (electropermeabilized) area increase. This behavior can only be attributed to a rise in the electric conductivity due to a higher number of pulses. Accordingly, we present a theoretical modeling of an EP protocol that predicts correctly the increment in the electric current density observed experimentally during the addition of pulses. The model also demonstrates that the electric current increase is due to a rise in the electric conductivity, in turn induced by temperature and pulse number, with no significant changes in the electric field distribution. The EP model introduced, based on a novel formulation of the electric conductivity, leads to a more realistic description of the EP phenomenon, hopefully providing more accurate predictions of treatment outcomes.

Treatments based on electroporation (EP) induce the formation of pores in cell membranes due to the application of pulsed electric fields. We present experimental evidence of the existence of pH fronts emerging from both electrodes during treatments based on tissue EP, for conditions found in many studies, and that these fronts are immediate and substantial. pH fronts are indirectly measured through the evanescence time (ET), defined as the time required for the tissue buffer to neutralize them. The ET was measured through a pH indicator imaged at a series of time intervals using a four-cluster hard fuzzy-c-means algorithm to segment pixels corresponding to the pH indicator at every frame. The ET was calculated as the time during which the number of pixels was 10% of those in the initial frame. While in EP-based treatments such as reversible (ECT) and irreversible electroporation (IRE) the ET is very short (though enough to cause minor injuries) due to electric pulse characteristics and biological buffers present in the tissue, in gene electrotransfer (GET), ET is much longer, enough to denaturate plasmids and produce cell damage. When any of the electric pulse parameters is doubled or tripled the ET grows and, remarkably, when any of the pulse parameters in GET is halved, the ET drops significantly. Reducing pH fronts has relevant implications for GET treatment efficiency, due to a substantial reduction of plasmid damage and cell loss.

We present experimental measurements and theoretical predictions of ion transport in agar gels during reversible electroporation (ECT) for conditions typical to many clinical studies found in the literature, revealing the presence of pH fronts emerging from both electrodes. These results suggest that pH fronts are immediate and substantial. Since they might give rise to tissue necrosis, an unwanted condition in clinical applications of ECT as well as in irreversible electroporation (IRE) and in electrogenetherapy (EGT), it is important to quantify their extent and evolution. Here, a tracking technique is used to follow the space-time evolution of these pH fronts. It is found that they scale in time as t(½), characteristic of a predominantly diffusive process. Comparing ECT pH fronts with those arising in electrotherapy (EChT), another treatment applying constant electric fields whose main goal is tissue necrosis, a striking result is observed: anodic acidification is larger in ECT than in EChT, suggesting that tissue necrosis could also be greater. Ways to minimize these adverse effects in ECT are suggested.