Suárez Cecilia, Soba Alejandro, Maglietti Felipe, Olaiz Nahuel, Marshall Guillermo
Laboratorio de Sistemas Complejos, Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina.
Centro de Simulación Computacional - CONICET y Comisión Nacional de Energia Atómica, Buenos Aires, Argentina.
PLoS One. 2014 Dec 1;9(12):e113413. doi: 10.1371/journal.pone.0113413. eCollection 2014.
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.
基于电通透（EP）的方法，如应用于医学、食品加工或环境管理中的那些方法，已经成熟且被广泛使用。施加的电压以及组织电导率对于评估最终的电通透面积进而评估EP效果至关重要。文献中的实验结果表明，在某些EP方法下，连续脉冲会增加组织电导率甚至通透量。在此，我们引入一个理论模型，该模型在基于EP的方法应用中考虑了这种效应，并通过实验测量对其进行验证。该理论模型通过一个非线性拉普拉斯方程描述电场分布，该方程具有一个取决于电场、温度和脉冲数量的可变电导率系数，以及用于描述温度变化的彭内生物热方程。在实验中，使用蔬菜组织模型（土豆片）来测量不同EP方法下的电流和组织电通透面积。实验测量表明，在连续脉冲期间且施加电压保持恒定时，电流密度和变黑（电通透）面积会增加。这种行为只能归因于由于脉冲数量增加导致的电导率上升。因此，我们提出了一个EP方法的理论模型，该模型能够正确预测在添加脉冲期间实验观察到的电流密度增加。该模型还表明，电流增加是由于电导率上升，而电导率上升又是由温度和脉冲数量引起的，电场分布没有显著变化。所引入的基于电导率新公式的EP模型，对EP现象给出了更现实的描述，有望为治疗结果提供更准确的预测。
