Sel Davorka, Mazeres Serge, Teissie Justin, Miklavcic Damijan
University of Ljubljana, Faculty of Electrical Engineering, SI-1000 Ljubljana, Slovenia.
IEEE Trans Biomed Eng. 2003 Nov;50(11):1221-32. doi: 10.1109/TBME.2003.818466.
Information about electric field distribution in tissue is very important for effective electropermeabilization. In heterogeneous tissues with complex geometry, finite-element (FE) models provide one of alternative sources of such information. In the present study, modeling of needle electrode geometry in the FE model was investigated in order to determine the most appropriate geometry by considering the need for frequent FE model computation present in electroporation models. The 8-faceted needle electrode geometry proposed--determined on a model with a single needle electrode pair by means of criteria function--consisted of the weighted sum of relative difference between measured and computed total current, the relative difference in CPU time spent on solving model, and the relative difference in cross section surface of electrodes. Such electrode geometry was further evaluated on physical models with needle arrays by comparison of computed total current and measured current. The agreement between modeled and measured current was good (within 9% of measurement), except in cases with very thin gel. For voltage above 50 V, a linear relationship between current and voltage was observed in measurements. But at lower voltages, a nonlinear behavior was detected resulting from side (electrochemical) effects at electrode-gel interface. This effect was incorporated in the model by introducing a 50-V shift which reduced the difference between the model and the measurement to less than 3%. As long as material properties and geometry are well described by FE model, current-based validation can be used for a rough model validation. That is a routine assay compared with imaging of electric field, which is otherwise employed for model validation. Additionally, current estimated by model, can be preset as maximum in electroporator in order to protect tissue against damage.
组织中电场分布的信息对于有效的电通透化非常重要。在具有复杂几何形状的异质组织中，有限元（FE）模型提供了此类信息的一种替代来源。在本研究中，对有限元模型中针电极几何形状的建模进行了研究，以便通过考虑电穿孔模型中频繁进行有限元模型计算的需求来确定最合适的几何形状。所提出的八面针电极几何形状——通过准则函数在具有单个针电极对的模型上确定——由测量和计算的总电流之间的相对差异、求解模型所花费的CPU时间的相对差异以及电极横截面表面的相对差异的加权和组成。通过比较计算的总电流和测量电流，在具有针阵列的物理模型上进一步评估了这种电极几何形状。除了在非常薄的凝胶情况下，建模电流与测量电流之间的一致性良好（在测量值的9%以内）。对于高于50 V的电压，在测量中观察到电流与电压之间的线性关系。但在较低电压下，检测到由于电极 - 凝胶界面的侧向（电化学）效应导致的非线性行为。通过引入50 V的偏移将这种效应纳入模型，这将模型与测量之间的差异减小到小于3%。只要有限元模型能够很好地描述材料特性和几何形状，基于电流的验证就可用于粗略的模型验证。这是一种与用于模型验证的电场成像相比的常规检测方法。此外，模型估计的电流可以在电穿孔仪中预设为最大值，以保护组织免受损伤。
