Labarbera Nicholas, Drapaca Corina
Department of Engineering Science & Mechanics, The Pennsylvania State University, 212 Earth-Engineering Sciences Bldg., University Park, 16802, PA, USA.
Center for Neural Engineering, The Pennsylvania State University, 409C Earth-Engineering Science Building, University Park, 16802, PA, USA.
Theor Biol Med Model. 2017 Nov 1;14(1):20. doi: 10.1186/s12976-017-0065-6.
One recent area of cancer research is irreversible electroporation (IRE). Irreversible electroporation is a minimally invasive procedure where needle electrodes are inserted into the body to ablate tumor cells with electricity. The aim of this paper is to propose a mathematical model that incorporates a tissue's conductivity increasing more in the direction of the electrical field as this has been shown to occur in experiments.
It was necessary to mathematically derive a valid form of the conductivity tensor such that it is dependent on the electrical field direction and can be easily implemented into numerical software. The derivation of a conductivity tensor that can take arbitrary functions for the conductivity in the directions tangent and normal to the electrical field is the main contribution of this paper. Numerical simulations were performed for isotropic-varying and anisotropic-varying conductivities to evaluate the importance of including the electrical field's direction in the formulation for conductivity.
By starting from previously published experimental results, this paper derived a general formulation for an anistropic-varying tensor for implementation into irreversible electroporation modeling software. The anistropic-varying tensor formulation allows the conductivity to take into consideration both electrical field direction and magnitude, as opposed to previous published works that only took into account electrical field magnitude. The anisotropic formulation predicts roughly a five percent decrease in ablation size for the monopolar simulation and approximately a ten percent decrease in ablation size for the bipolar simulations. This is a positive result as previously reported results found the isotropic formulation to overpredict ablation size for both monopolar and bipolar simulations. Furthermore, it was also reported that the isotropic formulation overpredicts the ablation size more for the bipolar case than the monopolar case. Thus, our results are following the experimental trend by having a larger percentage change in volume for the bipolar case than the monopolar case.
The predicted volume of ablated cells decreased, and could be a possible explanation for the slight over-prediction seen by isotropic-varying formulations.
癌症研究的一个最新领域是不可逆电穿孔（IRE）。不可逆电穿孔是一种微创手术，通过将针状电极插入体内，利用电流消融肿瘤细胞。本文的目的是提出一个数学模型，该模型考虑到组织的电导率在电场方向上增加得更多，因为实验已证明会出现这种情况。
有必要从数学上推导出电导率张量的有效形式，使其依赖于电场方向，并能轻松地应用于数值软件。本文的主要贡献在于推导出一个电导率张量，该张量在与电场相切和垂直的方向上可以采用任意的电导率函数。对各向同性变化和各向异性变化的电导率进行了数值模拟，以评估在电导率公式中纳入电场方向的重要性。
本文从先前发表的实验结果出发，推导出了一个用于不可逆电穿孔建模软件的各向异性变化张量的通用公式。与之前只考虑电场大小的已发表作品不同，各向异性变化张量公式允许电导率同时考虑电场方向和大小。对于单极模拟，各向异性公式预测消融尺寸大约减小5%，对于双极模拟，消融尺寸大约减小10%。这是一个积极的结果，因为先前报道的结果发现，对于单极和双极模拟，各向同性公式都会高估消融尺寸。此外，还报道了各向同性公式在双极情况下比单极情况下更高估消融尺寸。因此，我们的结果遵循了实验趋势，双极情况下的体积变化百分比比单极情况下更大。
预测的消融细胞体积减小，这可能是各向同性变化公式出现轻微高估的一个可能解释。
