Center for Bioengineering in the Service of Humanity and Society, School of Computer Science and Engineering, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel.
Biomed Eng Online. 2010 Feb 26;9:13. doi: 10.1186/1475-925X-9-13.
Irreversible electroporation (IRE) is a minimally invasive tissue ablation technique which utilizes electric pulses delivered by electrodes to a targeted area of tissue to produce high amplitude electric fields, thus inducing irreversible damage to the cell membrane lipid bilayer. An important application of this technique is for cancer tissue ablation. Mathematical modelling is considered important in IRE treatment planning. In the past, IRE mathematical modelling used a deterministic single value for the amplitude of the electric field required for causing cell death. However, tissue, particularly cancerous tissue, is comprised of a population of different cells of different sizes and orientations, which in conventional IRE are exposed to complex electric fields; therefore, using a deterministic single value is overly simplistic.
We introduce and describe a new methodology for evaluating IRE induced cell death in tissue. Our approach employs a statistical Peleg-Fermi model to correlate probability of cell death in heterogeneous tissue to the parameters of electroporation pulses such as the number of pulses, electric field amplitude and pulse length. For treatment planning, the Peleg-Fermi model is combined with a numerical solution of the multidimensional electric field equation cast in a dimensionless form. This is the first time in which this concept is used for evaluating IRE cell death in multidimensional situations.
We illustrate the methodology using data reported in literature for prostate cancer cell death by IRE. We show how to fit this data to a Fermi function in order to calculate the critical statistic parameters. To illustrate the use of the methodology, we simulated 2-D irreversible electroporation protocols and produced 2-D maps of the statistical distribution of cell death in the treated region. These plots were compared to plots produced using a deterministic model of cell death by IRE and the differences were noted.
In this work we introduce a new methodology for evaluation of tissue ablation by IRE using statistical models of cell death. We believe that the use of a statistical model rather than a deterministic model for IRE cell death will improve the accuracy of treatment planning for cancer treatment with IRE.
不可逆电穿孔（IRE）是一种微创组织消融技术，它利用电极向目标组织区域传递电脉冲，产生高幅度的电场，从而导致细胞膜脂质双层不可逆损伤。该技术的一个重要应用是用于癌症组织消融。数学建模被认为是 IRE 治疗计划中的重要环节。过去，IRE 数学建模使用一个确定性的单一数值来表示引起细胞死亡所需的电场幅度。然而，组织，特别是癌变组织，由不同大小和取向的不同细胞组成，在传统的 IRE 中，这些细胞会暴露在复杂的电场中；因此，使用确定性的单一数值过于简单化。
我们引入并描述了一种新的方法来评估组织中的 IRE 诱导细胞死亡。我们的方法采用统计的 Peleg-Fermi 模型，将异质组织中的细胞死亡概率与电穿孔脉冲的参数相关联，如脉冲数、电场幅度和脉冲长度。在治疗计划中，Peleg-Fermi 模型与多维电场方程的数值解相结合，该方程以无量纲形式表示。这是首次将该概念用于评估多维情况下的 IRE 细胞死亡。
我们使用文献中报道的前列腺癌细胞死亡的 IRE 数据来说明该方法。我们展示了如何将这些数据拟合到 Fermi 函数中，以计算临界统计参数。为了说明该方法的用途，我们模拟了 2-D IRE 不可逆电穿孔方案，并生成了处理区域中细胞死亡的统计分布的 2-D 图。将这些图与使用 IRE 细胞死亡的确定性模型生成的图进行了比较，并注意到了差异。
在这项工作中，我们引入了一种新的方法，用于使用细胞死亡的统计模型评估 IRE 引起的组织消融。我们相信，对于 IRE 细胞死亡，使用统计模型而不是确定性模型将提高癌症治疗中 IRE 治疗计划的准确性。
