Anistropically varying conductivity in irreversible electroporation simulations

Abstract

Background: 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. Method: 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. Results: 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. Conclusions: The predicted volume of ablated cells decreased, and could be a possible explanation for the slight over-prediction seen by isotropic-varying formulations.

Determination of lethal electric field threshold for pulsed field ablation in ex vivo perfused porcine and human hearts

“…The numerical model included an anisotropic representation of the tissue conductivity (67), and an electric field dependent increase in conductivity, using the built in COMSOL function for a smoothed Heaviside function with two continuous derivatives (68). Similarly, the anisotropy ratio in cardiac muscle has been previously described to be between 1.5 and 4 (69)(70)(71)(72).…”

Development and research of invasive and non-invasive electrodes for electrochemotherapy

“…Therefore, when a high enough voltage is applied, the dynamics of the tissue conductivity must be considered (Fig 1.8). The precise calculation of conductivity increase from initial σ0 to maximum σmax can be found using the smoothed Heaviside function, which is widely used in describing conductivity dynamics versus the applied electric field or the Gompertz curve (Labarbera and Drapaca, 2017). The process is apparent in the transition zone between RE (ERE) and IRE (EIRE) electric field thresholds for all mammalian tissues.…”