Development of a Multi-Pulse Conductivity Model for Liver Tissue Treated With Pulsed Electric Fields

Pulsed electric field treatment modalities typically utilize multiple pulses to permeabilize biological tissue. This electroporation process induces conductivity changes in the tissue, which are indicative of the extent of electroporation. In this study, we characterized the electroporation-induced conductivity changes using all treatment pulses instead of solely the first pulse as in conventional conductivity models. Rabbit liver tissue was employed to study the tissue conductivity changes caused by multiple, 100 μs pulses delivered through flat plate electrodes. Voltage and current data were recorded during treatment and used to calculate the tissue conductivity during the entire pulsing process. Temperature data were also recorded to quantify the contribution of Joule heating to the conductivity according to the tissue temperature coefficient. By fitting all these data to a modified Heaviside function, where the two turning points (E(0), E(1)) and the increase factor (A) are the main parameters, we calculated the conductivity as a function of the electric field (E), where the parameters of the Heaviside function (A and E(0)) were functions of pulse number (N). With the resulting multi-factor conductivity model, a numerical electroporation simulation can predict the electrical current for multiple pulses more accurately than existing conductivity models. Moreover, the saturating behavior caused by electroporation can be explained by the saturation trends of the increase factor A in this model. The conductivity change induced by electroporation has a significant increase at about the first 30 pulses, then tends to saturate at 0.465 S/m. The proposed conductivity model can simulate the electroporation process more accurately than the conventional conductivity model. The electric field distribution computed using this model is essential for treatment planning in biomedical applications utilizing multiple pulsed electric fields, and the method proposed here, relating the pulse number to the conductivity through the variables in the Heaviside function, may be adapted to investigate the effect of other parameters, like pulse frequency and pulse width, on electroporation.