However, even if the field distribution is the same, pulse parameters such as pulse number, pulse duration and the temporal mode of delivery of pulses affect the extent of electroporation. The resultant local electric field determines the extent of permeabilization-reversible and/or irreversible -or if thermal damage has occurred. For a given tissue type, electrode geometry and spacing, the applied voltage of these pulses generates an electric field distribution in tissue. These pulses are on the order of 100 µs in duration and generally delivered at a pulse repetition rate of 1 Hz through electrodes inserted directly into, or adjacent to, the target tissue.
#BIPOLAR SQUARE WAVE EQUATION SERIES#
Ĭonventional electroporation-based therapies (EBTs) involve the use of a series of high voltage, unipolar pulses: 8 for electrochemotherapy and 80 for IRE. IRE has shown great promise in the non-thermal ablation of tumors while obviating the need for adjuvant drugs. Alternatively, irreversible electroporation (IRE) is characterized by irreversible structural defects, chemical imbalances due to the influx and efflux of ions, and subsequent cell death. This effect is commonly used for introducing chemotherapeutic drugs into tumor cells during electrochemotherapy or for transfer of DNA molecules inside cells during electrogenetherapy. Electroporation is characterized as reversible when the pores reseal, the membrane recovers after treatment, and the cell survives. This increases cell permeability to molecules that before could not pass through the membrane and decreases membrane resistance. This paves way for modeling fields without prior characterization of non-linear tissue properties, and thereby simplifying electroporation procedures.Įlectroporation is a phenomenon in which transient nanoscale defects referred to as 'pores', form in the cell membrane in response to an externally applied electric field. The electric field distributions due to high-frequency, bipolar electroporation pulses can be closely approximated with the homogeneous analytical solution. The potato tissue lesions differed from the analytical solution by 39.7 ± 1.3 % ( x-axis) and 6.87 ± 6.26 % ( y-axis) for conventional unipolar pulses, and 15.46 ± 1.37 % ( x-axis) and 3.63 ± 5.9 % ( y-axis) for high- frequency bipolar pulses. Resultsįor high-frequency bipolar burst treatment, the thermal images closely mirrored the constant electric field contours. To analyze the dynamic impedance changes due to electroporation at different frequencies, electrical impedance measurements (1 Hz to 1 MHz) were made before and after the treatment of potato tissue. These values were compared to the analytical solution to quantify its ability to predict treatment outcomes. Second, potato ablations were performed and the lesion size was measured along the x- and y-axes. The analytical solution was overlaid on the thermal images for a qualitative assessment of the electric fields.
![bipolar square wave equation bipolar square wave equation](https://d3i71xaburhd42.cloudfront.net/ee4dcf8fd46d909d36533d45db242388b92dd38d/4-TableI-1.png)
First, pulses were applied to potato tuber tissue while an infrared camera was used to monitor the temperature distribution in real-time as a corollary to the electric field distribution.
![bipolar square wave equation bipolar square wave equation](https://media.springernature.com/lw785/springer-static/image/chp%3A10.1007%2F978-3-319-26779-1_5-1/MediaObjects/372556_0_En_5-1_Fig1_HTML.gif)
Two methods were used to examine the agreement between the analytical solution to Laplace's equation and the electric fields generated by 100 µs unipolar pulses and bursts of 1 µs bipolar pulses. Here, it is shown that the impedance changes during high-frequency, bipolar electroporation therapy are reduced, and the electric field distribution can be approximated using the analytical solution to Laplace's equation that is valid for a homogeneous medium of constant conductivity. These dynamic impedance changes, which depend on the tissue type and the applied electric field, need to be quantified a priori, making mathematical modeling complicated. In response to conventional, unipolar pulses, the electrical impedance of a tissue varies as a function of the local electric field, leading to a redistribution of the field. For electroporation-based therapies, accurate modeling of the electric field distribution within the target tissue is important for predicting the treatment volume.