Short microsecond pulses achieve homogeneous electroporation of elongated biological cells irrespective of their orientation in electric field

Abstract

In gene electrotransfer and cardiac ablation with irreversible electroporation, treated muscle cells are typically of elongated shape and their orientation may vary. Orientation of cells in electric field has been reported to affect electroporation, and hence electrodes placement and pulse parameters choice in treatments for achieving homogeneous effect in tissue is important. We investigated how cell orientation influences electroporation with respect to different pulse durations (ns to ms range), both experimentally and numerically. Experimentally detected electroporation (evaluated separately for cells parallel and perpendicular to electric field) via Ca²⁺ uptake in H9c2 and AC16 cardiomyocytes was numerically modeled using the asymptotic pore equation. Results showed that cell orientation affects electroporation extent: using short, nanosecond pulses, cells perpendicular to electric field are significantly more electroporated than parallel (up to 100-times more pores formed), and with long, millisecond pulses, cells parallel to electric field are more electroporated than perpendicular (up to 1000-times more pores formed). In the range of a few microseconds, cells of both orientations were electroporated to the same extent. Using pulses of a few microseconds lends itself as a new possible strategy in achieving homogeneous electroporation in tissue with elongated cells of different orientation (e.g. electroporation-based cardiac ablation).

Figure 1

Electroporation of H9c2 cells as monitored by Ca²⁺ uptake with fluorescent calcium indicator Fura-2 (ratio images). Cells were pulsed with single pulses of (A) 100 ns, 40 kV/cm, (B) 10 µs, 1000 V/cm, (C) 1 ms, 200 V/cm. Cells at 8 s after pulse application are encircled, brighter cells express higher levels of Ca²⁺ uptake. Scalebar: 100 µm. Arrow: the direction of the electric field.

Figure 2

Experimental results of electroporation of parallel and perpendicular cardiomyocytes H9c2 and AC16, using pulses of different durations (100 ns to 10 ms) at different electric field strength. (A) Parallel and perpendicular cells are elongated (a > 2b), and their longer axes (a) are oriented parallel or perpendicular to the electric field E, with 20° tolerance in angle. (B), (C) Experimental electroporation of cells of different orientations was monitored by calcium uptake with a fluorescent calcium indicator Fura-2, 8 s after the pulse application. Results are expressed as a median difference in Fura-2 340/380 ratio between parallel and perpendicular cells (lines), and individual measurements are shown for each electric field strength (crosses). When parallel cells are more affected than perpendicular, then the difference is a positive value. When perpendicular cells are more affected, then the results are below zero. B) Experimental results of H9c2 cells were obtained from 5–30 cells per experiment, an average of three independent experiments, except for 1 ms (repeated 4×), 10 ms (repeated 5×), 100 ns, 40 and 46.6 kV/cm (repeated 5×), 100 ns, 20 kV/cm (repeated 6×), and 100 ns, 26.6 kV/cm (repeated 9×). C) Experimental results of AC16 cells were obtained from 4–23 cells per experiment, an average of three independent experiments, except for 100 ns, 40 kV/cm (repeated 5×), 100 ns, 46.6 kV/cm (repeated 6×), 100 ns, 20 kV/cm (repeated 7×) and 100 ns, 26.6 kV/cm (repeated 7×). * - statistically significant differences from control (p < 0.05), the Kruskal-Wallis One Way Analysis of Variance on Ranks, followed by Multiple Comparisons versus Control Group (the Dunn’s Method). Results of statistical analyses are shown in the Appendix, Tables A1a and A1b.

Figure 3

Numerically determined number of pores formed on the cell membrane as a function of pulse duration when pulses of equivalent parameters are applied to two different cell geometries. (A) Short axis was one-quarter of the length of the long axis, and equivalent parameters were obtained with the hyperbolic equation (crossover at 6 µs), or (B) the Saulis pore equation (crossover at 3 µs). (C) Short axis was one half of the length of the long axis, and equivalent parameters were obtained with the hyperbolic equation (no crossover observed) or (D) the hyperbolic equation, scaled for a factor of 0.5 to take into account larger cell geometry (crossover at 4 µs).

Figure 4

A numerically determined ratio of the number of pores when cells orientation is parallel vs perpendicular. Different examples are shown: when a cell is of different geometry (ratio 1:2 and 1:4) and/or when equivalent pulse parameters are calculated as the hyperbolic equation, scaled hyperbolic equation or with the Saulis pore equation. We can see that in all cases with nanosecond pulses the perpendicular direction was more efficient in pore formation and the crossover was obtained in the range of 3 to 6 microseconds, depending on the cell geometry and applied an electric field. The black dashed line shows the ratio of 1 where perpendicular and parallel orientation are equivalent.

Figure 5

Number of pores formed as a function of the applied electric field when a single 100 µs long pulse is applied. The effect of different ratios of geometry is shown for the geometry ratios 2 (in red), 4 (in black) and 7 (in blue). For all, parallel orientation is in solid line and perpendicular in dashed. For all ratios and parallel orientation, the pores start forming at approximately the same electric field, while for perpendicular orientation, a higher electric field is needed for more elongated cells (ratio 7) than for less elongated cells (ratio 2) to achieve a similar level of electroporation.

Figure 6

Electrodes and waveforms of pulses used in the study. Electrodes for (A) 100 ns pulse application, and (B) for 1 µs – 10 ms pulse application. Waveforms of pulses used in the study: (C) 100 ns, 400 V (numerically calculated electric field of 26.6 kV/cm), (D) 1 µs, 1000 V (voltage-to-distance ratio 2500 V/cm), (E) 10 µs, 600 V (voltage-to-distance ratio 1500 V/cm), (F) 100 µs, 200 V (voltage-to-distance ratio 500 V/cm), (G) 1 ms, 80 V (voltage-to-distance ratio 200 V/cm), (H) 10 ms, 50 V (voltage-to-distance ratio 125 V/cm).

Figure 7

Geometry of the modeled spheroids. In the model, we modeled different spheroid geometries. (A) The modeled geometry of the cell with ratio 2× and (B) with the ratio 4×. (C) In experiments, cells were attached to the bottom of the dish and shaped like half of an elongated spheroid. However, due to the numerical symmetry of the problem, we modeled the cells as full spheroids.

Figure 8

Strength-duration curves which were used to scale the electric field to obtain equivalent pulse parameters. Black dotted line was obtained by optimizing the Saulis pore equation, the solid blue line is the hyperbolic equation, and the orange dash-dot line is the hyperbolic equation decreased for a factor of 0.5. Factor 0.5 was chosen to compensate for a smaller cell in calculations with ratio 4×.