FIGURE 1.
(A) 50 × 50 HF pulses. From left to right: 50 bursts were applied with a repetition frequency of 1 Hz; one burst with 200 μs total pulse on time and consisted of 50 bipolar pulses; one bipolar pulse of amplitude U consisted of a 2 μs long positive pulse, and a 2 μs long negative pulse (both of voltage U) with a 2 μs long interpulse delay. (B) 8 × 100 μs or 8 × 5 ms monopolar pulse of amplitude U and pulse duration of 100 μs or 5 ms were applied with a repetition frequency of 1 Hz
FIGURE 2.
Schematic of the model that describes electroporation and molecular transport. (A) The equivalent circuit, which considers electroporation (membrane pore/defect formation) to be a two-step process, as depicted in (B). The blue capacitance and resistance represent the intact cell membrane. When the electric field is applied, the cell membrane becomes permeable first to small ions, indicating the first porous state (N) of the membrane represented by green resistance. Then the membrane becomes permeable to small molecules, indicating the second porous state (M) of the membrane represented by magenta resistance. Reproduced from Sweeney et al.56 with permission.
TABLE 1.
Model parameters
| Parameter | Symbol | Value | Reference |
|---|---|---|---|
| Electroporation threshold voltage | U0 | 258 mV | 56 |
| Membrane thickness | h | 5 nm | 56 |
| Cell radius | r | 7.5 μm | 56 |
| Membrane time constant | τRC | 1 µs | 56 |
| Membrane permittivity | ɛm | 12 × 8.85 × 10−12 F/m | 56 |
| Solute radius | ρs | 0.58 nm | 58 |
| Defect radius | ρd | 0.8 nm | 56 |
| Solute radius/Defect radius | λm = ρs/ρd | 0.7250 | 56 |
| Solute diffusivity | D | 1.670 × 10−9 m2/s | 58,59 |
| Parameter in N formation rate | α | 2 × 10−6 | 56 |
| N relaxation rate | β | 4 × 10−8 | 56 |
| Relative permeabilzed conductance | γ | 1 × 106 | 56 |
| Parameter in M formation rate | δ | 1 × 10−3 | 56 |
| M relaxation rate | η | 4 × 10−9 | 56 |
| Permeability coefficient | ξ | 8.45 × 10−4 | 56 |
| Electroporation medium conductivity | σ | 1.4 S/m | * |
FIGURE 3.
Cell survival (solid) and cell membrane permeability (dashed) as a function of the electric field when (A) 50 × 50 HF pulses; (B) 8 × 100 μs pulses; (C) 8 × 5 ms pulses are used. The chosen optimal electric fields are encircled. Each data point presents the mean ± standard deviation from 3–4 experiments. * = statistically significant differences from control (p < 0.05) performing one-way ANOVA if the normality test passed or otherwise ANOVA on ranks. The light blue, red, and green asterisks are related to survival experiments.
FIGURE 4.
Cytotoxicity of cisplatin (A) and cisplatin molecules per cell (B) at different concentrations of cisplatin at a fixed electric field: 1.4 kV/cm for 50 × 50 HF pulses, 1.2 kV/cm for 8 × 100 μs pulses and 0.6 kV/cm for 8 × 5 ms pulses. Each data point presents the mean ± standard deviation from 3–4 experiments. *= statistically significant differences from control (p < 0.05) performing twoway ANOVA test. The color of the asterisk corresponds to the line color for a specific type of tested pulse. Cell survival as a function of cisplatin molecules per cell in combination with electroporation (C) our experimental data and (D) experimental data replotted from Vižintin et al.52 with permission.
FIGURE 5.
Comparison between the number of cisplatin molecules obtained experimentally (asterisks) and using the model (solid line) for (A) 50 × 50 HF pulses, (B) 8 × 100 μs pulses, (C) 8 × 5 ms pulses, (D) 1 × 200 ns pulses, and (E) 25 × 400 ns pulses. We used three different extracellular concentrations of cisplatin: 0 μM, 10 μM, 30 μM, and 50 μM.