Electric pulse shape impact on biological effects: A modeling study

Calculated plasma membrane voltage induced by applying electric pulses using capacitive coupling

“…Figure 4 shows the two-shell electrical model of the cell, which considers the cell as two concentric spheres with the plasma, or cell, membrane and nuclear envelope encompassing the cytoplasm and nucleoplasm, respectively. Each layer is defined by its permittivity, ε, and conductivity, σ [44,45]. Assuming perfectly spherical and evenly distributed cells in the buffer allows one to apply Maxwell's mixture formula to convert the effective permittivity of the suspension (or mixture), ε sus , to the effective permittivity of an individual cell, ε c , where each effective permittivity is complex and frequency-dependent and may in general be written as where i is the imaginary constant, ε * is the complex permittivity, ε o is the permittivity of free space, and ε′ and ε″ are the real and imaginary components of permittivity, respectively.…”

“…Assuming perfectly spherical and evenly distributed cells in the buffer allows one to apply Maxwell's mixture formula to convert the effective permittivity of the suspension (or mixture), ε sus , to the effective permittivity of an individual cell, ε c , where each effective permittivity is complex and frequency-dependent and may in general be written as where i is the imaginary constant, ε * is the complex permittivity, ε o is the permittivity of free space, and ε′ and ε″ are the real and imaginary components of permittivity, respectively. We follow the formulation presented by Feldman, et al to convert ε and σ of each individual cell component (the nucleoplasm, nuclear envelope, cytoplasm, and plasma membrane for a eukaryotic cell) to the complex permittivity of the cell c e ⁎ by including the inner radius of the cell (r cell ), the inner radius of the nucleus (r nuc ), the membrane thickness (t m ), and the thickness of the nuclear envelope (t ne ) using the two-shell model [44,45]. We then determine the complex permittivity of the cell suspension, ε sus , by using Maxwell's mixing equation [46] given by p p…”

“…where buf e ⁎ is the complex permittivity of the buffer and p is the volume fraction of the cells in the suspension. Table 1 summarizes the buffer permittivity and conductivity, cell volume fraction, and the physical and electrical properties of the two cancer and two normal cell types considered here [44,45].…”

“…As a sample calculation, we assess the impact of EPs with a peak voltage of 300 V on Jurkat cells, which are often used for EP analyses [5,10,12,45,50], using the capacitive coupling configuration shown in figure 1(b). Table 4 summarizes the pulse parameters used to assess the impact of rise-and dwell-times on cell membrane voltage behavior for a fixed fall-time of 5 ns with the pulse duration and rise-and fall-times chosen to be in a typical NSEP regime [49].…”

“…Figure 11(a) shows the membrane voltages for B-normal, T-normal, Daudi, and Jurkat cells following exposure to a capacitively coupled 100 V, 10 ns EP with 5 ns rise-and fall-times, demonstrating that the waveforms depend strongly on the dielectric and physical properties of the cells. These pulse parameters were chosen to resemble the 10 ns pulses used in various NSEP studies [5,10,45,50]. Figure 11(b) shows c e ¢ and c e calculated using the two-shell model over the relevant frequency range for calculating the plasma membrane voltage for these 10 ns pulses.…”