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Cell membrane thermal gradients induced by electromagnetic fields
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10.1063/1.4809642
/content/aip/journal/jap/113/21/10.1063/1.4809642
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/21/10.1063/1.4809642

Figures

Image of FIG. 1.
FIG. 1.

Simplified schematic of a spherical biological cell with a concentric spherical nucleus (e.g., Refs. ). The cell consists of five regions characterized by thermal conductivity (), electric conductivity (), and permittivity (): the nucleoplasm (np), nuclear envelope (ne), cytoplasm (cp), and cell membrane (m). The nuclear and cell radii are given by and , respectively, and thickness of the nuclear envelope and cell membrane are denoted by and , respectively.

Image of FIG. 2.
FIG. 2.

Lumped equivalent circuit for electric field application to biological cells, where , , , and are the resistances of the plasma membrane, cytoplasm, extracellular fluid, and load, respectively, is the plasma membrane capacitance, and is the applied voltage. Because is much less than the other resistances, it is neglected in analyses.

Image of FIG. 3.
FIG. 3.

Analytic calculation of the spatial evolution of the temperature across the cell for 10 ns (solid) and 10 s (dashed) pulses after (a) 18 ns, (b) 18 s, and (c) 85 s. The characteristic heat conduction frequency for each pulse condition is τ  = 3 × 10 s.

Image of FIG. 4.
FIG. 4.

Analytic calculation of the spatial evolution of the temperature gradient (∇) across the cell membrane ( = 1 represents the intersection of the membrane with the extracellular fluid) calculated for 10 ns (solid) and 10 s (dashed) pulses after (a) 18 ns, (b) 18 s, and (c) 85 s. The characteristic heat conduction frequency for each pulse condition is τ  = 3 × 10 s.

Image of FIG. 5.
FIG. 5.

(a) Time and (b) spatial dependence of a Gaussian heat source (with  = 0 the center of the cell) used for determining cell and membrane temperature gradients.

Image of FIG. 6.
FIG. 6.

Temperature across the cell and extracellular fluid normalized to the maximum temperature increase due to a single pulse of duration / = 0.01 at different (dimensionless) times using a 3D model of the cell. Arc length represents location with the center of the cell at zero and the inner edge of the membrane at one.

Image of FIG. 7.
FIG. 7.

Temperature gradient in the system normalized to the maximum ratio of the maximum temperature increase to cell radius for exposure to pulses of duration /  = 0.01 at different (dimensionless) times using a 3D model of the cell. Arc length represents location with the center of the cell at zero and the inner edge of the membrane at one.

Image of FIG. 8.
FIG. 8.

Temperature gradient normalized to the ratio of membrane temperature change due to a single pulse and the cell radius (Δ /) as a function of pulse duration normalized to thermal diffusion time. The analytic gradient law agrees well with 1D and 3D numerical calculations at longer pulses and permit estimation when numerical approaches diverge at shorter pulse duration due to meshing constraints.

Image of FIG. 9.
FIG. 9.

1D simulation (symbols) and analytic calculations (lines) of the maximum and minimum temperature gradient normalized to the ratio of membrane temperature change due to a single pulse and the cell radius (Δ /) as a function of time normalized to thermal diffusion time, , for pulse trains with duration  = 10 and pulse repetition times, , of 2.5 × 10 and 2.5 × 10 , where  = 7 × 10 s is the thermal diffusion time.

Tables

Generic image for table
Table I.

The parameters of the model cell under investigation. The physical quantities relate to the temperature of 320 K.

Generic image for table
Table II.

Maximum temperature difference, temperature gradient, and induced electric field across the cell membrane due to pulsed electric field application onto biological cells. Note that we apply Eq. (3) in the text to the multiple pulse conditions because the time between pulses far exceeds the thermal diffusion time.

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/content/aip/journal/jap/113/21/10.1063/1.4809642
2013-06-06
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Cell membrane thermal gradients induced by electromagnetic fields
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/21/10.1063/1.4809642
10.1063/1.4809642
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