Numerical Determination of Transmembrane Voltage Induced on Irregularly Shaped Cells

Pucihar, Gorazd; Kotnik, Tadej; Valič, Blaž; Miklavčič, Damijan

doi:10.1007/s10439-005-9076-2

Cited by 180 publications

(132 citation statements)

References 45 publications

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“…An electric field perturbed by one cell could have a secondary effect on neighboring cells. Simulation work has demonstrated that if two cells are located close to each other, they interact and alter each other's patterns and amounts of polarization, through perturbation of the extracellular electrical field [32,33]. Experimental work has also provided supportive evidence for such conclusions.…”

Section: Electric Field Distribution Around a Single Cellmentioning

confidence: 88%

“…First, the cell is represented as a spherical shell, and this oversimplification may be biologically simple, considering that the membrane polarization induced by an applied field is dependent on the complex geometrical structure of the membrane [40]. Future work should consider multi-compartment modeling or finite element meshes [22,23,32] to model this geometrical complexity. Second, both the extracellular medium and cytoplasmic environment are not truly homogenous [41,42].…”

Section: Future Directionsmentioning

confidence: 99%

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Influence of Cellular Properties on the Electric Field Distribution Around a Single Cell

Ye¹,

Cotic²,

Fehlings³

et al. 2012

PIER B

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Abstract-Electric fields have been widely used for the treatment of neurological diseases, using techniques such as non-invasive brain stimulation. An electric current controls cell excitability by imposing voltage changes across the cell membrane. At the same time, the presence of the cell itself causes a re-distribution of the local electric field. Computation of the electric field distribution at a single cell microscopic level is essential in understanding the mechanism of electric stimulation. In addition, the impact of the cellular biophysical properties on the field distribution in the vicinity of the cell should also be addressed. In this paper, we have begun by first computing the field distribution around and within a spherical model cell. The electric fields in the three regions differed by several orders of magnitude. The field intensity in the extracellular space was of the same order as that of the externally applied field, while in the membrane, it was calculated to be several thousand times greater than the applied field. In contrast, the field intensity inside the cell was greatly attenuated to approximately 1/133th of the applied field. We then performed a

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Section: Electric Field Distribution Around a Single Cellmentioning

confidence: 88%

Section: Future Directionsmentioning

confidence: 99%

Influence of Cellular Properties on the Electric Field Distribution Around a Single Cell

Ye¹,

Cotic²,

Fehlings³

et al. 2012

PIER B

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show abstract

“…In particular, the calculation of the transmembranar potential (TMP), which is the difference of the electric potentials through the membrane is of great interest in the modelization of the influency of electromagnetic fields on living cells [19]. Actually, a sufficiently large amplitude of the TMP leads to an increase of the cell membrane permeability [21], [23]. This phenomenon, called electropermeabilization, holds great potential for application in many fields of medicine.…”

Section: 1mentioning

confidence: 99%

“…To avoid these numerical difficulties and to perform computations in realistic shapes of cell, Pucihar et al [21] propose to replace the membrane by a condition on the boundary of the cytoplasm, using electromagnetic and optic considerations but they do not give any error estimate to prove the accuracy of their method.…”

Section: 1mentioning

confidence: 99%

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Asymptotics for steady‐state voltage potentials in a bidimensional highly contrasted medium with thin layer

Poignard

2007

Math Methods in App Sciences

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To cite this version:Clair Poignard. Asymptotics for steady state voltage potentials in a bidimensional highly contrasted medium with thin layer. Mathematical Methods in the Applied Sciences, Wiley, 2008, 31 (4) CLAIR POIGNARDAbstract. We study the behavior of steady state voltage potentials in two kinds of bidimensional media composed of material of complex permittivity equal to 1 (respectively α) surrounded by a thin membrane of thickness h and of complex permittivity α (respectively 1). We provide in both cases a rigorous derivation of the asymptotic expansion of steady state voltage potentials at any order as h tends to zero, when Neumann boundary condition is imposed on the exterior boundary of the thin layer. Our complex parameter α is bounded but may be very small compared to 1, hence our results describe the asymptotics of steady state voltage potentials in all heterogeneous and highly heterogeneous media with thin layer. The asymptotic terms of the potential in the membrane are given explicitly in local coordinates in terms of the boundary data and of the curvature of the domain, while these of the inner potential are the solutions to the so-called dielectric formulation with appropriate boundary conditions. The error estimates are given explicitly in terms of h and α with appropriate Sobolev norm of the boundary data. We show that the two situations described above lead to completely different asymptotic behaviors of the potentials.

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Quantitative assessment of dielectric parameters for membrane lipid bi‐layers from RF permittivity measurements

Merla¹,

Liberti²,

Apollonio³

et al. 2009

Bioelectromagnetics

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In this article, we propose and validate theoretical and experimental methods to quantitatively assess the Debye dielectric model of membrane lipid bi-layers. This consists of two steps: permittivity measurements of biological solutions (liposomes), and estimation of the model parameters by inverse application of the Effective Medium Theory. The measurements are conducted in the frequency domain between 100 MHz and 2 GHz using a modified coaxial connector, at the temperatures of 27 and 30 degrees C. Estimations have been performed using a three-layered model based on the Maxwell-Wagner formulation. Debye parameters (mean value +/- standard error) found from fitting experimental data are: epsilon(s) = 11.69 +/- 0.09, epsilon(infinity) = 4.00 +/- 0.07, f(relax) = 179.85 +/- 6.20 MHz and epsilon(s) = (1.1 +/- 0.1) x 10(-7) S/m. This model can be used in microdosimetric studies aiming to precisely determine the E-field distribution in a biological target down to the single cell level. In this context the use of an accurate membrane dielectric model, valid through a wide frequency range, is particularly appropriate.

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Numerical Determination of Transmembrane Voltage Induced on Irregularly Shaped Cells

Cited by 180 publications

References 45 publications

Influence of Cellular Properties on the Electric Field Distribution Around a Single Cell

Influence of Cellular Properties on the Electric Field Distribution Around a Single Cell

Asymptotics for steady‐state voltage potentials in a bidimensional highly contrasted medium with thin layer

Quantitative assessment of dielectric parameters for membrane lipid bi‐layers from RF permittivity measurements

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