Cylindrical cell membranes in uniform applied electric fields: validation of a transport lattice method

The frequency and time domain transmembrane voltage responses of a cylindrical cell in an external electric field are calculated using a transport lattice, which allows solution of a variety of biologically relevant transport problems with complex cell geometry and field interactions. Here we demonstrate the method for a cylindrical membrane geometry and compare results with known analytical solutions. Results of transport lattice simulations on a Cartesian lattice are found to have discrepancies with the analytical solutions due to the limited volume of the system model and approximations for the local membrane model on the Cartesian lattice. Better agreement is attained when using a triangular mesh to represent the geometry rather than a Cartesian lattice. The transport lattice method can be readily extended to more sophisticated cell, organelle, and tissue configurations. Local membrane models within a system lattice can also include nonlinear responses such as electroporation and ion-channel gating.     

Potential distribution for a spheroidal cell having a conductivemembrane in an electric field

When a cell is situated in a uniform electric field, the field is modified due to the relatively low conductance of the cell membrane compared to that of the surrounding fluids. In certain cases, such as in the estimation of internal and external electrokinetic forces, one requires a means of estimating the magnitude of the electric field inside and outside the cell. Most treatments consider the case when the membrane has zero conductivity, or the case of only a spherical cell. The authors solve Laplace's equation for the electric potential distribution inside and outside a cell having a prolate spheroidal shape and having a membrane with a finite, nonzero conductivity     

Biological cells with gap junctions in low-frequency electricfields

Biological effects have been observed from weak, low-frequency magnetic fields. It has been suggested that the observed effects are due to the induced currents and electric fields. The behavior of cells exposed to an electric field is investigated in this paper. The induced transmembrane potential (TMP) is examined in geometrically complex models of various cell configurations. The TMP is evaluated using the finite element method (FEM), a numerical technique that is well suited to complicated geometries. Because displacement currents can be neglected at very low frequencies, a FEM solver that considers only material conductivity is used. Therefore, our results apply only well below the relaxation frequency. Chains and clusters of gap-connected cells of various sizes are modeled. The conductivity and size of the gap junctions in the cell configurations are also varied. The results for small configurations are compared to models of ellipsoidal cells with shapes similar to those of the configurations. FEM estimates of TMPs in long, cylindrical cell chains are compared to the predictions of the leaky cable model. The FEM approach confirms that gap-junction-connected cells can be treated as a single similarly shaped cell. Gaps influence the potential in the interior of cell configurations, and these effects increase with gap size and conductivity. For configurations to which approximations such as the leaky cable model do not apply, the FEM approach can be used to estimate the TMP, if the model is adapted to fit within computational memory limits     

毫米波辐射下悬液细胞膜电压变化研究

根据有效介质理论,用Maxwell-Wagner等效公式计算细胞悬液中的平均场．然后基于时变场中单细胞膜电压第二计算模型,用场近似等效方法,建立了毫米场辐射下悬液中细胞膜电压计算模型．模型表明悬液细胞膜电压变化和毫米波的功率、频率、细胞半径、细胞排列及细胞的浓度有关。     

Magnetic resonance electrical impedance tomography for monitoring electric field distribution during tissue electroporation

Electroporation is a phenomenon caused by externally applied electric field of an adequate strength and duration to cells that results in the increase of cell membrane permeability to various molecules, which otherwise are deprived of transport mechanism. As accurate coverage of the tissue with a sufficiently large electric field presents one of the most important conditions for successful electroporation, applications based on electroporation would greatly benefit with a method of monitoring the electric field, especially if it could be done during the treatment. As the membrane electroporation is a consequence of an induced transmembrane potential which is directly proportional to the local electric field, we propose current density imaging (CDI) and magnetic resonance electrical impedance tomography (MREIT) techniques to measure the electric field distribution during electroporation. The experimental part of the study employs CDI with short high-voltage pulses, while the theoretical part of the study is based on numerical simulations of MREIT. A good agreement between experimental and numerical results was obtained, suggesting that CDI and MREIT can be used to determine the electric field during electric pulse delivery and that both of the methods can be of significant help in planning and monitoring of future electroporation based clinical applications.     

Analysis of Intense, Subnanosecond Electrical Pulse-Induced Transmembrane Voltage in Spheroidal Cells With Arbitrary Orientation

Self-consistent evaluations of the transmembrane potential (TMP) and possible membrane electroporation in spheroidal cells arising from an ultrashort, high-intensity pulse are reported. The present study couples the Laplace equation with Smoluchowski theory of pore formation, and uses double-shell models. It is shown that the response of prolate spheroids is faster than that of the sphere, with the outer membrane reaching its steady-state value in about ${2} {mu}$s. The simulation result also shows that the TMP across an inner organelle could exceed the value across the plasma membrane at least over the first $hbox{0.4}; {mu }$s or so, indicating a possibility of intracellular, electromanipulation of cells. The TMP induced by pulsed external voltages is predicted to be higher in oblate spheroids in comparison to both spherical and prolate spheroidal cells. This occurs due to flattening of the surface area.      

Numerical modeling of disordered mixture using pseudorandom simulations

The electrostatic effective permittivity of samples of three-dimensional random material consisting of equisized spheres is analyzed numerically. The electric field inside a cubical computation domain is calculated by using finite-element method and field calculation software Opera in a supercomputer. The spheres occupy random positions in the cubic computation cell. As the effective permittivity is analyzed numerically, the finite calculation domain makes the structure infinite and periodic. This kind of structure is called pseudorandom material. This study suggests that a relatively small computational domain (around five times the inclusion sphere radius) could be used when modeling random mixture, if the same samples are analyzed using three orthogonal field orientations. The effective permittivity as a function of the volume fraction of inclusions can be described with generalized mixing formula containing a parameter, which is fitted to numerical results.     

FDTD analysis of a gigahertz TEM cell for ultra-wideband pulse exposure studies of biological specimens

Gigahertz transverse electromagnetic (GTEM) transmission cells have been previously used to experimentally study exposure of biological cells to ultra-wideband (UWB), monopolar, electromagnetic pulses. Using finite-difference time-domain (FDTD) simulations we examine the time-dependent electric field waveforms and energy dose spatial distributions within a finite volume of biological cell culture medium during these experiments. The simulations show that when one or more flasks containing cell culture media are placed inside the GTEM cell, the uniform fields of the empty GTEM cell are significantly perturbed. The fields inside the cell culture medium, representing the fields to which the biological cells are exposed, are no longer monopolar and are spatially highly nonuniform. These effects result from a combination of refraction and distortion of the incident wave, combined with excitation of resonant eigenmodes within the cell culture medium volume. The simulations show that these distortions of the incident waveform may be mitigated by supporting the sample on a high permittivity pedestal and modifying the incident waveform to more closely approximate a Gaussian pulse. Under all simulated conditions, the estimated maximum temperature rises are completely negligible, ensuring that any experimentally observed unusual cell function or histopathology can be associated with nonthermal effects.     

Investigating membrane breakdown of neuronal cells exposed to nonuniform electric fields by finite-element modeling and experiments

High electric field strengths may induce high cell membrane potentials. At a certain breakdown level the membrane potential becomes constant due to the transition from an insulating state into a high conductivity and high permeability state. Pores are thought to be created through which molecules may be transported into and out of the cell interior. Membrane rupture may follow due to the expansion of pores or the creation of many small pores across a certain part of the membrane surface. In nonuniform electric fields, it is difficult to predict the electroporated membrane area. Therefore, in this study the induced membrane potential and the membrane area where this potential exceeds the breakdown level is investigated by finite-element modeling. Results from experiments in which the collapse of neuronal cells was detected were combined with the computed field strengths in order to investigate membrane breakdown and membrane rupture. It was found that in nonuniform fields membrane rupture is position dependent, especially at higher breakdown levels. This indicates that the size of the membrane site that is affected by electroporation determines rupture.     

A model study of electric field interactions between cardiacmyocytes

The transmission of excitation via electric field coupling was studied in a model comprising two myocytes abutted end-to-end and placed in an unbounded volume conductor. Each myocyte was modeled as a small cylinder of membrane (10 microns in diameter and 100 microns in length) capped at both ends. A Beeler-Reuter model modified for the Na+ current dynamics served to simulate the membrane ionic current. There was no resistive coupling between the myocytes and the intercellular junction consisted of closely apposed pre- and post-junctional membranes, separated by a uniform cleft distance. The membrane current crossing the prejunctional membrane during the action potential upstroke tends to flow out of the cleft, but it is partly prevented from doing so by the shunt resistance constituted by the cleft volume conductor. The prejunctional upstroke gives rise to a pulse of positive potential within the cleft which induces a small capacitive current across the post-junctional membrane to yield a small positive change in the intracellular potential in the post-junctional cell. The net result is an hyperpolarization of the post-junctional cleft membrane and a slight depolarization of the rest of the cell membrane since the extracellular potential outside of the cell is zero. The magnitude of this depolarization is quite small for a flat junctional membrane and it can be increased by membrane folding and interdigitation, so as to increase the junctional membrane area by a factor of 10 or more. Even then the post-junctional depolarization does not reach threshold when the extracellular potential around the post-junctional cell is effectively zero. Threshold depolarization occurs in the presence of a large decrease of post-junctional load, by increasing the junctional membrane capacitance and/or decreasing the volume of the post-junctional cell. Assuming that the normal resistive coupling between two cardiac myocytes is 1-4 M omega, our model study indicates that electric field coupling would then be about two orders of magnitude smaller. However, substantial enhancement of the efficacy of electric field transmission was observed in the case of cells with substantial junctional membrane folding.     

Effective conductivity of cell suspensions

Using finite-element method (FEM) effective conductivity of cell suspension was calculated for different cell volume fractions and membrane conductivities. Cells were modeled as spheres having equivalent conductivity and were organized in cubic lattices, layers and clusters. The results were compared to different analytical expressions for effective conductivity and they showed that Maxwell theory is valid also for higher volume fractions.     

Microdosimetry for nanosecond pulsed electric field applications: a parametric study for a single cell

A microdosimetric study of nanosecond pulsed electric fields, including dielectric dispersivity of cell compartments, is proposed in our paper. A quasi-static solution based on the Laplace equation was adapted to wideband signals and used to address the problem of electric field estimation at cellular level. The electric solution was coupled with an asymptotic electroporation model able to predict membrane pore density. An initial result of our paper is the relevance of the dielectric dispersivity, providing evidence that both the transmembrane potential and the pore density are strongly influenced by the choice of modeling used. We note the crucial role played by the dielectric properties of the membrane that can greatly impact on the poration of the cell. This can partly explain the selective action reported on cancerous cells in mixed populations, if one considers that tumor cells may present different dielectric responses. Moreover, these kinds of studies can be useful to determine the appropriate setting of nsPEF generators as well as for the design and optimization of new-generation devices.     

A fictitious domain method for conformal modeling of the perfectelectric conductors in the FDTD method

We present a fictitious domain method to avoid the staircase approximation in the study of perfect electric conductors (PEC) in the finite-difference time-domain (FDTD) method. The idea is to extend the electromagnetic field inside the PEC and to introduce a new unknown, the surface electric current density to ensure the vanishing of the tangential components of the electric field on the boundary of the PEC. This requires the use of two independent meshes: a regular three-dimensional (3-D) cubic lattice for the electromagnetic field and a triangular surface-patching for the surface electric current density. The intersection of these two meshes gives a simple coupling law between the electric field and the surface electric current density. An interesting property of this method is that it provides the surface electric current density at each time step. Furthermore, this method looks like FDTD with a special model for the PEC. Numerical results for several objects are presented     

Switching of Electrically Responsive,Light‐Sensitive Colloidal Suspensions of Anisotropic Pigment Particles

An unusual electro‐optical behavior of colloidal suspensions of dichroic, elongated (rod‐shaped) pigment particles is reported. These suspensions exhibit nematic liquid crystal order at low volume fraction of the suspended particles (<15 wt%) and show a strong electric and optical response to an external electric field. Additionally, the characteristics of the optical response can be reversibly manipulated by illuminating the sample with light in its absorption band. The suspensions show a number of interesting phenomena like homeotropic‐planar orientational transitions and light‐induced pattern formation.     

Evaluation of interactions of electric fields due to electrostatic discharge with human tissue

Electrostatic discharges (ESDs) produce in the human tissue very strong electric fields of short duration. Possible biophysical interactions are evaluated by comparing the fields in subcutaneous fat/skin to the thresholds for peripheral nerve stimulation, and by computations of membrane potential and electric fields in cytoplasm of a typical cell in bone marrow. It is found that a 4-A peak ESD event is capable of stimulation of nerves located in subcutaneous fat of the lower arm of the hand eliciting a spark, with tens of kV/m and pulse duration of approximately 80 ns. For the same ESD event, the transmembrane potential (TMP) reaches 32 mV with a pulse duration of approximately 200 ns (half-width duration). The electric field in the cytoplasm of a bone marrow cell changes from about 8.8 kV/m to--2 kV/m in about 200 ns.     

Backscatter RCS for TE and TM excitations of dielectric-filledcavity-backed apertures in two-dimensional bodies

Transverse electric (TE) and transverse magnetic (TM) scattering from dielectric-filled, cavity-backed apertures in two-dimensional bodies are treated using the method of moments technique to solve a set of combined-field integral equations for the equivalent induced electric and magnetic currents on the exterior of the scattering body and on the associated aperture. Results are presented for the backscatter radar cross section (RCS) versus the electrical size of the scatterer for two different dielectric-filled cavity-backed geometries. The first geometry is a circular cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the cylinder is dielectric filled and is also of circular cross section. The two cylinders (external and internal) are of different radii and their respective longitudinal axes are parallel but not collocated. The second is a square cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the square cylinder is dielectric-filled and is also of square cross section     

Electric fields in bone marrow substructures at power-line frequencies

Bone marrow is known to be responsible for leukemia. In order to study the hypothesis relating power-line frequencies electromagnetic fields and childhood leukemia from a subcellular perspective, two models of bone marrow substructures exposed to electric field are computed numerically. A set of cancellous bone data obtained from computed tomography scan is computed using both the finite element method (FEM) and scalar potential finite difference method. A maximum electric field enhancement of 50% is observed. Another model of bone marrow stroma cells is implemented only in FEM using thin film approximation. The transmembrane potential (TMP) change across the gap junctions is found to range from several to over 200 microV. The two results suggest that imperceptible contact currents can produce biologically significant TMP change at least in a limited number of bone marrow stroma cells.     

Theoretical and experimental analysis of electroporated membrane conductance in cell suspension

An intense electric field can be applied to increase the membrane conductance G(m) and consequently, the conductivity of cell suspension. This phenomenon is called electroporation. This mechanism is used in a wide range of medical applications, genetic engineering, and therapies. Conductivity measurements of cell suspensions were carried out during application of electric fields from 40 to 165 kV/m. Experimental results were analyzed with two electroporation models: the asymptotic electroporation model was used to estimate G(m) at the beginning and at the end of electric field pulse, and the extended Kinosita electroporation model to increase G(m) linearly in time. The maximum G(m) was 1-7 × 10(4) S/m(2), and the critical angle (when the G(m) is insignificant) was 50°-65°. In addition, the sensitivity of electroporated membrane conductance to extracellular and cytoplasmatic conductivity and cell radius has been studied. This study showed that external conductivity and cell radius are important parameters affecting the pore-opening phenomenon. However, if the cell radius is larger than 7 μm in low conductivity medium, the cell dimensions are not so important.     

Electro‐optical Materials: Switching of Electrically Responsive,Light‐Sensitive Colloidal Suspensions of Anisotropic Pigment Particles (Adv. Funct. Mater. 3/2011)

An unusual electro‐optical behavior of colloidal suspensions of dichroic, elongated (rod‐shaped) pigment particles is reported. These suspensions exhibit nematic liquid crystal order at low volume fraction of the suspended particles (<15 wt%) and show a strong electric and optical response to an external electric field. Additionally, the characteristics of the optical response can be reversibly manipulated by illuminating the sample with light in its absorption band. The suspensions show a number of interesting phenomena like homeotropic‐planar orientational transitions and light‐induced pattern formation.     

Modulation of conduction at points of axonal bifurcation by appliedelectric fields

This study investigated how weak electric fields, on the order of 100 mV/cm, modulate action potential conduction through points of axonal bifurcation in leech touch sensory neurons. Axonal branch points in neurons are ubiquitous structures, and they are sites of low safety-factor for action potential propagation. In this study calibrated electric fields were applied around excised ganglia from the leech central nervous system. The electric fields were generated by 500 ms constant current square waves applied to the bath containing the tissue. Microelectrode penetration of the neurons was used to: 1) record transmembrane potential changes in the cell body of the neuron that resulted from the external field; 2) monitor conduction block when action potentials, evoked in the periphery, propagated into the ganglion; 3) inject current directly into the cell in an experimental analysis of the mechanism by which the externally applied field produced block. Conduction block was reliably induced by electric fields too weak to reach threshold for firing action potentials. In an experimental analysis where block was produced by the direct intracellular injection of negative current, a reversed polarity field relieved it. This indicates that when the external field induces block, it does so by membrane hyperpolarization at the branch point.