Hidden realities of electrical injuries.

ABSTRACT: The clinical spectrum of electrical injury ranges from the absence of any external physical signs to severe and life-threatening trauma. This article discusses the fundamental concepts and misunderstandings surrounding electrical injuries and the best practices for evaluation and treatment.

Emergence of a large pore subpopulation during electroporating pulses.

Electroporation increases ionic and molecular transport through cell membranes by creating transient aqueous pores. These pores cannot be directly observed experimentally, but cell system modeling with dynamic electroporation predicts pore populations that produce cellular responses consistent with experiments. We show a cell system model's response that illustrates the life cycle of a pore population in response to a widely used 1 kV/cm, 100 µs trapezoidal pulse. Rapid pore creation occurs early in the pulse, followed by the gradual emergence of a subpopulation of large pores reaching ~30 nm radius. After the pulse, pores rapidly contract to form a single thermally broadened distribution of small pores (~1 nm radius) that slowly decays. We also show the response of the same model to pulses of 100 ns to 1 ms duration, each with an applied field strength adjusted such that a total of 10,000±100 pores are created. As pulse duration is increased, the pore size distributions vary dramatically and a distinct subpopulation of large pores emerges for pulses of microsecond and longer duration. This subpopulation of transient large pores is relevant to understanding rapid transport of macromolecules into and out of cells during a pulse.

A brief overview of electroporation pulse strength-duration space: a region where additional intracellular effects are expected.

Electroporation (EP) of outer cell membranes is widely used in research, biotechnology and medicine. Now intracellular effects by organelle EP are of growing interest, mainly due to nanosecond pulsed electric fields (nsPEF). For perspective, here we provide an approximate overview of EP pulse strength-duration space. This overview locates approximately some known effects and applications in strength-duration space, and includes a region where additional intracellular EP effects are expected. A feature of intracellular EP is direct, electrical redistribution of endogenous biochemicals among cellular compartments. For example, intracellular EP may initiate a multistep process for apoptosis. In this hypothesis, initial EP pulses release calcium from the endoplasmic reticulum, followed by calcium redistribution within the cytoplasm. With further EP pulses calcium penetrates mitochondrial membranes and causes changes that trigger release of cytochrome c and other death molecules. Apoptosis may therefore occur even in the presence of apoptotic inhibitors, using pulses that are smaller, but longer, than nsPEF.

Intracellular electroporation site distributions: modeling examples for nsPEF and IRE pulse waveforms.

We illustrate expected electroporation (EP) responses to two classes of large electric field pulses by employing systems models, one of a cell in vitro and the other of multiple cells in vivo. The first pulse class involves "nsPEF" (nanosecond pulsed electric fields). The durations are less than a microsecond, but the magnitudes are extremely large, often 10 kV/cm or more, and all of the pores remain small. The second class involves "IRE" (irreversible electroporation). Durations are many microseconds to several milliseconds, but with magnitudes smaller than 10 kV/cm, and a wide range of pore sizes evolves. A key feature of both pulse classes is non-thermal cell killing by multiple pulses without delivering external drugs or genes. For small pulses the models respond passively (no pore creation) providing negative controls. For larger pulses transient aqueous pore populations evolve. These greatly increase local membrane conductance temporarily, causing rapid redistribution of fields near and within cells. This complex electrical behavior is generally not revealed by experiments reporting biological end points resulting from cumulative ionic and molecular transport through cell membranes. The underlying, heterogeneous pore population distributions are also not obtained from typical experiments. Further, traditional EP applications involving molecular delivery are usually assumed to create pores solely in the outer, plasma membrane (PM). In contrast, our examples support the occurrence of intracellular EP by both nsPEF and IRE, but with different intracellular spatial distributions of EP sites.

Mechanisms for the intracellular manipulation of organelles by conventional electroporation.

Conventional electroporation (EP) changes both the conductance and molecular permeability of the plasma membrane (PM) of cells and is a standard method for delivering both biologically active and probe molecules of a wide range of sizes into cells. However, the underlying mechanisms at the molecular and cellular levels remain controversial. Here we introduce a mathematical cell model that contains representative organelles (nucleus, endoplasmic reticulum, mitochondria) and includes a dynamic EP model, which describes formation, expansion, contraction, and destruction for the plasma and all organelle membranes. We show that conventional EP provides transient electrical pathways into the cell, sufficient to create significant intracellular fields. This emerging intracellular electrical field is a secondary effect due to EP and can cause transmembrane voltages at the organelles, which are large enough and long enough to gate organelle channels, and even sufficient, at some field strengths, for the poration of organelle membranes. This suggests an alternative to nanosecond pulsed electric fields for intracellular manipulations.

In silico estimates of cell electroporation by electrical incapacitation waveforms.

We use a system model of a cell and approximate magnitudes of electrical incapacitation (EI) device waveforms to estimate conditions that lead to responses with or without electroporation (EP) of cell membranes near electrodes. Single pulse waveforms of Taser X26 and Aegis MK63 devices were measured using a resistive load. For the present estimates the digitized waveforms were scaled in magnitude according to the inverse square radial distance from two tissue-penetrating electrodes, approximated as hemispheres. The corresponding tissue level electric fields were then used as inputs to the cell system model. A dynamic pore model for membrane electroporation (EP) was assigned to many different sites on the cell plasma membrane (PM). EI devices generate sufficiently large transmembrane voltage, U(m)(t), such that pores were created, evolving into a heterogeneous and time-dependent pore population. These approximate responses suggest that both waveforms can cause PM EP. Peripheral nerve damage by EP is a candidate side effect. More extensive EP is expected from the Taser X26 than the Aegis MK63, mainly due to the approximately eight-fold difference in the peak magnitudes. In silico examination of EI waveforms by multiscale modeling is warranted, and can involve whole body, tissue and cell level models that now exist and are rapidly being improved.

Towards solid tumor treatment by nanosecond pulsed electric fields.

Local and drug-free solid tumor ablation by large nanosecond pulsed electric fields leads to supra-electroporation of all cellular membranes and has been observed to trigger nonthermal cell death by apoptosis. To establish pore-based effects as the underlying mechanism to inducing _apoptosis, we use a multicellular system model (spatial scale 100 microm) that has irregularly shaped liver cells and a multiscale liver tissue model (spatial scale 200 mm). Pore histograms for the multicellular model demonstrate the presence of only nanometer-sized pores due to nanosecond electric field pulses. The number of pores in the plasma membrane is such that the average tissue conductance during nanosecond electric field pulses is even higher than for longer irreversible electroporation pulses. It is shown, however, that these nanometer-sized pores, although numerous, only significantly change the permeability of the cellular membranes to small ions, but not to larger molecules. Tumor ablation by nanosecond pulsed electric fields causes small to moderate temperature increases. Thus, the underlying mechanism(s) that trigger cell death by apoptosis must be non-thermal electrical interactions, presumably leading to different ionic and molecular transport than for much longer irreversible electroporation pulses.

Membrane electroporation: The absolute rate equation and nanosecond time scale pore creation.

The recent applications of nanosecond, megavolt-per-meter electric field pulses to biological systems show striking cellular and subcellular electric field induced effects and revive the interest in the biophysical mechanism of electroporation. We first show that the absolute rate theory, with experimentally based parameter input, is consistent with membrane pore creation on a nanosecond time scale. Secondly we use a Smoluchowski equation-based model to formulate a self-consistent theoretical approach. The analysis is carried out for a planar cell membrane patch exposed to a 10 ns trapezoidal pulse with 1.5 ns rise and fall times. Results demonstrate reversible supraelectroporation behavior in terms of transmembrane voltage, pore density, membrane conductance, fractional aqueous area, pore distribution, and average pore radius. We further motivate and justify the use of Krassowska's asymptotic electroporation model for analyzing nanosecond pulses, showing that pore creation dominates the electrical response and that pore expansion is a negligible effect on this time scale.

Electrical behavior and pore accumulation in a multicellular model for conventional and supra-electroporation.

Extremely large but very short (20 kV/cm, 300 ns) electric field pulses were reported recently to non-thermally destroy melanoma tumors. The stated mechanism for field penetration into cells is pulse characteristic times faster than charge redistribution (displacement currents). Here we use a multicellular model with irregularly shaped, closely spaced cells to show that instead overwhelming pore creation (supra-electroporation) is dominant, with field penetration due to pores (ionic conduction currents) during most of the pulse. Moreover, the model's maximum membrane potential (about 1.2 V) is consistent with recent experimental observations on isolated cells. We also use the model to show that conventional electroporation resulting from 100 microsecond, 1 kV/cm pulses yields a spatially heterogeneous electroporation distribution. In contrast, the melanoma-destroying pulses cause nearly homogeneous electroporation of cells and their nuclear membranes. Electropores can persist for times much longer than the pulses, and are likely to be an important mechanism contributing to cell death.

How low should you go: novel device for nail trephination.

BACKGROUND: The most commonly used treatment for subungual hematomas is nail trephination, a technique that is not standardized and that poorly controls for trephination depth. OBJECTIVE: The objective was to test the safety and tolerance of a new device for nail trephination that uses innovative "mesoscission" or microcutting technology to create holes of specific depths in the nail plate without penetrating the nail bed. MATERIALS AND METHODS: Fourteen adult subjects with healthy toenails had five holes drilled in a random single-blind fashion at different test settings into their right great toenail with this device and were assessed for pain and pressure tolerance as well as perioperative and postoperative complications. RESULTS: Nail trephination with this device in this small pilot study was controlled and well tolerated. LIMITATIONS: The study population was small (n = 14) and the follow-up evaluation relied on patient self-report, which is not always reliable. The follow-up period was only 1 week and did not allow for evaluation of permanent nail plate deformity. CONCLUSION: Mesoscission may be a controlled and practical alternative to traditional nail trephining methods.

Three dimensional transport lattice model for describing action potentials in axons stimulated by external electrodes.

Conditions that stimulate action potentials in one or more nerves is of widespread interest. Axon and nerve models are usually based on two dimensional pre-specified lumped equivalents that assume where currents will flow. In contrast, here we illustrate creation of three dimensional (3D) system models with a transport lattice of interconnected local models for external and internal electrolyte and axon membrane. The transport lattice solves Laplace's equation in the extracellular medium and is coupled to the Hodgkin-Huxley model at local membrane sites. These space-filling models incorporate the geometric scale, which allows explicit representation of confined axons and external electrodes. The present results demonstrate feasibility of the basic approach. These models are spatially coarse and approximate, but can be straightforwardly improved. The transport lattice system models are modular and multiscale (spatial scales ranging from the membrane thickness of 5 nm to the axon segment length of 2 cm).

Model of a confined spherical cell in uniform and heterogeneous applied electric fields.

Cells exposed to electric fields are often confined to a small volume within a solid tissue or within or near a device. Here we report on an approach to describing the frequency and time domain electrical responses of a spatially confined spherical cell by using a transport lattice system model. Two cases are considered: (1) a uniform applied field created by parallel plane electrodes, and (2) a heterogeneous applied field created by a planar electrode and a sharp microelectrode. Here fixed conductivities and dielectric permittivities of the extra- and intracellular media and of the membrane are used to create local transport models that are interconnected to create the system model. Consistent with traditional analytical solutions for spherical cells in an electrolyte of infinite extent, in the frequency domain the field amplification, G(m) (f) is large at low frequencies, f<1 MHz. G(m) (f) gradually decreases above 1 MHz and reaches a lower plateau at about 300 MHz, with the cell becoming almost "electrically invisible". In the time domain the application of a field pulse can result in altered localized transmembrane voltage changes due to a single microelectrode. The transport lattice approach provides modular, multiscale modeling capability that here ranges from cell membranes (5 nm scale) to the cell confinement volume ( approximately 40 microm scale).

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.

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion.

BACKGROUND: Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. METHODS: We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42 degrees C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. RESULTS: The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45 degrees C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. CONCLUSIONS: The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue.

Electroporation of a lipid bilayer as a chemical reaction.

When a cell's transmembrane potential is increased from a physiological one to more than 370 mV, the transmembrane current increases more than hundredfold within a millisecond. This is due to the formation of conductive pores in the membrane. We construct a model in which we conceive of pore formation as a voltage sensitive chemical reaction. The model predicts the logarithm of the pore formation rate to increase proportionally to the square of the voltage. We measure currents through frog muscle cell membranes under 8 ms pulses of up to 440 mV. The experimental data appear consistent with the model.

Transdermal microconduits by microscission for drug delivery and sample acquisition.

BACKGROUND: Painless, rapid, controlled, minimally invasive molecular transport across human skin for drug delivery and analyte acquisition is of widespread interest. Creation of microconduits through the stratum corneum and epidermis is achieved by stochastic scissioning events localized to typically 250 microm diameter areas of human skin in vivo. METHODS: Microscissioning is achieved by a limited flux of accelerated gas: 25 microm inert particles passing through the aperture in a mask held against the stratum corneum. The particles scize (cut) tissue, which is removed by the gas flow with the sensation of a gentle stream of air against the skin. The resulting microconduit is fully open and may be between 50 and 200 microm deep. RESULTS: In vivo adult human tests show that microconduits reduce the electrical impedance between two ECG electrodes from approximately 4,000 Omega to 500 Omega. Drug delivery has been demonstrated in vivo by applying lidocaine to a microconduit from a cotton swab. Sharp point probing demonstrated full anaesthesia around the site within three minutes. Topical application without the microconduit required approximately 1.5 hours. Approximately 180 microm deep microconduits in vivo yielded blood sample volumes of several microl, with a faint pricking sensation as blood enters tissue. Blood glucose measurements were taken with two commercial monitoring systems. Microconduits are invisible to the unaided eye, developing a slight erythematous macule that disappears over days. CONCLUSION: Microscissioned microconduits may provide a minimally invasive basis for delivery of any size molecule, and for extraction of interstitial fluid and blood samples. Such microconduits reduce through-skin electrical impedance, have controllable diameter and depth, are fully open and, after healing, no foreign bodies were visible using through-skin confocal microscopy. In subjects to date, microscissioning is painless and rapid.

Electroporation of a multicellular system: asymptotic model analysis.

Quantitative understanding of electroporation in a multicellular system has been limited. The transient aqueous pore theory describes electroporation as the stochastic formation of hydrophilic pores in the presence of an applied electric field. We have used an asymptotic model for local membrane electroporation in a transport lattice system model to predict effects of a electrical pulse on a didactic multicellular model. We show that pulses of amplitude 0.2 to 2 kV/cm and duration 100 micros can cause extensive electroporation resulting in significant redistribution of transmembrane voltages.

Resealing dynamics of a cell membrane after electroporation.

The membrane of a living cell consists of a bilayer of amphipolar lipid molecules as well as much larger proteins. Transmembrane potentials of up to 120 mV are physiologic and well tolerated, but when the potential is more than 300 mV, this lipid bilayer is unstable. Pores are then formed through which measurable flow of ions can occur. We follow currents through frog muscle cell membranes under 4-ms pulses of up to 440 mV. We present a theory that allows us to describe the relaxation of the current back to zero after the pulse in terms of membrane parameters. We obtain a line tension of 3.6 x 10(-6) N, which is similar to that found in artificial lipid bilayers.