Distributed equivalent-circuit models for circular dispersive electrodes

Perspectives on setting limits for RF contact currents: a commentary

BACKGROUND

Limits for exposure to radiofrequency (RF) contact currents are specified in the two dominant RF safety standards and guidelines developed by the Institute of Electrical and Electronics Engineers (IEEE) and the International Commission on Non-Ionizing Radiation Protection (ICNIRP). These limits are intended to prevent RF burns when contacting RF energized objects caused by high local tissue current densities. We explain what contact currents are and review some history of the relevant limits with an emphasis on so-called "touch" contacts, i.e., contact between a person and a contact current source during touch via a very small contact area.

RESULTS

Contact current limits were originally set on the basis of controlling the specific absorption rate resulting from the current flowing through regions of small conductive cross section within the body, such as the wrist or ankle. More recently, contact currents have been based on thresholds of perceived heating. In the latest standard from the IEEE developed for NATO, contact currents have been based on two research studies in which thresholds for perception of thermal warmth or thermal pain have been measured. Importantly, these studies maximized conductive contact between the subject and the contact current source. This factor was found to dominate the response to heating wherein high resistance contact, such as from dry skin, can result in local heating many times that from a highly conductive contact. Other factors such as electrode size and shape, frequency of the current and the physical force associated with contact are found to introduce uncertainty in threshold values when comparing data across multiple studies.

CONCLUSIONS

Relying on studies in which the contact current is minimized for a given threshold does not result in conservative protection limits. Future efforts to develop limits on contact currents should include consideration of (1) the basis for the limits (perception, pain, tissue damage); (2) understanding of the practical conditions of real world exposure for contact currents such as contact resistance, size and shape of the contact electrode and applied force at the point of contact; (3) consistency of how contact currents are applied in research studies across different researchers; (4) effects of frequency.

Electrodes for high-definition transcutaneous DC stimulation for applications in drug delivery and electrotherapy, including tDCS

Transcutaneous electrical stimulation is applied in a range of biomedical applications including transcranial direct current stimulation (tDCS). tDCS is a non-invasive procedure where a weak direct current (<2 mA) is applied across the scalp to modulate brain function. High-definition tDCS (HD-tDCS) is a technique used to increase the spatial focality of tDCS by passing current across the scalp using <12 mm diameter electrodes. The purpose of this study was to design and optimize "high-definition" electrode-gel parameters for electrode durability, skin safety and subjective pain. Anode and cathode electrode potential, temperature, pH and subjective sensation over time were assessed during application of 2 mA direct current, for up to 22 min on agar gel or subject forearms. A selection of five types of solid-conductors (Ag pellet, Ag/AgCl pellet, rubber pellet, Ag/AgCl ring and Ag/AgCl disc) and seven conductive gels (Signa, Spectra, Tensive, Redux, BioGel, Lectron and CCNY-4) were investigated. The Ag/AgCl ring in combination with CCNY-4 gel resulted in the most favorable outcomes. Under anode stimulations, electrode potential and temperature rises were generally observed in all electrode-gel combinations except for Ag/AgCl ring and disc electrodes. pH remained constant for all solid-conductors except for both Ag and rubber pellet electrodes with Signa and CCNY-4 gels. Sensation ratings were independent of stimulation polarity. Ag/AgCl ring electrodes were found to be the most comfortable followed by Ag, rubber and Ag/AgCl pellet electrodes across all gels.

Spatiotemporal interactions in retinal prosthesis subjects

PURPOSE

Vision loss due to retinitis pigmentosa affects an estimated 15 million people worldwide. Through collaboration between Second Sight Medical Products, Inc., and the Doheny Eye Institute, six blind human subjects underwent implantation with epiretinal 4 x 4 electrode arrays designed to directly stimulate the remaining cells of the retina, with the goal of restoring functional vision by applying spatiotemporal patterns of stimulation. To better understand spatiotemporal interactions between electrodes during synchronous and asynchronous stimulation, the authors investigated how percepts changed as a function of pulse timing across the electrodes.

METHODS

Pulse trains (20, 40, 80, and 160 Hz) were presented on groups of electrodes with 800, 1600, or 2400 microm center-to-center separation. Stimulation was either synchronous (pulses were presented simultaneously across electrodes) or asynchronous (pulses were phase shifted). Using a same-different discrimination task, the authors were able to evaluate how the perceptual quality of the stimuli changed as a function of phase shifts across multiple electrodes.

RESULTS

Even after controlling for electric field interactions, subjects could discriminate between spatiotemporal pulse train patterns based on differences of phase across electrodes as small as 3 ms. These findings suggest that the quality of the percept is affected not only by electric field interactions but also by spatiotemporal interactions at the neural level.

CONCLUSIONS

During multielectrode stimulation, interactions between electrodes have a significant influence on the quality of the percept. Understanding how these spatiotemporal interactions at the neural level influence percepts during multielectrode stimulation is fundamental to the successful design of a retinal prosthesis.

Brightness as a function of current amplitude in human retinal electrical stimulation

PURPOSE

With the goal of eventually restoring functional vision in patients with retinal degenerative diseases, USC/Second Sight Medical Products, Inc. chronically implanted blind human subjects with a prototype epiretinal prosthesis consisting of a 4 x 4 array of 16 stimulating electrodes. To accurately represent a visual scene, a visual prosthesis must convey luminance information across a range of brightness levels. To achieve this, the brightness of phosphenes produced by an individual electrode should scale appropriately with luminance, and the same luminance should produce equivalently bright phosphenes across the entire electrode array. The goal was to examine how apparent brightness changes as a function of stimulation intensity across electrodes.

METHODS

As described in previous studies, electrical stimulation of intact cells of the neural retina using this prosthetic device reliably elicits visual percepts in human subjects blinded by retinitis pigmentosa. Here, apparent brightness for a range of electrical amplitudes was measured using both subjective magnitude rating and brightness-matching procedures in chronically implanted human subjects.

RESULTS

It was found that apparent brightness can be described as a power function of stimulation intensity. The same model can also predict brightness matching across electrodes.

CONCLUSIONS

These results suggest that a relatively simple model for scaling current across electrodes may be capable of producing equivalently bright phosphenes across an entire array. (ClinicalTrials.gov number, NCT00279500.).

Factors affecting perceptual thresholds in epiretinal prostheses

PURPOSE

The goal was to evaluate how perceptual thresholds are related to electrode impedance, electrode size, the distance of electrodes from the retinal surface, and retinal thickness in six subjects blind as a result of retinitis pigmentosa, who received epiretinal prostheses implanted monocularly as part of a U.S. Food and Drug Administration (FDA)-approved clinical trial.

METHODS

The implant consisted of an extraocular unit containing electronics for wireless data, power recovery, and generation of stimulus current, and an intraocular unit containing 16 platinum stimulating electrodes (260- or 520-microm diameter) arranged in a 4 x 4 pattern. The electrode array was held onto the retina by a small tack. Stimulation was controlled by a computer-based external system that allowed independent control over each electrode. Perceptual thresholds (the current necessary to see a percept on 79% of trials) and impedance were measured for each electrode on a biweekly basis. The distance of electrodes from the retinal surface and retinal thickness were measured by optical coherence tomography on a less regular basis.

RESULTS

Stimulation thresholds for detecting phosphenes correlated with the distance of the electrodes from the retinal surface, but not with electrode size, electrode impedance, or retinal thickness.

CONCLUSIONS

Maintaining close proximity between the electrode array and the retinal surface is critical in developing a successful retinal implant. With the development of chronic electrode arrays that are stable and flush on the retinal surface, it is likely that the influence of other factors such as electrode size, retinal degeneration, and subject age will become more apparent. (ClinicalTrials.gov number, NCT00279500.).

Sequential activation of a segmented ground pad reduces skin heating during radiofrequency tumor ablation: optimization via computational models

Radiofrequency (RF) ablation has become an accepted treatment modality for unresectable tumors. The need for larger ablation zones has resulted in increased RF generator power. Skin burns due to ground pad heating are increasingly limiting further increases in generator power, and thus, ablation zone size. We investigated a method for reducing ground pad heating in which a commercial ground pad is segmented into multiple ground electrodes, with sequential activation of ground electrode subsets. We created finite-element method computer models of a commercial ground pad (14 x 23 cm) and compared normal operation of a standard pad to sequential activation of a segmented pad (two to five separate ground electrode segments). A constant current of 1 A was applied for 12 min in all simulations. Time periods during sequential activation simulations were adjusted to keep the leading edge temperatures at each ground electrode equal. The maximum temperature using standard activation of the commercial pad was 41.7 degrees C. For sequential activation of a segmented pad, the maximum temperature ranged from 39.3 degrees C (five segments) to 40.9 degrees C (two segments). Sequential activation of a segmented ground pad resulted in lower tissue temperatures. This method may reduce the incidence of ground pad burns and enable the use of higher power generators during RF tumor ablation.

The dependence of spectral impedance on disc microelectrode radius

As microelectrodes gain widespread use for electrochemical sensing, biopotential recording, and neural stimulation, it becomes important to understand the dependence of electrochemical impedance on microelectrode size. It has been shown mathematically that a disc electrode, coplanar in an insulating substrate and exposed to a conducting media, exhibits an inhomogeneous current distribution when a potential step is applied. This distribution is known as the primary distribution, and its derivation also yielded an analytic solution for electrical resistance of the conducting media (R(s)), between the disc surface and a distant ground, which is inversely proportional to disk radius [R(s) = 1/(4kappar), where kappa is media conductivity and r is disk radius]. The dependence of spectral impedance on microelectrode radius, however, has not been explored. We verify the analytical solution for resistance using high-frequency (100 kHz) electrochemical impedance data from microelectrodes of varying radius (11-325 microm). For all disc radii, as we approach a lower frequency (--> 10 Hz), we observe a transition from radial to area dependence (e.g., 1/r --> 1/r2). We hypothesize that this transition is driven by the fact that the derivation of the primary distribution ignores concentration gradients, but that these gradients cannot be ignored at lower frequencies.

Impedance-gradient electrode reduces skin irritation induced by transthoracic defibrillation

A new type of disposable external defibrillation electrode has been developed to reduce the skin irritation commonly associated with defibrillation and synchronised cardioversion. This design employs an impedance gradient to reduce the proportion of current delivered to the electrode periphery. The temperature distribution under the new electrode was compared with that of four other types of commercially available electrodes after repeated high-energy biphasic defibrillation discharges to domestic swine. Skin temperature distributions were acquired using non-invasive thermography. Measurements of the maximum temperature rise at each electrode site, taken 3.6s after the fifth defibrillation discharge, demonstrated that the new impedance-gradient electrode produced 50-60% less skin heating than two of the three uniform-impedance electrode designs. Histological examination of erythematous sites excised 24 h after defibrillation quantified the associated skin damage using a scoring protocol developed for this study. In contrast to previous studies, histological examinations demonstrated second-degree skin burns following defibrillation. The new electrode design, however, induced 44-46% less skin damage than two of the traditional uniform-impedance electrodes.

Estimation of current density distribution under electrodes for external defibrillation

BACKGROUND

Transthoracic defibrillation is the most common life-saving technique for the restoration of the heart rhythm of cardiac arrest victims. The procedure requires adequate application of large electrodes on the patient chest, to ensure low-resistance electrical contact. The current density distribution under the electrodes is non-uniform, leading to muscle contraction and pain, or risks of burning. The recent introduction of automatic external defibrillators and even wearable defibrillators, presents new demanding requirements for the structure of electrodes.

METHOD AND RESULTS

Using the pseudo-elliptic differential equation of Laplace type with appropriate boundary conditions and applying finite element method modeling, electrodes of various shapes and structure were studied. The non-uniformity of the current density distribution was shown to be moderately improved by adding a low resistivity layer between the metal and tissue and by a ring around the electrode perimeter. The inclusion of openings in long-term wearable electrodes additionally disturbs the current density profile. However, a number of small-size perforations may result in acceptable current density distribution.

CONCLUSION

The current density distribution non-uniformity of circular electrodes is about 30% less than that of square-shaped electrodes. The use of an interface layer of intermediate resistivity, comparable to that of the underlying tissues, and a high-resistivity perimeter ring, can further improve the distribution. The inclusion of skin aeration openings disturbs the current paths, but an appropriate selection of number and size provides a reasonable compromise.

Finite element analyses of uniform current density electrodes for radio-frequency cardiac ablation

The high current density at the edge of a metal electrode causes hot spots, which can lead to charring or blood coagulation formation during radio-frequency (RF) cardiac ablation. We used finite element analysis to predict the current density distribution created by several electrode designs for RF ablation. The numerical results demonstrated that there were hot spots at the edge of the conventional tip electrode and the insulating catheter. By modifying the shape of the edge of the 5-mm tip electrode, we could significantly reduce the high current density at the electrode-insulator interface. We also studied the current density distribution produced by a cylindrically shaped electrode. We modified the shape of a cylindrical electrode by recessing the edge and filled in a coating material so that the overall structure was still cylindrical. We analyzed the effects of depth of recess and the electrical conductivity of the added material. The results show that more uniform current density can be accomplished by recessing the electrode, adding a curvature to the electrode, and by coating the electrode with a resistive material.

A single-channel implantable microstimulator for functional neuromuscular stimulation

This paper describes a single-channel implantable microstimulator for functional neuromuscular stimulation. This device measures 2 x 2 x 10 mm3 and can be inserted into paralyzed muscle groups by expulsion from a hypodermic needle. Power and data to the device are supplied from outside by RF telemetry using an amplitude-modulated 2-MHz RF carrier generated using a high-efficiency class-E transmitter. The transmitted signal carries a 5-b address which selects one of the 32 possible microstimulators. The selected device then delivers up to 2 microC of charge store in a tantalum chip capacitor for up to 200 microseconds (10 mA) into loads of < 800 omega through a high-current thin-film iridium-oxide (IrOx) electrode (approximately 0.3 mm2 in area). A bi-CMOS receiver circuitry is used to: generate two regulated voltage supplies (4.5 and 9 V), recover a 2-MHz clock from the carrier, demodulate the address code, and activate the output current delivery circuitry upon the reception of an external command. The overall power dissipation of the receiver circuitry is 45-55 mW. The implant is hermetically packaged using a custom-made glass capsule.

Spatial potential and current distributions along transvenous defibrillation electrodes: variation of electrode characteristics

The therapeutic efficacy of an endocardial defibrillation lead system can be improved by controlling the profile of current delivery through a suitable choice of electrode characteristics, which include the length, radius, number of conductor elements, electrode resistance, and point of connection to the voltage source. Such control will minimize tissue and lead damage during long-term use. In this study, a semianalytical model was developed to study cylindrical electrodes of different constructions in an idealized electrolytic medium. Simulations were performed to investigate the effects of varying the electrode characteristics on the spatial voltage and current distributions and interelectrode resistance for cylindrical electrodes of different constructions. The results show that, for transvenous electrodes of realistic dimensions, the current distributions are determined largely by the edge effects. The edge effects increase as the aspect ratio of the electrode (length/radius) decrease. The multiple edges resulting from wrapping conductor elements over a nonconducting base are found to increase the nonuniformity and the current density over the conductor-covered surface. The model is used to demonstrate two techniques of controlling the current distribution. The first method involve modifying the electrode resistivity profile and point of connection. In the second approach, the electrode surface is covered with a thin film having a model-computed resistance profile. By using either methods to produce isocurrent electrodes, the interelectrode resistance is found to increase.

A quasi-power theorem for bulk conductors: comments on rheoencephalography

A special case of Tellegen's theorem, the quasi-power theorem, can be readily developed for bulk conductors, and a bulk conductor analog of Cohn's theorem follows which allows prediction of sensitivity of impedance plethysmographic measurements to tissue impedance changes in a system of bulk conductors. An example addressing the effects of scalp and cranium on the inference of regional blood flow in brain tissue begs additional questions about the origins of the rheoencephalogram.