Towards a more accurate quasi-static approximation of the electric potential for neurostimulation with kilohertz-frequency sources. J Neural Eng 2023;20:10.1088/1741-2552/ad1612. [PMID: 38100821 PMCID: PMC10822676 DOI: 10.1088/1741-2552/ad1612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Objective.Our goal was to determine the conditions for which a more precise calculation of the electric potential than the quasi-static approximation may be needed in models of electrical neurostimulation, particularly for signals with kilohertz-frequency components.Approach.We conducted a comprehensive quantitative study of the differences in nerve fiber activation and conduction block when using the quasi-static and Helmholtz approximations for the electric potential in a model of electrical neurostimulation.Main results.We first show that the potentials generated by sources of unbalanced pulses exhibit different transients as compared to those of charge-balanced pulses, and this is disregarded by the quasi-static assumption. Secondly, relative errors for current-distance curves were below 3%, while for strength-duration curves these ranged between 1%-17%, but could be improved to less than 3% across the range of pulse duration by providing a corrected quasi-static conductivity. Third, we extended our analysis to trains of pulses and reported a 'congruence area' below 700 Hz, where the fidelity of fiber responses is maximal for supra-threshold stimulation. Further examination of waveforms and polarities revealed similar fidelities in the congruence area, but significant differences were observed beyond this area. However, the spike-train distance revealed differences in activation patterns when comparing the response generated by each model. Finally, in simulations of conduction-block, we found that block thresholds exhibited errors above 20% for repetition rates above 10 kHz. Yet, employing a corrected value of the conductivity improved the agreement between models, with errors no greater than 8%.Significance.Our results emphasize that the quasi-static approximation cannot be naively extended to electrical stimulation with high-frequency components, and notable differences can be observed in activation patterns. As well, we introduce a methodology to obtain more precise model responses using the quasi-static approach, retaining its simplicity, which can be a valuable resource in computational neuroengineering.

A partially averaged system to model neuron responses to interferential current stimulation

The interferential current (IFC) therapy is a noninvasive electrical neurostimulation technique intended to activate deep neurons using surface electrodes. In IFC, two independent kilohertz-frequency currents purportedly intersect where an interference field is generated. However, the effects of IFC on neurons within and outside the interference field are not completely understood, and it is unclear whether this technique can reliable activate deep target neurons without side effects. In recent years, realistic computational models of IFC have been introduced to quantify the effects of IFC on brain cells, but they are often complex and computationally costly. Here, we introduce a simplified model of IFC based on the FitzHugh-Nagumo (FHN) model of a neuron. By considering a modified averaging method, we obtain a non-autonomous approximated system, with explicit representation of relevant IFC parameters. For this approximated system we determine conditions under which it reliably approximates the complete FHN system under IFC stimulation, and we mathematically prove its ability to predict nonspiking states. In addition, we perform numerical simulations that show that the interference effect is observed only for a narrow set of IFC parameters and, in particular, for a beat frequency no higher than about 100 [Hz]. Our novel model tailored to the IFC technique contributes to the understanding of neurostimulation modalities using this type of signals, and can have implications in the design of noninvasive electrical stimulation therapies.

Multiscale entropy analysis of retinal signals reveals reduced complexity in a mouse model of Alzheimer's disease

Alzheimer's disease (AD) is one of the most significant health challenges of our time, affecting a growing number of the elderly population. In recent years, the retina has received increased attention as a candidate for AD biomarkers since it appears to manifest the pathological signatures of the disease. Therefore, its electrical activity may hint at AD-related physiological changes. However, it is unclear how AD affects retinal electrophysiology and what tools are more appropriate to detect these possible changes. In this study, we used entropy tools to estimate the complexity of the dynamics of healthy and diseased retinas at different ages. We recorded microelectroretinogram responses to visual stimuli of different nature from retinas of young and adult, wild-type and 5xFAD-an animal model of AD-mice. To estimate the complexity of signals, we used the multiscale entropy approach, which calculates the entropy at several time scales using a coarse graining procedure. We found that young retinas had more complex responses to different visual stimuli. Further, the responses of young, wild-type retinas to natural-like stimuli exhibited significantly higher complexity than young, 5xFAD retinas. Our findings support a theory of complexity-loss with aging and disease and can have significant implications for early AD diagnosis.

Creating a neuroprosthesis for active tactile exploration of textures

Intracortical microstimulation (ICMS) of the primary somatosensory cortex (S1) can produce percepts that mimic somatic sensation and, thus, has potential as an approach to sensorize prosthetic limbs. However, it is not known whether ICMS could recreate active texture exploration-the ability to infer information about object texture by using one's fingertips to scan a surface. Here, we show that ICMS of S1 can convey information about the spatial frequencies of invisible virtual gratings through a process of active tactile exploration. Two rhesus monkeys scanned pairs of visually identical screen objects with the fingertip of a hand avatar-controlled first via a joystick and later via a brain-machine interface-to find the object with denser virtual gratings. The gratings consisted of evenly spaced ridges that were signaled through individual ICMS pulses generated whenever the avatar's fingertip crossed a ridge. The monkeys learned to interpret these ICMS patterns, evoked by the interplay of their voluntary movements and the virtual textures of each object, to perform a sensory discrimination task. Discrimination accuracy followed Weber's law of just-noticeable differences (JND) across a range of grating densities; a finding that matches normal cutaneous sensation. Moreover, 1 monkey developed an active scanning strategy where avatar velocity was integrated with the ICMS pulses to interpret the texture information. We propose that this approach could equip upper-limb neuroprostheses with direct access to texture features acquired during active exploration of natural objects.

Nerve excitation using an amplitude-modulated signal with kilohertz-frequency carrier and non-zero offset

BACKGROUND

Incorporating kilohertz-frequency signals in transcutaneous electrical stimulation has been proposed as a means to overcome the impedance of the skin, thereby reaching deeper nerves. In particular, a transdermal amplitude modulated signal (TAMS), composed of a 210 kHz non-zero offset carrier modulated by rectangular pulses, was introduced recently for the treatment of overactive bladder. However, the contribution of the components of TAMS to nerve fiber activation has not been quantified.

METHODS

We conducted in vivo experiments and applied direct stimulation to the sciatic nerve of cats and rats. We measured electromyogram and compound action potential activity evoked by pulses, TAMS and modified versions of TAMS in which we varied the size of the carrier.

RESULTS

Nerve fiber activation using TAMS showed no difference with respect to activation with conventional pulse for carrier frequencies of 20 kHz and higher, regardless the relative amplitude of the carrier. For frequencies lower than 20 kHz, the offset needed to generate half of the maximal evoked response decreased significantly with respect to the pulse. Results of simulations in a computational model of nerve fiber stimulation using the same stimulation waveforms closely matched our experimental measurements.

CONCLUSION

Taken together, these results suggest that a TAMS with carrier frequencies >20 kHz does not offer any advantage over conventional pulses, even with larger amplitudes of the carrier, and this has implications for design of waveforms for efficient and effective transcutaneous stimulation.

Effects of frequency-dependent membrane capacitance on neural excitability

OBJECTIVE

Models of excitable cells consider the membrane specific capacitance as a ubiquitous and constant parameter. However, experimental measurements show that the membrane capacitance declines with increasing frequency, i.e., exhibits dispersion. We quantified the effects of frequency-dependent membrane capacitance, c(f), on the excitability of cells and nerve fibers across the frequency range from dc to hundreds of kilohertz.

APPROACH

We implemented a model of c(f) using linear circuit elements, and incorporated it into several models of neurons with different channel kinetics: the Hodgkin-Huxley model of an unmyelinated axon, the McIntyre-Richardson-Grill (MRG) of a mammalian myelinated axon, and a model of a cortical neuron from prefrontal cortex (PFC). We calculated thresholds for excitation and kHz frequency conduction block, the conduction velocity, recovery cycle, strength-distance relationship and firing rate.

MAIN RESULTS

The impact of c(f) on activation thresholds depended on the stimulation waveform and channel kinetics. We observed no effect using rectangular pulse stimulation, and a reduction for frequencies of 10 kHz and above using sinusoidal signals only for the MRG model. c(f) had minimal impact on the recovery cycle and the strength-distance relationship, whereas the conduction velocity increased by up to 7.9% and 1.7% for myelinated and unmyelinated fibers, respectively. Block thresholds declined moderately when incorporating c(f), the effect was greater at higher frequencies, and the maximum reduction was 11.5%. Finally, c(f) marginally altered the firing pattern of a model of a PFC cell, reducing the median interspike interval by less than 2%.

SIGNIFICANCE

This is the first comprehensive analysis of the effects of dispersive capacitance on neural excitability, and as the interest on stimulation with kHz signals gains more attention, it defines the regions over which frequency-dependent membrane capacitance, c(f), should be considered.

Volume conductor model of transcutaneous electrical stimulation with kilohertz signals

OBJECTIVE

Incorporating high-frequency components in transcutaneous electrical stimulation (TES) waveforms may make it possible to stimulate deeper nerve fibers since the impedance of tissue declines with increasing frequency. However, the mechanisms of high-frequency TES remain largely unexplored. We investigated the properties of TES with frequencies beyond those typically used in neural stimulation.

APPROACH

We implemented a multilayer volume conductor model including dispersion and capacitive effects, coupled to a cable model of a nerve fiber. We simulated voltage- and current-controlled transcutaneous stimulation, and quantified the effects of frequency on the distribution of potentials and fiber excitation. We also quantified the effects of a novel transdermal amplitude modulated signal (TAMS) consisting of a non-zero offset sinusoidal carrier modulated by a square-pulse train.

MAIN RESULTS

The model revealed that high-frequency signals generated larger potentials at depth than did low frequencies, but this did not translate into lower stimulation thresholds. Both TAMS and conventional rectangular pulses activated more superficial fibers in addition to the deeper, target fibers, and at no frequency did we observe an inversion of the strength-distance relationship. Current regulated stimulation was more strongly influenced by fiber depth, whereas voltage regulated stimulation was more strongly influenced by skin thickness. Finally, our model reproduced the threshold-frequency relationship of experimentally measured motor thresholds.

SIGNIFICANCE

The model may be used for prediction of motor thresholds in TES, and contributes to the understanding of high-frequency TES.

Mapping of somatostatin-28 (1-12) in the alpaca diencephalon

Using an immunocytochemical technique, we report for the first time the distribution of immunoreactive cell bodies and fibers containing somatostatin-28 (1-12) in the alpaca diencephalon. Somatostatin-28 (1-12)-immunoreactive cell bodies were only observed in the hypothalamus (lateral hypothalamic area, arcuate nucleus and ventromedial hypothalamic nucleus). However, immunoreactive fibers were widely distributed throughout the thalamus and hypothalamus. A high density of such fibers was observed in the central medial thalamic nucleus, laterodorsal thalamic nucleus, lateral habenular nucleus, mediodorsal thalamic nucleus, paraventricular thalamic nucleus, reuniens thalamic nucleus, rhomboid thalamic nucleus, subparafascicular thalamic nucleus, anterior hypothalamic area, arcuate nucleus, dorsal hypothalamic area, around the fornix, lateral hypothalamic area, lateral mammilary nucleus, posterior hypothalamic nucleus, paraventricular hypothalamic nucleus, suprachiasmatic nucleus, supraoptic hypothalamic nucleus, and in the ventromedial hypothalamic nucleus. The widespread distribution of somatostatin-28 (1-12) in the thalamus and hypothalamus of the alpaca suggests that the neuropeptide could be involved in many physiological actions.

A critical experimental study of the classical tactile threshold theory

Background

The tactile sense is being used in a variety of applications involving tactile human-machine interfaces. In a significant number of publications the classical threshold concept plays a central role in modelling and explaining psychophysical experimental results such as in stochastic resonance (SR) phenomena. In SR, noise enhances detection of sub-threshold stimuli and the phenomenon is explained stating that the required amplitude to exceed the sensory threshold barrier can be reached by adding noise to a sub-threshold stimulus. We designed an experiment to test the validity of the classical vibrotactile threshold. Using a second choice experiment, we show that individuals can order sensorial events below the level known as the classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance level. Nevertheless, our experimental results are above that chance level contradicting the definition of the classical tactile threshold.

Results

We performed a three alternative forced choice detection experiment on 6 subjects asking them first and second choices. In each trial, only one of the intervals contained a stimulus and the others contained only noise. According to the classical threshold assumptions, a correct second choice response corresponds to a guess attempt with a statistical frequency of 50%. Results show an average of 67.35% (STD = 1.41%) for the second choice response that is not explained by the classical threshold definition. Additionally, for low stimulus amplitudes, second choice correct detection is above chance level for any detectability level.

Conclusions

Using a second choice experiment, we show that individuals can order sensorial events below the level known as a classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance level. Nevertheless, our experimental results are above that chance level. Therefore, if detection exists below the classical threshold level, then the model to explain the SR phenomenon or any other tactile perception phenomena based on the psychophysical classical threshold is not valid. We conclude that a more suitable model of the tactile sensory system is needed.

Coincidence-enhanced stochastic resonance: experimental evidence challenges the psychophysical theory behind stochastic resonance

Stochastic resonance (SR) is the counterintuitive phenomenon in which noise enhances detection of sub-threshold stimuli. The SR psychophysical threshold theory establishes that the required amplitude to exceed the sensory threshold barrier can be reached by adding noise to a sub-threshold stimulus. The aim of this study was to test the SR theory by comparing detection results from two different randomly-presented stimulus conditions. In the first condition, optimal noise was present during the whole attention interval; in the second, the optimal noise was restricted to the same time interval as the stimulus. SR threshold theory predicts no difference between the two conditions because noise helps the sub-threshold stimulus to reach threshold in both cases. The psychophysical experimental method used a 300 ms rectangular force pulse as a stimulus within an attention interval of 1.5 s, applied to the index finger of six human subjects in the two distinct conditions. For all subjects we show that in the condition in which the noise was present only when synchronized with the stimulus, detection was better (p<0.05) than in the condition in which the noise was delivered throughout the attention interval. These results provide the first direct evidence that SR threshold theory is incomplete and that a new phenomenon has been identified, which we call Coincidence-Enhanced Stochastic Resonance (CESR). We propose that CESR might occur because subject uncertainty is reduced when noise points at the same temporal window as the stimulus.

[Controversy and reforms about the health system in Chile]

A worrying stabilization of infant mortality (19/1000) and maternal mortality (0.5/1000) rates has been observed in the last few years in Chile. The well known decrease in mortality from cardiovascular disease and cancer observed in developed countries has not taken place in Chile. An unacceptable 40% of people coming electively to peripheral clinics cannot get medical care and must seek attention in the emergency services. This deterioration of medical care to the Chilean population can be related to a cutback in national funds allocated to the public health system. The development of a private insurance system (ISAPRES) and the turnover of peripheral clinics to local government authorities has not been able to compensate for this. As a consequence an increasing discrimination of the quality of health care between the poor and rich sectors of the population has emerged. The wealthiest 10% of the population is consuming over 1/3 of the health resources. Poor districts are not able to provide the minimum to cover for medicines, vaccines and wage replacements during illness. The private sector spends 20% in administration and has not contributed to build new hospitals or to increase the number of beds available in the country. A significant modification of the current situation is urgently needed.