Analysis and Optimization of Pulse Dynamics for Magnetic Stimulation

Magnetic stimulation is a standard tool in brain research and has found important clinical applications in neurology, psychiatry, and rehabilitation. Whereas coil designs and the spatial field properties have been intensively studied in the literature, the temporal dynamics of the field has received less attention. Typically, the magnetic field waveform is determined by available device circuit topologies rather than by consideration of what is optimal for neural stimulation. This paper analyzes and optimizes the waveform dynamics using a nonlinear model of a mammalian axon. The optimization objective was to minimize the pulse energy loss. The energy loss drives power consumption and heating, which are the dominating limitations of magnetic stimulation. The optimization approach is based on a hybrid global-local method. Different coordinate systems for describing the continuous waveforms in a limited parameter space are defined for numerical stability. The optimization results suggest that there are waveforms with substantially higher efficiency than that of traditional pulse shapes. One class of optimal pulses is analyzed further. Although the coil voltage profile of these waveforms is almost rectangular, the corresponding current shape presents distinctive characteristics, such as a slow low-amplitude first phase which precedes the main pulse and reduces the losses. Representatives of this class of waveforms corresponding to different maximum voltages are linked by a nonlinear transformation. The main phase, however, scales with time only. As with conventional magnetic stimulation pulses, briefer pulses result in lower energy loss but require higher coil voltage than longer pulses.     

Effect of non-symmetric waveform on conduction block induced by high-frequency (kHz) biphasic stimulation in unmyelinated axon

The effect of a non-symmetric waveform on nerve conduction block induced by high-frequency biphasic stimulation is investigated using a lumped circuit model of the unmyelinated axon based on Hodgkin-Huxley equations. The simulation results reveal that the block threshold monotonically increases with the stimulation frequency for the symmetric stimulation waveform. However, a non-monotonic relationship between block threshold and stimulation frequency is observed when the stimulation waveform is non-symmetric. Constant activation of potassium channels by the high-frequency stimulation results in the increase of block threshold with increasing frequency. The non-symmetric waveform with a positive pulse 0.4–0.8 μs longer than the negative pulse blocks axonal conduction by hyperpolarizing the membrane and causes a decrease in block threshold as the frequency increases above 12–16 kHz. On the other hand, the non-symmetric waveform with a negative pulse 0.4–0.8 μs longer than the positive pulse blocks axonal conduction by depolarizing the membrane and causes a decrease in block threshold as the frequency increases above 40–53 kHz. This simulation study is important for understanding the potential mechanisms underlying the nerve block observed in animal studies, and may also help to design new animal experiments to further improve the nerve block method for clinical applications.     

Analysis of Pulsatile Retinal Movements by Spectral-Domain Low-Coherence Interferometry: Influence of Age and Glaucoma on the Pulse Wave

Recent studies have shown that ocular hemodynamics and eye tissue biomechanical properties play an important role in the pathophysiology of glaucoma. Nevertheless, better, non-invasive methods to assess these characteristics in vivo are essential for a thorough understanding of degenerative mechanisms. Here, we propose to measure ocular tissue movements induced by cardiac pulsations and study the ocular pulse waveform as an indicator of tissue compliance. Using a novel, low-cost and non-invasive device based on spectral-domain low coherence interferometry (SD-LCI), we demonstrate the potential of this technique to differentiate ocular hemodynamic and biomechanical properties. We measured the axial movement of the retina driven by the pulsatile ocular blood flow in 11 young healthy individuals, 12 older healthy individuals and 15 older treated glaucoma patients using our custom-made SD-OCT apparatus. The cardiac pulse was simultaneously measured through the use of an oximeter to allow comparison. Spectral components up to the second harmonic were obtained and analyzed. For the different cohorts, we computed a few parameters that characterize the three groups of individuals by analyzing the movement of the retinal tissue at two locations, using this simple, low-cost interferometric device. Our pilot study indicates that spectral analysis of the fundus pulsation has potential for the study of ocular biomechanical and vascular properties, as well as for the study of ocular disease.     

Evaluation of Intradural Stimulation Efficiency and Selectivity in a Computational Model of Spinal Cord Stimulation

Spinal cord stimulation (SCS) is an alternative or adjunct therapy to treat chronic pain, a prevalent and clinically challenging condition. Although SCS has substantial clinical success, the therapy is still prone to failures, including lead breakage, lead migration, and poor pain relief. The goal of this study was to develop a computational model of SCS and use the model to compare activation of neural elements during intradural and extradural electrode placement. We constructed five patient-specific models of SCS. Stimulation thresholds predicted by the model were compared to stimulation thresholds measured intraoperatively, and we used these models to quantify the efficiency and selectivity of intradural and extradural SCS. Intradural placement dramatically increased stimulation efficiency and reduced the power required to stimulate the dorsal columns by more than 90%. Intradural placement also increased selectivity, allowing activation of a greater proportion of dorsal column fibers before spread of activation to dorsal root fibers, as well as more selective activation of individual dermatomes at different lateral deviations from the midline. Further, the results suggest that current electrode designs used for extradural SCS are not optimal for intradural SCS, and a novel azimuthal tripolar design increased stimulation selectivity, even beyond that achieved with an intradural paddle array. Increased stimulation efficiency is expected to increase the battery life of implantable pulse generators, increase the recharge interval of rechargeable implantable pulse generators, and potentially reduce stimulator volume. The greater selectivity of intradural stimulation may improve the success rate of SCS by mitigating the sensitivity of pain relief to malpositioning of the electrode. The outcome of this effort is a better quantitative understanding of how intradural electrode placement can potentially increase the selectivity and efficiency of SCS, which, in turn, provides predictions that can be tested in future clinical studies assessing the potential therapeutic benefits of intradural SCS.     

2-ns Electrostimulation of Ca2+ Influx into Chromaffin Cells: Rapid Modulation by Field Reversal

Cellular effects of nanosecond-pulsed electric field exposures can be attenuated by an electric field reversal, a phenomenon called bipolar pulse cancellation. Our investigations of this phenomenon in neuroendocrine adrenal chromaffin cells show that a single 2-ns, 16 MV/m unipolar pulse elicited a rapid, transient rise in intracellular Ca²⁺ levels due to Ca²⁺ influx through voltage-gated calcium channels. The response was eliminated by a 2-ns bipolar pulse with positive and negative phases of equal duration and amplitude and fully restored (unipolar-equivalent response) when the delay between each phase of the bipolar pulse was 30 ns. Longer interphase intervals evoked Ca²⁺ responses that were greater in magnitude than those evoked by a unipolar pulse (stimulation). Cancellation was also observed when the amplitude of the second (negative) phase of the bipolar pulse was half that of the first (positive) phase but progressively lost as the amplitude of the second phase was incrementally increased above that of the first phase. When the amplitude of the second phase was twice that of the first phase, there was stimulation. By comparing the experimental results for each manipulation of the bipolar pulse waveform with analytical calculations of capacitive membrane charging/discharging, also known as accelerated membrane discharge mechanism, we show that the transition from cancellation to unipolar-equivalent stimulation broadly agrees with this model. Taken as a whole, our results demonstrate that electrostimulation of adrenal chromaffin cells with ultrashort pulses can be modulated with interphase intervals of tens of nanoseconds, a prediction of the accelerated membrane discharge mechanism not previously observed in other bipolar pulse cancellation studies. Such modulation of Ca²⁺ responses in a neural-type cell is promising for the potential use of nanosecond bipolar pulse technologies for remote electrostimulation applications for neuromodulation.     

Picosecond Pulse Electrical Field Suppressing Spike Firing in Hippocampal CA1 in Rat In Vivo

Picosecond pulse electrical fields (psPEFs), due to their high temporal-resolution accuracy and localization, were viewed as a potential targeted and noninvasive method for neuromodulation. However, few studies have reported psPEFs regulating neuronal activity in vivo. In this paper, a preliminary study on psPEFs regulating action potentials in hippocampus CA1 of rats in vivo was carried out. By analyzing the neuronal spike firing rate in hippocampus CA1 pre- and post-psPEF stimulation, effects of frequency, duration, and dosimetry of psPEFs were studied. The psPEF used in this study had a pulse width of 500 ps and a field strength of 1 kV/mm, established by 1 kV picosecond voltage pulses. Results showed that the psPEF suppressed spike firing in hippocampal CA1 neurons. The suppression effect was found to be significant except for 10 s, 10 Hz. For short-duration stimulation (10 s), the inhibition rate of spike firing increased with frequency. At longer stimulation durations (1 and 2 min), the inhibition rate increased and decreased alternately as the frequency increased. Despite this, the inhibition rate at high frequencies (5 and 10 kHz) was significantly larger than that at 10 and 100 Hz. A cumulative effect of psPEF on spike firing inhibition was found at low frequencies (10 and 100 Hz), which was saturated when frequency reached 500 Hz or higher. This paper conducts a study on psPEF regulating spike firing in hippocampal CA1 in vivo for the first time and guides subsequent study on psPEF achieving noninvasive neuromodulation. © 2020 Bioelectromagnetics Society     

A model of motor and sensory axon activation in the median nerve using surface electrical stimulation

Surface electrical stimulation has the potential to be a powerful and non-invasive treatment for a variety of medical conditions but currently it is difficult to obtain consistent evoked responses. A viable clinical system must be able to adapt to variations in individuals to produce repeatable results. To more fully study the effect of these variations without performing exhaustive testing on human subjects, a system of computer models was created to predict motor and sensory axon activation in the median nerve due to surface electrical stimulation at the elbow. An anatomically-based finite element model of the arm was built to accurately predict voltages resulting from surface electrical stimulation. In addition, two axon models were developed based on previously published models to incorporate physiological differences between sensory and motor axons. This resulted in axon models that could reproduce experimental results for conduction velocity, strength-duration curves and activation threshold. Differences in experimentally obtained action potential shape between the motor and sensory axons were reflected in the models. The models predicted a lower threshold for sensory axons than motor axons of the same diameter, allowing a range of sensory axons to be activated before any motor axons. This system of models will be a useful tool for development of surface electrical stimulation as a method to target specific neural functions.     

Possible origin of action potential and birefringence change in nerve axon

In this theory, we propose that the action potential and the birefringence change in nerve axon are both originated from dipole reorientation at the membrane surface under stimulation. The calculation is based upon a dipole distribution in two energy bands with a population ratior. Coincidence of the action potential with the birefringence change is predicted to occur whenr is in the order of 0.1 which corresponds to severalkT for the energy separation between the two bands. Furthermore, at any value ofr, there is always a small delay of the birefringence change behind the action potential. The theory not only is in good agreement with the recent optical observations in nerve but also indicates a possible physical origin of action potential, a long unresolved problem in neurophysiology.     

Reversible electrical breakdown of squid giant axon membrane

Charge pulse relaxation experiments were performed on squid giant axon. In the low voltage range, the initial voltage across squid axon membrane was a linear function of the injected charge. For voltages of the order of 1 V this relationship between injected charge and voltage across the membrane changes abruptly. Because of a high conductance state caused by these large electric fields the voltage across the membrane cannot be made large enough to exceed a critical value, Vc, defined as the breakdown voltage, Vc has for squid axon membrane a value of 1.1 V at 12 degrees C. During breakdown the specific membrane conductance exceeds 1 S. cm-2. Electrical breakdown produced by charge pulses of few microseconds duration have no influence on the excitability of the squid axon membrane. The resealing process of the membrane is so fast that a depolarizing breakdown is followed by the falling phase of a normal action potential. Thus, membrane voltages close to Vc open the sodium channels in few microseconds, but do not produce a decrease of the time constant of potassium activation large enough to cause the opening of a significant percentage of channels in a time of about 10 mus. It is probable that the reversible electrical breakdown is mainly caused by mechanical instability produced by electrostriction of the membrane (electrochemical model), but the decrease in the Born energy for ion injection into the membrane, accompanying the decrease in membrane thickness, may play also an important role. Because of the high conductance of the membrane during breakdown it seems very likely that this results in pore formation.     

A new algorithm for voltage clamp by iteration: A learning control of a nonlinear neuronal system

Voltage-clamp of excitable membrane allows the measurement of membrane currents associated with electrical potential changes across the membrane. However, it has been impossible in practice to apply the conventional analog feedback voltageclamp circuits to single electrode voltage clamping in central neurons. The reason for this is that the feedback system becomes unstable because of the positive feedback required for compensation of capacitative loss through the wall of the microelectrode. Park et al. (1981) proposed a new iterative technique to solve this problem. It requires that the potential to be clamped repeats itself with little or no change. The amount of current needed to clamp the membrane potential is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Since the feedback loop is open in real time, the system has great stability, and this advantage can be exploited in single electrode preparations. The computation algorithm which calculates the current waveform based on the voltage deviation during the last trial is the central part of the iterative voltage-clamp system. In this paper, we propose a new algorithm, which has several theoretical and practical advantages over the original one proposed by Park et al. First, two parameters used in the new algorithm are predetermined by a current-clamp experiment. Second, the speed of convergence of the new algorithm is faster than that of the Park's original algorithm. This was shown by computer simulation of iterative voltage clamp of artificial membrane following Hodgkin-Huxley equations for squid axon membrane and Rall's compartment model for a neuron with dendrites. Finally, we offer proof that the new algorithm is certain to converge for the general cases of voltage-clamp experiments with active membrane properties, synaptic membranes, etc. Consequently, the new algorithm for iterative voltage clamp is very suitable for single electrode voltage clamp in the central neurons. The new algorithm has been successfully applied to voltage-clamp experiments on rubrospinal neurons of cats (Tsukahara, Murakami, Kawato, Oda, and Etoh, in preparation).     

Effect of stimulus parameters in the treatment of seizures by electrical stimulation in the kainate animal model

Preliminary results from animal and clinical studies demonstrate that electrical stimulation of brain structures can reduce seizure frequency in patients with refractory epilepsy. Since most researchers derive stimulation parameters by trial and error, it is unclear what stimulation frequency, amplitude and duration constitutes a set of optimal stimulation parameters for aborting seizure activity in a given patient. In this investigation, we begin to quantify the independent effects of stimulation parameters on electrographic seizures, such that they could be used to develop an efficient closed-loop prosthesis that intervenes before the clinical onset of a seizure and seizure generalization. Biphasic stimulation is manually delivered to the hippocampus in response to a visually detected electrographic seizure. Such focal, responsive stimulation allows for anti-seizure treatment delivery with improved temporal and spatial specificity over conventional open-loop stimulation paradigms, with the possibility of avoiding tissue damage stemming from excessive exposure to electrical stimulation. We retrospectively examine the effects of stimulation frequency (low, medium and high), pulse-width (low and high) and amplitude (low and high) in seizures recorded from 23 kainic acid treated rats. We also consider the effects of total charge delivered and the rate of charge delivery, and identify stimulation parameter sets that induce after-discharges or more seizures. Among the stimulation parameters evaluated, we note 2 major findings. First, stimulation frequency is a key parameter for inhibiting seizure activity; the anti-seizure effect cannot be attributed to only the charge delivered per phase. Second, an after-discharge curve shows that as the frequency and pulse-width of stimulation increases, smaller pulse amplitudes are capable of eliciting an after-discharge. It is expected that stimulation parameter optimization will lead to devices with enhanced treatment efficacies and reduced side-effect profiles, especially when used in conjunction with seizure prediction or detection algorithms in a closed-loop control application.     

Responsive neuromodulators based on artificial neural networks used to control seizure-like events in a computational model of epilepsy

Deep brain stimulation (DBS) has been noted for its potential to suppress epileptic seizures. To date, DBS has achieved mixed results as a therapeutic approach to seizure control. Using a computational model, we demonstrate that high-complexity, biologically-inspired responsive neuromodulation is superior to periodic forms of neuromodulation (responsive and non-responsive) such as those implemented in DBS, as well as neuromodulation using random and random repetitive-interval stimulation. We configured radial basis function (RBF) networks to generate outputs modeling interictal time series recorded from rodent hippocampal slices that were perfused with low Mg2?/high K? solution. We then compared the performance of RBF-based interictal modulation, periodic biphasic-pulse modulation, random modulation and random repetitive modulation on a cognitive rhythm generator (CRG) model of spontaneous seizure-like events (SLEs), testing efficacy of SLE control. A statistically significant improvement in SLE mitigation for the RBF interictal modulation case versus the periodic and random cases was observed, suggesting that the use of biologically-inspired neuromodulators may achieve better results for the purpose of electrical control of seizures in a clinical setting.     

The mechanism of extracellular stimulation of nerve cells on an electrolyte-oxide-semiconductor capacitor

Extracellular excitation of neurons is applied in studies of cultured networks and brain tissue, as well as in neuroprosthetics. We elucidate its mechanism in an electrophysiological approach by comparing voltage-clamp and current-clamp recordings of individual neurons on an insulated planar electrode. Noninvasive stimulation of neurons from pedal ganglia of Lymnaea stagnalis is achieved by defined voltage ramps applied to an electrolyte/HfO₂/silicon capacitor. Effects on the smaller attached cell membrane and the larger free membrane are distinguished in a two-domain-stimulation model. Under current-clamp, we study the polarization that is induced for closed ion channels. Under voltage-clamp, we determine the capacitive gating of ion channels in the attached membrane by falling voltage ramps and for comparison also the gating of all channels by conventional variation of the intracellular voltage. Neuronal excitation is elicited under current-clamp by two mechanisms: Rising voltage ramps depolarize the free membrane such that an action potential is triggered. Falling voltage ramps depolarize the attached membrane such that local ion currents are activated that depolarize the free membrane and trigger an action potential. The electrophysiological analysis of extracellular stimulation in the simple model system is a basis for its systematic optimization in neuronal networks and brain tissue.     

Right or left ear reference changes the voltage of frontal and parietal somatosensory evoked potentials

Short-latency cortical somatosensory evoked potentials (SEPs) to left median nerve stimulation were recorded with either the left or right earlobe as reference. With a right earlobe reference the voltage of the parietal N20 and P27 was reduced while the voltage of the frontal P20 and N30 was enhanced. The effects were consistent, but their size varied with the SEP component considered and also among the subjects. Analysis of SEPs at different scalp sites and at either earlobe suggested that the ear contralateral to the side stimulated picked up transient potential differences, depending a.o. on side asymmetry and geometry of the neural generators as disclosed in topographic mapping. For example, the right ear potential can be shifted negatively by the right N20 field evoked by left median nerve stimulation. The changes involve the absolute potential values, but not the time features of the gradients of potential fields. Scalp current density (SCD) maps are not affected. The results are pertinent for current discussions about which reference to use and document the practical recommendation of recording short-latency cortical SEPs with a reference at the ear ipsilateral (not contralateral) to the side of stimulation.     

Frequency change-induced alternative potential waveform dependence of membrane damage to cells cultured on an electrode surface

In the present study, alternative potential stimulation with rectangular pulse, sine and triangular waveforms at 10 and 100Hz was applied to cells cultured on an ITO electrode. As a result, we found that the alternating potential waveform dependence induced by the frequency on membrane damage of cells cultured on an electrode surface. The cell membrane damage was promoted by a rectangular pulse wave in comparison with sine and triangular waves, when alternating electrical potentials of 0 to +1.0V at 100Hz were loaded. In contrast, this waveform dependence was not observed when the frequency was 10Hz. Furthermore, it was found that cell membrane damage was induced at positive potentials more than +0.8V under the present experimental conditions.     

动态神经元的网络模型——Ⅲ.电路实现

在动态神经元网络数学模型的基础上,利用模拟有源器件与数学开关电路组成的硬件系统来达到模拟生物神经元的目的。模拟的结果表明：这个硬件具有神经元脉冲发放的动态过程,系统中每部分的输出信号分别对应于突触后电位、感受器电位、始段分级电位和轴突上脉冲发放等波形,与生物实验资料相似,是一个比计算机仿真更接近实际的连续模型,它将为小型神经元网络的动态特性分析提供了更直观,更可靠的手段。     

Biophysical mechanisms of transient optical stimulation of peripheral nerve

A new method for in vivo neural activation using low-intensity, pulsed infrared light exhibits advantages over standard electrical means by providing contact-free, spatially selective, artifact-free stimulation. Here we investigate the biophysical mechanism underlying this phenomenon by careful examination of possible photobiological effects after absorption-driven light-tissue interaction. The rat sciatic nerve preparation was stimulated in vivo with a Holmium:yttrium aluminum garnet laser (2.12 microm), free electron laser (2.1 microm), alexandrite laser (750 nm), and prototype solid-state laser nerve stimulator (1.87 microm). We systematically determined relative contributions from a list of plausible interaction types resulting in optical stimulation, including thermal, pressure, electric field, and photochemical effects. Collectively, the results support our hypothesis that direct neural activation with pulsed laser light is induced by a thermal transient. We then present data that characterize and quantify the spatial and temporal nature of this required temperature rise, including a measured surface temperature change required for stimulation of the peripheral nerve (6 degrees C-10 degrees C). This interaction is a photothermal effect from moderate, transient tissue heating, a temporally and spatially mediated temperature gradient at the axon level (3.8 degrees C-6.4 degrees C), resulting in direct or indirect activation of transmembrane ion channels causing action potential generation.     

Nanosecond pulsed electric field generators for the study of subcellular effects

Modeling and experimental studies have shown that pulsed electric fields of nanosecond duration and megavolt per meter amplitude affect subcellular structures but do not lead to the formation of large pores in the outer membrane. This "intracellular electromanipulation" requires the use of pulse generators which provide extremely high power but low energy pulses. In this study, we describe the concept of the required pulsed power sources, their design, operation, and the necessary diagnostics. Two types of pulse generators based on the Blumlein line principle have been developed and are described here. One system is designed to treat a large number of cells in cuvettes holding volumes from 0.1 to 0.8 ml. Pulses of up to 40 kV amplitude, with a duration of 10 ns and a rise time close to 1 ns can be applied to the cuvette. For an electrode gap of 1 mm this voltage corresponds to an average electric field of 40 MV/m. The second system allows for real time observation of individual cells under a microscope. It generates pulses of 10-300 ns duration with a rise time of 3.5 ns and voltage amplitudes up to 1 kV. Connected to a microreactor with an electrode gap of 100 microm, electric fields up to 10 MV/m are applied.     

节律性听觉刺激下的神经振荡同步化及其应用

大脑的感觉、情绪、认知等功能与其神经振荡模式有密切的联系。通过施加节律性刺激可以调控大脑的神经振荡模式,进而影响个体感受、情绪状态和认知功能等。与近年来常见的非侵入性电刺激和磁刺激相比,同样依赖于外部刺激输入的节律性感觉刺激具有成本低、易操作等优点,被认为是一种极具潜力的神经调控手段。本文以节律性听觉刺激为例,系统综述了不同类型的节律性听觉刺激如何影响大脑的神经振荡模式,进而影响相关状态和功能;并通过总结外部节律性听觉刺激对个体感知觉、情绪与认知功能的影响,讨论其生理机制和应用前景。