Recruitment of dorsal column fibers in spinal cord stimulation: influence of collateral branching

A systematic review of computational models for the design of spinal cord stimulation therapies: from neural circuits to patient-specific simulations

Seventy years ago, Hodgkin and Huxley published the first mathematical model to describe action potential generation, laying the foundation for modern computational neuroscience. Since then, the field has evolved enormously, with studies spanning from basic neuroscience to clinical applications for neuromodulation. Computer models of neuromodulation have evolved in complexity and personalization, advancing clinical practice and novel neurostimulation therapies, such as spinal cord stimulation. Spinal cord stimulation is a therapy widely used to treat chronic pain, with rapidly expanding indications, such as restoring motor function. In general, simulations contributed dramatically to improve lead designs, stimulation configurations, waveform parameters and programming procedures and provided insight into potential mechanisms of action of electrical stimulation. Although the implementation of neural models are relentlessly increasing in number and complexity, it is reasonable to ask whether this observed increase in complexity is necessary for improved accuracy and, ultimately, for clinical efficacy. With this aim, we performed a systematic literature review and a qualitative meta-synthesis of the evolution of computational models, with a focus on complexity, personalization and the use of medical imaging to capture realistic anatomy. Our review showed that increased model complexity and personalization improved both mechanistic and translational studies. More specifically, the use of medical imaging enabled the development of patient-specific models that can help to transform clinical practice in spinal cord stimulation. Finally, we combined our results to provide clear guidelines for standardization and expansion of computational models for spinal cord stimulation.

Lumbar trans-spinal direct current stimulation: A modeling-experimental approach to dorsal root ganglia stimulation

Introduction

The excitability of spinal motor neurons (MN) can be altered through subthreshold currents, such as transcutaneous spinal direct-current stimulation (tsDCS). Current evidence shows that tsDCS can interfere with ascending somatosensory pathways and lower motor neurons' (LMN) excitability, which points to its therapeutic potential for repairing altered spinal responses. We aim to define the best tsDCS montage for maximizing the electric field (E-field) in the lumbar spinal cord (L-SC) by computer modeling; and to apply this montage to measure the effect on LMN excitability and somatosensory evoked potentials (SSEP).

Methods

A human volume conductor model was obtained from an available database. The E-field distribution was calculated considering three different electrode settings aiming at maximizing the field at L-SC and right dorsal root ganglia (DRG). The best electrode setting was then selected and applied in a blind crossover pseudo-randomized study including 14 subjects. tsDCS was delivered for 15 min (cathodal vs. sham) over L2 vertebra level (4 mA, 144 mC/cm²), and its effect on F-waves, H-reflex (including homosynaptic depression, HD) and SSEPs was investigated in the lower limbs.

Results

All simulated montages showed higher current density and E-field magnitudes between the electrodes (>0.15 V/m), with a major longitudinal component and with rostral-caudal direction. The induced E-field involved the sensory ganglia and was maximum in the right T8-left L2 montage, which was the one selected for the experimental protocol. We disclosed a statistically significant increase of the H-reflex amplitude at 0.1 Hz, after cathodal tsDCS (c-tsDCS) on both sides. No other significant change was observed.

Discussion

Our results can suggest the c-tsDCS applied to the L-SC and DRG can modulate synaptic efficiency increasing lower motor neurons response to Ia fibers excitation. The possible implications of our findings for treating clinical conditions will be addressed in future studies.

Theoretical model of external spinal cord stimulation

In this paper, a simple theoretical model of the excitation of action potentials of multiple motor pools by stimulating current pulses over the lumbosacral regions of the spinal cord is presented. The present model is consistent with known experimental data.

Simultaneous 10 kHz and 40 Hz spinal cord stimulation increases dorsal horn inhibitory interneuron activity

Since 1967, spinal cord stimulation (SCS) has been used to manage chronic intractable pain of the trunk and limbs. Low-intensity, paresthesia-free, 10 kHz SCS has demonstrated statistically- and clinically-superior long-term pain relief compared to conventional SCS. 10 kHz SCS has been proposed to operate via selective activation of inhibitory interneurons in the superficial dorsal horn. In contrast, 40 Hz SCS is presumed to operate largely via dorsal column fiber activation. To determine if these mechanisms may be implemented synergistically, we examined the effect of each type of stimulation both independently and simultaneously on putatively inhibitory and putatively excitatory neurons in the superficial dorsal horn. When 10 kHz SCS was applied relatively caudally to the measured spinal segment, simultaneous with 40 Hz SCS applied relatively rostrally to that spinal segment, inhibitory interneurons demonstrated a median increase of 26 spikes/s compared to their baseline firing rates. Median firing rate increases of inhibitory interneurons were 8.7 and 5.1 spikes/s during 40 Hz SCS applied rostrally and 10 kHz SCS applied caudally, respectively. By comparison, the median firing rate of excitatory interneurons increased by 4.1 spikes/s during simultaneous 40 Hz SCS applied rostrally and 10 kHz SCS applied caudally. Median firing rate increases of excitatory interneurons were 13 and 0.8 spikes/s during 40 Hz SCS applied rostrally and 10 kHz SCS applied caudally, respectively. This suggests that simultaneously applying 10 kHz SCS caudally and 40 Hz SCS rostrally may provide greater pain relief than either type of SCS alone by increasing the firing rates of inhibitory interneurons, albeit with greater excitatory interneuron activation.

Neural Recruitment During Conventional, Burst, and 10-kHz Spinal Cord Stimulation for Pain

Spinal cord stimulation (SCS) is a popular neurostimulation therapy for severe chronic pain. To improve stimulation efficacy, multiple modes are now used clinically, including conventional, burst, and 10-kHz SCS. Clinical observations have produced speculation that these modes target different neural elements and/or work via distinct mechanisms of action. However, in humans, these hypotheses cannot be conclusively answered via experimental methods. Therefore, we utilized computational modeling to assess the response of primary afferents, interneurons, and projection neurons to conventional, burst, and 10-kHz SCS. We found that local cell thresholds were always higher than afferent thresholds, arguing against direct recruitment of these local cells. Furthermore, although we observed relative threshold differences between conventional, burst, and 10-kHz SCS, the recruitment order was the same. Finally, contrary to previous reports, axon collateralization produced complex changes in activation thresholds of primary afferents. These results motivate future work to contextualize clinical observations across SCS paradigms. PERSPECTIVE: This article presents the first computational modeling study to investigate neural recruitment during conventional, burst, and 10-kilohertz spinal cord stimulation for chronic pain within a single modeling framework. The results provide insight into these treatments' unknown mechanisms of action and offer context to interpreting clinical observations.

The plasticity of nerve fibers: the prolonged effects of polarization of afferent fibers

The review surveys various aspects of the plasticity of nerve fibers, in particular the prolonged increase in their excitability evoked by polarization, focusing on a long-lasting increase in the excitability of myelinated afferent fibers traversing the dorsal columns of the spinal cord. We review the evidence that increased axonal excitability 1) follows epidurally applied direct current (DC) as well as relatively short (5 or 10 ms) current pulses and synaptically evoked intrinsic field potentials; 2) critically depends on the polarization of branching regions of afferent fibers at the sites where they bifurcate and give off axon collaterals entering the spinal gray matter in conjunction with actions of extrasynaptic GABA_A membrane receptors; and 3) shares the feature of being activity-independent with the short-lasting effects of polarization of peripheral nerve fibers. A comparison between the polarization evoked sustained increase in the excitability of dorsal column fibers and spinal motoneurons (plateau potentials) indicates the possibility that they are mediated by partly similar membrane channels (including noninactivating type L Cav⁺⁺ 1.3 but not Na⁺ channels) and partly different mechanisms. We finally consider under which conditions transspinally applied DC (tsDCS) might reproduce the effects of epidural polarization on dorsal column fibers and the possible advantages of increased excitability of afferent fibers for the rehabilitation of motor and sensory functions after spinal cord injuries.NEW & NOTEWORTHY This review supplements previous reviews of properties of nerve fibers by surveying recent experimental evidence for their long-term plasticity. It also extends recent descriptions of spinal effects of DC by reviewing effects of polarization of afferent nerve fibers within the dorsal columns, the mechanisms most likely underlying the long-lasting increase in their excitability and possible clinical implications.

Recruitment of upper-limb motoneurons with epidural electrical stimulation of the cervical spinal cord

Epidural electrical stimulation (EES) of lumbosacral sensorimotor circuits improves leg motor control in animals and humans with spinal cord injury (SCI). Upper-limb motor control involves similar circuits, located in the cervical spinal cord, suggesting that EES could also improve arm and hand movements after quadriplegia. However, the ability of cervical EES to selectively modulate specific upper-limb motor nuclei remains unclear. Here, we combined a computational model of the cervical spinal cord with experiments in macaque monkeys to explore the mechanisms of upper-limb motoneuron recruitment with EES and characterize the selectivity of cervical interfaces. We show that lateral electrodes produce a segmental recruitment of arm motoneurons mediated by the direct activation of sensory afferents, and that muscle responses to EES are modulated during movement. Intraoperative recordings suggested similar properties in humans at rest. These modelling and experimental results can be applied for the development of neurotechnologies designed for the improvement of arm and hand control in humans with quadriplegia.

The efficacy of epidural electrical stimulation (EES) to engage arm muscles and improve movement after spinal cord injury is still unclear. Here, the authors investigated how EES can recruit upper-limb motor neurons by combining computational modelling with experiments in non-human primates.

Anatomical and technical factors affecting the neural response to epidural spinal cord stimulation

OBJECTIVE

Spinal cord stimulation (SCS) is a common neurostimulation therapy to treat chronic pain. Computational models represent a valuable tool to study the potential mechanisms of action of SCS and to optimize the design and implementation of SCS technologies. However, it is imperative that these computational models include the appropriate level of detail to accurately predict the neural response to SCS and to correlate model predictions with clinical outcomes. Therefore, the goal of this study was to investigate several anatomic and technical factors that may affect model-based predictions of neural activation during thoracic SCS.

APPROACH

We developed computational models that consisted of detailed finite element models of the lower thoracic spinal cord, surrounding tissues, and implanted SCS electrode arrays. We positioned multicompartment models of sensory axons within the spinal cord to calculate the activation threshold for each sensory axon. We then investigated how activation thresholds changed as a function of several anatomical variables (e.g. spine geometry, dorsal rootlet anatomy), stimulation type (i.e. voltage-controlled vs. current-controlled), electrode impedance, lead position, lead type, and electrical properties of surrounding tissues (e.g. dura conductivity, frequency-dependent conductivity).

MAIN RESULTS

Several anatomic and modeling factors produced significant percent differences or errors in activation thresholds. Rostrocaudal positioning of the cathode with respect to the vertebrae had a large effect (up to 32%) on activation thresholds. Variability in electrode impedance produced significant changes in activation thresholds for voltage-controlled stimulation (38% to 51%), but had little effect on activation thresholds for current-controlled stimulation (less than 13%). Changing the dura conductivity also produced significant differences in activation thresholds.

SIGNIFICANCE

This study demonstrates several anatomic and technical factors that can affect the neural response to SCS. These factors should be considered in clinical implementation and in future computational modeling studies of thoracic SCS.

Branching points of primary afferent fibers are vital for the modulation of fiber excitability by epidural DC polarization and by GABA in the rat spinal cord

The aim of the study was to examine whether the sustained increases in the excitability of afferent fibers traversing the dorsal columns evoked by their polarization depend on the branching points of these fibers. To this end, the effects of epidural polarization were compared in four spinal regions in deeply anesthetized rats; two with the densest collateralization of muscle afferent fibers (above motor nuclei and Clarke's column) and two where the collateralization is more sparse (rostral and caudal to motor nuclei, respectively. The degree of collateralization in different segments was reconstructed in retrogradely labeled afferent fibers in the rat. Nerve volleys evoked in peripheral nerves by electrical stimulation of the dorsal columns within these regions were used as a measure of the excitability of the stimulated fibers. Potent increases in the excitability were evoked by polarization above motor nuclei and Clarke's column, both during constant direct current (DC) polarization (1 µA for 1 min) and for at least 30 min following DC polarization. Smaller excitability increases occurred during the polarization within other regions and were thereafter either absent or rapidly declined after its termination. The postpolarization increases in excitability were counteracted by the GABA_A receptor antagonist bicuculline and the _α5GABA_A extrasynaptic receptor antagonist L655708 and enhanced by the GABA_A receptor agonist muscimol and by ionophoretically applied GABA. As extrasynaptic _α5GABA_A receptors have been found close to Na channels within branching points, these results are consistent with the involvement of branching points in the induction of the sustained postpolarization increases in fiber excitability.NEW & NOTEWORTHY Polarization of sensory fibers traversing dorsal columns of the spinal cord may considerably increase the excitability of these fibers. We show that this involves the effects of current at branching points of afferent fibers and depends on extrasynaptic effects of GABA. These results contribute to our understanding of the mechanism underlying plasticity of activation of nerve fibers and may be used to increase the effectiveness of epidural stimulation in humans and recovery of spinal functions.

Reduced order models of myelinated axonal compartments

The paper presents a hierarchical series of computational models for myelinated axonal compartments. Three classes of models are considered, either with distributed parameters (2.5D EQS-ElectroQuasi Static, 1D TL-Transmission Lines) or with lumped parameters (0D). They are systematically analyzed with both analytical and numerical approaches, the main goal being to identify the best procedure for order reduction of each case. An appropriate error estimator is proposed in order to assess the accuracy of the models. This is the foundation of a procedure able to find the simplest reduced model having an imposed precision. The most computationally efficient model from the three geometries proved to be the analytical 1D one, which is able to have accuracy less than 0.1%. By order reduction with vector fitting, a finite model is generated with a relative difference of 10^- 4 for order 5. The dynamical models thus extracted allow an efficient simulation of neurons and, consequently, of neuronal circuits. In such situations, the linear models of the myelinated compartments coupled with the dynamical, non-linear models of the Ranvier nodes, neuronal body (soma) and dendritic tree give global reduced models. In order to ease the simulation of large-scale neuronal systems, the sub-models at each level, including those of myelinated compartments should have the lowest possible order. The presented procedure is a first step in achieving simulations of neural systems with accuracy control.

Cervical trans-spinal direct current stimulation: a modelling-experimental approach

Background

Trans-spinal direct current stimulation (tsDCS) is a non-invasive technique with promising neuromodulatory effects on spinal cord (SC) circuitry. Computational studies are essential to guide effective tsDCS protocols for specific clinical applications. This study aims to combine modelling and experimental studies to determine the electrode montage that maximizes electric field (E-field) delivery during cervical tsDCS.

Methods

Current and E-field distributions in the cervical SC were predicted for four electrode montages in a human realistic model using computational methods. A double-blind crossover and randomized exploratory study was conducted using the montage that maximized E-field delivery. tsDCS was applied for 15 min in 10 healthy subjects (anodal, cathodal, sham, with polarity assigned to the cervical electrode), with a current intensity of 2.5 mA, resulting in a total current charge density delivery of 90 mC/cm². Upper limb motor (transcranial magnetic stimulation) and sensory evoked potentials (MEP, SEP), M-waves, H-reflex and F-wave responses were analysed. Central and peripheral conduction times were determined using MEP. Repeated measures ANOVA and Friedman test were used for statistical analysis (significance level α = 0.05).

Results

All montages presented higher current density and E-field magnitudes in the cervical SC region between the electrodes. However, electrodes at C3 and T3 spinous processes (C3-T3) originated the highest E-field magnitude (0.50 V/m). Using C3-T3 montage we observed significant changes in N9 SEP latency (p = 0.006), but significance did not persist in pairwise comparisons (sham-anodal: p = 0.022; sham-cathodal: p = 0.619; anodal-cathodal: p = 0.018; α = 0.017, Bonferroni corrected). MEP latency and central motor conduction time (CMCT) modified significantly on stimulation (p = 0.007 and p = 0.015, respectively). In addition, pairwise comparisons confirmed significant differences between sham and cathodal conditions after Bonferroni correction for MEP latency (sham-anodal: p = 0.868; sham-cathodal: p = 0.011; anodal-cathodal: p = 0.023) and CMCT (sham-anodal: p = 0.929; sham-cathodal: p = 0.010; anodal-cathodal: p = 0.034).

Conclusions

Computational models predicted higher E-field delivery in the cervical SC for the C3-T3 montage. Polarity-dependent effects in motor responses were reported using this montage consistent with spinal motor modulation. tsDCS experimental protocol designs should be guided by modelling studies to improve effectiveness.

The Quasi-uniform assumption for Spinal Cord Stimulation translational research

BACKGROUND

Quasi-uniform assumption is a general theory that postulates local electric field predicts neuronal activation. Computational current flow model of spinal cord stimulation (SCS) of humans and animal models inform how the quasi-uniform assumption can support scaling neuromodulation dose between humans and translational animal.

NEW METHOD

Here we developed finite element models of cat and rat SCS, and brain slice, alongside SCS models. Boundary conditions related to species specific electrode dimensions applied, and electric fields per unit current (mA) predicted.

RESULTS

Clinically and across animal, electric fields change abruptly over small distance compared to the neuronal morphology, such that each neuron is exposed to multiple electric fields. Per unit current, electric fields generally decrease with body mass, but not necessarily and proportionally across tissues. Peak electric field in dorsal column rat and cat were ∼17x and ∼1x of clinical values, for scaled electrodes and equal current. Within the spinal cord, the electric field for rat, cat, and human decreased to 50% of peak value caudo-rostrally (C5-C6) at 0.48 mm, 3.2 mm, and 8 mm, and mediolaterally at 0.14 mm, 2.3 mm, and 3.1 mm. Because these space constants are different, electric field across species cannot be matched without selecting a region of interest (ROI).

COMPARISON WITH EXISTING METHOD

This is the first computational model to support scaling neuromodulation dose between humans and translational animal.

CONCLUSIONS

Inter-species reproduction of the electric field profile across the entire surface of neuron populations is intractable. Approximating quasi-uniform electric field in a ROI is a rational step to translational scaling.

Electric Field Distribution during Non-Invasive Electric and Magnetic Stimulation of the Cervical Spinal Cord. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2019;2019:5898-5901. [PMID: 31947192 DOI: 10.1109/embc.2019.8857129]

Experimental studies on transcutaneous spinal cord direct current and magnetic stimulation (tsDCS and tsMS) show promising results in the neuromodulation of spinal sensory and motor pathways, with possible application in spinal functional rehabilitation. Modelling studies on the electric field (EF) distribution during tsDCS and tsMS are powerful tools to understand the underlying biophysics and to select and optimize stimulation protocols for a specific clinical target. The study presented here compares the EF during cervical tsDCS and tsMS. The EF predictions show the same spatial profiles along the cervical spinal cord using both types of stimulation. tsMS presents higher average magnitudes per spinal segment, with a maximum value of 14.61 V/m, whereas tsDCS is approximately 30 times lower, reaching 0.44 V/m. According to previous studies, tsDCS and tsMS induce EF values which are sufficient for spinal neuromodulation.

Dorsal root ganglion stimulation for chronic pain modulates Aβ-fiber activity but not C-fiber activity: A computational modeling study

OBJECTIVE

The goal of this project was to use computational models to investigate which types of primary sensory neurons are modulated by dorsal root ganglion stimulation (DRGS) to provide pain relief.

METHODS

We modeled DRGS by coupling an anatomical finite element model of a human L5 dorsal root ganglion to biophysical models of primary sensory neurons. We calculated the stimulation amplitude needed to elicit an action potential in each neuron, and examined how DRGS affected sensory neuron activity.

RESULTS

We showed that within clinical ranges of stimulation parameters, DRGS drives the activity of large myelinated Aβ-fibers but does not directly activate small nonmyelinated C-fibers. We also showed that the position of the active and return electrodes and the polarity of the stimulus pulse influence neural activation.

CONCLUSIONS

Our results indicate that DRGS may provide pain relief by activating pain-gating mechanisms in the dorsal horn via repeated activation of large myelinated afferents.

SIGNIFICANCE

Understanding the mechanisms of action of DRGS-induced pain relief may lead to innovations in stimulation technologies that improve patient outcomes.

Computational Study of the Effect of Electrode Polarity on Neural Activation Related to Paresthesia Coverage in Spinal Cord Stimulation Therapy

OBJECTIVE

Using computer simulation, we investigated the effect of electrode polarity on neural activation in spinal cord stimulation and propose a new strategy to maximize the activating area in the dorsal column (DC) and, thus, paresthesia coverage in clinical practice.

MATERIALS AND METHODS

A new three-dimensional spinal cord model at the T10 vertebral level was developed to simulate neural activation induced by the electric field distribution produced by different typical four-contact electrode polarities in single- and dual-lead stimulation. Our approach consisted of the combination of a finite element model of the spinal cord developed in COMSOL Multiphysics and a nerve fiber model implemented in MATLAB. Five evaluation parameters were evaluated, namely, the recruitment ratio, the perception and discomfort thresholds, and the activating area and depth. The results were compared quantitatively.

RESULTS

The dual-guarded cathode presents the maximum activating area and depth in single- and dual-lead stimulation. However, the lowest value of the ratio between the perception threshold in DC and the perception threshold in the dorsal root (DR) is achieved when the guarded cathode is programmed. Although the two versions of bipolar polarity (namely bipolar 1 and bipolar 2) produce higher activating area and depth than the guarded cathode, they are suitable for producing DR stimulation. Similarly, dual-lead stimulation is likely to activate DR fibers because the electrodes are closer to these fibers.

CONCLUSIONS

The results suggest that the activating area in the DC is maximized by using the dual-guarded cathode both in single- and dual-lead stimulation modes. However, DC nerve fibers are preferentially stimulated when the guarded cathode is used. According to these results, the new electrode programming strategy that we propose for clinical practice first uses the dual-guarded cathode, but, if the DR nerve fibers are activated, it then uses guarded cathode polarity.

Mechanisms of spinal cord stimulation for the treatment of pain: Still in the dark after 50 years

Background and Objective

Despite the value of spinal cord stimulation (SCS) in treating some patients with focal neuropathic pain, technological advances in stimulator design and treatment protocols have not correlated with significant improvements in clinical outcomes. This may be because incomplete understanding of the mechanisms underlying SCS precludes improvement in clinical efficacy. In this brief review, we (a) review phenomenological effects of SCS, (b) review the literature on proposed spinal sites of action of SCS and (c) propose a novel hypothesis of mechanism of action.

Results

Dorsal columns, dorsal roots and dorsal horns have each been proposed as spinal sites of action of SCS. We suggest that evidence in favour of the dorsal columns or dorsal roots as the primary mediators of SCS is weak and propose that the dorsal horn is the crucial site of action. Furthermore, we hypothesize that, based on their location, and neurochemical and morphological properties, dorsal horn islet cells may mediate the effects of SCS.

Conclusions

The precise spinal mechanisms of action of SCS are still unknown. Dorsal horn islet cells have properties that position them to play a key role in analgesic effects of electrical stimulation. Understanding the mechanisms responsible for positive SCS effects are needed for successful translation into clinical dividends.

Significance

We review possible spinal mechanisms of action of spinal cord stimulation for neuropathic pain, proposing that direct modulation of dorsal horn neurons is crucial. We suggest that mechanistic insights are needed for translation into more favourable clinical outcomes.

Quantifying axonal responses in patient-specific models of subthalamic deep brain stimulation

Medical imaging has played a major role in defining the general anatomical targets for deep brain stimulation (DBS) therapies. However, specifics on the underlying brain circuitry that is directly modulated by DBS electric fields remain relatively undefined. Detailed biophysical modeling of DBS provides an approach to quantify the theoretical responses to stimulation at the cellular level, and has established a key role for axonal activation in the therapeutic mechanisms of DBS. Estimates of DBS-induced axonal activation can then be coupled with advances in defining the structural connectome of the human brain to provide insight into the modulated brain circuitry and possible correlations with clinical outcomes. These pathway-activation models (PAMs) represent powerful tools for DBS research, but the theoretical predictions are highly dependent upon the underlying assumptions of the particular modeling strategy used to create the PAM. In general, three types of PAMs are used to estimate activation: 1) field-cable (FC) models, 2) driving force (DF) models, and 3) volume of tissue activated (VTA) models. FC models represent the "gold standard" for analysis but at the cost of extreme technical demands and computational resources. Consequently, DF and VTA PAMs, derived from simplified FC models, are typically used in clinical research studies, but the relative accuracy of these implementations is unknown. Therefore, we performed a head-to-head comparison of the different PAMs, specifically evaluating DBS of three different axonal pathways in the subthalamic region. The DF PAM was markedly more accurate than the VTA PAMs, but none of these simplified models were able to match the results of the patient-specific FC PAM across all pathways and combinations of stimulus parameters. These results highlight the limitations of using simplified predictors to estimate axonal stimulation and emphasize the need for novel algorithms that are both biophysically realistic and computationally simple.

Transcutaneous spinal direct current stimulation of the lumbar and sacral spinal cord: a modelling study

OBJECTIVE

Our aim was to perform a computational study of the electric field (E-field) generated by transcutaneous spinal direct current stimulation (tsDCS) applied over the thoracic, lumbar and sacral spinal cord, in order to assess possible neuromodulatory effects on spinal cord circuitry related with lower limb functions.

APPROACH

A realistic volume conductor model of the human body consisting of 14 tissues was obtained from available databases. Rubber pad electrodes with a metallic connector and a conductive gel layer were modelled. The finite element (FE) method was used to calculate the E-field when a current of 2.5 mA was passed between two electrodes. The main characteristics of the E-field distributions in the spinal grey matter (spinal-GM) and spinal white matter (spinal-WM) were compared for seven montages, with the anode placed either over T10, T8 or L2 spinous processes (s.p.), and the cathode placed over right deltoid (rD), umbilicus (U) and right iliac crest (rIC) areas or T8 s.p. Anisotropic conductivity of spinal-WM and of a group of dorsal muscles near the vertebral column was considered.

MAIN RESULTS

The average E-field magnitude was predicted to be above 0.15 V m^-1 in spinal cord regions located between the electrodes. L2-T8 and T8-rIC montages resulted in the highest E-field magnitudes in lumbar and sacral spinal segments (>0.30 V m^-1). E-field longitudinal component is 3 to 6 times higher than the ventral-dorsal and right-left components in both the spinal-GM and WM. Anatomical features such as CSF narrowing due to vertebrae bony edges or disks intrusions in the spinal canal correlate with local maxima positions.

SIGNIFICANCE

Computational modelling studies can provide detailed information regarding the electric field in the spinal cord during tsDCS. They are important to guide the design of clinical tsDCS protocols that optimize stimulation of application-specific spinal targets.

Spinal Cord Stimulation in Chronic Pain: Mode of Action

STUDY DESIGN

Literature review.

OBJECTIVE

A review of the literature that presents a perspective on mechanisms of actions behind spinal cord stimulation (SCS) therapy for chronic pain.

SUMMARY OF BACKGROUND DATA

SCS is an effective therapeutic alternative for the treatment of intractable chronic pain. Its application has been mostly based on the gate control theory of pain. Computational models have been fundamental on the understanding of clinical observations and the design of therapies that provide optimal neuromodulation. Research has provided insight into the involvement of specific neurotransmitters that support segmental and supraspinal mechanisms of action.

METHODS

A literature review was performed with emphasis on mechanisms of action for SCS including the effects of electrical fields on spinal cord structures based on computational models and preclinical and clinical explorations.

RESULTS

This review provides background on the development of SCS, which has been driven around a paresthesia-based paradigm as a result of the gate control theory. A review of computational models emphasizes their importance on our current understanding of the mechanism of action and clinical optimization of therapy. Electrophysiology and molecular biology have provided a closer, yet narrow, view of the effect of SCS on neurotransmitters and their receptors, which have led to the formulation of segmental and supraspinal mechanisms. Literature supporting the involvement of glial cells in chronic pain and their characteristic response to electrical fields should motivate further investigation of mechanisms involving neuroglia. Finally, a review of recent results paresthesia-free strategies should encourage research on mechanisms of action.

CONCLUSION

The mechanisms of SCS have been extensively studied and several consistent phenomena have emerged. The activation of A-beta fibers to induce paresthesia also involve neurotransmitter release via segmental and supraspinal pathways. Despite advancements, much remains to be understood, particularly as new stimulation strategies are developed.

LEVEL OF EVIDENCE

N /A.

Epidural Stimulation of Rat Spinal Cord at Lumbosacral Segment Using a Surface Electrode: A Computer Simulation Study

Clinical research indicates that the epidural spinal cord stimulation (ESCS) at lumbosacral segment has shown potential for promoting locomotor recovery in patients with incomplete spinal cord injury. However, the underlying neural mechanism needs to be determined by animal experiments. In order to refine experimental protocols, we used a finite element simulation to investigate the activation of nerve fibers in a rat spinal cord model. Our model is composed of a volume conductor model from L1 to S2 spinal segments and the McIntyre-Richard-Grill axon model, which is used to investigate the threshold of selected spinal fibers with different diameters at varied locations and predict the neural responses of any target fibers with bipolar electrode configuration. Mathematical modeling suggests that the electrode-fiber distance may play an important role in the recruitment of nerve fibers, whereas longer pulse width predicted greater activity of spinal root fibers and dorsal column fibers, as well as may exert an effective influence on the motor system by the ability to increase and even "steer" spatial selectivity with deeper penetration into the dorsal columns. The spikes were initiated at sites along the nerve fibers depending on which component was closest to the cathode among the longitudinal part of the fiber, its entrance into spinal cord, or strong bending at the entry. Our simulation results show good agreement with the previous findings from animal studies. It is concluded that the computational ESCS model is a valuable tool to obtain a better insight into the immediately evoked electrophysiological phenomena in animal models, and provides further guidelines for conducting animal experiments to enhance the exploration of basic neural mechanisms.

Analyzing the tradeoff between electrical complexity and accuracy in patient-specific computational models of deep brain stimulation

OBJECTIVE

Deep brain stimulation (DBS) is an adjunctive therapy that is effective in treating movement disorders and shows promise for treating psychiatric disorders. Computational models of DBS have begun to be utilized as tools to optimize the therapy. Despite advancements in the anatomical accuracy of these models, there is still uncertainty as to what level of electrical complexity is adequate for modeling the electric field in the brain and the subsequent neural response to the stimulation.

APPROACH

We used magnetic resonance images to create an image-based computational model of subthalamic DBS. The complexity of the volume conductor model was increased by incrementally including heterogeneity, anisotropy, and dielectric dispersion in the electrical properties of the brain. We quantified changes in the load of the electrode, the electric potential distribution, and stimulation thresholds of descending corticofugal (DCF) axon models.

MAIN RESULTS

Incorporation of heterogeneity altered the electric potentials and subsequent stimulation thresholds, but to a lesser degree than incorporation of anisotropy. Additionally, the results were sensitive to the choice of method for defining anisotropy, with stimulation thresholds of DCF axons changing by as much as 190%. Typical approaches for defining anisotropy underestimate the expected load of the stimulation electrode, which led to underestimation of the extent of stimulation. More accurate predictions of the electrode load were achieved with alternative approaches for defining anisotropy. The effects of dielectric dispersion were small compared to the effects of heterogeneity and anisotropy.

SIGNIFICANCE

The results of this study help delineate the level of detail that is required to accurately model electric fields generated by DBS electrodes.

Review: Bioelectrical mechanisms in spinal cord stimulation

OBJECTIVES

The aim of this review is to make specialists in a variety of disciplines familiar with basic aspects of spinal cord stimulation and the role of mathematical modeling in understanding its mechanisms of action and the solution of basic problems.

METHODS

The paper is divided into five sections. The content of each section also covers aspects of various disciplines. Most aspects are presented in an unusual way, likely resulting in new viewpoints and further developments in the growing field of neuromodulation.

RESULTS

A special, integrating role is the mathematical modeling of spinal cord stimulation and the simulation studies of various aspects, such as the stimulation in axial low-back pain.

CONCLUSIONS

In particular the conclusions from several computer simulation studies are relevant and of interest to specialists in many disciplines.

Computational analysis of kilohertz frequency spinal cord stimulation for chronic pain management

BACKGROUND

Kilohertz frequency spinal cord stimulation (KHFSCS) is an emerging therapy for treating refractory neuropathic pain. Although KHFSCS has the potential to improve the lives of patients experiencing debilitating pain, its mechanisms of action are unknown and thus it is difficult to optimize its development. Therefore, the goal of this study was to use a computer model to investigate the direct effects of KHFSCS on specific neural elements of the spinal cord.

METHODS

This computer model consisted of two main components: (1) finite element models of the electric field generated by KHFSCS and (2) multicompartment cable models of axons in the spinal cord. Model analysis permitted systematic investigation into a number of variables (e.g., dorsal cerebrospinal fluid thickness, lead location, fiber collateralization, and fiber size) and their corresponding effects on excitation and conduction block thresholds during KHFSCS.

RESULTS

The results of this study suggest that direct excitation of large-diameter dorsal column or dorsal root fibers require high stimulation amplitudes that are at the upper end or outside of the range used in clinical KHFSCS (i.e., 0.5 to 5 mA). Conduction block was only possible within the clinical range for a thin dorsal cerebrospinal fluid layer.

CONCLUSIONS

These results suggest that clinical KHFSCS may not function through direct activation or conduction block of dorsal column or dorsal root fibers. Although these results should be validated with further studies, the authors propose that additional concepts and/or alternative hypotheses should be considered when examining the pain relief mechanisms of KHFSCS.

Computational Study of Subdural Cortical Stimulation: Effects of Simulating Anisotropic Conductivity on Activation of Cortical Neurons

Subdural cortical stimulation (SuCS) is an appealing method in the treatment of neurological disorders, and computational modeling studies of SuCS have been applied to determine the optimal design for electrotherapy. To achieve a better understanding of computational modeling on the stimulation effects of SuCS, the influence of anisotropic white matter conductivity on the activation of cortical neurons was investigated in a realistic head model. In this paper, we constructed pyramidal neuronal models (layers 3 and 5) that showed primary excitation of the corticospinal tract, and an anatomically realistic head model reflecting complex brain geometry. The anisotropic information was acquired from diffusion tensor magnetic resonance imaging (DT-MRI) and then applied to the white matter at various ratios of anisotropic conductivity. First, we compared the isotropic and anisotropic models; compared to the isotropic model, the anisotropic model showed that neurons were activated in the deeper bank during cathodal stimulation and in the wider crown during anodal stimulation. Second, several popular anisotropic principles were adapted to investigate the effects of variations in anisotropic information. We observed that excitation thresholds varied with anisotropic principles, especially with anodal stimulation. Overall, incorporating anisotropic conductivity into the anatomically realistic head model is critical for accurate estimation of neuronal responses; however, caution should be used in the selection of anisotropic information.

Principles of cord activation during spinal cord stimulation

OBJECTIVES

This study aims to review some of the basic principles of extracellular electrical stimulation used in spinal cord stimulation therapy for intractable pain.

MATERIALS AND METHODS

Spinal cord stimulation has been used therapeutically for more than 40 years. We present the basic principles of extracellular stimulation on which the therapy is based, describe electrode operation and current configurations, and explain the implications of these technological advances for the clinical application of spinal cord stimulation.

RESULTS

Computational studies of coupled electric field and neuron models have significantly advanced our understanding of the therapeutic effects of neurostimulation. Neurostimulation is intended to obtain maximal selectivity of desired neural elements while avoiding those resulting in side-effects. Preferential stimulation of the dorsal columns is achieved with a narrow spacing between electrodes using bipolar or tripolar electrode configurations. Stimulus parameters such as amplitude and pulse width may be used to selectively control which neuronal elements are excited during stimulation.

CONCLUSIONS

A better understanding of the interaction between electric fields and the targeted neural elements may guide the selection of stimulation parameters in contemporary neurostimulators and lead to continuing advances in engineering solutions for therapeutic spinal cord stimulation.

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.

Mechanisms and models of spinal cord stimulation for the treatment of neuropathic pain

Spinal cord stimulation (SCS) is an established and cost-effective therapy for treating severe chronic pain. However, despite over 40 years of clinical practice and the development of novel electrode designs and treatment protocols, increases in clinical success, defined as the proportion of patients that experience 50% or greater self-reported pain relief, have stalled. An incomplete knowledge of the neural circuits and systems underlying chronic pain and the interaction of SCS with these circuits may underlie this plateau in clinical efficacy. This review summarizes prior work and identifies gaps in our knowledge regarding the neural circuits related to pain and SCS in the dorsal horn, supraspinal structures, and the Pain Matrix. In addition, this review discusses and critiques current experimental and computational models used to investigate and optimize SCS. Further research into the interactions between SCS and pain pathways in the nervous system using animal and computational models is a fruitful approach to improve this promising therapy.

Mechanism of dorsal column stimulation to treat neuropathic but not nociceptive pain: analysis with a computational model

OBJECTIVE

Stimulation of axons within the dorsal columns of the human spinal cord has become a widely used therapy to treat refractory neuropathic pain. The mechanisms have yet to be fully elucidated and may even be contrary to standard "gate control theory." Our hypothesis is that a computational model provides a plausible description of the mechanism by which dorsal column stimulation (DCS) inhibits wide dynamic range (WDR) cell output in a neuropathic model but not in a nociceptive pain model.

MATERIALS AND METHODS

We created a computational model of the human spinal cord involving approximately 360,000 individual neurons and dendritic processing of some 60 million synapses--the most elaborate dynamic computational model of the human spinal cord to date. Neuropathic and nociceptive "pain" signals were created by activating topographically isolated regions of excitatory interneurons and high-threshold nociceptive fiber inputs, driving analogous regions of WDR neurons. Dorsal column fiber activity was then added at clinically relevant levels (e.g., Aβ firing rate between 0 and 110 Hz by using a 210-μsec pulse width, 50-150 Hz frequency, at 1-3 V amplitude).

RESULTS

Analysis of the nociceptive pain, neuropathic pain, and modulated circuits shows that, in contradiction to gate control theory, 1) nociceptive and neuropathic pain signaling must be distinct, and 2) DCS neuromodulation predominantly affects the neuropathic signal only, inhibiting centrally sensitized pathological neuron groups and ultimately the WDR pain transmission cells.

CONCLUSION

We offer a different set of necessary premises than gate control theory to explain neuropathic pain inhibition and the relative lack of nociceptive pain inhibition by using retrograde DCS. Hypotheses regarding not only the pain relief mechanisms of DCS were made but also regarding the circuitry of pain itself, both nociceptive and neuropathic. These hypotheses and further use of the model may lead to novel stimulation paradigms.

Current approaches to model extracellular electrical neural microstimulation

Nowadays, high-density microelectrode arrays provide unprecedented possibilities to precisely activate spatially well-controlled central nervous system (CNS) areas. However, this requires optimizing stimulating devices, which in turn requires a good understanding of the effects of microstimulation on cells and tissues. In this context, modeling approaches provide flexible ways to predict the outcome of electrical stimulation in terms of CNS activation. In this paper, we present state-of-the-art modeling methods with sufficient details to allow the reader to rapidly build numerical models of neuronal extracellular microstimulation. These include (1) the computation of the electrical potential field created by the stimulation in the tissue, and (2) the response of a target neuron to this field. Two main approaches are described: First we describe the classical hybrid approach that combines the finite element modeling of the potential field with the calculation of the neuron's response in a cable equation framework (compartmentalized neuron models). Then, we present a “whole finite element” approach allowing the simultaneous calculation of the extracellular and intracellular potentials, by representing the neuronal membrane with a thin-film approximation. This approach was previously introduced in the frame of neural recording, but has never been implemented to determine the effect of extracellular stimulation on the neural response at a sub-compartment level. Here, we show on an example that the latter modeling scheme can reveal important sub-compartment behavior of the neural membrane that cannot be resolved using the hybrid approach. The goal of this paper is also to describe in detail the practical implementation of these methods to allow the reader to easily build new models using standard software packages. These modeling paradigms, depending on the situation, should help build more efficient high-density neural prostheses for CNS rehabilitation.

A computational model for epidural electrical stimulation of spinal sensorimotor circuits

Epidural electrical stimulation (EES) of lumbosacral segments can restore a range of movements after spinal cord injury. However, the mechanisms and neural structures through which EES facilitates movement execution remain unclear. Here, we designed a computational model and performed in vivo experiments to investigate the type of fibers, neurons, and circuits recruited in response to EES. We first developed a realistic finite element computer model of rat lumbosacral segments to identify the currents generated by EES. To evaluate the impact of these currents on sensorimotor circuits, we coupled this model with an anatomically realistic axon-cable model of motoneurons, interneurons, and myelinated afferent fibers for antagonistic ankle muscles. Comparisons between computer simulations and experiments revealed the ability of the model to predict EES-evoked motor responses over multiple intensities and locations. Analysis of the recruited neural structures revealed the lack of direct influence of EES on motoneurons and interneurons. Simulations and pharmacological experiments demonstrated that EES engages spinal circuits trans-synaptically through the recruitment of myelinated afferent fibers. The model also predicted the capacity of spatially distinct EES to modulate side-specific limb movements and, to a lesser extent, extension versus flexion. These predictions were confirmed during standing and walking enabled by EES in spinal rats. These combined results provide a mechanistic framework for the design of spinal neuroprosthetic systems to improve standing and walking after neurological disorders.

Field distribution of epidural electrical stimulation

Epidural electrical stimulation has been applied in clinics for many years. However, there is still a concern about possible injury to spinal nerves. This study investigated electrical field and current density distribution during direct epidural electrical stimulation. Field distribution models were theoretically deduced, while the distribution of potentials and current were analyzed. The current density presented an increase of 70-80%, with one peak value ranging from -85° to 85° between the two stimulated poles. The effect of direct epidural electrical stimulation is mainly on local tissue surrounding the electrodes, concentrated around the two stimulated positions.

Staggered Transverse Tripoles With Quadripolar Lateral Anodes Using Percutaneous and Surgical Leads in Spinal Cord Stimulation

BACKGROUND:

In spinal cord stimulation for low-back pain, the use of electrode arrays with both low-power requirements and selective activation of target dorsal column (DC) fibers is desired. The aligned transverse tripolar lead configuration offers the best DC selectivity. Electrode alignment of the same configuration using 3 parallel percutaneous leads is possible, but compromised by longitudinal migration, resulting in loss of DC selectivity. This loss might be repaired by using the adjacent anodal contacts on the lateral leads.

OBJECTIVE:

To investigate if stimulation using adjacent anodal contacts on the lateral percutaneous leads of a staggered transverse tripole can restore DC selectivity.

METHODS:

Staggered transverse tripoles with quadripolar lateral anodes were modeled on the low-thoracic vertebral region (T10–T12) of the spinal cord using (a) percutaneous lead with staggered quadripolar lateral anodal configuration (PERC QD) and (b) laminotomy lead with staggered quadripolar lateral anodal configuration (LAM QD), of the same contact dimensions. The commercially available LAM 565 surgical lead with 16 widely spaced contacts was also modeled. For comparison with PERC QD, staggered transverse tripoles with dual lateral anodes were modeled by using percutaneous lead with staggered dual lateral anodal configuration (PERC ST).

RESULTS:

The PERC QD improved the depth of DC penetration and enabled selective recruitment of DCs in comparison with PERC ST. Mediolateral selectivity of DCs could not be achieved with the LAM 565.

CONCLUSION:

Stimulation using PERC QD improves anodal shielding of dorsal roots and restores DC selectivity. Based on our modeling study, we hypothesize that, in clinical practice, LAM QD can provide an improved performance compared with the PERC QD. Our model also predicts that the same configuration realized on the commercial LAM 565 surgical lead with widely spaced contacts cannot selectively stimulate DCs essential in treating low-back pain.

A study of electrode placement at the cervical and upper thoracic nerve roots using an anatomic trans-spinal approach

Objective. Since 1996 we have placed temporary catheters at the cervical nerve roots in chronic pain patients for the treatment of radiculopathy and complex regional pain syndrome. We investigated the possibility of placing electrodes both at the cervical spinal nerve and dorsal root ganglion for the purpose of neuromodulation. Methods. Anatomic and technical feasibility studies were performed on 4 human cadavers to examine the placement of electrodes at the cervical nerve roots. We proposed a novel trans-spinal approach to the cervical and upper thoracic nerve roots. We tested various approaches and insertion techniques. We collected radiographic images of the essential steps involved in this technique. Results. Successful placement was accomplished in 3 of the 4 cadavers at the C3, C4, C5, C6, C7, C8, T1, and T2 nerve roots. For placement at C5 to T2, we used a trans-spinal approach entering at the corresponding contralateral interlaminar space. However, due to the anatomy of the cervical nerve roots, vertebral artery, cervical plexus, and occiput, it was necessary to use a different technique for the upper cervical nerve roots. For placement at the C3 and C4 nerve roots, we made the initial insertion between the C1 and C2 lamina using curved needles which were advanced in a caudal direction transversing the median plane of the spine to arrive at the contralateral inter vertebral foramen of either C3 or C4. We were unable to cannulate either C1 or C2 in any of the cadavers. The required equipment included fluoroscopy, contrast dye, directable guide wires, electrodes, and curved needles. Conclusions. In human cadavers, a percutaneous technique was successful in the placement of neurostimulator electrodes at the cervical and upper thoracic nerve roots using a novel trans-spinal approach. New smaller electrode systems that can be placed in a transforaminal position safely may be needed.

Technical performance of percutaneous and laminectomy leads analyzed by modeling

The objective of this study was to compare the technical performance of laminectomy and percutaneous spinal cord stimulation leads with similar contact spacing by computer modeling. Monopolar and tripolar (guarded cathode) stimulation with both lead types in a low-thoracic spine model was simulated using UT-SCS software. Dorsal column and dorsal root fiber thresholds were calculated as well as the area of recruited fibers in the dorsal columns, the rostrocaudal span of recruited dorsal root fibers and the energy consumption at discomfort threshold. Tripolar stimulation is superior to monopolar stimulation in the recruitment of the dorsal columns, a percutaneous lead recruits a ∼12% larger dorsal column area than a laminectomy lead does. This difference is reduced when the contact spacing of the lead models is the same. A percutaneous lead with significant wire impedance (140 Ohms) consumes ∼115-240% more energy, whereas the same lead with negligible wire impedance consumes ∼40-85% more energy. A deterioration of all performance parameters is predicted when a percutaneous lead is placed more dorsally in the epidural tissue. When positioned next to the dura mater, a percutaneous lead has a similar performance (fiber recruitment in the dorsal columns and the dorsal roots) as a laminectomy lead with similar contact spacing, but substantially higher energy consumption. The superior clinical performance of the laminectomy lead is most probably due to the difference in volume and insertion technique of the two lead types.

Technical performance of percutaneous leads for spinal cord stimulation: a modeling study

Objective  To compare the technical performance of different percutaneous lead types for spinal cord stimulation. Methods  Using the ut-scs software (University of Twente's spinal cord stimulation), lead models having similar characteristics such as the 3487A PISCES-Quad (PQ), 3887 PISCES-Quad Compact (PC), 3888 PISCES-Quad Plus (PP) (Medtronic Inc., Minneapolis, MN), and the AB SC2108 (AB) (Advanced Bionics Corp., Valencia, CA) were simulated in monopolar and tripolar (guarded cathode) combinations on a single lead, placed just outside the dorsal dura mater and both centered on the spinal cord midline, and at 1 mm lateral. The influence of displacing a lead dorsally in the epidural fat was examined as well. Finally, dual leads both aligned and offset were modeled. Several parameters were calculated to allow a quantitative comparison of the performances. Results  When programmed as a guarded cathode, the AB lead recruits nerve fibers in an ~25% larger dorsal column area than the PQ. However, the AB has an ~160% higher energy consumption. The performance of the PC is between the AB and PQ, whereas the PP is suitable only for dorsal root stimulation. Displacing a single lead off midline or dorsally decreases its ability to recruit fibers in the dorsal columns. Similarly, dual lead combinations are less capable when compared to single lead centered on the spinal cord midline just outside the dura mater. Conclusions  Complex pain syndromes are treated best with lead having a small contact spacing, being programmed as a tripole (guarded cathode) and centered on the spinal cord midline just outside the dura mater. This is because dorsal column fiber recruitment is more extensive than with any other combinations, including dual leads. Improved recruitment of dorsal column fibers is accompanied by increased energy consumption.

Analysis of spinal cord stimulation and design of epidural electrodes by computer modeling

This paper is an overview of the results of computer modeling of spinal cord stimulation, started ten years ago at the University of Twente, The Netherlands. Results are given of the analysis of various geometrical factors, including spinal anatomy, which influence the effect of spinal cord stimulation on nerve fiber recruitment and paresthesia coverage. In a second phase, the computer model was used for the design of new electrode configurations expected to give a better paresthesia coverage in the management of chronic pain. Two new electrode types are presented: the narrow bi-/tripole and the transverse tripole. The latter also enables adjusting the body area affected with paresthesia by means of a dual channel pulse generator giving simultaneous pulses, thereby limiting surgical interventions for electrode repositioning.

Analysis of induced electrical currents from magnetic field coupling inside implantable neurostimulator leads

Background

Over the last decade, the number of neurostimulator systems implanted in patients has been rapidly growing. Nearly 50, 000 neurostimulators are implanted worldwide annually. The most common type of implantable neurostimulators is indicated for pain relief. At the same time, commercial use of other electromagnetic technologies is expanding, making electromagnetic interference (EMI) of neurostimulator function an issue of concern. Typically reported sources of neurostimulator EMI include security systems, metal detectors and wireless equipment. When near such sources, patients with implanted neurostimulators have reported adverse events such as shock, pain, and increased stimulation. In recent in vitro studies, radio frequency identification (RFID) technology has been shown to inhibit the stimulation pulse of an implantable neurostimulator system during low frequency exposure at close distances. This could potentially be due to induced electrical currents inside the implantable neurostimulator leads that are caused by magnetic field coupling from the low frequency identification system.

Methods

To systematically address the concerns posed by EMI, we developed a test platform to assess the interference from coupled magnetic fields on implantable neurostimulator systems. To measure interference, we recorded the output of one implantable neurostimulator, programmed for best therapy threshold settings, when in close proximity to an operating low frequency RFID emitter. The output contained electrical potentials from the neurostimulator system and those induced by EMI from the RFID emitter. We also recorded the output of the same neurostimulator system programmed for best therapy threshold settings without RFID interference. Using the Spatially Extended Nonlinear Node (SENN) model, we compared threshold factors of spinal cord fiber excitation for both recorded outputs.

Results

The electric current induced by low frequency RFID emitter was not significant to have a noticeable effect on electrical stimulation.

Conclusions

We demonstrated a method for analyzing effects of coupled magnetic field interference on implantable neurostimulator system and its electrodes which could be used by device manufacturers during the design and testing phases of the development process.

Modeling extracellular electrical neural stimulation: from basic understanding to MEA-based applications

Extracellular electrical stimulation of neural networks has been widely used empirically for decades with individual electrodes. Since recently, microtechnology provides advanced systems with high-density microelectrode arrays (MEAs). Taking the most of these devices for fundamental goals or developing neural prosthesis requires a good knowledge of the mechanisms underlying electrical stimulation. Here, we review modeling approaches used to determine (1) the electric potential field created by a stimulation and (2) the response of an excitable cell to an applied field. Computation of the potential field requires solving the Poisson equation. While this can be performed analytically in simple electrode-neuron configurations, numerical models are required for realistic geometries. In these models, special care must be taken to model the potential drop at the electrode/tissue interface using appropriate boundary conditions. The neural response to the field can then be calculated using compartmentalized cell models, by solving a cable equation, the source term of which (called activating function) is proportional to the second derivative of the extracellular field along the neural arborization. Analytical and numerical solutions to this equation are first presented. Then, we discuss the use of approximated solutions to intuitively predict the neuronal response: Either the "activating function" or the "mirror estimate", depending on the pulse duration and the cell space constant. Finally, we address the design of optimal electrode configurations allowing the selective activation of neurons near each stimulation site. This can be achieved using either multipolar configurations, or the "ground surface" configuration, which can be easily integrated in high-density MEAs. Overall, models highlighting the mechanisms of electrical microstimulation and improving stimulating devices should help understanding the influence of extracellular fields on neural elements and developing optimized neural prostheses for rehabilitation.