Evaluating the impact of the deep brain stimulation induced electric field on subthalamic neurons: A computational modelling study

Local neuroanatomical and tract-based proxies of optimal subcallosal cingulate deep brain stimulation

BACKGROUND

Deep brain stimulation of the subcallosal cingulate area (SCC-DBS) is a promising neuromodulatory therapy for treatment-resistant depression (TRD). Biomarkers of optimal target engagement are needed to guide surgical targeting and stimulation parameter selection and to reduce variance in clinical outcome.

OBJECTIVE/HYPOTHESIS

We aimed to characterize the relationship between stimulation location, white matter tract engagement, and clinical outcome in a large (n = 60) TRD cohort treated with SCC-DBS. A smaller cohort (n = 22) of SCC-DBS patients with differing primary indications (bipolar disorder/anorexia nervosa) was utilized as an out-of-sample validation cohort.

METHODS

Volumes of tissue activated (VTAs) were constructed in standard space using high-resolution structural MRI and individual stimulation parameters. VTA-based probabilistic stimulation maps (PSMs) were generated to elucidate voxelwise spatial patterns of efficacious stimulation. A whole-brain tractogram derived from Human Connectome Project diffusion-weighted MRI data was seeded with VTA pairs, and white matter streamlines whose overlap with VTAs related to outcome ('discriminative' streamlines; Puncorrected < 0.05) were identified using t-tests. Linear modelling was used to interrogate the potential clinical relevance of VTA overlap with specific structures.

RESULTS

PSMs varied by hemisphere: high-value left-sided voxels were located more anterosuperiorly and squarely in the lateral white matter, while the equivalent right-sided voxels fell more posteroinferiorly and involved a greater proportion of grey matter. Positive discriminative streamlines localized to the bilateral (but primarily left) cingulum bundle, forceps minor/rostrum of corpus callosum, and bilateral uncinate fasciculus. Conversely, negative discriminative streamlines mostly belonged to the right cingulum bundle and bilateral uncinate fasciculus. The best performing linear model, which utilized information about VTA volume overlap with each of the positive discriminative streamline bundles as well as the negative discriminative elements of the right cingulum bundle, explained significant variance in clinical improvement in the primary TRD cohort (R = 0.46, P < 0.001) and survived repeated 10-fold cross-validation (R = 0.50, P = 0.040). This model was also able to predict outcome in the out-of-sample validation cohort (R = 0.43, P = 0.047).

CONCLUSION(S)

These findings reinforce prior indications of the importance of white matter engagement to SCC-DBS treatment success while providing new insights that could inform surgical targeting and stimulation parameter selection decisions.

Toward a cerebello-thalamo-cortical computational model of spinocerebellar ataxia

Computational neural network modelling is an emerging approach for optimization of drug treatment of neurological disorders and fine-tuning of rehabilitation strategies. In the current study, we constructed a cerebello-thalamo-cortical computational neural network model to simulate a mouse model of cerebellar ataxia (pcd^5J mice) by manipulating cerebellar bursts through reduction of GABAergic inhibitory input. Cerebellar output neurons were projected to the thalamus and bidirectionally connected with the cortical network. Our results showed that reduction of inhibitory input in the cerebellum orchestrated the cortical local field potential (LFP) dynamics to generate specific motor outputs of oscillations of the theta, alpha, and beta bands in the computational model as well as in mouse motor cortical neurons. The therapeutic potential of deep brain stimulation (DBS) was tested in the computational model by increasing the sensory input to restore cortical output. Ataxia mice showed normalization of the motor cortex LFP after cerebellum DBS. We provide a novel approach to computational modelling to investigate the effect of DBS by mimicking cerebellar ataxia involving degeneration of Purkinje cells. Simulated neural activity coincides with findings from neural recordings of ataxia mice. Our computational model could thus represent cerebellar pathologies and provide insight into how to improve disease symptoms by restoring neuronal electrophysiological properties using DBS.

Structuro-functional surrogates of response to subcallosal cingulate deep brain stimulation for depression

Subcallosal cingulate deep brain stimulation (SCC-DBS) produces long-term clinical improvement in approximately half of patients with severe treatment-resistant depression (TRD). We hypothesized that both structural and functional brain attributes may be important in determining responsiveness to this therapy. In a TRD SCC-DBS cohort, we retrospectively examined baseline and longitudinal differences in MRI-derived brain volume (n = 65) and 18F-fluorodeoxyglucose-PET glucose metabolism (n = 21) between responders and non-responders. Support-vector machines (SVMs) were subsequently trained to classify patients' response status based on extracted baseline imaging features. A machine learning model incorporating pre-operative frontopolar, precentral/frontal opercular, and orbitofrontal local volume values classified binary response status (12 months) with 83% accuracy (leave-one-out cross-validation (LOOCV): 80% accuracy) and explained 32% of the variance in continuous clinical improvement. It was also predictive in an out-of-sample SCC-DBS cohort (n = 21) with differing primary indications (bipolar disorder/anorexia nervosa) (76% accuracy). Adding pre-operative glucose metabolism information from rostral anterior cingulate cortex and temporal pole improved model performance, enabling it to predict response status in the TRD cohort with 86% accuracy (LOOCV: 81% accuracy) and explain 67% of clinical variance. Response-related patterns of metabolic and structural post-DBS change were also observed, especially in anterior cingulate cortex and neighbouring white matter. Areas where responders differed from non-responders - both at baseline and longitudinally - largely overlapped with depression-implicated white matter tracts, namely uncinate fasciculus, cingulum bundle, and forceps minor/rostrum of corpus callosum. The extent of patient-specific engagement of these same tracts (according to electrode location and stimulation parameters) also served as a predictor of TRD response status (72% accuracy; LOOCV: 70% accuracy) and augmented performance of the volume-based (88% accuracy; LOOCV: 82% accuracy) and combined volume/metabolism-based SVMs (100% accuracy; LOOCV: 94% accuracy). Taken together, these results indicate that responders and non-responders to SCC-DBS exhibit differences in brain volume and metabolism, both pre- and post-surgery. Baseline imaging features moreover predict response to treatment (particularly when combined with information about local tract engagement) and could inform future patient selection and other clinical decisions.

Probabilistic Mapping of Deep Brain Stimulation: Insights from 15 Years of Therapy

Deep brain stimulation (DBS) depends on precise delivery of electrical current to target tissues. However, the specific brain structures responsible for best outcome are still debated. We applied probabilistic stimulation mapping to a retrospective, multidisorder DBS dataset assembled over 15 years at our institution (n_total = 482 patients; n_{Parkinson disease} = 303; n_dystonia = 64; n_tremor = 39; n_{treatment-resistant depression/anorexia nervosa} = 76) to identify the neuroanatomical substrates of optimal clinical response. Using high-resolution structural magnetic resonance imaging and activation volume modeling, probabilistic stimulation maps (PSMs) that delineated areas of above-mean and below-mean response for each patient cohort were generated and defined in terms of their relationships with surrounding anatomical structures. Our results show that overlap between PSMs and individual patients' activation volumes can serve as a guide to predict clinical outcomes, but that this is not the sole determinant of response. In the future, individualized models that incorporate advancements in mapping techniques with patient-specific clinical variables will likely contribute to the optimization of DBS target selection and improved outcomes for patients. ANN NEUROL 2021;89:426-443.

Closed-Loop Implantable Therapeutic Neuromodulation Systems Based on Neurochemical Monitoring

Closed-loop or intelligent neuromodulation allows adjustable, personalized neuromodulation which usually incorporates the recording of a biomarker, followed by implementation of an algorithm which decides the timing (when?) and strength (how much?) of stimulation. Closed-loop neuromodulation has been shown to have greater benefits compared to open-loop neuromodulation, particularly for therapeutic applications such as pharmacoresistant epilepsy, movement disorders and potentially for psychological disorders such as depression or drug addiction. However, an important aspect of the technique is selection of an appropriate, preferably neural biomarker. Neurochemical sensing can provide high resolution biomarker monitoring for various neurological disorders as well as offer deeper insight into neurological mechanisms. The chemicals of interest being measured, could be ions such as potassium (K⁺), sodium (Na⁺), calcium (Ca²⁺), chloride (Cl⁻), hydrogen (H⁺) or neurotransmitters such as dopamine, serotonin and glutamate. This review focusses on the different building blocks necessary for a neurochemical, closed-loop neuromodulation system including biomarkers, sensors and data processing algorithms. Furthermore, it also highlights the merits and drawbacks of using this biomarker modality.

A Network Model of Local Field Potential Activity in Essential Tremor and the Impact of Deep Brain Stimulation

Essential tremor (ET), a movement disorder characterised by an uncontrollable shaking of the affected body part, is often professed to be the most common movement disorder, affecting up to one percent of adults over 40 years of age. The precise cause of ET is unknown, however pathological oscillations of a network of a number of brain regions are implicated in leading to the disorder. Deep brain stimulation (DBS) is a clinical therapy used to alleviate the symptoms of a number of movement disorders. DBS involves the surgical implantation of electrodes into specific nuclei in the brain. For ET the targeted region is the ventralis intermedius (Vim) nucleus of the thalamus. Though DBS is effective for treating ET, the mechanism through which the therapeutic effect is obtained is not understood. To elucidate the mechanism underlying the pathological network activity and the effect of DBS on such activity, we take a computational modelling approach combined with electrophysiological data. The pathological brain activity was recorded intra-operatively via implanted DBS electrodes, whilst simultaneously recording muscle activity of the affected limbs. We modelled the network hypothesised to underlie ET using the Wilson-Cowan approach. The modelled network exhibited oscillatory behaviour within the tremor frequency range, as did our electrophysiological data. By applying a DBS-like input we suppressed these oscillations. This study shows that the dynamics of the ET network support oscillations at the tremor frequency and the application of a DBS-like input disrupts this activity, which could be one mechanism underlying the therapeutic benefit.

Essential tremor (ET) is acknowledged to be the most common movement disorder affecting 1% of the population. Although the underlying mechanisms remain elusive, the thalamus, cortex and cerebellum are implicated in the underlying pathology. More recently, it has been shown that ET can be successfully treated by deep brain stimulation (DBS). This clinical treatment involves the surgical implantation of electrodes into the brain, through which current is applied. However, the mechanisms of how DBS achieves clinical benefit continue to be debated. A key question is whether ET can be modeled as a pathological network behavior as has been suggested previously. If so, we can then ask how DBS would modulate this brain activity. Our study combines: (i) simultaneous electrophysiological recordings from the brain and muscle; (ii) computational modelling; (iii) mathematical analysis. We found that the network supports oscillations in the tremor range, and the application of high frequency DBS switches this to low amplitude, high-frequency activity. We propose that our model can be used to predict DBS parameter settings that suppress pathological network activity and consequently tremor. In summary, we provide the first population level model of essential tremor including the effect of DBS on network behaviour.

Electrode Position and Current Amplitude Modulate Impulsivity after Subthalamic Stimulation in Parkinsons Disease-A Computational Study

Background: Subthalamic Nucleus Deep Brain Stimulation (STN-DBS) is highly effective in alleviating motor symptoms of Parkinson's disease (PD) which are not optimally controlled by dopamine replacement therapy. Clinical studies and reports suggest that STN-DBS may result in increased impulsivity and de novo impulse control disorders (ICD).

Objective/Hypothesis: We aimed to compare performance on a decision making task, the Iowa Gambling Task (IGT), in healthy conditions (HC), untreated and medically-treated PD conditions with and without STN stimulation. We hypothesized that the position of electrode and stimulation current modulate impulsivity after STN-DBS.

Methods: We built a computational spiking network model of basal ganglia (BG) and compared the model's STN output with STN activity in PD. Reinforcement learning methodology was applied to simulate IGT performance under various conditions of dopaminergic and STN stimulation where IGT total and bin scores were compared among various conditions.

Results: The computational model reproduced neural activity observed in normal and PD conditions. Untreated and medically-treated PD conditions had lower total IGT scores (higher impulsivity) compared to HC (P < 0.0001). The electrode position that happens to selectively stimulate the part of the STN corresponding to an advantageous panel on IGT resulted in de-selection of that panel and worsening of performance (P < 0.0001). Supratherapeutic stimulation amplitudes also worsened IGT performance (P < 0.001).

Conclusion(s): In our computational model, STN stimulation led to impulsive decision making in IGT in PD condition. Electrode position and stimulation current influenced impulsivity which may explain the variable effects of STN-DBS reported in patients.

Innovations in deep brain stimulation methodology

Deep brain stimulation is a powerful clinical method for movement disorders that no longer respond satisfactorily to pharmacological management, but its progress has been hampered by stagnation in technological procedure solutions and device development. Recently, the combined research efforts of bioengineers, neuroscientists, and clinicians have helped to better understand the mechanisms of deep brain stimulation, and solutions for the translational roadblock are emerging. Here, we define the needs for methodological advances in deep brain stimulation from a neurophysiological perspective and describe technological solutions that are currently evaluated for near-term clinical application. © 2016 International Parkinson and Movement Disorder Society.

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

Theoretical Optimization of Stimulation Strategies for a Directionally Segmented Deep Brain Stimulation Electrode Array

Programming deep brain stimulation (DBS) systems currently involves a clinician manually sweeping through a range of stimulus parameter settings to identify the setting that delivers the most robust therapy for a patient. With the advent of DBS arrays with a higher number and density of electrodes, this trial and error process becomes unmanageable in a clinical setting. This study developed a computationally efficient, model-based algorithm to estimate an electrode configuration that will most strongly activate tissue within a volume of interest. The cerebellar-receiving area of motor thalamus, the target for treating essential tremor with DBS, was rendered from imaging data and discretized into grid points aligned in approximate afferent and efferent axonal pathway orientations. A finite-element model (FEM) was constructed to simulate the volumetric tissue voltage during DBS. We leveraged the principle of voltage superposition to formulate a convex optimization-based approach to maximize activating function (AF) values at each grid point (via three different criteria), hence increasing the overall probability of action potential initiation and neuronal entrainment within the target volume. For both efferent and afferent pathways, this approach achieved global optima within several seconds. The optimal electrode configuration and resulting AF values differed across each optimization criteria and between axonal orientations. This approach only required a set of FEM simulations equal to the number of DBS array electrodes, and could readily accommodate anisotropic-inhomogeneous tissue conductances or other axonal orientations. The algorithm provides an efficient, flexible determination of optimal electrode configurations for programming DBS arrays.

A programmable high-voltage compliance neural stimulator for deep brain stimulation in vivo

Deep brain stimulation (DBS) is one of the most effective therapies for movement and other disorders. The DBS neurosurgical procedure involves the implantation of a DBS device and a battery-operated neurotransmitter, which delivers electrical impulses to treatment targets through implanted electrodes. The DBS modulates the neuronal activities in the brain nucleus for improving physiological responses as long as an electric discharge above the stimulation threshold can be achieved. In an effort to improve the performance of an implanted DBS device, the device size, implementation cost, and power efficiency are among the most important DBS device design aspects. This study aims to present preliminary research results of an efficient stimulator, with emphasis on conversion efficiency. The prototype stimulator features high-voltage compliance, implemented with only a standard semiconductor process, without the use of extra masks in the foundry through our proposed circuit structure. The results of animal experiments, including evaluation of evoked responses induced by thalamic electrical stimuli with our fabricated chip, were shown to demonstrate the proof of concept of our design.

Effects of antidromic and orthodromic activation of STN afferent axons during DBS in Parkinson's disease: a simulation study

Recent studies suggest that subthalamic nucleus (STN)-Deep Brain Stimulation (DBS) may exert at least part of its therapeutic effect through the antidromic suppression of pathological oscillations in the cortex in 6-OHDA treated rats and in parkinsonian patients. STN-DBS may also activate STN neurons by initiating action potential propagation in the orthodromic direction, similarly resulting in suppression of pathological oscillations in the STN. While experimental studies have provided strong evidence in support of antidromic stimulation of cortical neurons, it is difficult to separate relative contributions of antidromic and orthodromic effects of STN-DBS. The aim of this computational study was to examine the effects of antidromic and orthodromic activation on neural firing patterns and beta-band (13-30 Hz) oscillations in the STN and cortex during DBS of STN afferent axons projecting from the cortex. High frequency antidromic stimulation alone effectively suppressed simulated beta activity in both the cortex and STN-globus pallidus externa (GPe) network. High frequency orthodromic stimulation similarly suppressed beta activity within the STN and GPe through the direct stimulation of STN neurons driven by DBS at the same frequency as the stimulus. The combined effect of both antidromic and orthodromic stimulation modulated cortical activity antidromically while simultaneously orthodromically driving STN neurons. While high frequency DBS reduced STN beta-band power, low frequency stimulation resulted in resonant effects, increasing beta-band activity, consistent with previous experimental observations. The simulation results indicate effective suppression of simulated oscillatory activity through both antidromic stimulation of cortical neurons and direct orthodromic stimulation of STN neurons. The results of the study agree with experimental recordings of STN and cortical neurons in rats and support the therapeutic potential of stimulation of cortical neurons.

Reversing the polarity of bipolar stimulation in deep brain stimulation for essential tremor: a theoretical explanation for a useful clinical intervention

The quadripolar electrodes used for deep brain stimulation are designed to give flexibility in contact configuration, optimize therapeutic effect, and minimize side-effects. A patient with essential tremor did not tolerate a bipolar setting due to the emergence of a pulling sensation in her face. However, when the polarity of the contacts was reversed, a 70% higher voltage was tolerated. Using an electric field model, we predicted that this effect was due to the proximity of the topmost contact to the internal capsule. Post-operative imaging supported this prediction. These results demonstrate how a multi-disciplinary approach allows us to optimize parameter settings.

Artificial neural network based characterization of the volume of tissue activated during deep brain stimulation

OBJECTIVE

Clinical deep brain stimulation (DBS) systems can be programmed with thousands of different stimulation parameter combinations (e.g. electrode contact(s), voltage, pulse width, frequency). Our goal was to develop novel computational tools to characterize the effects of stimulation parameter adjustment for DBS.

APPROACH

The volume of tissue activated (VTA) represents a metric used to estimate the spatial extent of DBS for a given parameter setting. Traditional methods for calculating the VTA rely on activation function (AF)-based approaches and tend to overestimate the neural response when stimulation is applied through multiple electrode contacts. Therefore, we created a new method for VTA calculation that relied on artificial neural networks (ANNs).

MAIN RESULTS

The ANN-based predictor provides more accurate descriptions of the spatial spread of activation compared to AF-based approaches for monopolar stimulation. In addition, the ANN was able to accurately estimate the VTA in response to multi-contact electrode configurations.

SIGNIFICANCE

The ANN-based approach may represent a useful method for fast computation of the VTA in situations with limited computational resources, such as a clinical DBS programming application on a tablet computer.

Spatiotemporal visualization of deep brain stimulation-induced effects in the subthalamic nucleus

Deep brain stimulation (DBS) is a successful surgical therapy used to treat the disabling symptoms of movement disorders such as Parkinson's disease. It involves the chronic stimulation of disorder-specific nuclei. However, the mechanisms that lead to clinical improvements remain unclear. Consequently, this slows the optimization of present-day DBS therapy and hinders its future development and application. We used a computational model to calculate the distribution of electric potential induced by DBS and study the effect of stimulation on the spiking activity of a subthalamic nucleus (STN) projection neuron. We previously showed that such a model can reveal detailed spatial effects of stimulation in the vicinity of the electrode. However, this multi-compartmental STN neuron model can fire in either a burst or tonic mode and, in this study, we hypothesized that the firing mode of the cell will have a major impact on the DBS-induced effects. Our simulations showed that the bursting model exhibits behaviour observed in studies of high-frequency stimulation of STN neurons, such as the presence of a silent period at stimulation offset and frequency-dependent stimulation effects. We validated the model by simulating the clinical parameter settings used for a Parkinsonian patient and showed, in a patient-specific anatomical model, that the region of affected tissue is consistent with clinical observations of the optimal DBS site. Our results demonstrated a method of quantitatively assessing neuronal changes induced by DBS, to maximize therapeutic benefit and minimize unwanted side effects.

Simulation of cortico-basal ganglia oscillations and their suppression by closed loop deep brain stimulation

A new model of deep brain stimulation (DBS) is presented that integrates volume conduction effects with a neural model of pathological beta-band oscillations in the cortico-basal ganglia network. The model is used to test the clinical hypothesis that closed-loop control of the amplitude of DBS may be possible, based on the average rectified value of beta-band oscillations in the local field potential. Simulation of closed-loop high-frequency DBS was shown to yield energy savings, with the magnitude of the energy saved dependent on the strength of coupling between the subthalamic nucleus and the remainder of the cortico-basal ganglia network. When closed-loop DBS was applied to a strongly coupled cortico-basal ganglia network, the stimulation energy delivered over a 480 s period was reduced by up to 42%. Greater energy reductions were observed for weakly coupled networks, as the stimulation amplitude reduced to zero once the initial desynchronization had occurred. The results provide support for the application of closed-loop high-frequency DBS based on electrophysiological biomarkers.

Explaining clinical effects of deep brain stimulation through simplified target-specific modeling of the volume of activated tissue

BACKGROUND AND PURPOSE

Although progress has been made in understanding the optimal anatomic structures as target areas for DBS, little effort has been put into modeling and predicting electromagnetic field properties of activated DBS electrodes and understanding their interactions with the adjacent tissue. Currently, DBS is performed with the patient awake to assess the effectiveness and the side effect spectrum of stimulation. This study was designed to create a robust and rather simple numeric and visual tool that provides sufficient and practical relevant information to visualize the patient's individual VAT.

MATERIALS AND METHODS

Multivariate polynomial fitting of previously obtained data from a finite-element model, based on a similar DBS system, was used. The model estimates VAT as a first-approximation sphere around the active DBS contact, using stimulation voltages and individual tissue-electrode impedances. Validation uses data from 2 patients with PD by MR imaging, DTI, fiber tractography, and postoperative CT data.

RESULTS

Our model can predict VAT for impedances between 500 and 2000 Ω with stimulation voltages up to 10 V. It is based on assumptions for monopolar DBS. Evaluation of 2 DBS cases showed a convincing correspondence between predicted VAT and neurologic (side) effects (internal capsule activation).

CONCLUSIONS

Stimulation effects during DBS can be readily explained with this simple VAT model. Its implementation in daily clinical routine might help in understanding the types of tissues activated during DBS. This technique might have the potential to facilitate DBS implantations with the patient under general anesthesia while yielding acceptable clinical effectiveness.

Effect of dispersive conductivity and permittivity in volume conductor models of deep brain stimulation

The aim of this study was to examine the effect of dispersive tissue properties on the volume-conducted voltage waveforms and volume of tissue activated during deep brain stimulation. Inhomogeneous finite-element models were developed, incorporating a distributed dispersive electrode-tissue interface and encapsulation tissue of high and low conductivity, under both current-controlled and voltage-controlled stimulation. The models were used to assess the accuracy of capacitive models, where material properties were estimated at a single frequency, with respect to the full dispersive models. The effect of incorporating dispersion in the electrical conductivity and relative permittivity was found to depend on both the applied stimulus and the encapsulation tissue surrounding the electrode. Under current-controlled stimulation, and during voltage-controlled stimulation when the electrode was surrounded by high-resistivity encapsulation tissue, the dispersive material properties of the tissue were found to influence the voltage waveform in the tissue, indicated by RMS errors between the capacitive and dispersive models of 20%-38% at short pulse durations. When the dispersive model was approximated by a capacitive model, the accuracy of estimates of the volume of tissue activated was very sensitive to the frequency at which material properties were estimated. When material properties at 1 kHz were used, the error in the volume of tissue activated by capacitive approximations was reduced to -4.33% and 11.10%, respectively, for current-controlled and voltage-controlled stimulations, with higher errors observed when higher or lower frequencies were used.