A multi-scale computational model of the effects of TMS on motor cortex

Circuits in the motor cortex explain oscillatory responses to transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a popular method used to investigate brain function. Stimulation over the motor cortex evokes muscle contractions known as motor evoked potentials (MEPs) and also high-frequency volleys of electrical activity measured in the cervical spinal cord. The physiological mechanisms of these experimentally derived responses remain unclear, but it is thought that the connections between circuits of excitatory and inhibitory neurons play a vital role. Using a spiking neural network model of the motor cortex, we explained the generation of waves of activity, so called 'I-waves', following cortical stimulation. The model reproduces a number of experimentally known responses including direction of TMS, increased inhibition, and changes in strength. Using populations of thousands of neurons in a model of cortical circuitry we showed that the cortex generated transient oscillatory responses without any tuning, and that neuron parameters such as refractory period and delays influenced the pattern and timing of those oscillations. By comparing our network with simpler, previously proposed circuits, we explored the contributions of specific connections and found that recurrent inhibitory connections are vital in producing later waves that significantly impact the production of motor evoked potentials in downstream muscles (Thickbroom, 2011). This model builds on previous work to increase our understanding of how complex circuitry of the cortex is involved in the generation of I-waves.

Multipulse transcranial magnetic stimulation of human motor cortex produces short-latency corticomotor facilitation via two distinct mechanisms

Single-pulse transcranial magnetic stimulation (TMS) of the precentral hand representation (M1_HAND) can elicit indirect waves in the corticospinal tract at a periodicity of ∼660 Hz, called I-waves. These descending volleys are produced by transsynaptic excitation of fast-conducting corticospinal axons in M1_HAND. Paired-pulse TMS can induce short-interval intracortical facilitation (SICF) of motor evoked potentials (MEPs) at interpulse intervals that match I-wave periodicity. This study examined whether short-latency corticospinal facilitation engages additional mechanisms independently of I-wave periodicity. In 19 volunteers, one to four biphasic TMS pulses were applied to left M1_HAND with interpulse intervals adjusted to the first peak or trough of the individual SICF curve at different intensities to probe the intensity-response relationship. Multipulse TMS_HAND at individual peak latency facilitated MEP amplitudes and reduced resting motor threshold (RMT) compared with single pulses. Multipulse TMS_HAND at individual trough latency also produced a consistent facilitation of MEPs and a reduction of RMT. Short-latency facilitation at trough latency was less pronounced, but the relative difference in facilitation decreased with increasing stimulus intensity. Increasing the pulse number had only a modest effect. Two mechanisms underlie short-latency facilitation caused by biphasic multipulse TMS_HAND. One intracortical mechanism is related to I-wave periodicity and engages fast-conducting direct projections to spinal motoneurons. A second corticospinal mechanism does not rely on I-wave rhythmicity and may be mediated by slower-conducting indirect pyramidal tract projections from M1_HAND to spinal interneurons. The latter mechanism deserves more attention in studies of the corticomotor system and its link to manual motor control using the MEP.NEW & NOTEWORTHY TMS pairs evoke SICF at interpulse intervals (IPIs) that match I-wave periodicity. Biphasic bursts with IPIs at the latency of the first peak facilitate MEPs and reduce corticomotor threshold. Bursts at the latency of the first trough facilitate MEPs and reduce corticomotor threshold to a lesser extent. TMS bursts facilitate corticomotor excitability via two mechanisms: SICF-dependently via fast-conducting direct projections from M1_HAND to spinal motoneurons and SICF-independently, probably through slower-conducting indirect pyramidal tract projections.

TMS with fast and accurate electronic control: Measuring the orientation sensitivity of corticomotor pathways

BACKGROUND

Transcranial magnetic stimulation (TMS) coils allow only a slow, mechanical adjustment of the stimulating electric field (E-field) orientation in the cerebral tissue. Fast E-field control is needed to synchronize the stimulation with the ongoing brain activity. Also, empirical models that fully describe the relationship between evoked responses and the stimulus orientation and intensity are still missing.

OBJECTIVE

We aimed to (1) develop a TMS transducer for manipulating the E-field orientation electronically with high accuracy at the neuronally meaningful millisecond-level time scale and (2) devise and validate a physiologically based model describing the orientation selectivity of neuronal excitability.

METHODS

We designed and manufactured a two-coil TMS transducer. The coil windings were computed with a minimum-energy optimization procedure, and the transducer was controlled with our custom-made electronics. The electronic E-field control was verified with a TMS characterizer. The motor evoked potential amplitude and latency of a hand muscle were mapped in 3° steps of the stimulus orientation in 16 healthy subjects for three stimulation intensities. We fitted a logistic model to the motor response amplitude.

RESULTS

The two-coil TMS transducer allows one to manipulate the pulse orientation accurately without manual coil movement. The motor response amplitude followed a logistic function of the stimulus orientation; this dependency was strongly affected by the stimulus intensity.

CONCLUSION

The developed electronic control of the E-field orientation allows exploring new stimulation paradigms and probing neuronal mechanisms. The presented model helps to disentangle the neuronal mechanisms of brain function and guide future non-invasive stimulation protocols.

Multi-scale modeling toolbox for single neuron and subcellular activity under Transcranial Magnetic Stimulation

BACKGROUND

Transcranial Magnetic Stimulation (TMS) is a widely used non-invasive brain stimulation method. However, its mechanism of action and the neural response to TMS are still poorly understood. Multi-scale modeling can complement experimental research to study the subcellular neural effects of TMS. At the macroscopic level, sophisticated numerical models exist to estimate the induced electric fields. However, multi-scale computational modeling approaches to predict TMS cellular and subcellular responses, crucial to understanding TMS plasticity inducing protocols, are not available so far.

OBJECTIVE

We develop an open-source multi-scale toolbox Neuron Modeling for TMS (NeMo-TMS) to address this problem.

METHODS

NeMo-TMS generates accurate neuron models from morphological reconstructions, couples them to the external electric fields induced by TMS, and simulates the cellular and subcellular responses of single-pulse and repetitive TMS.

RESULTS

We provide examples showing some of the capabilities of the toolbox.

CONCLUSION

NeMo-TMS toolbox allows researchers a previously not available level of detail and precision in realistically modeling the physical and physiological effects of TMS.

A probabilistic transcranial magnetic stimulation localization method

Objective.Transcranial magnetic stimulation (TMS) can be used to safely and noninvasively activate brain tissue. However, the characteristic parameters of the neuronal activation have been largely unclear. In this work, we propose a novel neuronal activation model and develop a method to infer its parameters from measured motor evoked potential signals.Approach.The connection between neuronal activation due to an induced electric field and a measured motor threshold is modeled. The posterior distribution of the model parameters are inferred from measurement data using Bayes' formula. The measurements are the active motor thresholds obtained with multiple stimulating coil locations, and the parameters of the model are the location, preferred direction of activation, and threshold electric field value of the activation site. The posterior distribution is sampled using a Markov chain Monte Carlo method. We quantify the plausibility of the model by calculating the marginal likelihood of the measured thresholds. The method is validated with synthetic data and applied to motor threshold measurements from the first dorsal interosseus muscle in five healthy participants.Main results.The method produces a probability distribution for the activation location, from which a minimal volume where the activation occurs with 95% probability can be derived. For eight or nine stimulating coil locations, the smallest such a volume obtained was approximately 100 mm³. The 95% probability volume intersected the pre-central gyral crown and the anterior wall of the central sulcus, and the preferred direction was perpendicular to the central sulcus, both findings being consistent with the literature. Furthermore, it was not possible to rule out if the activation occurred either in the white or grey matter. In one participant, two distinct activations sites were found while others exhibited a unique site.Significance.The method is both generic and robust, and it lays a foundation for a framework that enables accurate analysis and characterization of TMS activation mechanisms.

Mapping of multiple muscles with transcranial magnetic stimulation: absolute and relative test-retest reliability

The spatial accuracy of transcranial magnetic stimulation (TMS) may be as small as a few millimeters. Despite such great potential, navigated TMS (nTMS) mapping is still underused for the assessment of motor plasticity, particularly in clinical settings. Here, we investigate the within-limb somatotopy gradient as well as absolute and relative reliability of three hand muscle cortical representations (MCRs) using a comprehensive grid-based sulcus-informed nTMS motor mapping. We enrolled 22 young healthy male volunteers. Two nTMS mapping sessions were separated by 5-10 days. Motor evoked potentials were obtained from abductor pollicis brevis (APB), abductor digiti minimi, and extensor digitorum communis. In addition to individual MRI-based analysis, we studied normalized MNI MCRs. For the reliability assessment, we calculated intraclass correlation and the smallest detectable change. Our results revealed a somatotopy gradient reflected by APB MCR having the most lateral location. Reliability analysis showed that the commonly used metrics of MCRs, such as areas, volumes, centers of gravity (COGs), and hotspots had a high relative and low absolute reliability for all three muscles. For within-limb TMS somatotopy, the most common metrics such as the shifts between MCR COGs and hotspots had poor relative reliability. However, overlaps between different muscle MCRs were highly reliable. We, thus, provide novel evidence that inter-muscle MCR interaction can be reliably traced using MCR overlaps while shifts between the COGs and hotspots of different MCRs are not suitable for this purpose. Our results have implications for the interpretation of nTMS motor mapping results in healthy subjects and patients with neurological conditions.

A Physical Perspective to the Inductive Function of Myelin-A Missing Piece of Neuroscience

Starting from the inductance in neurons, two physical origins are discussed, which are the coil inductance of myelin and the piezoelectric effect of the cell membrane. The direct evidence of the coil inductance of myelin is the opposite spiraling phenomenon between adjacent myelin sheaths confirmed by previous studies. As for the piezoelectric effect of the cell membrane, which has been well-known in physics, the direct evidence is the mechanical wave accompany with action potential. Therefore, a more complete physical nature of neural signals is provided. In conventional neuroscience, the neural signal is a pure electrical signal. In our new theory, the neural signal is an energy pulse containing electrical, magnetic, and mechanical components. Such a physical understanding of the neural signal and neural systems significantly improve the knowledge of the neurons. On the one hand, we achieve a corrected neural circuit of an inductor-capacitor-capacitor (LCC) form, whose frequency response and electrical characteristics have been validated by previous studies and the modeling fitting of artifacts in our experiments. On the other hand, a number of phenomena observed in neural experiments are explained. In particular, they are the mechanism of magnetic nerve stimulations and ultrasound nerve stimulations, the MRI image contrast issue and Anode Break Excitation. At last, the biological function of myelin is summarized. It is to provide inductance in the process of neural signal, which can enhance the signal speed in peripheral nervous systems and provide frequency modulation function in central nervous systems.

Simulation of transcranial magnetic stimulation in head model with morphologically-realistic cortical neurons

BACKGROUND

Transcranial magnetic stimulation (TMS) enables non-invasive modulation of brain activity with both clinical and research applications, but fundamental questions remain about the neural types and elements TMS activates and how stimulation parameters affect the neural response.

OBJECTIVE

To develop a multi-scale computational model to quantify the effect of TMS parameters on the direct response of individual neurons.

METHODS

We integrated morphologically-realistic neuronal models with TMS-induced electric fields computed in a finite element model of a human head to quantify the cortical response to TMS with several combinations of pulse waveforms and current directions.

RESULTS

TMS activated with lowest intensity intracortical axonal terminations in the superficial gyral crown and lip regions. Layer 5 pyramidal cells had the lowest thresholds, but layer 2/3 pyramidal cells and inhibitory basket cells were also activated at most intensities. Direct activation of layers 1 and 6 was unlikely. Neural activation was largely driven by the field magnitude, rather than the field component normal to the cortical surface. Varying the induced current direction caused a waveform-dependent shift in the activation site and provided a potential mechanism for experimentally observed differences in thresholds and latencies of muscle responses.

CONCLUSIONS

This biophysically-based simulation provides a novel method to elucidate mechanisms and inform parameter selection of TMS and other cortical stimulation modalities. It also serves as a foundation for more detailed network models of the response to TMS, which may include endogenous activity, synaptic connectivity, inputs from intrinsic and extrinsic axonal projections, and corticofugal axons in white matter.

Coupling Magnetically Induced Electric Fields to Neurons: Longitudinal and Transverse Activation

We present a theory and computational models to couple the electric field induced by magnetic stimulation to neuronal membranes. Based on the characteristics of magnetically induced electric fields and the modified cable equation that we developed previously, quasipotentials are derived as a simple and accurate approximation for coupling of the electric fields to neurons. The conventional and modified cable equations are used to simulate magnetic stimulation of long peripheral nerves by circular and figure-8 coils. Activation thresholds are obtained over a range of lateral and vertical coil positions for two nonlinear membrane models representing unmyelinated and myelinated straight axons and also for undulating myelinated axons. For unmyelinated straight axons, the thresholds obtained with the modified cable equation are significantly lower due to transverse polarization, and the spatial distributions of thresholds as a function of coil position differ significantly from predictions by the activating function. However, the activation thresholds of unmyelinated axons obtained with either cable equation are very high and beyond the output capabilities of conventional magnetic stimulators. For myelinated axons, threshold values are similar for both cable equations and within the range of magnetic stimulators. Whereas the transverse field contributes negligibly to the activation thresholds of myelinated fibers, axonal undulation can significantly increase or decrease thresholds depending on coil position. The analysis provides a rigorous theoretical foundation and implementation methods for the use of the cable equation to model neuronal response to magnetically induced electric fields. Experimentally observed stimulation with the electric fields perpendicular to the nerve trunk cannot be explained by transverse polarization and is likely due to nerve fiber undulation and other geometrical inhomogeneities.

Direct Electrical Stimulation in Electrocorticographic Brain-Computer Interfaces: Enabling Technologies for Input to Cortex

Electrocorticographic brain computer interfaces (ECoG-BCIs) offer tremendous opportunities for restoring function in individuals suffering from neurological damage and for advancing basic neuroscience knowledge. ECoG electrodes are already commonly used clinically for monitoring epilepsy and have greater spatial specificity in recording neuronal activity than techniques such as electroencephalography (EEG). Much work to date in the field has focused on using ECoG signals recorded from cortex as control outputs for driving end effectors. An equally important but less explored application of an ECoG-BCI is directing input into cortex using ECoG electrodes for direct electrical stimulation (DES). Combining DES with ECoG recording enables a truly bidirectional BCI, where information is both read from and written to the brain. We discuss the advantages and opportunities, as well as the barriers and challenges presented by using DES in an ECoG-BCI. In this article, we review ECoG electrodes, the physics and physiology of DES, and the use of electrical stimulation of the brain for the clinical treatment of disorders such as epilepsy and Parkinson’s disease. We briefly discuss some of the translational, regulatory, financial, and ethical concerns regarding ECoG-BCIs. Next, we describe the use of ECoG-based DES for providing sensory feedback and for probing and modifying cortical connectivity. We explore future directions, which may draw on invasive animal studies with penetrating and surface electrodes as well as non-invasive stimulation methods such as transcranial magnetic stimulation (TMS). We conclude by describing enabling technologies, such as smaller ECoG electrodes for more precise targeting of cortical areas, signal processing strategies for simultaneous stimulation and recording, and computational modeling and algorithms for tailoring stimulation to each individual brain.

Biophysically realistic neuron models for simulation of cortical stimulation

OBJECTIVE

We implemented computational models of human and rat cortical neurons for simulating the neural response to cortical stimulation with electromagnetic fields.

APPROACH

We adapted model neurons from the library of Blue Brain models to reflect biophysical and geometric properties of both adult rat and human cortical neurons and coupled the model neurons to exogenous electric fields (E-fields). The models included 3D reconstructed axonal and dendritic arbors, experimentally-validated electrophysiological behaviors, and multiple, morphological variants within cell types. Using these models, we characterized the single-cell responses to intracortical microstimulation (ICMS) and uniform E-field with dc as well as pulsed currents.

MAIN RESULTS

The strength-duration and current-distance characteristics of the model neurons to ICMS agreed with published experimental results, as did the subthreshold polarization of cell bodies and axon terminals by uniform dc E-fields. For all forms of stimulation, the lowest threshold elements were terminals of the axon collaterals, and the dependence of threshold and polarization on spatial and temporal stimulation parameters was strongly affected by morphological features of the axonal arbor, including myelination, diameter, and branching.

SIGNIFICANCE

These results provide key insights into the mechanisms of cortical stimulation. The presented models can be used to study various cortical stimulation modalities while incorporating detailed spatial and temporal features of the applied E-field.

The effects of transcranial alternating current stimulation (tACS) at individual alpha peak frequency (iAPF) on motor cortex excitability in young and elderly adults

Transcranial alternating current stimulation (tACS) can modulate brain oscillations, cortical excitability and behaviour. In aging, the decrease in EEG alpha activity (8–12 Hz) in the parieto-occipital and mu rhythm in the motor cortex are correlated with the decline in cognitive and motor functions, respectively. Increasing alpha activity using tACS might therefore improve cognitive and motor function in the elderly. The present study explored the influence of tACS on cortical excitability in young and old healthy adults. We applied tACS at individual alpha peak frequency for 10 min (1.5 mA) to the left motor cortex. Transcranial magnetic stimulation was used to assess the changes in cortical excitability as measured by motor-evoked potentials at rest, before and after stimulation. TACS increased cortical excitability in both groups. However, our results also suggest that the mechanism behind the effects was different, as we observed an increase and decrease in intracortical inhibition in the old group and young group, respectively. Our results indicate that both groups profited similarly from the stimulation. There was no indication that tACS was more effective in conditions of low alpha power, that is, in the elderly.

Multi-Scale Computational Models for Electrical Brain Stimulation

Electrical brain stimulation (EBS) is an appealing method to treat neurological disorders. To achieve optimal stimulation effects and a better understanding of the underlying brain mechanisms, neuroscientists have proposed computational modeling studies for a decade. Recently, multi-scale models that combine a volume conductor head model and multi-compartmental models of cortical neurons have been developed to predict stimulation effects on the macroscopic and microscopic levels more precisely. As the need for better computational models continues to increase, we overview here recent multi-scale modeling studies; we focused on approaches that coupled a simplified or high-resolution volume conductor head model and multi-compartmental models of cortical neurons, and constructed realistic fiber models using diffusion tensor imaging (DTI). Further implications for achieving better precision in estimating cellular responses are discussed.

Morphology controls how hippocampal CA1 pyramidal neuron responds to uniform electric fields: a biophysical modeling study

Responses of different neurons to electric field (EF) are highly variable, which depends on intrinsic properties of cell type. Here we use multi-compartmental biophysical models to investigate how morphologic features affect EF-induced responses in hippocampal CA1 pyramidal neurons. We find that the basic morphologies of neuronal elements, including diameter, length, bend, branch, and axon terminals, are all correlated with somatic depolarization through altering the current sources or sinks created by applied field. Varying them alters the EF threshold for triggering action potentials (APs), and then determines cell sensitivity to suprathreshold field. Introducing excitatory postsynaptic potential increases cell excitability and reduces morphology-dependent EF firing threshold. It is also shown that applying identical subthreshold EF results in distinct polarizations on cell membrane with different realistic morphologies. These findings shed light on the crucial role of morphologies in determining field-induced neural response from the point of view of biophysical models. The predictions are conducive to better understanding the variability in modulatory effects of EF stimulation at the cellular level, which could also aid the interpretations of how applied fields activate central nervous system neurons and affect relevant circuits.

The Effect of a Transcranial Channel as a Skull/Brain Interface in High-Definition Transcranial Direct Current Stimulation-A Computational Study

A transcranial channel is an interface between the skull and brain; it consists of a biocompatible and highly conductive material that helps convey the current induced by transcranial direct current stimulation (tDCS) to the target area. However, it has been proposed only conceptually, and there has been no concrete study of its efficacy. In this work, we conducted a computational investigation of this conceptual transcranial model with high-definition tDCS, inducing focalized neuromodulation to determine whether inclusion of a transcranial channel performs effectively. To do so, we constructed an anatomically realistic head model and compartmental pyramidal neuronal models. We analyzed membrane polarization by extracellular stimulation and found that the inclusion of a transcranial channel induced polarization at the target area 11 times greater than conventional HD-tDCS without the transcranial channel. Furthermore, the stimulation effect of the transcranial channel persisted up to approximately 80%, even when the stimulus electrodes were displaced approximately 5 mm from the target area. We investigated the efficacy of the transcranial channel and found that greatly improved stimulation intensity and focality may be achieved. Thus, the use of these channels may be promising for clinical treatment.

A multi-scale computational model of the effects of TMS on motor cortex

The detailed biophysical mechanisms through which transcranial magnetic stimulation (TMS) activates cortical circuits are still not fully understood. Here we present a multi-scale computational model to describe and explain the activation of different pyramidal cell types in motor cortex due to TMS. Our model determines precise electric fields based on an individual head model derived from magnetic resonance imaging and calculates how these electric fields activate morphologically detailed models of different neuron types. We predict neural activation patterns for different coil orientations consistent with experimental findings. Beyond this, our model allows us to calculate activation thresholds for individual neurons and precise initiation sites of individual action potentials on the neurons’ complex morphologies. Specifically, our model predicts that cortical layer 3 pyramidal neurons are generally easier to stimulate than layer 5 pyramidal neurons, thereby explaining the lower stimulation thresholds observed for I-waves compared to D-waves. It also shows differences in the regions of activated cortical layer 5 and layer 3 pyramidal cells depending on coil orientation. Finally, it predicts that under standard stimulation conditions, action potentials are mostly generated at the axon initial segment of cortical pyramidal cells, with a much less important activation site being the part of a layer 5 pyramidal cell axon where it crosses the boundary between grey matter and white matter. In conclusion, our computational model offers a detailed account of the mechanisms through which TMS activates different cortical pyramidal cell types, paving the way for more targeted application of TMS based on individual brain morphology in clinical and basic research settings.