Elsevier

Clinical Neurophysiology

Volume 132, Issue 2, February 2021, Pages 412-428
Clinical Neurophysiology

Modeling motor-evoked potentials from neural field simulations of transcranial magnetic stimulation

https://doi.org/10.1016/j.clinph.2020.10.032Get rights and content

Highlights

  • A model of motor-evoked potential formation gives a realistic electromyogram in response to TMS.

  • The model reproduces effects of short-interval intracortical inhibition, intracortical facilitation and long-interval intracortical inhibition.

  • A link between existing neural field modeling and realistic outcome measures of TMS is provided.

Abstract

Objective

To develop a population-based biophysical model of motor-evoked potentials (MEPs) following transcranial magnetic stimulation (TMS).

Methods

We combined an existing MEP model with population-based cortical modeling. Layer 2/3 excitatory and inhibitory neural populations, modeled with neural-field theory, are stimulated with TMS and feed layer 5 corticospinal neurons, which also couple directly but weakly to the TMS pulse. The layer 5 output controls mean motoneuron responses, which generate a series of single motor-unit action potentials that are summed to estimate a MEP.

Results

A MEP waveform was generated comparable to those observed experimentally. The model captured TMS phenomena including a sigmoidal input–output curve, common paired pulse effects (short interval intracortical inhibition, intracortical facilitation, long interval intracortical inhibition) including responses to pharmacological interventions, and a cortical silent period. Changes in MEP amplitude following theta burst paradigms were observed including variability in outcome direction.

Conclusions

The model reproduces effects seen in common TMS paradigms.

Significance

The model allows population-based modeling of changes in cortical dynamics due to TMS protocols to be assessed in terms of changes in MEPs, thus allowing a clear comparison between population-based modeling predictions and typical experimental outcome measures.

Introduction

Transcranial Magnetic Stimulation (TMS) is a non-invasive form of brain stimulation used for the study of brain function and for clinical treatments of brain disorders such as depression (Hallett, 2007, Ziemann et al., 2008, Pascual-Leone et al., 2000, Lefaucheur et al., 2014). Applying a single TMS pulse at sufficient intensity over the primary motor cortex results in firing of layer 5 corticospinal neurons due mainly to transsynaptic activation from layer 2/3 interneurons and horizontal fibres, but also direct activation of the neurons by the pulse at high enough intensities (Hallett, 2007, Di Lazzaro et al., 2012). The descending volley of activity gives a measurable motor response in peripheral muscles targeted by the stimulated region, known as a motor-evoked potential (MEP) (Hallett, 2000). MEPs have been widely used as a measure of the excitability of the corticomotor system in TMS studies, and have revealed several well known neural phenomena related to TMS, such as periods of net inhibition and excitation using paired pulse protocols (i.e. short and long interval intracortical inhibition [SICI; LICI], and intracortical facilitation [ICF]) (Valls-Solé et al., 1992, Kujirai et al., 1993), and a cortical silent period observed when TMS is given during a voluntary contraction. Furthermore, MEPs are used to assess changes in cortical excitability resulting from repetitive TMS (rTMS) protocols (Di Lazzaro et al., 2008), which are thought to induce plasticity in cortical circuits through mechanisms similar to long-term potentiation and depression (LTP/D) (Cooke and Bliss, 2006). However, despite nearly 30 years of research, it remains unclear how microscale mechanisms underlying plasticity occurring at synaptic level (e.g. LTP/D) manifest when large populations of neurons are activated as with TMS (Parkin et al., 2015, Matheson et al., 2016).

Biophysically-informed models provide a mathematical description of TMS and other neurostimulation effects that can be used to better understand TMS phenomena (Seo and Jun, 2017, Wilson et al., 2018). Models typically describe biophysical processes with equations. Existing models include descriptions of the shape and timecourse of the magnetic and induced electric fields due to TMS, including realistic human head geometries (Thielscher et al., 2011, Deng et al., 2013, Opitz et al., 2013, Tang et al., 2016, Bungert et al., 2016), large networks of spiking neurons (Esser et al., 2005), detailed descriptions of spiking of single neurons and small networks of neurons (Traub et al., 2003, Rusu et al., 2014, Moezzi et al., 2017), population-based descriptions of neural firing rates (Deco et al., 2008, Pinotsis et al., 2014) and plasticity effects (Fung et al., 2013, Wilson et al., 2016).

Modeling of the processes underlying TMS-induced effects has been undertaken through several stategies (Seo and Jun, 2017, Wilson et al., 2018). Esser et al. (2005) have constructed a low-level model of 33 thousand neurons in the cortex and thalamus with five million synaptic connections. The model demonstrates biologically-plausible spontaneous activity and evoked responses, notably I-waves. More detailed multicompartment models for single neurons or small groups of neurons have also been used, to study bursting phenomena in more detail (Traub et al., 2003). Rusu et al. (2014) used a detailed model of a layer 5 neuron, fed by a small population of layer 2/3 single-compartment cells. The hypothesis is that interactions between layer 2/3 and layer 5 cells are purely feed-forward (no resonance loops or chains of excitatory and inhibitory cells), and a spike generated in the layer 2/3 cells affects the layer 5 cell after a certain time (Triesch et al., 2015). Under this hypothesis, I-waves could be reproduced. However, the mechanism for generation of the I-waves in this model differs from the more conventional view that I-waves are a result of repetitive input to layer 5 cells from a resonanting circuit.

While models of individual neurons have proven useful in capturing TMS-related phenomena, there are several notable limitations. First, the high number of parameters (e.g. values determining receptor conductances, synapse weights, conduction delays etc. for each neuron/synapse) can pose problems in constraining the model, thereby increasing the risk of over-fitting. Second, the complexity of these models often comes with a high computational cost, which greatly increases the time required for simulations. Finally, the models have largely focused on generating corticospinal output which is suitable for capturing I-wave activity, but does not generalise to MEPs measured at peripheral muscles, which is by far the most common experimental method for assessing TMS-evoked activity of the motor system.

While the dynamics of evoked responses in the brain involves highly nonlinear processes, modeling these need not be complicated. Population-based modeling (Deco et al., 2008, Pinotsis et al., 2014), including neural mass or neural field approaches, considers firing rates of populations of cells, rather than detailed dynamics of many individual cells. As such, population-based models have far fewer parameters, and are less computationally expensive than models of individual neurons. Neural field modeling is well suited to TMS because a TMS pulse excites many thousands of neurons over an area of several centimeters-squared. Neural field approaches have been used to model cortical plasticity following repetitive TMS, a lasting change in strengths of connections between neurons (Huang et al., 2011, Fung et al., 2013, Fung and Robinson, 2014, Wilson et al., 2016). In these works, plasticity has been included using rules which capture either phenomenological descriptions of plasticity (e.g. spike timing dependent plasticity), or physiological theories (e.g. calcium dependent plasticity) (Shouval et al., 2002).

Population-based cortical modeling of TMS has been hard to interpret in relation to human experiments. For example, most models have evaluated changes in synaptic weights between excitatory neural populations following rTMS but it remains unclear how these changes would impact the amplitude of MEPs. To address this failing in the existing literature, population based models must be combined with models of the motor system.

Li et al. (2012) have described MEP amplitude and shape in terms of a sum of individual motor unit responses, with thresholds for the motor units distributed exponentially. Such an approach has the benefit of simplicity, with few parameters. However, it describes only the motoneuron response, not the processes that feed it, and misses biophysical detail such as motor unit synchrony. Moezzi et al. (2017) have developed this further; they have used the hypothesis and I-wave model of Rusu et al. (2014) to simulate MEP formation following TMS using a population of layer 2/3 excitatory and inhibitory neurons, feeding layer 5 cortical cells and motoneurons. They reproduced MEP responses that matched closely those measured experimentally; however, this was under similar limitations to other individual neuron models in terms of a large parameter space and high computational cost. In contrast, Goetz et al. (2019) have used a statistical model based on experimental data to compile a MEP model, although this model was not biophysical in the sense that it only modeled the distribution of MEPs, not the biological processes underlying MEP generation.

The aim of this study was to develop an MEP model that can be used alongside a general population-based neural field model of single-pulse, paired-pulse and repetitive TMS, thereby linking population-based model predictions of the effects of TMS with commonly-used experimental outcomes for the first time. To achieve this aim, we have combined the approach of Moezzi et al. (2017) with neural field modeling. Specifically, we model the layer 2/3 and layer 5 populations with population-based dynamics. Firing rates of motoneurons are described as functions of the layer 5 firing rate, and a train of motoneuron firings is reconstructed. Each motounit contributes a motounit action potential (MUAP). Thus MEP activity is determined. This approach provides a much-needed link between population-based models of cortical dynamics, and models of MEP activity, thereby allowing a direct comparison between model outputs and human experiments. To test the generalizability of our MEP model, we first assess whether we can capture well known single and paired-pulse MEP phenomena. We then evaluate how sensitive our MEP model is to changes in synaptic weights predicted by population-based rTMS models of plasticity.

Section snippets

Methods

We have combined a neural field approach (Fung and Robinson, 2014, Wilson et al., 2016) with existing models of MEP formation (Li et al., 2012, Moezzi et al., 2017). The scheme is shown schematically in Fig. 1.

Motor evoked potential at rest

A simulated EMG at rest is shown in Fig. 3 by the black lines. A stimulation intensity of 780 s−1 (120% RMT) has been used with a pulse length of 0.5 ms (Wilson et al., 2016). Broadly, these parameters result in activation of around 39% of neurons, of similar magnitude to the fraction of neurons reported to respond to single TMS in non-human primates (Romero et al., 2019). Part (a) gives a plot of the EMG as a function of time (stimulation is at 0 s); the MEP is indicated. The corresponding

Discussion

We have developed a biophysical model of MEPs following TMS to the motor cortex by combining a population-based model of cortical activity and an individual neuron model of motor output. The model captures many common features of MEPs including input–output characteristics, responses to paired-pulse paradigms, a silent period with voluntary contraction and changes in MEPs following plasticity-inducing TBS paradigms. It provides unique insights into how micro/mesoscale mechanisms, such as

Conclusions

We have demonstrated how a biophysically plausible nonlinear model of MEPs can be combined with the output of a population-based model of cortical neurons in order to produce a description of MEPs due to TMS. The final MEP activity is realistic in terms of variation with intensity and muscle contraction, and demonstrates the known amplitude and interval-dependent effects in paired-pulse stimulation. The MEP model is also sensitive to changes in synaptic weight predicted by a model of

Author statement

MTW constructed the model, carried out most of the modeling, and led the writing of the manuscript. BM provided guidance on the modeling approach. NCR provided experimental background and contributed to the manuscript.

Declaration of Competing Interest

We declare no conflict of interest in this work.

Acknowledgments

NCR is supported by an Australian Research Council DECRA fellowship (DE180100741). We thank Mitchell Goldsworthy for access to the raw data of Goldsworthy et al. (2016).

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