A Model of TMS-induced I-waves in Motor Cortex

Abstract

Background

Transcranial magnetic stimulation (TMS) allows to manipulate neural activity non-invasively, and much research is trying to exploit this ability in clinical and basic research settings. In a standard TMS paradigm, single-pulse stimulation over motor cortex produces repetitive responses in descending motor pathways called I-waves. However, the details of how TMS induces neural activity patterns in cortical circuits to produce these responses remain poorly understood. According to a traditional view, I-waves are due to repetitive synaptic inputs to pyramidal neurons in layer 5 (L5) of motor cortex, but the potential origin of such repetitive inputs is unclear.

Objective/hypothesis

Here we aim to test the plausibility of an alternative mechanism behind D- and I-wave generation through computational modeling. This mechanism relies on the broad distribution of conduction delays of synaptic inputs arriving at different parts of L5 cells' dendritic trees and their spike generation mechanism.

Methods

Our model consists of a detailed L5 pyramidal cell and a population of layer 2 and 3 (L2/3) neurons projecting onto it with synapses exhibiting short-term depression. I-waves are simulated as superpositions of spike trains from a large population of L5 cells.

Results

Our model successfully reproduces all basic characteristics of I-waves observed in epidural responses during in vivo recordings of conscious humans. In addition, it shows how the complex morphology of L5 neurons might play an important role in the generation of I-waves. In the model, later I-waves are formed due to inputs to distal synapses, while earlier ones are driven by synapses closer to the soma. Finally, the model offers an explanation for the inhibition and facilitation effects in paired-pulse stimulation protocols.

Conclusions

In contrast to previous models, which required either neural oscillators or chains of inhibitory interneurons acting upon L5 cells, our model is fully feed-forward without lateral connections or loops. It parsimoniously explains findings from a range of experiments and should be considered as a viable alternative explanation of the generating mechanism of I-waves.

Introduction

Non-invasive brain stimulation techniques such as transcranial magnetic stimulation (TMS) have gained much attention in recent years after promising results in treating several neurological disorders such as depression or stroke [1], [2]. The ability to influence brain activity non-invasively is very appealing, but it has been difficult to establish how exactly TMS activates different types of neurons in cortical circuits. In a standard single-pulse paradigm a TMS coil is placed over the motor cortex. The fluctuating magnetic field induces an electric field, which affects the excitability of central motor pathways and causes a strong depolarization of large neuronal populations. As a result of single-pulse TMS but also single-pulse transcranial electric stimulation (TES), high-frequency (∼600 Hz) descending volleys of activity are observed at electrodes in the epidural space [3], [4], [5], [6]. Early studies [7], [8], [9] using different stimulation types and comparing spike latencies have shown that weak electrical stimuli generated brief single waves. They suggested that such waves originate as a result of direct stimulation of pyramidal tract neurons and therefore these waves were termed D-waves. With strong cortical stimuli the D-wave was usually followed by three or four subsequent waves considered to have an indirect origin and thought to be the result of action potentials (APs) from presynaptic fibers impinging on the dendritic tree of pyramidal tract neurons. They were therefore termed I-waves. In humans, the descending cortical volleys of activity were initially recorded in anaesthetized subjects from the surface of the spinal cord during surgery. More recently, they have been recorded in conscious subjects with no central nervous system (CNS) abnormality who had spinal cord electrodes implanted for the treatment of chronic pain. Such opportunities are uncommon and thus the effects of TMS are usually studied by using needle electromyography (EMG) recordings or by observing limb movements. However, such recordings give little insight into the effects of magnetic stimulation on populations of cortical neurons. Several theories regarding the mechanism responsible for the generation of I-waves have been proposed, but none of them has gained widespread acceptance [7], [10], [11]. In one of the proposed models, TMS causes the activation of a large pool of cortical cells that fire according to their intrinsic membrane properties and act as a resonating circuit that directly activates layer 5 (L5) cells. Such a model however has been argued to require a second, indirect activation of layer 2 and 3 (L2/3) cells. In another proposed model, TMS activates chains of inhibitory and excitatory neurons providing waves of activation and inhibition to L5. It is unclear, however, what the anatomical basis for such hypothesized chains should be. Here we aim to test the plausibility of an alternative mechanism behind D- and I-wave generation through computational modeling that relies on the broad distribution of conduction delays of synaptic inputs arriving at different parts of L5 cells' dendritic trees and their spike generation mechanism. We constructed a model consisting of a morphologically detailed L5 cell stimulated by a pool of L2/3 excitatory and inhibitory cells in a 4:1 ratio [12] (Fig. 1). These cells project uniformly onto the basal and apical dendrites of the L5 cell. Ion channel kinetics were modeled using a modified Hodgkin–Huxley formalism [13], while neurotransmission is mediated by excitatory voltage-independent and voltage-dependent channels together with inhibitory channels (see Methods section). The model offers a viable explanation of the generation of D- and I-waves and accounts for their frequency and timing. According to the model, the generation of I-waves is the product of intrinsic and extrinsic factors. Synchronous volleys of excitatory and inhibitory post-synaptic potentials (EPSPs and IPSPs) from L2/3 cells interact on the complex dendritic tree of the L5 cell. In response, the L5 cell's spiking mechanism generates brief trains of action potentials at typical I-wave frequencies. We explore how the anatomical details of L5 cells play an important role in I-wave generation. Specifically, we show how by removing distal dendritic branches later I-waves are abolished. Thus, our model is consistent with the claim that individual I-waves have different generating mechanisms with early and late I-waves being supported by distinct pathways [9], [14]. As shown in the following, our model reproduces findings from a range of experiments including pharmacological or behavioral modulation of I-waves and facilitation and inhibition effects observed in paired-pulse stimulation protocols. Overall, we find that the proposed model is a viable and parsimonious alternative to previous attempts to explain the mechanisms behind D- and I-wave generation.