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Mechanism of neural interference by transcranial magnetic stimulation: network or single neuron?
Mechanism of neural interference
by transcranial magnetic stimulation:
network or single neuron?
Yoichi Miyawaki
RIKEN Brain Science Institute
Wako, Saitama 351-0198, JAPAN
yoichi miyawaki@brain.riken.jp
Masato Okada
RIKEN Brain Science Institute
PRESTO, JST
Wako, Saitama 351-0198, JAPAN
okada@brain.riken.jp
Abstract
This paper proposes neural mechanisms of transcranial magnetic stim-
ulation (TMS). TMS can stimulate the brain non-invasively through a
brief magnetic pulse delivered by a coil placed on the scalp, interfering
with specic cortical functions with a high temporal resolution. Due to
these advantages, TMS has been a popular experimental tool in various
neuroscience elds. However, the neural mechanisms underlying TMS-
induced interference are still unknown; a theoretical basis for TMS has
not been developed. This paper provides computational evidence that in-
hibitory interactions in a neural population, not an isolated single neuron,
play a critical role in yielding the neural interference induced by TMS.
1
Introduction
Transcranial magnetic stimulation (TMS) is an experimental tool for stimulating neurons
via brief magnetic pulses delivered by a coil placed on the scalp. TMS can non-invasively
interfere with neural functions related to a target cortical area with high temporal accuracy.
Because of these unique and powerful features, TMS has been popular in various elds,
including cognitive neuroscience and clinical application. However, despite its utility, the
mechanisms of how TMS stimulates neurons and interferes with neural functions are still
unknown. Although several studies have modeled spike initiation and inhibition with a
brief magnetic pulse imposed on an isolated single neuron [1][2], it is rather more plausible
to assume that a large number of neurons are stimulated massively and simultaneously
because the spatial extent of the induced magnetic eld under the coil is large enough for
this to happen.
In this paper, we computationally analyze TMS-induced effects both on a neural population
level and on a single neuron level. Firstly, we demonstrate that the dynamics of a simple
excitatory-inhibitory balanced network well explains the temporal properties of visual per-
cept suppression induced by a single pulse TMS. Secondly, we demonstrate that sustained
inhibitory effect by a subthreshold TMS is reproduced by the network model, but not by an
isolated single neuron model. Finally, we propose plausible neural mechanisms underlying
TMS-induced interference with coordinated neural activities in the cortical network. Figure 1: A) The network architecture. TMS was delivered to all neurons uniformly
and simultaneously. B) The bistability in the network. The afferent input consisted of
a suprathreshold transient and subthreshold sustained component leads the network into
the bistable regime. The parameters used here are
= 0.1, = 0.25, J
0
= 73, J
2
=
110, and T = 1.
2
Methods
2.1
TMS on neural population
2.1.1
Network model for feature selectivity
We employed a simple excitatory-inhibitory balanced network model that is well analyzed
as a model for a sensory feature detector system [3] (Fig. 1A): m
d
dt m(, t)
= m(, t) + g[h(, t)]
(1)
h
(, t) = 2
2
d
J ( )m( , t) + h
ext
(, t)
(2)
J
( ) = J
0
+ J
2
cos 2( )
(3)
h
ext
(, t) = c(t)[1 + cos 2(
0
)]
(4)
Here, m
(, t) is the activity of neuron and
m
is the microscopic characteristic time
analogous to the membrane time constant of a neuron (Here we set
m
= 10 ms). g
[h] is a
quasi-linear output function,
g
[h] =
0
(h < T ) (h T ) (T h < T + 1/)
1
(h T + 1/)
(5)
where T is the threshold of the neuron, is the gain factor, and h
(, t) is the input to neuron
. For simplicity, we assume that m
(, t) has a periodic boundary condition (/2
/
2), and the connections of each neuron are limited to this periodic range. 0
is a stimulus feature to be detected, and the afferent input, h
ext
(, t), has its maximal
amplitude c
(t) at =
0
. We assume a static visual stimulus so that
0
is constant during
the stimulation (Hereafter we set
0
= 0). is an afferent tuning coefcient, describing
how the afferent input to the target population has already been localized around
0
(0
1/2).
The synaptic weight from neuron to , J
( ), consists of the uniform inhibition
J
0
and a feature-specic interaction J
2
. J
0
increases an effective threshold and regulates
the whole network activity through all-to-all inhibition. J
2
facilitates neurons neighboring
in the feature space and suppresses distant ones through a cosine-type connection weight. Through these recurrent interactions, the activity prole of the network evolves and sharp-
ens after the afferent stimulus onset.
The most intuitive and widely accepted example representable by this model is the orienta-
tion tuning function of the primary visual cortex [3][4][5]. Assuming that the coded feature
is the orientation of a stimulus, we can regard as a neuron responding to angle , h
ext
as
an input from the lateral geniculate nucleus (LGN), and J as a recurrent interaction in the
primary visual cortex (V1).
Because the synaptic weight and afferent input have only the 0th and 2nd Fourier compo-
nents, the network state can be fully described by the two order parameters m
0
and m
2
,
which are 0th- and 2nd-order Fourier coefcients of m
(, t). The macroscopic dynamics
of the network is thus derived by Fourier transformation of m
(, t), m
d
dt m
0
(t) = m
0
(t) + 2
2
d
g[h(, t)]
(6) m
d
dt m
2
(t) = m
2
(t) + 2
2
d
g[h(, t)] cos 2
(7)
where m
0
(t) represents the mean activity of the entire network and m
2
(t) represents the
degree of modulation of the activity prole of the network. h
(, t) is also described by the
order parameter,
h
(, t) = J
0
m
0
(t) + c(t)(1 ) + ( c(t) + J
2
m
2
(t)) cos 2
(8)
Substituting Eq.8 into Eq.6 and 7, the network dynamics can be calculated numerically.
2.1.2
TMS induction
We assumed that the TMS perturbation would be constant for all neurons in the network
because the spatial extent of the neural population that we were dealing with is small com-
pared with the spatial gradient of the induced electric eld. Thus we modied the input
function as
h
(, t) = h(, t) + I
TMS
(t). Eq.6 to 8 were also modied accordingly by re-
placing h with
h. Here we employ a simple rectangular input (amplitude: I
TMS
, duration:
D
TMS
) as a TMS-like perturbation (see the middle graph of Fig. 2A).
2.1.3
Bistability and afferent input model
TMS applied to the occipital area after visual stimulus presentation typically suppresses its
visual percept [6][7][8]. To determine whether the network model produces suppression
similar to the experimental data, we applied a TMS-like perturbation at various timings
after the afferent onset and examined whether the nal state was suppressed or not. For this
purpose, the network must hold two equilibria for the same afferent input condition and
reach one of them depending on the specic timing and intensity of TMS. We thus chose
proper sets of , J
0
, and J
2
that operated the network in the non-linear regime. In addition,
we employed an afferent input model consisting of suprathreshold transient (amplitude:
A
t
> T , duration: D
t
) and subthreshold sustained (amplitude: A
s
< T ) components (see
the bottom graph of Fig. 2A). This is the simplest input model to lead the network into
the bistable range (Fig. 1B), yet it still captures the common properties of neural signals in
brain areas such as the LGN and visual cortex.
2.2
TMS on single neuron
2.2.1
Compartment model of cortical neuron
We also examined the effect of TMS on an isolated single neuron by using a compartment
model of a neocortical neuron analyzed by Mainen and Sejnowski [9]. The model included
Figure 2: A) The time course of the order parameters, the perturbation, and the afferent in-
put. B) The network state in the order parameters plane. The network bifurcates depending
on the induction timing of the perturbation and converges to either of the attractors. Two
examples of TMS induction timing (10 and 20 ms after the afferent onset) are shown here.
The dotted lines indicate the control condition without the perturbation in both graphs.
the following membrane ion channels: a low density of Na
+
channels in soma and den-
drites and a high density in the axon hillock and the initial segment, fast K
+
channels in
soma but not in dendrites, slow calcium- and voltage-dependent K
+
channels in soma and
dendrites, and high-threshold Ca
2+
channels in soma and dendrites. We examined several
types of cellular morphology as Mainens report but excluded axonal compartments in or-
der to evaluate the effect of induced current only from dendritic arborization. We injected a
constant somatic current and o