Proceedings of 20 121CME International Conference on Complex Medical Engineering

July I - 4, Kobe, Japan

Models of cortico-basal ganglia circuits and synaptic plasticity for transcranial magnetic stimulation

Yu-yang Yen, Lee-ray Chen, Institute of Systems Neuroscience,

National Tsing Hua University,

Hsinchu City, Taiwan, R.O.C.

Ying-zu Huang, Department of Neurology,

Chang-Gung Memorial Hospital,

Linkou, Taiwan, R.O.C.

Chung-Chuan Lo * Institute of Systems Neuroscience,

National Tsing Hua University,

Hsinchu City, Taiwan, R.O.C.

Abstract- Transcranial magnetic simulations (TMS) is an

effective tool for studying pathophysiology of dystonia as well as

various other movement or cognitive functions of the brain. To

study how TMS induces complex neuronal responses and

plasticity, we built computational models for primary motor

cortex, basal ganglia and synaptic plasticity. Our models have

successfully reproduced neuronal responses to TMS,

corresponding neural plasticity induced by a number of

repetitive TMS protocols and different signal pathways in basal

ganglia. With integration of the three models into a unified large­

scale model (work in progress), we will be able to provide insights

into neuronal mechanisms underlying the effectiveness of TMS

and pathophysiology of dystonia.

Index Terms- TMS, rTMS, TBS, dystonia, basal ganglia, motor cortex, synaptic plasticity

I. INTRODUCTION

Dystonia is a neurological movement disorder characterized by abnormal postures of the affected body part. A large number of studies of dystonia showed a widespread reduction in the excitability of inhibitory circuits in the motor system and an increase in the responsiveness of motor cortex to transcranial magnetic simulations (TMS) that targets synaptic plasticity [1], [2]. TMS has been used to probe pathophysiology of dystonia as well as to give a temporary relief of its symptoms. However, the underlying neuronal mechanism of the effects of TMS in dystonia is still not clear. To address the issue, we built computational models of neural circuits using detailed single neuron and synapse models with an aim to reproduce the neuronal responses of normal subjects and patients with dystonia to TMS.

The present study consists of three parts. The first part involves in building a neural circuit model of motor cortex, where TMS is typically applied. The model is based on Esser et al. 2005 [3].

In addition to cortical circuit dynamics, synaptic plasticity is also believed to contribute in the complex neuronal responses to TMS. We had previously published a phenomenological model [4] describing how theta-burst TMS (i.e. TBS) pulses change the intracellular calcium concentration [Ca

2+] and how the time course of [Ca

2+] produces synaptic

plasticity. In the second part of the present study, we went on to extend the model by implementing a calcium-dependent plasticity model (CaDP) [5], which includes detailed calcium dynamics at the cellular and molecular levels. We further

included a model of pre-synaptic short-term plasticity and showed that it plays a crucial role in reproducing complex pattern of neuronal plasticity induced by various repetitive TMS protocols.

In addition to cortical abnormality, basal ganglia had also been reported as an important brain structure involved in dystonia [6-9]. The major input structure, striatum, contains two subtypes of medium spiny neurons (MSNs) which are defined by the type of the dopamine receptor (D 1 or D2) expressed on the cell membrane. DI MSNs project to substantia nigra pars reticulate (SNr) and form a "direct" pathway. When DI MSNs are activated, they directly inhibit SNr which in turn disinhibits thalamus. D2 MSNs innervate external globus pallidas (GPe), which inhibits SNr. The MSNs -> GPe -> SNr projection is called the "indirect" pathway because D2 MSNs indirectly modulate SNr through GPe. Opposite to the direct pathway, an increased activity in D2 MSNs causes an elevated activity in SNr neurons. A number of motor disorders including dystonia are associated with the malfunction of dopamine homeostasis or unbalanced direct/indirect pathways. In the present study, we tested our model by simulating the response of basal ganglia and thalamus when a motor signal is delivered from the motor cortex to both DI and D2 MSNs in striatum with and without the presence of dopamine.

II. METHODS

A. Simulation Environment

The neural circuit models were developed using Neural Simulation Tool (NEST) [10]. The simulator is compiled and configured in official standard setup with Python2.6 as pyNEST package in Ubuntu 10.04 LTS; OpenMP was used for parallel computing. We used the HT neuron model [3] provided in NEST as our single neuron model.

B. Cortical Neural Network Model

The network model (Fig. I) and the single neuron model were developed based on a previous cortical model for single­pulse TMS [3]. The primary motor cortical network consists of three cortical layers: L2/3, L5 and L6. Ll and L6 layers are not modeled because they are relatively thin and neurons are sparse comparing to the other layers. In addition to the primary motor cortex, the network also contains a reticular nucleus and a

This work is supported by NHRl grant NHRI-EX99-99 13EC and NSC grant 98-23 1 1-8-007 -005-MY3. * To whom correspondence should be addressed. Dr. Chung-Chuan Lo, e-mail: cclo@mx.nthu.edu.tw; phone: +886-3-57420 14

978-1-4673-1618-7112/$31.00 ©2012 IEEE 96

Pallid as (external)

Figure I. A schematics of the corti co-basal ganglia-thalamocortical network. In the present study we separately modeled the thalamocortical networks, the basal ganglia networks and the detailed synaptic plasticity to address different aspects of the neuronal effects of TMS. With combination of the three compoenets (work in progress), the integrated model will be able to provide insights into the pathophysiology of dystonia

motor thalamus module. The cortical layers receive background noise as well as inputs from reticular nucleus and motor thalamus. In the simulated network, we set the smallest structure as the topographic element which consists of one inhibitory neuron and two excitatory neurons. A patch of 5x5 topographic elements forms a slice in a cortical column. A cortical column is formed by three vertically aligned slices, which correspond to three cortical layers. Neurons form synaptic connections with neighboring neurons with probability following a Gaussian distribution. Reduced from the cortical network model in Esser et al. 2005 [3], our model contains only 2x2 cortical columns while still being able to produce observed cortical and epidural response (Fig. 2) to single TMS pulse. The reduced model enables us to simulate network activities under various stimulation protocols for minutes or longer with a reasonable computational time.

C. Synaptic Plasticity at Cellular and Molecular Level

The pre-synaptic short-term plasticity model was developed based on Hempel et al. 2000 [11], which modeled vesicle depletion and generation at the pre-synaptic terminal due to spike inputs. Synaptic efficiency at the pre-synaptic terminal is determined by facilitation factor Fstp and depression factor Dstp:

(1)

where go is the maximum synaptic weight. Fstp increases by a small amount upon each spike input but decays to 0 slowly when no spike event occurs. Dstp, on the other hand, decreases by a small amount for each spike input and recovers to 1 when there is no spike. In our model, the short-term plasticity changes excitatory post-synaptic potentials, thus in turn affects the calcium dynamics which involves in the spike-timing dependent plasticity.

The model of calcium dependent plasticity was developed based on Rubin et at. 2005 [5]. The model detects the time course of [Ca

2+] at three levels: high (> 4IlM), moderate

97

(2.6�0.6IlM) and low « 0.61lM). The potentiation factor P serves as the high calcium concentration detector and it is activated when [Ca2+] goes around or above 41lM. The depression factor D serves as the moderate [Ca

2+] detector

when the calcium concentration stays in the moderate level for a long enough time. From the molecular biology point of view, P factor simulates long term potentiation (L TP) induced by high [Ca2+], including the weak influence of protein phosphatase 1 (PPl) on calmodulin-dependent protein kinase II (CaMKII) [12]. Meanwhile, D factor simulates long-term depression (LTD) induced by moderate [Ca

2+] with an

inhibition on phosphoprotein phosphatase 1 (PPl) by protein kinase A (PKA). Finally, the P factor and the D factor together determine the change of synaptic strength W described by

W'(P,D) = ( aw _ P. W)/r 1 + exp((P - p)/kp) 1 + exp((D - dJ/kd) • (2)

We note that Equation 2 describes the post-synaptic weight change. The total synaptic weight (Wsyn) is calculated by combining the presynaptic and postsynaptic weights:

Wsyn = goFs,pl)s,p(Wo + W(P, D)) (3)

where Wo is the baseline weight at the postsynaptic site.

D. Neural Circuit Model of Basal Ganglia

The basal ganglia model we built focused on simulating detailed spiking activity and plasticity. The model consists of all major structures of basal ganglia except for substantia nigra pars compacta (SNc) because in the study we do not need the detailed activity of dopaminergic neurons which locate in SNc. The effects of Dl or D2 activation on MSNs are very complex [13] and here we focused on their effects on the excitability of MSNs. When Dl receptors are activated by dopamine, they make Dl MSNs more excitable; hence facilitate the cortico­striatal information transmission. In contrast, when D2 receptors are activated, they reduce the excitability of D2 MSNs which suppress the cortico-striatal information transmission.

E. rTMS & TBS Simulating Patterns

A single TMS pulse is simulated by injecting a short pulse of direct current to 25% of randomly selected pre-synaptic terminals in the cortical network. In the present study we modeled several TMS protocol:

• 1 Hz rTMS (repetitive TMS) - One stimulus is given in every 1000 ms for a total of 150 stimuli, which produce a LTD-like effect. The protocol is modified from [14].

• 6 Hz rTMS - six stimuli are given in every 1000 ms for a total of 150 stimuli, which produce a LTP-like effect. The protocol is modified from [15].

• Intermittently theta-burst TMS (iTBS) - A 2-sec train of 3-pulse 50Hz bursts given every 200 ms repeated

every 10 seconds for 20 cycles (600 pulses in total). The protocol produces a LTP-like effect.

• Intermediate TBS (imTBS) - A 5-sec train of 3-pulse 50Hz bursts given every 200 ms repeated every 15 seconds for 8 cycles (600 pulses in total). The protocol produces no-significant plasticity change.

• Continuously TBS (cTBS) - A 40 sec uninterrupted train of 3-pulse 50Hz bursts (600 pulses in total). This produces a LTD-like effect.

III. RESULTS

A. Single-Pulse TMS Response on Cortical Model

Previous studies [16], [17] showed that a single TMS pulse produces several recordable indirect waves (I-waves). We successfully reproduced the I-waves induced by TMS in our cortical model (Fig. 2). The thick lines in Fig. 2 indicate the average membrane potentials in the corresponding cortical layers. The red thick line of layer 5 excitatory neuron represents signal output from motor cortex, i.e. epidural recorded signals. The color contour plots indicate the membrane potential (color) of 100 neurons in corresponding cortical layers. Red indicates a higher membrane potential while blue indicates a lower membrane potential. Vertical black lines mark the onset time of the TMS pulse.

B. Activation of Motor Pathways in Basal Ganglia Model

Our simulations showed that with a high level of dopamine, Dl MSNs are strongly activated but D2 MSNs are not. The activated direct pathway inhibits SNr but activates thalamus (Tp) (Fig. 3 right column). This results in an excitatory input to motor cortex, or a "Go" event. In contrast, with a reduced level of dopamine, D2 MSNs are strongly activated but DI MSNs are not. This activates the indirect pathway and increases the activity of SNr which in turn inhibits thalamus. As a consequence, the cortico-striatal input does not reach motor cortex and forms a "No Go" event (Fig. 3 left colwnn).

C. Short-Term Depression Model

We tested our model of short-term plasticity using a single spike and a transient high frequency spike train input (Fig. 4). A single pre-synaptic spike produces an excitatory post­synaptic potential (EPSP) of �5mV while w ith the transient spike train input (60 Hz for 400 ms), the EPSP decreases (below 4m V). The result indicates that the post-synaptic neuron receives less and less neuron transmitter due to rapid spiking induced vesicle depletion.

The pre-synaptic calcium level in Fig. 4 affects the synaptic facilitation. With a high frequency spike input, Dstp decreases to a small value rapidly which dominants the weight change. After a 3000ms recovery period without spike input, Dstp recovers. The remaining calcium level raises F stp and increases the weight, therefore creates an EPSP with full amplitude.

98

-80 Membrane Potential (mV) -35 Figure 2. Simulated neural responses to a single TMS pulse in layer 2/3,

layer 5 and thalamus. Each of the color contour plots show the activity (membrane potential) of 100 neurons as functions of time. Curves above each contour plot indicate the population averaged membrane potential. The black vertical lines marke the onset time of the single TMS pulse.

DIMSN

D2MSN

GPe

GPi/SNr -----

Thalamus

I �� DIMSN

I: j D2MSN

rs:: ::;;J GPi/SNr

l � Thalamus

..... Dopamine neuron activated

- Dopamine neuron deactivated

Figure 3. Activation (firing rate) of direct (right column) and indirect (left column) pathways in the basal ganglia circuit.

-60rnV Post-synaptic

Membrane

Potential -66rnV 20rnV Pre-synaptic

Membrane

Potential -60rnV 2.5 Pre-synaptic

Calcium

level (11M)

1.0 lCf pstPT

Pstp & Dstp j U

"p

0.0 Time (ms) 1000 2000 3000 4000

Figure 4. Short-Term synaptic plasticity. A high frequency spike train input produces less and less post-synaptic responses. After a short (-3000ms) recovery period, a single spike input elicits a strong post-synaptic response again.

D. Plasticities induced by different rTMS protocols

Previous studies [14-16] showed that a stimulus frequency above 5 Hz are (called high frequency rTMS) tends to induce synaptic facilitation; while a frequency less than 5 Hz (low frequency rTMS) tends to depress synapses.

By combining pre-synaptic short-term plasticity and post­synaptic long-term plasticity, we were able to reproduce synaptic weight changes (Fig. 5) that are consistent with reported plasticity with different rTMS frequencies.

E. Plasticities induced by different TBS protocols

The combined plasticity model can further explain the TBS induced plasticity which the traditional STDP model could not explain. We modeled three TBS paradigms which induce three different patterns of plasticity respectively (Fig 6).

Consistent with observations, iTBS induces LTP, imTBS does not produce a significant weight change, and cTBS depresses synapses. Our result showed that there is a short initial depression followed by a facilitation of synaptic weight in all three protocols. The initial depression is caused by vesicle depletion, and the later facilitation is induced by the raised calcium level. After the initial depression and the later facilitation, the weight changes start to develop different patterns between the three TBS protocols. In iTBS and imTBS simulations, the weight is mainly determined by the calcium dependent plasticity. The calcium level in iTBS trials repeatedly rises before it decays to a certain level which induces significant depression. While the imTBS trials have sufficient interval between stimuli to induce depression which compensates the potentiation, result in an unchanged synaptic weight in terms of large time scale. In cTBS, the presynaptic neuron fires with short inter-spike intervals, and depletes vesicles. This causes pre-synaptic depression and decreases the amount of neuron transmitter being released. As a consequence, the post-synaptic calcium level only maintains at the mid-low range, which induces post-synaptic depression.

Post-synaptic

Membrane

Potential

Pre-synaptic

Membrane

Potential

iTBS 30.0 L--69 . 2 -

::: IIII IIII

22.6 -68.8 --

Low frequency (1 Hz) rTMS �:�����tiC -631 � 11111111IIIII Potential -66.9

:��:,�' .] IIIIIIIIIIIIII W.Ohl }=mmmnnnmmm Calcium Level (11M) Time(s)

6.0 3.0 0.0 IJJJJ.JJJJJ.JJi

5 10

High frequency (6 Hz) rTMS

2.6 _____ 2 .0 .../.------------------------------1 .• 6.0 3.0 �\_/IIIIII,\U_""II'II/IIIIIIM 0.0 '--_______ _

5 10 Figure 5. rTMS-induced plasticity in single neuron model. Low frequency

rTMS produces synaptic depression while high frequency rTMS facilitates synapses ..

IV. CONCLUSIONS

Neural plasticity is a central aspect of the effects of TMS as it provides the potential to probe and further to treat neurological movement disorders. By combining pre-synaptic short-term and post-synaptic long-term plasticity, we have built a model of synaptic plasticity. The novel approach enables us to reproduce the diverse pattern of plasticity induced by several TMS paradigms, including rTMS with a high or low frequency (Fig. 5), iTBS, imTBS, and cTBS (Fig. 6).

In addition to the model of synaptic plasticity, we have built a primary motor cortex network with detailed layers and column structures. Under the stimulation of single-pUlse TMS, the model exhibits neuronal responses resembling I-waves reported in various studies (Fig. 2). We are working on integrating the plasticity model with the cortical network model with an aim to reproduce the realistic neuronal responses to various TMS protocols. Furthermore, we will add

imTBS cTBS

L -M_' __ .UIIIIIillIm -66.9 30.0 ---- -69.2 1lIlIllJlllllJlllllJllllillWillWlJJIJIJlJJIJIJWJlJJUllliUllllllJJJ

Weight ::f�nmmmmu : t�

1.4 1.4

'OM Calcium � Level hiM) 3.0 0.0 5 10

6.0

15 10 Time (second)

25 0.0 '-----"5 ---�1"0-------Figure 6. TBS-induced synaptic plasticity. iTBS produces strong but brief calcium elevations which induce synaptic facilitation. cTBS produces tonic

calcium elevation at a medium level which depresses synapses. imTBS procudes a calcium time course in between iTBS and cTBS and hence produces no synaptic change.

99

the presented basal ganglia model into the integrated neural system which will help us to study the circuit mechanism and pathogenesis of dystonia as well as other movement disorders that involve basal ganglia.

ACKNOWLEDGMENT

Y.-Y. Y. and L.-R. C. thank Mr. Wen-Wei Liao and Mr. Yen-Nan Lin for their help in python programming.

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