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ORIGINAL RESEARCH
published: 08 August 2017
doi: 10.3389/fncom.2017.00073
Frontiers in Computational Neuroscience | www.frontiersin.org 1August 2017 | Volume 11 | Article 73
Edited by:
Ehud Kaplan,
Icahn School of Medicine at Mount
Sinai, United States
Reviewed by:
James B. Fallon,
Bionics Institute, Australia
Jun Ma,
Lanzhou University of Technology,
China
*Correspondence:
Miad Faezipour
mfaezipo@ bridgeport.edu
Received: 17 May 2017
Accepted: 25 July 2017
Published: 08 August 2017
Citation:
Daneshzand M, Faezipour M and
Barkana BD (2017) Computational
Stimulation of the Basal Ganglia
Neurons with Cost Effective Delayed
Gaussian Waveforms.
Front. Comput. Neurosci. 11:73.
doi: 10.3389/fncom.2017.00073
Computational Stimulation of the
Basal Ganglia Neurons with Cost
Effective Delayed Gaussian
Waveforms
Mohammad Daneshzand 1, Miad Faezipour 1*and Buket D. Barkana 2
1D-BEST Lab, Departments of Computer Science and Engineering and Biomedical Engineering, University of Bridgeport,
Bridgeport, CT, United States, 2Department of Electrical Engineering, University of Bridgeport, Bridgeport, CT, United States
Deep brain stimulation (DBS) has compelling results in the desynchronization of the
basal ganglia neuronal activities and thus, is used in treating the motor symptoms of
Parkinson’s disease (PD). Accurate definition of DBS waveform parameters could avert
tissue or electrode damage, increase the neuronal activity and reduce energy cost which
will prolong the battery life, hence avoiding device replacement surgeries. This study
considers the use of a charge balanced Gaussian waveform pattern as a method to
disrupt the firing patterns of neuronal cell activity. A computational model was created
to simulate ganglia cells and their interactions with thalamic neurons. From the model,
we investigated the effects of modified DBS pulse shapes and proposed a delay period
between the cathodic and anodic parts of the charge balanced Gaussian waveform to
desynchronize the firing patterns of the GPe and GPi cells. The results of the proposed
Gaussian waveform with delay outperformed that of rectangular DBS waveforms used
in in-vivo experiments. The Gaussian Delay Gaussian (GDG) waveforms achieved lower
number of misses in eliciting action potential while having a lower amplitude and shorter
length of delay compared to numerous different pulse shapes. The amount of energy
consumed in the basal ganglia network due to GDG waveforms was dropped by 22%
in comparison with charge balanced Gaussian waveforms without any delay between
the cathodic and anodic parts and was also 60% lower than a rectangular charged
balanced pulse with a delay between the cathodic and anodic parts of the waveform.
Furthermore, by defining a Synchronization Level metric, we observed that the GDG
waveform was able to reduce the synchronization of GPi neurons more effectively than
any other waveform. The promising results of GDG waveforms in terms of eliciting
action potential, desynchronization of the basal ganglia neurons and reduction of energy
consumption can potentially enhance the performance of DBS devices.
Keywords: deep brain stimulation, Parkinson’s Disease, basal ganglia network, energy efficiency, neuronal
activity, Gaussian waveform with delay, synchronization level
Daneshzand et al. Computational Stimulation of the Basal Ganglia
INTRODUCTION
Parkinson’s disease is associated with a complex variation
in neuronal spiking patterns in the basal ganglia such as
more observed burst and oscillatory patterns (Levy et al.,
2000). Experimental recordings of patients with Parkinson’s
disease (PD) show an increase in burst firing patterns and
synchronization in the Sub Thalamic Nucleus (STN) and Globus
Pallidus inturnus (GPi) while a decrease in the firing rate
of Globus Pallidus externus (GPe; Bergman et al., 1994; Nini
et al., 1995; Wichmann et al., 1999). This synchronization
happening in the beta range might be a source to intensify
motor symptoms of PD (Brown, 2007; Rivlin-Etzion et al.,
2010). In order to explain the original oscillation in PD,
two hypotheses have been proposed in retrospective studies.
The first one is based on in-vitro recordings of the STN-
GPe network and suggests that low frequency oscillation is
due to the reciprocally connected STN-GPe network behaving
as a pacemaker (Reck et al., 2009). The second hypothesis
claims that the abnormal correlated burst firing pattern is
due to dopamine depletion of presynaptic neurons, which
increases the effect of GABAergic transmission from GPe to STN
(Baufreton and Mark, 2008). Researchers suggest that irregular
firing in the basal ganglia neurons, characterizing neurological
disorder such as PD, may arise locally and then propagate
throughout the brain. But the underlying mechanism remains
unclear. Tang et al. (2016) constructed a minimal neuron-
astrocyte network model by connecting a neurons chain and an
astrocytes chain to investigate the local propagation of abnormal
firings.
Neuromodulation is a fast growing field of study focusing
on methods of interfering with neuronal activity. Electrical
stimulation such as Deep Brain Stimulation (DBS) influences
a wide variety of mechanisms at neuronal and system level
(Deniau et al., 2010). Parameter configuration of DBS differs from
patient to patient and requires experimental and computational
models for obtaining a decent efficiency (St George et al.,
2010). DBS disrupts the oscillatory activity of cells within the
basal ganglia (Tass, 2003; Modolo et al., 2008). The previous
hypotheses about the mechanism of DBS were based on the
idea of regularizing pathological activity through entrainment
and synaptic modifications (Rubin and Terman, 2004; Dorval
et al., 2010), while recent studies elucidated that DBS on STN
causes complex changes in the firing rate of efferent structures
(Humphries and Gurney, 2012).
Experimental studies investigated the effect of DBS on the
single cell level (Hashimoto et al., 2003), but there are vast
unknown information that can be extracted from neural network
activity and its reaction to stimulation. There are several
existing neural mass models aiming to understand ambiguities
of DBS in the network level (So et al., 2012; Summerson et al.,
2015). Terman et al. (2002) focused on synaptic interaction
between STN and GPe to describe and compare normal and
PD conditions. Along all the computational models used in
retrospective studies, we used a modified version of the basal
ganglia network (So et al., 2012) to investigate the effect of DBS
parameters.
The neuronal electrical activities depend on a periodical force
current or high frequency periodic DBS signals (Lv and Ma,
2016; Lv et al., 2016). High frequency DBS (more than 100 Hz)
has more therapeutic effect than low frequency stimulations,
and this effect would increase if pulses are given at a specific
phase (McConnell et al., 2012). Efficient stimulus waveforms
must be able to elicit action potentials that subsequently lead
to the release of neurotransmitters while minimizing the side
effects such as tissue damage, charge injection decrease, and
increase in energy consumption (Lilly et al., 1955; Sahin and
Tie, 2007; Jezernik et al., 2010). Recent stimulators have used
charge balanced waveforms with short duration, high amplitude
followed by long duration, low amplitude pulses. One of the
optimal DBS waveforms which decreases energy consumption is
an exponentially growing pulse by Jezernik and Manfred (2005).
Wongsarnpigoon and Grill (2010) found a Gaussian waveform
using the genetic algorithm to be the most optimal waveform.
Most of the implanted stimulators generate a high frequency
pulse train (Coffey, 2009). In order to have a charge balanced
efficient stimulus pulse for PD, these pulses should have the
amplitude around 3 V and a frequency of 130 Hz (Moro et al.,
2002). A prolonged delay between the two parts of the charge
balanced stimulation pulse improves activation of the resting
neurons while entrainment of the bursting neurons (Hofmann
et al., 2011).
In this work, we investigated the effect of this delay on more
energy efficient waveforms in a biologically detailed network of
the basal ganglia neurons. Optimized waveforms could prolong
battery life, reduce the frequency of recharge intervals and reduce
the cost and risk of battery replacement surgeries. The main
contributions of this research can be listed below.
1. A combinational DBS waveform with a delay between the
anodic and cathodic phases is proposed.
2. This modification of the DBS waveform allows for less energy
consumption by the stimulus pulse train along with the
reduction of the number of times that DBS waveform fails to
elicit an action potential.
3. Experimental results show that this new DBS waveform can
activate the basal ganglia neurons with lower amplitude and
shorter duration of delay compared to previously used DBS
signals such as rectangular pulses.
4. This new waveform modification also improves the synchrony
of DBS pulses with firing of the basal ganglia neurons; i.e., it
was able to elicit an action potential on the applied neuron
with almost every pulse of the DBS signal.
5. Thorough analytic study of the desynchronization of the basal
ganglia cells under PD condition has been carried out.
MATERIALS AND METHODS
With the aid of differential equations, mathematical cell models
provide an insight through synaptic and injected currents such
as DBS and also regarding how these external currents affect the
membrane voltage of cells. In addition, these models can be used
to test the effects of DBS waveforms on neuronal firing patterns.
Frontiers in Computational Neuroscience | www.frontiersin.org 2August 2017 | Volume 11 | Article 73
Daneshzand et al. Computational Stimulation of the Basal Ganglia
TABLE 1 | Previous works.
Works Methodology Advantages Disadvantages cons
Rubin and Terman,
2004
Original RT model based on
Hudgkin–Huxley equations.
Able to reproduce both pathological and
physiological activities of STN, GPe, GPi,
and Thalamic cells.
Does not consider the effect of sensory
motor cortex excitatory inputs.
Pirini et al., 2009 Enhanced Rubin and Terman (RT) model
with the effect of Striatum cells on the
network and Rectangular DBS on different
neuronal targets.
Representation of direct pathways of the
basal ganglia cells.
Some phenomena like electrode to neuron
distance, effects of somas, dendrites and
axons, synaptic activation/inactivation
effects, and neurotransmitter depletion are
not considered by this work.
Foutz and McIntyre,
2010
Energy efficient non-rectangular DBS
waveform.
Examining the neuronal activation energy
in both intracellular and extracellular
stimulation.
Proposed waveforms are hampered by
increased charge requirements, which
may limit potential savings in battery life.
Wongsarnpigoon and
Grill, 2010
Guassian energy efficient DBS waveform
with Genetic Algorithm.
Ability to find the optimal DBS waveform
parameters with the Genetic Algorithm.
Lack of DBS targeting consideration.
Hofmann et al., 2011 Charge balanced DBS waveforms with
introduction of a gap between cathodic
and anodic phases.
Modified DBS waveforms showed a
considerably increased efficiency in terms
of activation and entrainments of neuronal
activities.
Considering these DBS waveforms on a
single compartment model rather than
neuronal population network. Only
considers rectangular pulses.
So et al., 2012 Enhanced RT model with rectangular DBS
waveforms.
High ability to reconstruct the biological
phenomena happening in the basal
ganglia cells.
The model does not consider 3
dimensional orientations of different nuclei
and the position of the stimulating
electrode.
Summerson et al.,
2015
Various charge balanced DBS waveforms
implemented on a new cortical model.
High complexity and accuracy of model
with considering the layer V into the model.
Irregular DBS waveform used does not
provide the mean to understand the effect
of DBS waveforms parameters.
Holt et al., 2016 Closed loop approach of Deep Brain
Stimulation on the HM (Hahn and
McIntyre, 2010) model.
Considers the closed loop phasic
stimulation which enables applying the
DBS waveform at a proper time.
The complexity of neuronal network is not
fully addressed by the model.
Table 1 shows some of the most comprehensive retrospective
studies. Some of these works focused on achieving a biological
compatible neuronal model while others tested the effect of DBS
waveforms along with the model structure. The model used in
this research is a slightly modified version of the basal ganglia
network proposed by So et al. (2012) due to its ability to consider
the contribution of local cells in the basal ganglia under DBS
currents.
Basal Ganglia Network Model
This model adopts the basic differential equations of cells by
Hodgkin and Huxley (1952) in an interconnected manner to
stimulate involving neurons in the basal ganglia such as STN,
GPe, GPi, and Thalamic (Th) neurons. In our modified model,
synaptic currents between neurons are showed in the form of the
equation below:
Iion =gionmM
∞hN
∞(V−Eion) (1)
where gion is the conductance variable of each ion to or from the
cell and mM
∞and hN
∞are activation and inactivation functions
varying slightly for each ion involved in the cell (Hodgkin
and Huxley, 1952). Vis the membrane potential and Eion is
the equilibrium potential of the ion. Each group of cells are
represented by the modified Hudgkin Huxley model as explained
in the following sections:
Thalamic Neurons
Thalamic cells receive inhibitory inputs from GPi cells and
respond to that with an induced firing rate. In order to
generate the subthreshold charge and discharge of thalamic cells,
a depolarizing current is applied to the resting potential of
Thalamic cells. The membrane potential of Thalamic cells are
defined by this equation based on So et al. (2012).
CTh
dV
dt = −IL−INa −IK−IT−IGPi→Th +ISMC (2)
where the conductance values for Leaky, Sodium, Potassium
and T-type low threshold spiking currents are 0.05, 3, 5, and
5mS
cm2and the equilibrium potentials are −70, 50, −75, and
0 mV, respectively. ISMC is the sensory motor cortex current
representing the effect of other cells in the cortex on Thalamic
neurons. ISMC is defined as the normal distributed pulse train
with a frequency of 14 Hz and coefficient variance of 0.2 with
each pulse having the amplitude of 3 µA
cm2and duration of 5 ms, in
order to generate the unordinary signal train of the motor cortex.
IGPi→Th represents the inhibitory currents from a GPi neuron
to each Thalamic neuron with the conductance of 0.17 mS
cm2and
equilibrium potential of −85 mV.
STN Neurons
STN neurons receive many ionic currents including inhibitory
projections from GPe cells, DBS currents and a constant bias
current Ibias, which is the accumulated synaptic current from
Frontiers in Computational Neuroscience | www.frontiersin.org 3August 2017 | Volume 11 | Article 73
Daneshzand et al. Computational Stimulation of the Basal Ganglia
other brain regions. STN neurons have low rate of firing without
an external stimulus (Bevan and Wilson, 1999; So et al., 2012).
The equation governing the membrane potential of STN cells is
as follows.
CSTN
dV
dt = −IL−INa −IK−Ica−IT−IGPe→STN
+IDBS +Ibias (3)
where the conductance values for Leaky, Sodium, Potassium,
Calcium, and T-type low threshold spiking currents are 2.25,
37, 45, 2, and 0.5 mS
cm2and the equilibrium potentials are −60,
55, −80, 140, and 0 mV, respectively. IGPe→STN represents the
inhibitory currents from 2 GPe neurons to each STN neuron
with the conductance of 0.5 mS
cm2and equilibrium potential of −85
mV. Ibias is set to 29 µA
cm2for the healthy case and 20 µA
cm2for the
Parkinsonian case and finally, IDBS is the deep brain stimulus used
in the model.
GPe and GPi Neurons
The firing activity of Globus Pallidus Pars neurons increases with
an increased stimulus signal and follows a continuous monotonic
pattern (Kita and Kita, 2011; So et al., 2012). Equations (4) and (5)
represent the GPe and GPi neurons in this computational model.
CGPE
dV
dt = −IL−INa −IK−Ica−IT−ISTN→GPe +IGPe→GPe
+IDBS +Ibias (4)
CGPi
dV
dt = −IL−INa −IK−Ica−IT−ISTN→GPi+IGPe→GPi
+IDBS +Ibias (5)
where the conductance values for Leaky, Sodium, Potassium,
Calcium and T-type low threshold spiking currents are 0.1,
120, 30, 0.15, and 0.5 mS
cm2and the equilibrium potentials are
−65, 55, −80, 120, and 0 mV, respectively and these values are
the same for GPe and GPi neurons. ISTN→GPe represents the
excitatory currents from two STN neurons to each GPe neuron
with the conductance of 0.15 mS
cm2and equilibrium potential of
0 mV. IGPe→GPe represents the inhibitory currents from two GPe
neurons to each GPe neuron with the conductance of 0. 5 mS
cm2
and equilibrium potential of −85 mV. ISTN→GPi represents the
excitatory currents from two STN neurons to each GPi neuron
with the conductance of 0.15 mS
cm2and equilibrium potential of
0 mV. IGPe→GPe shows the inhibitory currents from two GPe
neurons to each GPi neuron with the conductance of 0.5 mS
cm2
and equilibrium potential of −85 mV. Ibias is set to 20 µA
cm2for
the healthy case and 8 µA
cm2for the Parkinsonian case in Equation
(4), 22 µA
cm2for the healthy case and 12 µA
cm2for the Parkinsonian
case in Equation (5).
Basal Ganglia Network and Synaptic
Connections
The basal ganglia network proposed by So et al. (2012) claimed
that running the model with 100 cells in each population would
cause a small alteration of results in comparison with a smaller
TABLE 2 | Number of connections between neuronal populations.
From population iTo population jSynaptic type
2 STN 1 GPE Excitatory
2 GPe 1 GPe Inhibitory
2 STN 1 GPi Excitatory
2 GPe 1 GPi Inhibitory
2 GPe 1 STN Inhibitory
1 GPi 1 Th Inhibitory
Number of excitatory/inhibitory synapsis between populations in the basal ganglia
model. The first column indicates the number of presynaptic neurons connecting to a
postsynaptic neuron in the second column.
FIGURE 1 | Basal Ganglia connectivity model. The model consists of four cell
types with 1,000 single compartment model neurons in each type. Inhibitory
connections are shown with (•) and excitatory inputs are shown with (N). The
sensory motor cortex pulse train is defined as an excitatory input to the
thalamic cells from the accumulation of firing cells in the sensory motor cortex.
STN, GPe, and GPi neuronal pools are subjected to Deep Brain Stimulation
(DBS) in this model.
network with 16 cells in each population. Since a rectangular
pulse shape similar to DBS was applied, increasing the network
size will influence the DBS waveform capability. In our model, we
set TH, STN, GPe and GPi populations, each with 1,000 neurons.
The connection between these populations arises in conformity
with the topological structure of the connectivity within the basal
ganglia and thalamic cells (Smith et al., 1998). We assumed the
synaptic connectivity between each population of neurons to be
in the form of Equation (1) and in this regard, the number of
connections from each type of neuron to other types is shown in
Table 2.
Each GPe cell has inhibitory projections to two STN, GPi,
and GPe neurons while each STN neuron has two excitatory
connections to two GPe and two GPi neurons, as shown
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
in Figure 1. GPi neurons act as an output connection to
Thalamic neurons with one inhibitory connection. This model
also considers an irregular frequency pulse train as an input to
the thalamic cells, exemplar of the accumulated current from the
sensory motor cortex region. The pulse train has an amplitude of
3µA
cm2and duration of 5 ms. The basal ganglia network by So et al.
(2012) also considers a network current which is viewed as the
input current Ibias from other brain regions to STN, GPe, and GPi
cells which plays a significant role in the computational model to
determine the healthy or Parkinsonian response of the network.
FIGURE 2 | DBS waveforms. Three biphasic pulses with and without delay between the anodic and cathodic phases are used in this basal ganglia model. A delay
elevates the threshold for the activation of neurons while making the network more resistant to the anodic phase. For both with and without delay Sinusoid and
Gaussian waveforms, energy consumption would be lower compared to rectangular pulse shapes. For all waveforms, the cathodic, delay, and anodic phases have
amplitudes of 200, 0, and −20 µAand a duration of 0.3, 0.7, and 1 ms, respectively.
FIGURE 3 | Cost evaluation of DBS waveforms. (A) STN, GPe, and GPi neuronal response to Pulse, Pulse Delay Pulse (PDP), Sinusoid, Sinusoid Delay Sinusoid
(SDS), Gaussian and Gaussian Delay Gaussian (GDG) DBS waveforms plus Healthy, and Parkinsonian’s Disease (PD) conditions. The network consists of 1,000
neurons in each cell type and the firing rates are averaged over multiple runs. (B) Total energy consumption of each DBS waveform of a network size of 1,000 neurons
in each cell type. Waveforms with delays (PDP, SDS, and GDG) had less number of misses in eliciting an action potential while being relatively more energy efficient
than the cathodic DBS waveforms. (C) The network size alters the accuracy of DBS waveforms in evoking action potentials while it is consistent with the energy
consumption value. GDG waveforms show the lowest number of misses as the network size increases from 100 to 1,000 and they have a lower error on multiple runs
of the network. Pulse, PDP, Sinusoid, and GDG waveforms are more sensitive to the network size while SDS and Gaussian waveforms reflect more steady responses
in terms of the number of misses with network size variation.
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
FIGURE 4 | Firing patterns of the Basal Ganglia neurons. Raster changes of firing patterns from healthy and PD conditions to DBS implemented waveforms. PD
decreases the firing rate of Thalamic, GPe and GPi neurons. Rectangular Pulses will adjust the neuronal response of Thalamic, GPe, and GPi neurons while failing to
follow up with the STN firing in the Healthy condition. PDP, Sinusoid, SDS, Gaussian, and GDG will increase the firing rate of STN, GPe, and GPi cells compared to the
PD condition and they also eradicate the synchronization of GPe and GPi neurons. GDG waveform results of GPe firing rates were promising as it simply adjusts itself
to GPe firing pattern under Healthy conditions.
FIGURE 5 | Mutual information. For STN and GPe neurons, the firing patterns
under GDG waveforms (YGDG) had the most amount of MI with YH. Also for
STN neurons, DBS waveforms with delay (YPDP,YSDS , and YGDG) had higher
MI compared to normal DBS waveforms (YPulse,YSinusoid ,YGaussian). YPDP
had more MI with YHthan normal pulses for all neurons. YSDS for GPe and
GPi shared lower MI with YHfor both STN and GPe, while having lower MI for
GPi cells.
By reducing this current going to STN, GPe, and GPi cells, an
elevated bursting pattern and synchronization of GPe/GPi cells
would emerge. Examination of deep brain signals were further
achieved by applying customized pulse shapes to STN, GPe, and
GPi cells, and compared with the typical rectangular waveform
used in retrospective studies (Hofmann et al., 2011; So et al.,
2012; Kang and Lowery, 2013; Summerson et al., 2015). It’s been
studied recently that fluctuations of neuronal action potentials
generate a magnetic field potential. The effect of any external
force such as electromagnetic radiation could be described by
an input current in the neuronal loop (Lv and Ma, 2016; Lv
et al., 2016). The DBS currents in our work induces the firing
of a group of the basal ganglia neurons by generating repetitive
(loop like) pulses. Generally, the effect of any external force
such as electromagnetic radiation or DBS, could be modeled
by an additive transmembrane current. Lv and Ma (2016) and
Lv et al. (2016) proposed a dimensionless Hindmarsh-Rose
model, considering magnetic flux in their model. Their model
is greatly reliable for bifurcation analysis while being capable of
reproducing chaotic firing activities within some neurons.
DBS Waveforms
Many studies have attempted to examine the therapeutic
effects of DBS waveforms on patients with Parkinson’s disease
(Berney et al., 2002; Hashimoto et al., 2003; Rizzone et al.,
2014) along with more computationally based studies such as
Wongsarnpigoon and Grill (2010),Foutz and McIntyre (2010),
So et al. (2012),Summerson et al. (2015),Kang and Lowery
(2013), and Hofmann et al. (2011). However, the effect of DBS
pulse modification with a delay in a complex network of the basal
ganglia has not been fully investigated. A typical waveform to be
used as DBS consists of a Cathodal pulse followed by a longer
extent of an Anodal pulse (Coffey, 2009).
In order to achieve a charge balanced Gaussian waveform
we must carefully define the width ratio between the cathodic
and anodic pulse, which in our study, we established as 1:3.3 to
guarantee enough time for the depolarization of the membrane
potential to have the maximum efficiency of DBS. We compared
a group of waveforms with a delay between the cathodic and
anodic phases in the computational network of the basal ganglia
to see how the DBS signals can activate the resting neurons along
with the reduction of neuronal synchronization. These signals
are rectangular pulses, sinusoid, and Gaussian along with three
biphasic waveforms with a delay between the cathodic and anodic
parts, which we call Pulse Delay Pulse (PDP), Sinusoid Delay
Sinusoid (SDS), and Gaussian Delay Gaussian (GDG) waveforms.
All these waveforms were able to decrease the synchronization
of GPe and GPi cells with a cathodic amplitude of 200 µA.
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
The pulse duration of the cathodic phases were 0.3 ms which
were enough to elicit an action potential with minimum energy
consumption (Wongsarnpigoon and Grill, 2010). The anodic
phase of the amplitude was −20 µAand a duration of 1 ms was
assigned. The delay of 0.7 ms showed a promising value for the
activation of resting neurons in our basal ganglia network. These
values were used to be consistent with previous studies (Foutz
and McIntyre, 2010; Wongsarnpigoon and Grill, 2010; So et al.,
2012; Summerson et al., 2015) and to have a better comparison of
energy consumption for each waveform, but as we show further
in this study, the cathodic and anodic amplitudes along with the
delay length can be varied to reach the optimal DBS waveforms.
Placing a delay between the cathodic and anodic phases had
been studied by Hofmann et al. (2011) with only a rectangular
pulse gap pulse waveform implemented on a simple Hodgkin-
Huxley and a Morris-Lacar model (Hodgkin and Huxley, 1952;
Morris and Lecar, 1981), however it does not consider the
interactive behavior of STN, GPe, and GPi neurons (Detorakis
et al., 2015). They considered the effect of this DBS waveform by
switching the cathodic and anodic phases, hence two waveforms
of cathodic gap anodic (CGA) and anodic gap cathodic (AGC)
were explored. They concluded that the AGC signals show a
complex behavior in terms of threshold amplitude for action
potential generation vs. gap duration. Therefore in this study, we
defined our DBS signals in the form of a cathodic phase followed
by a delay and then followed by an anodic phase. With this
configuration, we were able to achieve the activation of resting
neurons while having a fixed optimum delay length. The effect of
a Gaussian delay Gaussian waveform has not been studied before
which we showed is the most practical waveform for deep brain
stimulation in terms of energy consumption, desynchronization
of GPe/GPi cells, and performance of proper elicitation of action
potential within the network. Figure 2 shows the waveforms we
used in the computational basal ganglia model.
The anodic phase must have a lower amplitude with a longer
duration to counter balance the effect of a short length but
high amplitude cathodic pulse. With this configuration, we
can minimize the tissue damage of patients going under DBS
implantation (Harnack et al., 2004; DiLorenzo et al., 2014; Cogan
et al., 2016). Interfering the DBS waveform with a delay between
the cathodic and anodic parts also increases the threshold for the
activation of neurons and will make the network less influenced
by the anodic phase (Mortimer, 1990).
RESULTS
Cost Function
We applied different pulse shapes as deep brain stimulators to
investigate the energy consumed along with the number of times
that the DBS signals failed to elicit an action potential. The
cost function would simply accumulate these two criteria as the
equation below:
C=IW
I(t)2Z(t)dt +M(6)
where I(t) is the DBS current waveform, Z(t) is the constant
impedance set to 1 k,Wis the width of the waveform used
and Mis the number of misses in eliciting an action potential
(each miss is considered with the penalty of 3 nJ). Each pulse
of DBS tends to evoke an action potential on the implanted
FIGURE 6 | Phase locking values. Higher results of PLV were obtained with DBS waveforms modified with delay for all cell types. The firing pattern of all neurons was
relatively more locked to healthy conditions under Gaussian and GDG waveforms.
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
cell such as STN, GPe, or GPi. Ideally, the ratio of DBS pulse
to neuron action potential is 1:1, but since this ratio in PD
might not be exactly equal, variable Mcomes into picture. The
width of waveforms is kept similar to each other to have a
unified and fair comparison of cost functions. We use the basic
pulse, Sinusoid and Gaussian (Wongsarnpigoon and Grill, 2010)
waveforms and compare them to the modified waveforms with
a delay between the cathodic and anodic phases, called Pulse
delay Pulse (PDP), Sinusoid delay Sinusoid (SDS), and Gaussian
Delay Gaussian (GDG). Figure 3 shows the DBS waveforms
implemented in the computational network of the basal ganglia
along with the amount of energy consumed by each waveform. As
previously shown in Wongsarnpigoon and Grill (2010), Gaussian
signals for DBS guarantee the minimum energy consumption
compared to any other signal form such as pulse, rectangular,
ramp, exponential, and sinusoid. Adding a delay followed by an
anodic phase to the Gaussian waveform will slightly decrease
the energy efficiency but provides lower error in eliciting action
potentials. In Figure 3A, the neuronal responses of STN, GPe
and GPi cells in the basal ganglia network are illustrated. There
are two firing patterns for Healthy and Parkinsonian’s Disease
(PD) conditions along with the six types of DBS waveforms
implemented. DBS waveforms were able to activate the basal
ganglia neurons while suppressing the amplitude of spikes in STN
neurons which is an output to GPi neurons (Hashimoto et al.,
2003). STN neurons fired almost the same under all of the DBS
waveforms, which shows that the stimulation of DBS neurons are
independent of the DBS pulse shape. The lower amplitude of STN
neurons is similar to the physical observation in Hollerman et al.
(1992).
Synchronized responses of GPe and GPi neurons observed
under PD condition were eliminated by all DBS waveforms
although Gaussian and GDG waveforms were able to achieve
more precise desynchronization. Beurrier et al. (1999)
demonstrated that the increased firing rate of GPe and GPi
neurons might be due to the depolarization of STN neurons. The
network used in Figures 3A,B consists of 1,000 neurons in each
cell type (Thalamic, STN, GPe, and GPi). The amount of energy
consumed by GDG was almost one third of the rectangular
pulse. Generally, waveforms with a delay between the cathodic
and anodic parts (PDP, SDS, and GDG) showed less number
of misses in eliciting an action potential every time they were
implemented (Figure 3B). The results of energy consumption of
these waveforms were almost consistent with the network size,
but the number of misses in eliciting an action potential dropped
by incrementing the network size as it went from 100 neurons in
each cell type up to 1,000 (Figure 3C). We numerically evaluated
the energy and number of misses on different network sizes to
determine the consistency of the network. The error bars in
Figure 3B state that through numerous runs of the network
with different DBS waveforms, GDG showed the most persistent
results.
Firing Patterns of Basal Ganglia Neurons
From the recording of the neuronal firing rates in monkeys
(Bergman et al., 1994; Boraud et al., 1998; Wichmann and Soares,
2006), we expect to see an increase in the firing rate of GPi and
STN neurons after implementing the DBS signals, while GPe
neurons show the reduced firing rate. In Figure 4, the mean
firing rate of STN, GPe, and GPi cells increased from the PD
FIGURE 7 | Synchronization level of GPi neurons. (A) Neuronal firing pattern of two GPi cells are shown for a duration of 200 mS. The blue and red boxes show the
windows used to detect the APs inside them. Panel (B) shows the corresponding number of APs for each window. The number of APs for the red and blue boxes are
shown in red and blue, respectively. The correlation coefficient between the discrete functions obtained from (B) is then calculated. A total of 1,000 GPi firing
responses will produce 1,000 discrete functions as (B) and therefore a 1,000 by 1,000 correlation coefficient matrix is achieved for all GPi neurons.
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
condition to the DBS implemented condition. From Healthy to
PD condition, a decrease in the rate of GPe neurons is observable
which is consistent with the recording data (So et al., 2012). All six
DBS waveform types successfully increased the rate of spiking in
Thalamic, STN, GPe, and GPi cells, however the amount of this
boost in neuronal firing was lower for GPe neurons under the
stimulation of a GDG waveform, which promises better results
in diminishing the effects of Parkinson’s disease (Wichmann
et al., 1994). The relative increase in firing rates of GPe and
GPi cells from PD to DBS implemented conditions corresponded
to the experimental recordings in which the GDG and PDG
waveforms in our model reached the highest comparability to
the actual data (Hashimoto et al., 2003). The firing rate of
Thalamic neurons decreases from healthy to PD condition while
it increases after applying DBS, adjusted to Healthy conditions.
Summerson et al. (2015) investigated the average firing rate of
cells in the basal ganglia under regular and irregular rectangular
pulse DBS waveforms. The rate did not differ noticeably in both
cases proving that DBS has a uniform effect on the firing rate of
single neurons, but with various waveform shapes and the effect
of Delay between cathodic and anodic phases, GPi neurons tend
to fire more. This increased firing pattern is due to counteracting
the regularization period (Delay plus the anodic phase) and is
essential to improve the outgoing signals from the basal ganglia
to the thalamic neurons (Humphries and Gurney, 2012).
Synchronization of brain waves is the basis of functional
connectivity for neural decoding (Fell and Axmacher, 2011).
Changes in synchronization causes brain disorders like PD (Plenz
and Kital, 1999; Moazami-Goudarzi et al., 2008). There are
several bivariate techniques to study the synchronization in
firing patterns of brain cells (Jalili et al., 2014), namely, the
mutual information, phase locking (Guevara et al., 2005; Sakkalis
et al., 2009; Rummel et al., 2011) and synchronization levels
based on the correlation coefficient (Pirini et al., 2009). STN,
GPe, and GPi neurons fire with various patterns under different
DBS waveforms, therefore the similarity and synchronization
of these firing responses compared to the firing patterns of
these neurons under healthy condition is investigated by the
bivariate techniques mentioned above. Based on Lv and Ma
(2016) and Lv et al. (2016), appropriate external radiation can
change the initial bursting of neurons into a switching mode of
tonic and burst firing. This shows a promising finding in PD
since many neurons tend to fire in switching mode due to PD.
Also, in our work, the basal ganglia neurons under DBS showed
numerous firing patterns and low DBS frequency signals were
observed to fluctuate the neuronal activity into more switching
patterns. Ma et al. (2017) stated that bursting synchronization
under flux coupling could enhance with increasing external
force current. Here, we also showed that DBS waveforms
could affect the firing of population of neurons. For the STN
neurons firing rate in Figure 4, we can see that once the
amplitude of the DBS current is sufficient, the regular bursting
emerges.
Mutual Information
Based on the correlation and coherence definitions, it seems that
the relation between YHand YDBS of the basal ganglia neurons
has non-linear characteristics, hence the mutual information can
be more useful. The Mutual Information (MI) between two firing
patterns is defined as below:
MI (YH,YDBS)=XM
i=1XM
j=1Pij
YHYDBS ln( Pij
YHYDBS
Pi
YHPj
YDBS
) (7)
where Pij
YHYDBS is the estimated joint probability of the outcomes
iand jfor the signals and Pi
YHis the estimated probability
distribution of the ith outcome of YH. For STN and GPe neurons,
the firing patterns under GDG waveforms (YGDG) had the
most amount of MI with YH. Moreover, for STN neurons, DBS
waveforms with delay (YPDP,YSDS and YGDG ), had higher MI
compared to normal DBS waveforms (YPulse,YSinusoid,YGaussian).
YPDP had more MI with YHthan normal pulses for all neurons.
YSDS for GPe and GPi shared lower MI with YHfor both STN and
GPe, while having lower MI for GPi cells (Figure 5).
Phase Locking Value
In order to understand the phase synchrony between DBS
induced firing of STN, GPe, and GPi with the healthy condition,
we used the Phase Locking Value (PLV; Aydore et al., 2013). First
of all, we must extract the instantaneous phases from the signals
using a Hilbert transform as below:
ϕY=tan−1(H(Y)
Y) (8)
where H(Y) is the Hilbert transform of signal Y. In order to see
how well the firing patterns of STN, GPe, and GPi neurons under
DBS (YDBS) is phase locked to the healthy condition (YH), we can
use the following measure:
PLV (YH,YDBS)=1
L
XL
i=1ej(ϕYH−ϕYDBS )
(9)
Figure 6 shows the result of PLVs for STN, GPe, and GPi neurons
under various DBS waveforms in comparison with YH. For
all neurons under DBS waveform with delay (YPDP,YSDS , and
YGDG), the PLV results were higher than firing under normal
DBS (YPulse,YSinusoid ,YGaussian), which shows that adding
the delay in a charge balanced DBS waveform might provide
more synchronized firing patterns to the healthy condition.
The firing pattern of all neurons was relatively more locked
to healthy conditions under Gaussian and GDG waveforms
(YGaussian and YGDG). In PD condition, the PLV showed more
tonic responses for all neurons which indicates the ability of the
basal ganglia model to represent the irregular phases in which
cells fire due to PD.
Synchronization Level
GPi neurons tend to fire in a synchronized manner
due to Parkinson’s disease while DBS waveforms have a
desynchronization effect on these firing patterns. The correlation
between firing pattern of GPi neurons does not provide a
meaningful metric to evaluate the level of synchronization due
to extraneous low amplitude action potentials (AP) existing
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
between the desired APs (Figure 7). Therefore, we applied a
correlation coefficient analysis based on the desired APs of
these neurons in order to measure the synchronization level
among GPi neurons (Pirini et al., 2009). First of all, assuming a
population of 1,000 GPi neurons, we extracted the number of
action potentials for each non-overlapping frame (15 ms) for
all GPi neurons. These APs were obtained by a threshold value
of −20 mV. This would give us a function of the number of
APs based on each frame for every GPi neuron (Figure 7). The
reason for using non-overlapping windows is to avoid counting
any AP more than once. Equation (10) shows the number of APs
for neuron iin kconsecutive frames:
Fij=APw(k)(10)
APw(k)represents the number of action potentials calculated in
the kth frame. In the next step, the correlation coefficient of
these functions is defined for all GPi neurons. The correlation
coefficient between 1,000 of functions Fiis calculated in Equation
(11).
ρFi,Fj=PL
t=1(Fi−mean (Fi))(Fj−mean Fj)
qPL
t=1(Fi−mean (Fi))2PL
t=1(Fj−mean Fj)2
(11)
Lis the number of elements in each function. For a GPi
population of 1,000 neurons, a 1,000 by 1,000 elements
correlation matrix MCbetween all GPi neurons is generated
using Equation (11).
The total number of values in matrix MCwith significant
correlation (α≤0.05) is called NSwhile the total number of
elements in MCis denoted by NT. The synchronization level (SL)
for the GPi neurons is finally derived by the equation below:
SL =NS
NT
(12)
Table 3 shows the SL values of GPi neurons for different
conditions. SL was calculated as 0.2 for the healthy condition.
The low SL value shows that the synchronization of GPi
neurons is low. The SL value was calculated as 0.733 for PD
cases. This result shows an increased synchronization of GPi
neurons. Higher synchronization due to PD was reported in
Hammond et al. (2007) and Brown et al. (2004). However, it
was not expressed quantitatively. The SL value proposed by this
work allows for quantitative analysis to be performed. All DBS
waveforms were able to reduce the SL of GPi neurons. The
delay within the DBS signals (PDP, SDS, and GDG) reduced the
SL values further, which shows that the delay in DBS signals
could desynchronize the GPi firing patterns more effectively
compared to normal DBS waveforms (including Rectangular
Pulse, Sinusoid, and Gaussian). GDG waveforms had the lowest
SL among all well-known DBS signal shapes. This states that
Gaussian DBS waveforms are as efficient as rectangular pulses in
term of desynchronization of GPi neurons. Also, charge balanced
Gaussian waveforms with a delay between the cathodic and
anodic phases can reduce the synchronization of GPi neurons
TABLE 3 | Synchronization level of GPi neurons.
Condition SL
Healthy 0.2
PD 0.733
Rectangular Pulse 0.112
PDP 0.0889
Sinusoid 0.156
SDS 0.133
Gaussian 0.111
SDS 0.067
due to PD even further in comparison with normal charge
balanced DBS waveforms without delay.
Effect of Delay on Optimal DBS Waveforms
The six DBS waveforms were examined for the capability
of activating the resting neurons within the basal ganglia.
Modification of delay length will provide a lower amplitude
waveform in order to elicit an action potential. The main reason
for this phenomenon is that the anodic phase will reverse the
depolarization effect of the cathodic phase but with a delay in
between, the cathodic phase has sufficient time to depolarize
the membrane potential. Lower amplitude cathodic phases are
able to depolarize the membrane potential but the process needs
more time before the suppressive effect of the anodic phase
(Hofmann et al., 2011), therefore a tolerable delay length is
obligated to meet the desired condition. What we observed was
that having a longer delay, reduces the amplitude of the DBS
signal capable of eliciting AP’s. Therefore, the total amount of
energy is decreased. Although most of the energy consumption
is related to the peak of the signal rather than its shape (see
Equation 6; Wongsarnpigoon and Grill, 2010), showed that
shape of the DBS pulse in population models, also contributes
to this matter. This was also shown in our population model
in which Gaussian signals with or without delay had lower
effective amplitudes compared to other waveforms, as shown in
Figure 8.
To study the delay effect in our basal ganglia network, we
used three DBS waveforms with a variant delay length between
the cathodic and anodic phases. The effect of delay length is
seen on the waveform amplitude capable of eliciting an action
potential. The Gaussian Delay Gaussian waveforms (GDG) were
able to decrease the cathodic amplitude for eliciting an action
potential because the cathodic Gaussian waveform will depolarize
the membrane of the basal ganglia cells while the gradual decrease
of the following anodic Gaussian phase will act as an additional
delay for the depolarization process by creating a less sensitive
waveform to the anodic phase (Figure 8A). The GDG waveforms
reached the delay threshold faster than SDS and PDP. In this
figure, the duration of the anodic phase was 3.3 times of the
cathodic phase and the ratio of the cathodic to anodic phases
is set to 10:1. The threshold of the delay to reach the amplitude
of 200 µA, capable of eliciting action potentials was 0.32, 0.43,
and 0.65 mS with respect to GDG, SDS, and PDP waveforms.
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
The obtained cathodic amplitude to elicit an action potential for
PDP waveform was 30% lower than previous studies (So et al.,
2012), while SDS and GDG had even lower amplitudes than PDP.
The optimal values for these waveforms are shown in Figure 8B.
GDG had the lowest cathodic amplitude while functioning with
relatively lower amplitude in the anodic phase compared to the
SDS waveform (−19 µAfor GDG anodic and −23 µAfor SDS).
Lv et al. (2016) proves that the discharge mode of neuronal firing
could be dominated by angular frequency when low amplitude is
used in the external forcing current. Similar results in our work
explain how introducing delay in the DBS current can reduce the
amplitude of the external forcing current (DBS).
It is necessary to evaluate the performance of DBS waveforms
to see if the frequency of bursting neurons lock or synchronize
to the DBS frequency. We investigated the capability of
various pulse shapes to synchronize with the neuronal activity
during simulation. We used the PLV metric to calculate
the synchronization of bursting neurons with the input DBS
waveform as explained by Equation (9). The 3 different DBS
waveforms examined here were PDP, SDS and GDG. The results
of synchronization (PLV) were obtained based on the delay
length and the amplitude of the DBS signal. As shown in Figure 9,
we increased the delay length from 0 to 1.2 mS with steps of 0.05
mS and also the amplitude of DBS signal was set to 190 µAand
increased with steps of 1 µAup to 210 µA. DBS frequency was
set to 130 Hz and for each pair of delay length and amplitude,
the PLV of the specified DBS waveform with the firing pattern
of the desired neurons was obtained. We will discuss the effect
of each DBS waveform shape on STN, GPe, and GPi neurons,
but based on Figure 9, we can say that: for small amplitudes,
the synchronization was low (PLV ≤0.2) meaning that neuronal
firing was not adapted with the input DBS signal. Increasing
the amplitude did not increase the synchronization for zero or
small values of the delay length (PLV ≤0.5). Moreover, DBS
waveforms with long delay but low amplitude, failed to achieve
high synchronization (PLV ≤0.6). Once the amplitude and delay
length were sufficiently increased, near optimal synchronization
was observed (PLV ≥0.9). Furthermore, it has been shown that
the anodic phase of the DBS waveform has a hyper polarization
effect (Hofmann et al., 2011). Hyperpolarization helps enhancing
the speed of relaxation of the neurons and faster relaxation
implies a more bursting pattern. Increased bursting pattern of
neurons advances the synchronization with the input DBS. The
delay also provides enough relaxation time, hence higher delay
length with sufficient amplitude followed by the anodic phase,
leads to more synchronization of bursting neurons with the input
stimuli.
The PLVs of STN burst firing with PDP, SDS, and
GDG waveforms are shown in Figures 9A–C, respectively.
Synchronization of STN neurons with PDP occurred at delay
length and amplitude higher than 0.8 mS and 203 µA(PLV ≥
0.9). Under SDS input, synchronization occurred at a slightly
smaller delay length and amplitude. The desired PLV of STN
neurons with GDG input stimuli happened at delay length of
0.7 mS and amplitude of 192 µA. The slow increasing slope
of Gaussian anodic phase in GDG waveform acts as an extra
delay, therefore, higher synchronization with lower delay length
is achievable between GDG input and STN burst firing. For
PDP, SDS, and GDG waveforms, GPe neurons showed low
synchronization and only for a short period of delay length,
high synchronization was observed (Figures 9D–F). Generally,
synchronization of GPe burst firing with the input DBS signal
was low due to the fact that the DBS signals are targeted to
STN neurons in this model. Also, the inhibitory connections
between GPe and STN neurons might have disruptive effect on
the burst firing patterns of GPe neurons causing these neurons
not to accommodate the DBS signal. The PLV results of GPi
neurons with the input DBS were more consistent with STN
neurons since they receive direct excitatory connections from
STN (Figure 1). High synchronization (PLV ≥0.8) for GPi
neurons under PDP input happened at a delay length more than
0.9 mS and amplitudes higher than 200 µA(Figure 9G). For
SDS waveforms, to achieve high synchronization with GPi firing
(PLV ≥0.8), the delay length and amplitude must be higher than
0.8 mS and 200 µA, respectively, as shown in Figure 9H. GDG
signals outperformed PDP and SDS as their high synchronization
with GPi firings (PLV ≥0.8) occurred at a delay length longer
than 0.6 mS and amplitudes higher than 198 µA.
We can summarize the synchronization effect of different DBS
signal shapes with neuronal burst firing as follows:
•The anodic phase of DBS waveforms act as a hyper polarizer,
causing reduction of neuronal relaxation time and therefore,
speeding up the bursting frequency. Faster bursting leads to
more synchronization of the DBS signal and neuronal firings.
•GDG waveforms were able to achieve high PLVs with neuronal
burst firing while having a shorter delay length compared
to PDP and SDS specifications. The slowly uprising anodic
Gaussian phase of GDG waveforms compensate for the shorter
delay length.
•High synchronization of GDG waveforms and neuronal burst
firing (PLV ≥0.7) was obtained with a lower cathodic
amplitude, which makes them more energy efficient compared
to SDS or PDP waveforms.
•As shown in Figure 9, if the delay length is long enough,
all neuron types under any DBS waveforms show very high
synchronization (PLV ≥0.9). This shows the high effectiveness
achieved by adding the delay between the cathodic and anodic
phases of the DBS signal.
•Increasing the delay length diminishes the need for high
amplitude DBS signals and will reduce the side effect of
stimulation currents.
In general, the anodic phase opposes the neural depolarization
caused by the cathodic phase. Therefore, higher amplitude
(more energy) is needed to evoke action potentials from
neurons. Interphase delays in our model basically give enough
depolarization time (reducing the need of higher DBS peaks)
and also the slow uprising anodic phase of the GDG waveforms
provides extra time for depolarization, making GDG the most
efficient signal. Figure 10 depicts the effect of delay length and
frequency of stimulation on the consumed energy. In this Figure,
we defined a normalized energy threshold (NET) based on the
Delay Length (DL) and Frequency of stimulation (Fs). Energy
threshold was the minimum energy consumed by the DBS signal
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
FIGURE 8 | Optimal amplitude of DBS waveforms. (A) The effective cathodic amplitude to elicit an action potential for Gaussian Delay Gaussian (GDG), Sinusoid
Delay Sinusoid (SDS), and rectangular Pulse Delay Pulse (PDP) DBS waveforms. The threshold of delay to reach the amplitude of 200 µA, capable of eliciting action
potentials was 0.32, 0.43, and 0.65 mS with respect to GDG, SDS, and PDP waveforms. Vertical dashed lines show the delay threshold values for each waveform.
Delay sizes larger than these values lead to the same amplitude values and thus were unnecessary to plot. The GDG waveforms reached a lower delay threshold
faster than SDS and PDP. (B) Optimal waveform shapes used in our basal ganglia network. The amplitude and duration ratio of the cathodic to anodic phases were
10:1 and 3.3:1, respectively.
FIGURE 9 | PLV of neuronal response with the DBS input. (A) STN neurons under PDP-DBS showed low PLV. Under SDS and GDG, higher PLV was obtained with
shorter delay length and lower amplitude of the DBS signal, as seen in (B,C). Under PDP, SDS and GDG waveforms, GPe neurons showed low synchronization and
only for a short period of delay length, high synchronization was observed in (D–F). The PLV results of GPi neurons with the input DBS were more consistent with STN
neurons since they receive direct excitatory connections from STN. High synchronization for GPi neurons under PDP input happened at high amplitude and long delay
lengths (G). For SDS waveforms, to achieve high synchronization with GPi firing, the delay length and amplitude were a bit lower than PDP waveforms (H). GDG
signals outperformed PDP and SDS, as their high synchronization with GPi firings occurred at a much shorter delay length and lower amplitudes (I).
that caused at least 50% of the DBS pulses to elicit spikes. Then,
we normalized the energy threshold to a range between 0 and 1.
Higher values in this range indicate more energy consumed by
the stimulation signal. For PDP waveforms, as long as the DL is
short (DL <0.2 mS), increase in Fs does not affect the NET (NET
>0.7). Once the DL is large enough (DL >0.25 mS), we see a
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
FIGURE 10 | Normalized energy threshold (NET) for different DBS waveforms based on the frequency of stimulation (Fs) and delay length (DL). High frequencies
cause pulses to get closer in time. In this case, the interaction between successive pulses lead to a blocking condition where the anodic phase of one pulse
hyperpolarizes the membrane voltage, thus raising the threshold of the action potential for the next pulse. Therefore, an efficient DBS waveform can be determined
according to a trade-off between the delay length and the frequency of DBS, as changes in frequency alters the effect of the delay.
reduction of NET, especially at frequencies around 140 Hz. The
DL of SDS signals showed an interesting behavior, where for 0.2
mS <DL <0.35 mS, small NET appeared (NET <0.3) for almost
all frequencies. Fs >120 Hz along with DL <0.2 mS resulted
in a high NET (NET >0.8). The reason for this phenomenon
is that higher frequencies indicate that pulses are getting closer
in time. In this case, the interaction between successive pulses
lead to a blocking condition where the anodic phase of one pulse
hyperpolarizes the membrane voltage, thus raising the threshold
of the action potential for the next pulse (Weitz et al., 2014).
The same condition happens if the delay length is too large and
successive pulses are getting close to one another. For a range
of 0.2 mS <DL <0.3 mS and 30 Hz <Fs <140 Hz, NET
was lowered (NET <0.2) under GDG stimulation. Comparing
SDS to GDG, the maximum effective DL was dropped from 0.35
to 0.3 mS, which is due to the delay-like effect of the anodic
Gaussian phase, as explained before. According to the results,
we conclude that there must be a trade-off between DL and the
frequency of DBS, as changes in frequency alters the effect of
delay. Therefore, efficient delay lengths should be selected with
regards to the frequency of stimulation.
DISCUSSION
The results of this study show how modification of DBS
waveforms in the network of the basal ganglia can be beneficial
in comparison with standard rectangular DBS used in surgeries.
Although, previous studies investigated the effect of a delay
between the cathodic and anodic phases of DBS waveforms
(Hofmann et al., 2011), examining the effect of Gaussian
waveform with delay has not been fully investigated. Moreover,
we implemented this signal modification on a more complex
network of the basal ganglia, considering the interactions
between various cell types. The computational model of the basal
ganglia used in this research has some limitations which must
be considered in the future. For example, neuronal firing of this
model reproduced some of the experimentally observed firings
and not all. For healthy and Parkinsonian’s conditions, the firing
rates of STN and GPi were slightly lower than the reported trends
in the literature (So et al., 2012). In addition, this model does
not consider the three dimensional orientation of various nuclei
or the direction of neuronal projections. Although improving
the model can lead to better understanding of the underlying
mechanism of DBS, the model used is still able to generate
the spiking rate and firing patterns for investigating DBS signal
shapes. Moreover, a significant future work would be to consider
the magnetic flux parameter in this neuronal population model.
Neuronal firing under DBS current might be more accurate in
the existence of a field of stimuli rather than current stimuli,
hence it should be further investigated by the stability analysis
of collective neuronal behavior (Lv et al., 2016).
The duration of the delay must be set delicately. Long delay
length diminishes the need for high amplitude DBS signals and
will reduce the side effect of stimulation current, but delay
durations over 2 mS might not be safe for stimulation (Merrill
et al., 2005). The optimal delay length can be set in a closed
loop approach for each patient (Holt et al., 2016). By considering
a Gaussian pulse shape for the anodic phase, we were able
to reduce the delay period to 0.3 mS, which is safe to be
used without tissue damaging effects of the stimulation. This
is computationally studied in our work, although testing these
pulse shapes experimentally is out of the scope of this paper, it is
necessary to be done in future. The issue with rectangular pulses
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Daneshzand et al. Computational Stimulation of the Basal Ganglia
used in DBS is that their ability will decline with shorter delay
lengths unless the amplitude of the pulse is also lowered relative
to the reduction of the delay length. In this case, these pulses
might not be effective in eliciting action potential (Cogan, 2008).
DBS waveforms in Figure 8 showed that they will be able to elicit
action potential with a shorter length of delay while maintaining
the cathodic amplitude adequate to depolarize the membrane
potential of the basal ganglia cells. The slowly uprising anodic
Gaussian phase of GDG waveforms compensate for the shorter
delay length. The anodic phase of the DBS waveforms also act as
a hyper polarizer, causing reduction of neuronal relaxation time
and therefore speeding up the bursting frequency. Faster bursting
leads to more synchronization of DBS signals and neuronal
firings. In addition, based on the results of Figure 9, GDG
waveforms were able to achieve high PLVs with neuronal burst
firing while having a shorter delay length compared to PDP and
SDS specifications. In general, for all DBS waveforms in Figure 9,
the proposed delay between the cathodic and anodic phases
lead to higher synchronization and effectiveness. As a future
direction, one can examine the effect of skewness and kurtosis of
Gaussian waveforms which might have direct relation with the
amount of PLV between the DBS waveform and the neuronal
firings. It’s been shown that GDG waveforms can achieve better
results in terms of synchronization with the neuronal burst firing
while having lower amplitudes. Effective low amplitude GDG
waveforms decreases the energy consumption and therefore
provides a longer life time of Implantable Pulse Generators (IPG),
avoiding costly replacement surgeries (Hely et al., 2008).
A rectangular pulse with delay between the cathodic and
anodic parts (PDP) consumed 11% less energy than a normal
rectangular cathodic pulse (495 to 439 nJ) in our computational
network of the basal ganglia cells with 1,000 neurons in each
type. This amount of reduction was 7% for the sinusoidal pulse
with delay (SDS) compared to the normal sinusoid pulse (180
to 167 nJ). For Gaussian delay Gaussian (GDG), the reduction
of energy consumption of 22.5% (114 to 88.3 nJ) was achieved.
Along all these waveforms, GDG was the most effective pulse
shape to reduce the energy consumption. The GDG reduced
the energy by 60% compared to a rectangular pulse delay pulse
(PDP) waveform. In this research, we focused on the temporal
specifications of the stimulus pulse as it strongly influences the
performance of the treatment. More specifically, we aimed to
see if modified DBS signals can reduce the amount of energy
transmitted by the electrode, while being able to activate neurons
within the basal ganglia region. It is crucial to consider all
parameters of DBS signal specification such as amplitude, delay
length, and frequency of stimulation as they all eventually play a
significant role in the circuit design. Additionally, the total energy
consumed by the DBS device also depends on the device pace
maker circuitry, wiring and electrode specifications which must
also be studied. Finally, the improvement of biophysical basal
ganglia models such as considering the Autapse connections as
described in Lv et al. (2016), along with various specifications of
DBS signals, can provide a compelling tool for the investigation
of Parkinson’s disease.
AUTHOR CONTRIBUTIONS
MD, MF, and BB came up with the ideas and discussed
the analysis thoroughly. MD performed the simulations under
the supervision of MF and BB. MD, MF, and BB wrote the
manuscript.
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Conflict of Interest Statement: The authors declare that the research was
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Copyright © 2017 Daneshzand, Faezipour and Barkana. This is an open-access
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