Abstract and Figures

Neuronal entropy changes are observed in the basal ganglia circuit in Parkinson's disease (PD). These changes are observed in both single unit recordings from globus pallidus (GP) neurons and in local field potential (LFP) recordings from the subthalamic nucleus (STN). These changes are hypothesized as representing changes in the information coding capacity of the network, with PD resulting in a reduction in the coding capacity of the basal ganglia network. Entropy changes in the LFP and in single unit recordings are investigated in a detailed physiological model of the cortico-basal ganglia network during STN deep brain stimulation (DBS). The model incorporates extracellular stimulation of STN afferent fibers, with both orthodromic and antidromic activation, and simulation of the LFP detected at a differential recording electrode. LFP sample entropy and beta-band oscillation power were found to be altered following the application of DBS. The ring pattern entropy of GP neurons in the network were observed to decrease during high frequency stimulation and increase during low frequency stimulation. Simulation results were consistent with experimentally reported changes in neuronal entropy during DBS.
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Changes in Neuronal Entropy in a Network Model of the Cortico-Basal
Ganglia during Deep Brain Stimulation
John E. Fleming1,Student Member, IEEE and Madeleine M. Lowery1,Member, IEEE
Abstract Neuronal entropy changes are observed in the
basal ganglia circuit in Parkinson’s disease (PD). These changes
are observed in both single unit recordings from globus pallidus
(GP) neurons and in local field potential (LFP) recordings from
the subthalamic nucleus (STN). These changes are hypothesized
as representing changes in the information coding capacity of
the network, with PD resulting in a reduction in the coding
capacity of the basal ganglia network. Entropy changes in the
LFP and in single unit recordings are investigated in a detailed
physiological model of the cortico-basal ganglia network during
STN deep brain stimulation (DBS). The model incorporates
extracellular stimulation of STN afferent fibers, with both
orthodromic and antidromic activation, and simulation of the
LFP detected at a differential recording electrode. LFP sample
entropy and beta-band oscillation power were found to be
altered following the application of DBS. The firing pattern
entropy of GP neurons in the network were observed to
decrease during high frequency stimulation and increase during
low frequency stimulation. Simulation results were consistent
with experimentally reported changes in neuronal entropy
during DBS.
Parkinson’s disease (PD) is a neurodegenerative disease
characterized by a triad of motor symptoms; bradykinesia,
akinesia, and tremor. Recent research has focused on identi-
fying signals from the central and peripheral nervous system
which can be used to quantify the disease state and symptom
severity. These signals are commonly referred to as disease
‘biomarkers’. Clinical and experimental studies have identi-
fied several potential biomarkers for PD, such as increased
oscillatory activity in the beta frequency band (13-30 Hz)
recorded from the cortico-basal ganglia circuit [1], beta-
gamma band (60-200 Hz) phase-amplitude coupling in the
primary motor cortex [2], and changes in neuronal entropy
in the basal ganglia network [3]. Deep brain stimulation is
an effective treatment for PD which has been shown to have
measurable effects on these biomarkers. These effects include
reducing beta-band oscillatory activity [1], reducing beta-
gamma band phase-amplitude coupling [2], and regularizing
neural firing rates in the basal ganglia network [4], [5].
Firing pattern entropy, calculated using single unit record-
ings from the basal ganglia network, and sample entropy,
calculated from the STN local field potential (LFP), are two
entropy measures with observable changes during PD. Firing
pattern entropy quantifies an upper bound on the information
*Research supported by the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme
1John E. Fleming and Madeleine M. Lowery are with the Neuromus-
cular Systems Laboratory, School of Electrical & Electronic Engineering,
University College Dublin, Ireland (e-mail: john.fleming@ucdconnect.ie).
embedded in a spike train. Spike trains from globus pallidus
(GP) neurons are shown to have increased firing pattern
entropy during PD, with this being reduced to near healthy
levels during effective DBS [3]–[6]. Sample entropy is a
measure for assessing the complexity of physiological time
series signals. In [7], it was shown that there was an inverse
relationship between beta-band oscillation power and beta-
band sample entropy in the STN LFP. Furthermore, in [7]
LFP sample entropy was utilized to distinguish between PD
patients who experienced freezing of gait episodes and those
who did not.
Computational modelling allows the investigation of net-
work dynamics which may be difficult to access during
clinical practice. Here a computational model of the cortico-
basal ganglia network is utilized to investigate changes in
basal ganglia neuronal entropy during DBS. Single unit
recordings from GP neurons are utilized to assess changes
in firing pattern entropy, while the STN LFP is simulated to
assess changes in sample entropy and beta-band oscillatory
activity during DBS. The results from the computational
model are compared with results from clinical and experi-
mental studies. Quantifying changes in basal ganglia entropy
may lead to an improved understanding of the relationship
between oscillatory activity and entropy in the network, and
how this relationship is modified during PD and DBS.
A physiologically based model of the cortico-basal ganglia
network incorporating extracellular DBS and simulation of
the STN LFP was utilized [8]. The structure of the network
model is presented in Fig. 1 and includes the closed loop
formed between the cortex, basal ganglia and thalamus.
The major model components include single compartment,
conductance-based biophysical models of the STN, globus
pallidus externa (GPe), globus pallidus interna (GPi) and
thalamus, each of which have been validated and employed
in previous modelling studies [8]–[10]. The cortex is repre-
sented by a network of interneurons and multi-compartment
cortical neurons. Each component is described in greater
detail below.
Six hundred cells consisting of one hundred STN, GPe,
GPi, thalamic, interneuron and cortical neurons were con-
nected through excitatory and inhibitory synapses, AMPA
and GABAa, respectively. The STN neurons received direct
excitatory input from the cortex via the hyperdirect path-
way and inhibitory input from the GPe. Each STN neuron
received excitatory input from five cortical neurons and
inhibitory input from two GPe neurons. Each GPe neuron
received inhibitory input from one other GPe neurons and
excitatory input from two STN neurons. Each GPi neuron
received excitatory input from a single STN neuron and
inhibitory input from a single GPe neuron. Each thalamic
neuron received inhibitory input from a single GPi neuron.
Cortical neurons received excitatory input from a single tha-
lamic neuron and inhibitory input from a single interneuron.
Interneurons received excitatory input from a single cortical
axon. All connections within the network were randomly
Interneurons Soma
Figure 1. Schematic diagram of the cortico-basal ganglia
model. Excitatory and inhibitory connections are indicated
with a + or –, respectively.
The presence of pathologically exaggerated beta oscilla-
tions in the cortico-basal ganglia network, typically observed
in PD, were simulated by varying synaptic gains within the
network in accordance with [11]. An increased cortical drive
to the STN, due to strengthening of the hyperdirect pathway,
led to the emergence of beta oscillations within the network
and the STN LFP.
A. Cortex
The model used to simulate the cortex consisted of cor-
tical neurons and interneurons. The cortical neuron model
included a soma, axon initial segment (AIS), main axon, and
axon collateral. The cortical neuron soma and interneuron
models are based on the regular spiking neuron model
developed by Pospischil et al. [12]. The model used to
simulate the AIS, main axon, and axon collateral is based
on results from the experimental and modeling study in [13].
The membrane potentials of the cortical compartments and
interneurons are described by
syn (1)
Where Cmis the membrane capacitance, Ilis the leak
current, INa is the sodium current, IKis the potassium
current, IKd is D potassium current, IMis a slow, voltage-
dependent potassium current, and Isyn are synaptic currents.
The cortical soma model excluded the IKd current. The
cortical AIS, main axon and axon collateral segments did
not include the IMcurrent. Finally, cortical interneurons did
not include either the IKd or IMcurrents. Further details
regarding the parameters used can be found in [12], [13].
B. Subthalamic Nucleus
The STN model incorporates a physiological representa-
tion of STN neurons developed by Otsuka et al. [14]. The
model captures the generation of plateau potentials, which
are believed to play an important role in generating STN
bursting activity in PD. The membrane potential of an STN
neuron is given by
syn (2)
Where Cmis the membrane capacitance, Ilis the leak
current, INa is a sodium current, IKis a Kv3-type potassium
current, IAis a voltage dependent A-type potassium current,
ILis an L-type long lasting calcium current, ICaKis a
calcium activated potassium current, and Isyn are synaptic
currents. Further details can be found in [14].
C. Globus Pallidus and Thalamus
The models used to simulate GPe, GPi, and thalamic
neurons are based on those presented by Rubin and Terman
in [15]. The membrane potential of a GP neuron is described
syn (3)
Where Cmis the membrane capacitance, Ilis the leak
current, INa is the sodium current, IKis a potassium current,
INa is a sodium current, ITis a low-threshold T-type calcium
current, ICa is a voltage-dependent afterhyperpolarizaation
potassium current, and Isyn are synaptic currents. Thalamic
neurons were modelled similarly, with the exception of
excluding ICa and IAH P in the thalamic model. Further
details regarding the GPe, GPi, and thalamus models can
be found in [15].
D. Synapses
Individual synaptic currents, Ik
syn, were described by
syn =Rk(VmErev ) (4)
Where Ik
syn is the kth synaptic current, Rkrepresents
the kinetics of the onset and decay of current following a
presynaptic spike for synapse k, and Erev is the reversal
potential for the appropriate type of synapse. Further details
regarding the synaptic models can be found in [16].
E. Application of DBS and LFP Simulation
The extracellular potential due to a current source, Ix, at
time twas calculated as
Vx(t) = Ix(t)
Where σis the conductivity of a homogenous, isotropic
medium representing brain tissue. The distance from a point
in extracellular space to the current source Ix, or vice versa,
is given as rx.
For simulating the voltage applied to cortical collaterals
due to a monopolar stimulation electrode, rxwas the dis-
tance between each collateral segment and the stimulation
electrode, while Ixwas a square wave current source with
130 Hz frequency, 60 s pulse width and varying amplitude.
Cortical collaterals were assigned a random position in a
2 mm radius of extracellular space around the stimulation
To simulate the recording of the LFP using a differ-
ential recording electrode, STN neurons, like the cortical
collaterals, were assigned positions in a 2 mm radius of
extracellular space around the stimulation electrode. Each
recording electrode was positioned 1.365 mm away from the
stimulation electrode, with each recording electrode being
placed either side of the stimulation electrode. The LFP
recorded at each recording electrode was then calculated
as the summation of the total extracellular voltages due to
each STN neuron’s synaptic currents in the extracellular
space, where Ixcorresponds to the synaptic currents of an
STN neuron of distance rxaway from one of the recording
F. LFP Sample Entropy
Sample Entropy was calculated as the negative natural
logarithm of the estimated conditional probability that two
sequences similar for mpoints remain similar at the next
point, where self-matches are not included in calculating the
probability [17]. It is defined as
SampEn(m, r, N) = ln[Am+1(r)/Am(r)] (6)
Where Am+1(r)represents the number of vector pairs
(within the time series) of length m+ 1 whose mutual
distance is less than a tolerance r, and Am(r)equals the
number of vector pairs (within the time series) of length
mwhose mutual distance is less than r. Here the length
of the vector pairs, m, denotes the embedding dimension.
The mutual distance between the vector pairs was calculated
using the Chebyshev distance between the pairs, with mand
rset to 4 and 20% of the standard deviation of the data
G. Firing Pattern Entropy
The firing pattern entropy of a spike train was calculated
by binning the inter spike intervals of the train in logarithmic
time, as in [18]. The leftmost and rightmost bin edges were
set just below, or just above, the smallest and largest inter
spike intervals observed, respectively, in each population.
The entropy of the spike train was then calculated using
Shannon Entropy
H(X) =
PIS Iilog2(PISIi) (7)
Where His the entropy of spike train X,PISIiis the
probability of inter spike interval ioccurring in the spike
train, and Nis the number of inter spike interval bins.
H. Simulation Details
The model was implemented in Python using the API
package PyNN [19] with NEURON v7.6.5 as the model
simulator. A timestep of 0.01 ms was used for simulations.
Post-processing was done using custom scripts in MATLAB
(The MathWorks, Inc., Natick, MA). To examine LFP sample
entropy the LFP was first down-sampled and low-pass fil-
tered at 100Hz to remove stimulation artifact. To examine the
magnitude of beta-band oscillations in the LFP the LFP was
band-pass filtered between 10 and 35 Hz, full-wave rectified
and averaged by low-pass filtering at 2 Hz.
A. LFP Sample Entropy
The effect of varying stimulation amplitude on the STN
LFP sample entropy was investigated using a fixed frequency
and pulse width of 130 Hz and 60 µs, respectively, Fig. 2 (a).
A progressive increase in the sample entropy was observed
as the stimulation amplitude increased. For comparison, the
corresponding magnitude of beta-band oscillations in the
LFP is given in Fig. 2 (b).
DBS Amplitude (mA)
Figure 2. Normalized STN LFP (a) sample entropy and (b)
beta-band oscillation power as a function of DBS amplitude.
B. Firing Pattern Entropy
The effect of varying stimulation frequency on the firing
pattern entropy of GPe and GPi neurons was investigated
using a fixed amplitude and pulse width of 3 mA and 60
µs, respectively. Fig. 3 shows the cumulative distribution
of the firing pattern entropy for each population. Firing
pattern entropy was reduced following the application of
high frequency stimulation (HFS), with a frequency of 130
Hz, and increased following the application of low frequency
stimulation (LFS), with a frequency of 20 Hz.
Entropy (bits/spike)
Cumulative Distribution Function
Figure 3. Cumulative distributions of the firing pattern en-
tropy for the (a) GPe and (b) GPi neuron populations due to
high frequency and low frequency stimulation.
The aim of this study was to investigate changes in
neuronal entropy due to extracellular DBS in a computational
model of the cortico-basal ganglia network during PD. The
model includes extracellular stimulation of cortical afferent
fibers projecting to the STN and simulation of the resulting
LFP. This allows for comparison with clinical and exper-
imental results which have previously investigated entropy
changes in the cortico-basal ganglia network during PD.
Sample entropy was observed to have an inverse rela-
tionship with beta-band oscillation power, Fig. 2. In [7],
an inverse relationship was observed between beta-band
sample entropy and beta-band oscillation power taken from
STN LFP recordings in freely moving patients during three
movement tasks. Here, a distinction was not made between
frequency bands when calculating sample entropy. However,
effective DBS did result in similar behaviour, with beta-band
power decreasing, and sample entropy increasing in the LFP
for increasing DBS amplitude.
Firing pattern entropy in GP neurons decreased during
HFS, and increased during LFS of the STN, Fig. 3. These
results agree with those presented in [4]–[6] and support the
hypothesis that effective DBS regularizes firing patterns in
GP neurons.
The computational model presented displays changes in
neuronal entropy consistent with those presented in clinical
and experimental literature. These results suggest that inves-
tigation into basal ganglia entropy changes during PD and
DBS may elucidate the relationship between network entropy
and oscillation power during disease progression. Moreover,
these results support further investigation of the utilization
of entropy-based measures in closed-loop DBS strategies.
[1] A. A. K¨
uhn, et al., ”High-Frequency Stimulation of the Subthalamic
Nucleus Suppresses Oscillatory βActivity in Patients with Parkinsons
Disease in Parallel with Improvement in Motor Performance”, J.
Neurosci., vol. 28, no. 24, pp. 6165-6173, Jun. 2008.
[2] C. De Hemptinne, et al., ”Therapeutic deep brain stimulation reduces
cortical phase-amplitude coupling in Parkinsons disease”, Nat. Neu-
rosci., vol. 18, no. 5, pp. 779-786, 2015.
[3] A. D. Dorval, A. Muralidharan, A. L. Jensen, K. B. Baker, and J. L.
Vitek, ”Information in Pallidal Neurons Increases with Parkinsonian
Severity”, Parkinson & Rel. Dis., vol. 21, no. 11, pp. 1355-1361, 2015.
[4] A. D. Dorval, G. S. Russo, T. Hashimoto, W. Xu, W. M. Grill, and J.
L. Vitek, ”Deep Brain Stimulation Reduces Neuronal Entropy in the
MPTP-Primate Model of Parkinsons Disease”, J. Neurophysiol., vol.
100, no. 5, pp. 2807-2818, 2008.
[5] A. D. Dorval and W. M. Grill, ”Deep brain stimulation of the
subthalamic nucleus reestablishes neuronal information transmission
in the 6-OHDA rat model of parkinsonism.”, J. Neurophysiol., vol.
111, no. 10, pp. 1949-59, May 2014
[6] A. D. Dorval, A. M. Kuncel, M. J. Birdno, D. A. Turner, and W. M.
Grill, ”Deep Brain Stimulation Alleviates Parkinsonian Bradykinesia
by Regularizing Pallidal Activity”, J. Neurophysiol., vol. 104, no. 2,
pp. 911-921, 2010.
[7] J. Syrkin-Nikolau, et al., ”Subthalamic neural entropy is a feature of
freezing of gait in freely moving people with Parkinsons disease”,
Neurobiol. Dis., vol. 108, no. June, pp. 288-297, 2017.
[8] E. M. Dunn and M. M. Lowery, ”A model of the cortico-basal ganglia
network and local field potential during deep brain stimulation”, 2015
7th Int. IEEE/EMBS Conf. Neural Eng., pp. 848-851, 2015.
[9] G. Kang and M. M. Lowery, ”Interaction of oscillations, and their
suppression via deep brain stimulation, in a model of the cortico-
basal ganglia network”, IEEE Trans. Neural Syst. Rehabil. Eng., vol.
21, no. 2, pp. 244-253, 2013.
[10] G. Kang and M. M. Lowery, ”Effects of antidromic and orthodromic
activation of STN afferent axons during DBS in Parkinsons disease:
a simulation study”, Front. Comput. Neurosci., vol. 8, no. 32, 2014.
[11] R. J. Moran, et al., ”Alterations in brain connectivity underlying beta
oscillations in parkinsonism”, PLoS Comput. Biol., vol. 7, no. 8, 2011.
[12] M. Pospischil, et al., ”Minimal Hodgkin-Huxley type models for
different classes of cortical and thalamic neurons”, Biol. Cybern., vol.
99, no. 4-5, pp. 427-441, Nov. 2008.
[13] A. J. Foust, Y. Yu, M. Popovic, D. Zecevic, and D. A. Mccormick,
”Somatic Membrane Potential and Kv1 Channels Control Spike Re-
polarization in Cortical Axon Collaterals and Presynaptic Boutons”,
vol. 31, no. 43, pp. 15490-15498, 2011.
[14] T. Otsuka, T. Abe, T. Tsukagawa, and W. J. Song, ”Conductance-Based
Model of the Voltage-Dependent Generation of a Plateau Potential in
Subthalamic Neurons”, J. Neurophys., vol. 92, no. 1, 2004.
[15] J. E. Rubin and D. Terman, ”High Frequency Stimulation of the
Subthalamic Nucleus Eliminates Pathological Thalamic Rhythmicity
in a Computational Model”, J. Comput. Neurosci., vol. 16, no. 3, pp.
211-235, 2004.
[16] A. Destexhe, Z. F. Mainen, and T. J. Sejnowski, ”An Efficient Method
for Computing Synaptic Conductances Based on a Kinetic Model of
Receptor Binding”, Neural Comp., vol. 6, pp. 14–18, 1994.
[17] J. S. Richman and J. R. Moorman, ”Physiological time-series analysis
using approximate entropy and sample entropy”, Am. J. Physiol. Circ.
Physiol., vol. 278, no. 6, pp. H2039-H2049, 2000.
[18] A. D. Dorval, ”Probability Distributions of the Logarithm of
Inter–Spike Intervals yield Accurate Entropy Estimates from Small
Datasets”, J. Neurosci. Methods, vol. 173, no. 1, pp. 129-139, 2009.
[19] A. P. Davison, ”PyNN: a common interface for neuronal network
simulators”, Front. Neuroinform., vol. 2, no. January, pp. 1-10, 2008.
... Axon collaterals were positioned within the STN, parallel to one another, and orientated to project in the direction. The axon and collateral model was based on that used previously by Lowery and Kang 27,38 with membrane parameters based on an experimental study in mice developed by Foust et al. 39 . This model captures the threshold of activation of the axon and collateral by considering the properties of the model neuron along with the electrode geometry, the electrode-tissue-interface, and the heterogeneity and electrical properties of brain tissue incorporated in the rat DBS FEM model. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A c c e p t e d M a n u s c r i p t 16 Multi-compartment axon collaterals were simulated to be 500 µm long with a diameter of 0.5 µm and were comprised of 11 segments with 10 nodes. ...
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Objective: During deep brain stimulation (DBS) the electrode-tissue interface forms a critical path between device and brain tissue. Although changes in the electrical double layer and glial scar can impact stimulation efficacy, the effects of chronic DBS on the electrode-tissue interface have not yet been established. Approach: In this study, we characterised the electrode-tissue interface surrounding chronically implanted DBS electrodes in rats and compared the impedance and histological properties at the electrode interface in animals that received daily stimulation and in those where no stimulation was applied, up to eight weeks post-surgery. A computational model was developed based on the experimental data, which allowed the dispersive electrical properties of the surrounding encapsulation tissue to be estimated. The model was then used to study the effect of stimulation-induced changes in the electrode-tissue interface on the electric field and neural activation during voltage- and current-controlled stimulation. Main results: Incorporating the observed changes in simulations in silico, we estimated the frequency-dependent dielectric properties of the electrical double layer and surrounding encapsulation tissue. Through simulations we show how stimulation-induced changes in the properties of the electrode-tissue interface influence the electric field and alter neural activation during voltage-controlled stimulation. A substantial increase in the number of stimulated collaterals, and their distance from the electrode, was observed during voltage-controlled stimulation with stimulated ETI properties. In vitro examination of stimulated electrodes confirmed that high frequency stimulation leads to desorption of proteins at the electrode interface, with a concomitant reduction in impedance. Significance: The demonstration of stimulation-induced changes in the electrode-tissue interface has important implications for future DBS systems including closed-loop systems where the applied stimulation may change over time. Understanding these changes is particularly important for systems incorporating simultaneous stimulation and sensing, which interact dynamically with brain networks.
... In previous studies, PET results indicated that PHM is associated with changes in metabolic activity of the Gpi [26,27], especially because the Gpi is considered vulnerable to hypoxic brain damage [28,29]. It is known that globus pallidus (GP) neurons in the network decrease during high-frequency stimulation and increase during low frequency stimulation [30]. Although high-frequency stimulation targeting the Gpi has been reported in a few studies, in the present study, an increase in myoclonus ratings at high stimulation frequencies was observed, which is not in line with previous findings. ...
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Post-hypoxic myoclonus (PHM) and Lance–Adams syndrome (LAS) are rare conditions following cardiopulmonary resuscitation. The aim of this study was to identify functional activity in the cerebral cortex after a hypoxic event and to investigate alterations that could be modulated by deep brain stimulation (DBS). A voxel-based subtraction analysis of serial positron emission tomography (PET) scans was performed in a 34-year-old woman with chronic medically refractory PHM that improved with bilateral globus pallidus internus (Gpi) DBS implanted three years after the hypoxic event. The patient required low-frequency stimulation to show myoclonus improvement. Using voxel-based statistical parametric mapping, we identified a decrease in glucose metabolism in the prefrontal lobe including the dorsolateral, orbito-, and inferior prefrontal cortex, which was suspected to be the origin of the myoclonus from postoperative PET/magnetic resonance imaging (MRI) after DBS. Based on the present study results, voxel-based subtraction of PET appears to be a useful approach for monitoring patients with PHM treated with DBS. Further investigation and continuous follow-up on the use of PET analysis and DBS treatment for patients with PHM are necessary to help understanding the pathophysiology of PHM, or LAS.
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This study presents a computational model of closed-loop control of deep brain stimulation (DBS) for Parkinson's disease (PD) to investigate clinically viable control schemes for suppressing pathological beta-band activity. Closed-loop DBS for PD has shown promising results in preliminary clinical studies and offers the potential to achieve better control of patient symptoms and side effects with lower power consumption than conventional open-loop DBS. However, extensive testing of algorithms in patients is difficult. The model presented provides a means to explore a range of control algorithms in silico and optimize control parameters before preclinical testing. The model incorporates (i) the extracellular DBS electric field, (ii) antidromic and orthodromic activation of STN afferent fibers, (iii) the LFP detected at non-stimulating contacts on the DBS electrode and (iv) temporal variation of network beta-band activity within the thalamo-cortico-basal ganglia loop. The performance of on-off and dual-threshold controllers for suppressing beta-band activity by modulating the DBS amplitude were first verified, showing levels of beta suppression and reductions in power consumption comparable with previous clinical studies. Proportional (P) and proportional-integral (PI) closed-loop controllers for amplitude and frequency modulation were then investigated. A simple tuning rule was derived for selecting effective PI controller parameters to target long duration beta bursts while respecting clinical constraints that limit the rate of change of stimulation parameters. Of the controllers tested, PI controllers displayed superior performance for regulating network beta-band activity whilst accounting for clinical considerations. Proportional controllers resulted in undesirable rapid fluctuations of the DBS parameters which may exceed clinically tolerable rate limits. Overall, the PI controller for modulating DBS frequency performed best, reducing the mean error by 83% compared to DBS off and the mean power consumed to 25% of that utilized by open-loop DBS. The network model presented captures sufficient physiological detail to act as a surrogate for preclinical testing of closed-loop DBS algorithms using a clinically accessible biomarker, providing a first step for deriving and testing novel, clinically suitable closed-loop DBS controllers.
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Introduction: The motor symptoms of Parkinson's disease (PD) present with pathological neuronal activity in the basal ganglia. Although neuronal firing rate changes in the globus pallidus internus (GPi) and externus (GPe) are reported to underlie the development of PD motor signs, firing rates change inconsistently, vary confoundingly with some therapies, and are poor indicators of symptom severity. Methods: We explored the relationship between parkinsonian symptom severity and the effectiveness with which pallidal neurons transmit information. We quantify neuronal entropy and information - alternatives to firing rate and correlations respectively - in and between GPe and GPi neurons using a progressive, 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine, non-human primate model of PD. Results: Neuronal entropy and symptom severity were not linearly correlated: in both pallidal segments, entropy increased from naive to moderate parkinsonism, but decreased with further progression to the severely parkinsonian condition. In contrast, information transmitted from GPe to GPi increased consistently with symptom severity. Furthermore, antidromic information from GPi to GPe increased substantially with symptom severity. Together, these findings suggest that as parkinsonian severity increases, more and more information enters GPe and GPi from common sources, diminishing the relative importance of the orthodromic GPe to GPi connection. Conclusions: With parkinsonian progression, the direct and indirect pathways lose their independence and start to convey redundant information. We hypothesize that a loss of parallel processing impairs the ability of the network to select and implement motor commands, thus promoting the hypokinetic symptoms of PD.
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Deep brain stimulation (DBS) is increasingly applied for the treatment of brain disorders, but its mechanism of action remains unknown. Here we evaluate the effect of basal ganglia DBS on cortical function using invasive cortical recordings in Parkinson's disease (PD) patients undergoing DBS implantation surgery. In the primary motor cortex of PD patients, neuronal population spiking is excessively synchronized to the phase of network oscillations. This manifests in brain surface recordings as exaggerated coupling between the phase of the beta rhythm and the amplitude of broadband activity. We show that acute therapeutic DBS reversibly reduces phase-amplitude interactions over a similar time course as that of the reduction in parkinsonian motor signs. We propose that DBS of the basal ganglia improves cortical function by alleviating excessive beta phase locking of motor cortex neurons.
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Recent studies suggest that subthalamic nucleus (STN)-Deep Brain Stimulation (DBS) may exert at least part of its therapeutic effect through the antidromic suppression of pathological oscillations in the cortex in 6-OHDA treated rats and in parkinsonian patients. STN-DBS may also activate STN neurons by initiating action potential propagation in the orthodromic direction, similarly resulting in suppression of pathological oscillations in the STN. While experimental studies have provided strong evidence in support of antidromic stimulation of cortical neurons, it is difficult to separate relative contributions of antidromic and orthodromic effects of STN-DBS. The aim of this computational study was to examine the effects of antidromic and orthodromic activation on neural firing patterns and beta-band (13-30 Hz) oscillations in the STN and cortex during DBS of STN afferent axons projecting from the cortex. High frequency antidromic stimulation alone effectively suppressed simulated beta activity in both the cortex and STN-globus pallidus externa (GPe) network. High frequency orthodromic stimulation similarly suppressed beta activity within the STN and GPe through the direct stimulation of STN neurons driven by DBS at the same frequency as the stimulus. The combined effect of both antidromic and orthodromic stimulation modulated cortical activity antidromically while simultaneously orthodromically driving STN neurons. While high frequency DBS reduced STN beta-band power, low frequency stimulation resulted in resonant effects, increasing beta-band activity, consistent with previous experimental observations. The simulation results indicate effective suppression of simulated oscillatory activity through both antidromic stimulation of cortical neurons and direct orthodromic stimulation of STN neurons. The results of the study agree with experimental recordings of STN and cortical neurons in rats and support the therapeutic potential of stimulation of cortical neurons.
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Growing evidence suggests that synchronized neural oscillations in the cortico-basal ganglia network may play a critical role in the pathophysiology of Parkinson's disease. In this study, a new model of the closed loop network is used to explore the generation and interaction of network oscillations and their suppression through deep brain stimulation (DBS). Under simulated dopamine depletion conditions, increased gain through the hyperdirect pathway resulted in the interaction of neural oscillations at different frequencies in the cortex and subthalamic nucleus (STN), leading to the emergence of synchronized oscillations at a new intermediate frequency. Further increases in synaptic gain resulted in the cortex driving synchronous oscillatory activity throughout the network. When DBS was added to the model a progressive reduction in STN power at the tremor and beta frequencies was observed as the frequency of stimulation was increased, with resonance effects occurring for low frequency DBS ( 40 Hz) in agreement with experimental observations. The results provide new insights into the mechanisms by which synchronous oscillations can arise within the network and how DBS may suppress unwanted oscillatory activity.
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Past models of somatosensory cortex have successfully demonstrated map formation and subsequent map reorganization following localized repetitive stimuli or deafferentation. They provide an impressive demonstration that fairly simple assumptions about ...
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The shape of action potentials invading presynaptic terminals, which can vary significantly from spike waveforms recorded at the soma, may critically influence the probability of synaptic neurotransmitter release. Revealing the conductances that determine spike shape in presynaptic boutons is important for understanding how changes in the electrochemical context in which a spike is generated, such as subthreshold depolarization spreading from the soma, can modulate synaptic strength. Utilizing recent improvements in the signal-to-noise ratio of voltage-sensitive dye imaging in mouse brain slices, we demonstrate that intracortical axon collaterals and en passant presynaptic terminals of layer 5 pyramidal cells exhibit a high density of Kv1 subunit-containing ion channels, which generate a slowly inactivating K(+) current critically important for spike repolarization in these compartments. Blockade of the current by low doses of 4-aminopyridine or α-dendrotoxin dramatically slows the falling phase of action potentials in axon collaterals and presynaptic boutons. Furthermore, subthreshold depolarization of the soma broadened action potentials in collaterals bearing presynaptic boutons, an effect abolished by blocking Kv1 channels with α-dendrotoxin. These results indicate that action potential-induced synaptic transmission may operate through a mix of analog-digital transmission owing to the properties of Kv1 channels in axon collaterals and presynaptic boutons.
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Cortico-basal ganglia-thalamocortical circuits are severely disrupted by the dopamine depletion of Parkinson's disease (PD), leading to pathologically exaggerated beta oscillations. Abnormal rhythms, found in several circuit nodes are correlated with movement impairments but their neural basis remains unclear. Here, we used dynamic causal modelling (DCM) and the 6-hydroxydopamine-lesioned rat model of PD to examine the effective connectivity underlying these spectral abnormalities. We acquired auto-spectral and cross-spectral measures of beta oscillations (10-35 Hz) from local field potential recordings made simultaneously in the frontal cortex, striatum, external globus pallidus (GPe) and subthalamic nucleus (STN), and used these data to optimise neurobiologically plausible models. Chronic dopamine depletion reorganised the cortico-basal ganglia-thalamocortical circuit, with increased effective connectivity in the pathway from cortex to STN and decreased connectivity from STN to GPe. Moreover, a contribution analysis of the Parkinsonian circuit distinguished between pathogenic and compensatory processes and revealed how effective connectivity along the indirect pathway acquired a strategic importance that underpins beta oscillations. In modelling excessive beta synchrony in PD, these findings provide a novel perspective on how altered connectivity in basal ganglia-thalamocortical circuits reflects a balance between pathogenesis and compensation, and predicts potential new therapeutic targets to overcome dysfunctional oscillations.
Methods: Synchronous STN local field potentials (LFPs), shank angular velocities, and ground reaction forces were measured in fourteen PD subjects (eight Freezers) off medication, OFF deep brain stimulation (DBS), using an investigative, implanted, sensing neurostimulator (Activa® PC+S, Medtronic, Inc.). Tasks included standing still, instrumented forward walking, stepping in place on dual forceplates, and instrumented walking through a turning and barrier course. Results: During locomotion without FOG, Freezers showed lower beta (13-30Hz) power (P=0.036) and greater beta Sample Entropy (P=0.032), than Non-Freezers, as well as greater gait asymmetry and arrhythmicity (P<0.05 for both). No differences in alpha/beta power and/or entropy were evident at rest. During periods of FOG, Freezers showed greater alpha (8-12Hz) Sample Entropy (P<0.001) than during walking without FOG. Conclusions: A novel turning and barrier course was superior to FW in eliciting FOG. Greater unpredictability in subthalamic beta rhythms was evident during stepping without freezing episodes in Freezers compared to Non-Freezers, whereas greater unpredictability in alpha rhythms was evident in Freezers during FOG. Non-linear analysis of dynamic neural signals during gait in freely moving people with PD may yield greater insight into the pathophysiology of FOG; whether the increases in STN entropy are causative or compensatory remains to be determined. Some beta LFP power may be useful for rhythmic, symmetric gait and DBS parameters, which completely attenuate STN beta power may worsen rather than improve FOG.
Oscillatory neural activity in the beta frequency band (12-30 Hz) is elevated in Parkinson's disease and is correlated with the associated motor symptoms. These oscillations, which can be monitored through the local field potential (LFP) recorded by a deep brain stimulation (DBS) electrode, can give insight into the mechanisms of action, as well as treatment efficacy, of DBS. A detailed physiological model of the cortico-basal ganglia network during DBS of the subthalamic nucleus (STN) is presented. The model incorporates extracellular stimulation of STN afferent fibers, with both orthodromic and antidromic activation, and the LFP detected at the electrode. Pathological beta-band oscillations within the cortico-basal ganglia network were simulated and found to be attenuated following the application of DBS. The effects of varying DBS parameters, including pulse amplitude, duration and frequency, on the LFP at the DBS electrode were then assessed. The model presented here can be further used to understand the interaction of DBS with the complex dynamics of the cortico-basal ganglia network and subsequent changes observed in the LFP.
Pathophysiological activity of basal ganglia neurons accompanies the motor symptoms of Parkinson's disease. High frequency (>90 Hz) deep brain stimulation (DBS) reduces parkinsonian symptoms, but the mechanisms remain unclear. We hypothesize that parkinsonism-associated electrophysiological changes constitute an increase in neuronal firing pattern disorder and a concomitant decrease in information transmission through the ventral basal ganglia; and that effective DBS alleviates symptoms by decreasing neuronal disorder while simultaneously increasing information transfer through the same regions. We tested these hypotheses in the freely behaving, 6-hydroxydopamine-lesioned rat model of hemiparkinsonism. Following the onset of parkinsonism, mean neuronal firing rates were unchanged in spite of a significant increase in firing pattern disorder (i.e., neuronal entropy), in both the globus pallidus and substantia nigra pars reticulata. This increase in neuronal entropy was reversed by symptom-alleviating DBS. While increases in signal entropy are most commonly indicative of similar increases in information transmission, directed information through both regions was substantially reduced (>70%) following the onset of parkinsonism. Again, this decrease in information transmission was partially reversed by DBS. Together, these results suggest that the parkinsonian basal ganglia are rife with entropic activity, and incapable of functional information transmission. Further, they indicate that symptom-alleviating DBS works by lowering the entropic noise floor, enabling more information-rich signal propagation. In this view, the symptoms of parkinsonism may be more a default mode, normally overridden by healthy basal ganglia information. When that information is abolished by parkinsonian pathophysiology, hypokinetic symptoms emerge.