Download Stimulation-Induced Functional Decoupling (SIFD)

Linking brain dynamics, neural
mechanisms and deep brain
stimulation
Anne Beuter and Julien Modolo
Laboratoire d’Intégration du Matériau au Système
UMR CNRS 5218
University of Bordeaux
May 16th, 2008
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Outline
1.
2.
3.
4.
Parkinson’s disease (PD), Basal ganglia (BG), and
deep brain stimulation (DBS)
Mathematical model: population based approach
Can we explain DBS paradoxes?
Conclusion
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1. Parkinson’s disease (PD), Basal
ganglia (BG), and deep brain
stimulation (DBS)
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Parkinson’s disease (PD) and Deep
brain stimulation (DBS)

PD: 800 000 persons in Europe (65 000 new cases each year),
6 millions in the world

DBS: Standard and efficient symptomatic procedure to
improve motor symptoms

Main targets: Vim, GPi, STN (favorite)

Mechanisms of DBS: many hypotheses proposed, but
mechanisms still unclear today
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Static model of the network
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(Fig from McIntyre, 2005)
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Static model of the network (2)
Direct pathway
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(Fig modified from McIntyre, 2005)
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Static model of the network (3)
Indirect pathway
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(Fig modified from McIntyre, 2005)
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Static model of the network (4)
Hyperdirect
pathway
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(Fig modified from McIntyre, 2005)
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(Rubin, 2008)
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Zoom on basal ganglia
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Modolo J., Mosekilde E., Beuter A., J Physiol Paris, 2007
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Deep brain stimulation (DBS)
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McIntyre et al (2005)
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Deep brain stimulation (DBS) – stimulator off
(from Johns Hopkins Parkinson's Disease and Movement Disorders Center )
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Deep brain stimulation (DBS) – stimulator on
(from Johns Hopkins Parkinson's Disease and Movement Disorders Center )
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PD, DBS and paradoxes

Reversibility of symptoms (sleep, somnanbulism or
emergencies, pharmacology, DBS) PD = dynamical disease
(Beuter et al, 1995), defined by Mackey and Glass (1977)

Lesion versus stimulation: excitation and/or inhibition of the
stimulated area?

Frequency dependent stimulation effect
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Paradox 1: Reversibility of symptoms

PD: reversible under DBS or L-DOPA, symptoms re-appear
is DBS or L-DOPA is stopped.

 DBS acts on a control parameter of the motor loop
network to re-etablish physiological dynamics.
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Role of the STN-GPe complex in basal ganglia

STN and GPe: tightly interconnected nuclei

STN: main excitatory structure in basal ganglia

STN  weak activity in healthy state, strong and synchronous
activity between 3 and 8 Hz in PD

STN-GPe: can oscillate spontaneously, « bad pacemaker » ?
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The subthalamic nucleus: the prefered target
Levesque and Parent (2005)
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Parent et al. (1995)
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Goal: understand these paradoxes to
elucidate DBS mechanisms
Our methodology is:

Develop a mathematical model

Formulate candidate physiological mechanisms interpreted at several
scales of description

Confront with numerical simulations, experimental and clinical
observations
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Philosophy of the modelling approach

A multi-scale description: DBS current impacts the cellular,
population and « network of populations » levels (Beuter and
Modolo, 2007)

A dynamical description with a fine temporal resolution:
functional models are useful, but not sufficient (static)

A model not too cumbersome easily re-used by other
researchers in the field
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Paradox 1 (cont’d)
Single neurons
Neuronal network
Neuron 1
Neuron 2
…..
Coupling
Emerging activity
(physio/pathological)
Neuron N
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Paradox 1 (cont’d)
Single neurons
Neuronal network
Neuron 1
Neuron 2
Coupling
…..
Emerging activity
(physio/pathological)
Neuron N
DBS
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Paradox 1 (cont’d)
Single neurons
Neuronal network
Neuron 1
Neuron 2
…..
Disruption of
coupling
Emerging activity
(physio/pathological)
Neuron N
 Stimulation-Induced Functional Decoupling.
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2. Mathematical model:
population based approach
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A reminder on the Hodgkin-Huxley model
• Hodgkin & Huxley (1952):
Study of the giant squid axon, measurement of the
membrane potential under different stimulation
currents + ionic channels hypothesis.
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Izhikevich, 2007
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Modelling the effects of DBS with a
population based model

Why? : Complex systems imply numerous
interactions between the elements of the
system: analytical solving is difficult or
impossible.

Key concept : Average interaction for each
element.

Previous models: mainly based on the LIF
model (Nykamp and Tranchina, 2000;
Omurtag et al., 2000).

Advantages: multi-scale, dynamic model.
(Fig from Paul De Koninck Laboratory)
 Seems appropriate to model the effects of DBS in PD.
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A simplification: the Izhikevich model
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Izhikevich, 2003
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From single neuron to neuronal population
What do we need to describe a neuronal population of N neurons?
1) A population density function (number of neurons per state)
such as
2) Quantify neuronal individual dynamics (using the Izhikevich model)
3) Quantify neuronal interactions (using a mean-field variable)
If: N neurons, W afferences per neuron on average
Then: if M spikes at time t, each neuron receives (W/N)*M spikes
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Population equations
General form of a conservation equation
Population density
Neural flux
Mean-field variable
Detailed form of the main population equation
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Individual dynamics
Neural interactions
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Where is biology in the equations?
Synaptic events modelled by instantaneous « jumps » of amplitude ε in the membrane
potential
v(t)
Excitatory spike
ε
Rest
ε
Membrane potential
Inhibitory spike
t
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Where is biology in the equations?
Reception rate of neurotransmitters for each neuron: included in the spike reception rate
This holds too for the neurotransmitters production rate. The mean-field variable
expresses as:
Mean connectivity degree
Number of
neurons
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Axonal conduction
delays
Past activity of
the network
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Modelling the DBS stimulation current
Train of biphasic, charge-balanced pulses such as those used in Medtronic® stimulators
IDBS(t)
Simplification: DBS current
modelled as a current directly
injected through the membrane
t
Izhikevich model for STN
cells (Modolo et al., 2008)
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Multiscale properties of the approach
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Modolo J., Mosekilde E., Beuter A., J Physiol Paris, 2007
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Modelling the subthalamo-pallidal network

Terman and Rubin (2002, sophisticated and realistic cell
models), Gillies and Willshaw (2004, firing rate model)

The STN-GPe complex activity pattern can change under
the following conditions:



Inhibition from Striatum to GPe increases
Intra-GPe inhibitory synapses weaken
Relevance of modelling the STN-GPe network during DBS:
currently not measured experimentally
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Mathematical model of the subthalamopallidal complex
System of PDE describing the dynamics of STN and GPe depending on
connectivity, delays and individual firing patterns:
Individual population dynamics
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Modolo, Henry, Beuter, J Biol Phys (submitted)
Populations coupling
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STN and GPe neurons modelling

STN neurons with new parameters for the Izhikevich model
1) Spontaneous
spiking activity
2) Increased spiking
frequency under
excitatory input
3) Post-inhibitory
bursting
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Modolo, Henry, Beuter, J Biol Phys (submitted)
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STN and GPe dynamics
« Physiological » state
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« Pathological » state
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3. Can we explain DBS paradoxes?
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Paradox 1: Why do STN stimulation and
lesion produce similar benefits?

DBS: intuitively increases the firing rate of STN neurons.

Lesion: destruction of the STN (subthalamotomy), thus completely
suppresses STN activity, dramatically improves tremor (BUT is not
reversible!)

How can we explain this paradox? We propose the following
mechanism:
 Stimulation-Induced Functional Decoupling (SIFD): DBS current
neutralizes the impact of glutamatergic synapses within the STN
(cortical afferences or axon collaterals within the STN).
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Paradox 1 (cont’d)
We propose the following mechanism:
Stimulation Induced Functional Decoupling (SIFD) is the situation where neuronal
interactions become negligible with regards to individual neuronal dynamics. Thus, the
network becomes «unwired» and neurons seem independent from one another.
Mathematically speaking:
Individual neuronal
dynamics (+DBS)
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Neuronal interactions
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Paradox 1 (cont’d)
Supression of internal
excitatory connections.
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Response of STN model cells to DBS with/without excitatory coupling.
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Paradox 1 (cont’d)
From cortex
To GPi
Illustration of Stimulation-Induced
Functional Decoupling (SIFD).
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Paradox 1 (cont’d)
Intuitively, electrical stimulation of neurons should increase spiking activity
(assumed in Rubin and Terman, 2004)
However: in vivo recordings in MPTP monkeys show a decrease in STN neurons
activity! (Meissner et al., 2005)
Furthermore: GPi cells (target of STN cells) are activated at high-frequency
(Hashimoto et al., 2003)  how is this compatible?
McIntyre et al. (2004): DBS inhibits STN somas, and excites STN axons
soma
axon
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No DBS
DBS
No DBS
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Decrease of somatic
activity during DBS
(model, top;
experimental data in
humans, bottom)
(McIntyre et al., 2004)
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Paradox 1 (cont’d)

Let us list STN neurons dynamical properties:

Dampened oscillations of their membrane potential (Bergman et al., 1994)

Post-inhibitory bursts of action potentials (Bevan et al., 2002)

Two stable equilibria (bistability) (Kass and Mintz, 2006)
 STN neurons have their equilibrium near an Andronov-Hopf bifurcation
(Izhikevich, 2007) and can be classified as resonators.
 Eigen-frequency of STN neurons: low-frequency, thus: high-frequency (≥100 Hz)
can delay or decrease the response.
 STN neurons dynamical properties underlie their activity decrease during DBS
(Modolo and Beuter, in preparation).
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Paradox 2: Why are DBS effects frequencydependent?

Low-frequency (<20 Hz) DBS: has no effect on motor function,
sometimes worsens symptoms (Timmermann et al., 2007).

High-frequency DBS (>100 Hz): provides dramatic relief of
symptoms.

Modolo et al. (2008): low-frequency DBS current may cause a
resonance with STN neurons eigen-frequency.

 Low-frequency DBS appears to exacerbate pathological
activity, while high-frequency DBS suppresses it.
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Paradox 2 (cont’d)
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Model results. (Modolo, Henry, Beuter, J Biol Phys, submitted)
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How does DBS facilitate motor function?

DBS appears to mimic lesions by decreasing STN activity, and
lesions improve motor function.

Synaptic decoupling between motor cortex and STN during DBS
via SIFD.

Lalo et al. 2008  decrease bêta coupling between M1 and STN
during the execution of movement (experimental study).

Our interpretation: the STN becomes functionnaly decoupled
from M1 following SIFD, facilitating the execution of movement.
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Confirmation of insights from simulations

DBS mimics the decoupling of the STN from internal excitatory
connections and maybe from cortex, that normally occurs in the
presence of dopamine (Magill et al., 2001)

The effects of DBS are frequency-dependent, i.e., the stimulation
frequency is close or away from the resonance frequency of the
stimulated area (Timmermann et al., 2007)
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4. Conclusion
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Conclusion: a cascade of SIFDs?
Cortical
afferent spikes
Afferences from primary motor cortex (M1)
Cancellation by
collision
Antidromic
activation (Li
et al., 2007)
Axonal activation of GPi efferences
Efferences to GPi
Decreased somatic activity
SIFD
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Acknowledgements (model)
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Dr A. Garenne
Dr J. Henry
University of Bordeaux 2
University of Bordeaux 1
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Acknowledgements
Financial support of the project

BioSim European Network Of Excellence, No AB LSHB-CT-2004005137, Professor Erik Mosekilde, coordinator

Aquitaine Region (France), No 20051399003AB
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Recent publications

Modolo, Henry, Beuter. Dynamics of the subthalamo-pallidal complex during deep brain
stimulation in Parkinson’s disease, J Biol Phys, submitted.

Modolo, Mosekilde, Beuter. New insights offered by a computational model of deep
brain stimulation, J Physiol Paris, 101:58–65, 2007.

Modolo, Garenne, Henry, Beuter. Development and validation of a population based
model based on a discontinuous membrane potential neuron, J Integr Neurosci,
6(4):625–655, 2007.

Pascual, Modolo, Beuter. Is a computational model useful to understand the effects of
deep brain stimulation in Parkinson’s disease? J Integr Neurosci, 5(4) :551–559, 2006.
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Appendix
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The diffusion approximation
Let us remind the main population equation
In the limit
(EPSP low amplitude), the interaction term expresses as
which gives a Fokker-Planck equation
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Multiscale properties of the approach
• Infinite number of neurons
• Identical dynamical behaviour
24/05/2017Modolo
J., Mosekilde E., Beuter A., J Physiol Paris, 2007
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Population equations
In summary, each population is described by a population density function
Where the mean-field variable expresses as
24/05/2017Modolo
J., Garenne A., Henry J., Beuter A., J Integr Neurosci, 2007
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Boundary conditions
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