* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Stimulation-Induced Functional Decoupling (SIFD)
Synaptogenesis wikipedia , lookup
Theta model wikipedia , lookup
Aging brain wikipedia , lookup
Neural engineering wikipedia , lookup
Electrophysiology wikipedia , lookup
Environmental enrichment wikipedia , lookup
Neuroplasticity wikipedia , lookup
Mirror neuron wikipedia , lookup
Biochemistry of Alzheimer's disease wikipedia , lookup
Multielectrode array wikipedia , lookup
Types of artificial neural networks wikipedia , lookup
Neurotransmitter wikipedia , lookup
Stimulus (physiology) wikipedia , lookup
Haemodynamic response wikipedia , lookup
Central pattern generator wikipedia , lookup
Activity-dependent plasticity wikipedia , lookup
Single-unit recording wikipedia , lookup
Transcranial direct-current stimulation wikipedia , lookup
Nonsynaptic plasticity wikipedia , lookup
Development of the nervous system wikipedia , lookup
Neural coding wikipedia , lookup
Neural oscillation wikipedia , lookup
Clinical neurochemistry wikipedia , lookup
Holonomic brain theory wikipedia , lookup
Neuroanatomy wikipedia , lookup
Feature detection (nervous system) wikipedia , lookup
Molecular neuroscience wikipedia , lookup
Pre-Bötzinger complex wikipedia , lookup
Channelrhodopsin wikipedia , lookup
Premovement neuronal activity wikipedia , lookup
Optogenetics wikipedia , lookup
Neuropsychopharmacology wikipedia , lookup
Synaptic gating wikipedia , lookup
Neurostimulation wikipedia , lookup
Biological neuron model wikipedia , lookup
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 24/05/2017 1 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 24/05/2017 2 1. Parkinson’s disease (PD), Basal ganglia (BG), and deep brain stimulation (DBS) 24/05/2017 3 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 24/05/2017 4 Static model of the network 24/05/2017 (Fig from McIntyre, 2005) 5 Static model of the network (2) Direct pathway 24/05/2017 (Fig modified from McIntyre, 2005) 6 Static model of the network (3) Indirect pathway 24/05/2017 (Fig modified from McIntyre, 2005) 7 Static model of the network (4) Hyperdirect pathway 24/05/2017 (Fig modified from McIntyre, 2005) 8 (Rubin, 2008) 24/05/2017 9 Zoom on basal ganglia 24/05/2017 Modolo J., Mosekilde E., Beuter A., J Physiol Paris, 2007 10 Deep brain stimulation (DBS) 24/05/2017 11 McIntyre et al (2005) 24/05/2017 12 Deep brain stimulation (DBS) – stimulator off (from Johns Hopkins Parkinson's Disease and Movement Disorders Center ) 24/05/2017 13 Deep brain stimulation (DBS) – stimulator on (from Johns Hopkins Parkinson's Disease and Movement Disorders Center ) 24/05/2017 14 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 24/05/2017 15 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. 24/05/2017 16 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 » ? 24/05/2017 17 The subthalamic nucleus: the prefered target Levesque and Parent (2005) 24/05/2017 Parent et al. (1995) 18 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 24/05/2017 19 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 24/05/2017 20 Paradox 1 (cont’d) Single neurons Neuronal network Neuron 1 Neuron 2 ….. Coupling Emerging activity (physio/pathological) Neuron N 24/05/2017 21 Paradox 1 (cont’d) Single neurons Neuronal network Neuron 1 Neuron 2 Coupling ….. Emerging activity (physio/pathological) Neuron N DBS 24/05/2017 22 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. 24/05/2017 23 2. Mathematical model: population based approach 24/05/2017 24 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. 24/05/2017 Izhikevich, 2007 25 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. 24/05/2017 26 A simplification: the Izhikevich model 24/05/2017 Izhikevich, 2003 27 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 24/05/2017 28 Population equations General form of a conservation equation Population density Neural flux Mean-field variable Detailed form of the main population equation 24/05/2017 Individual dynamics Neural interactions 29 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 24/05/2017 30 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 24/05/2017 Axonal conduction delays Past activity of the network 31 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) 24/05/2017 32 Multiscale properties of the approach 24/05/2017 Modolo J., Mosekilde E., Beuter A., J Physiol Paris, 2007 33 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 24/05/2017 34 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 24/05/2017 Modolo, Henry, Beuter, J Biol Phys (submitted) Populations coupling 35 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 24/05/2017 Modolo, Henry, Beuter, J Biol Phys (submitted) 36 STN and GPe dynamics « Physiological » state 24/05/2017 « Pathological » state 37 3. Can we explain DBS paradoxes? 24/05/2017 38 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). 24/05/2017 39 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) 24/05/2017 Neuronal interactions 40 Paradox 1 (cont’d) Supression of internal excitatory connections. 24/05/2017 Response of STN model cells to DBS with/without excitatory coupling. 41 Paradox 1 (cont’d) From cortex To GPi Illustration of Stimulation-Induced Functional Decoupling (SIFD). 24/05/2017 42 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 24/05/2017 No DBS DBS No DBS 43 Decrease of somatic activity during DBS (model, top; experimental data in humans, bottom) (McIntyre et al., 2004) 24/05/2017 44 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). 24/05/2017 45 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. 24/05/2017 46 Paradox 2 (cont’d) 24/05/2017 Model results. (Modolo, Henry, Beuter, J Biol Phys, submitted) 47 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. 24/05/2017 48 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) 24/05/2017 49 4. Conclusion 24/05/2017 50 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 24/05/2017 51 Acknowledgements (model) 24/05/2017 Dr A. Garenne Dr J. Henry University of Bordeaux 2 University of Bordeaux 1 52 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 24/05/2017 53 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. 24/05/2017 54 Appendix 24/05/2017 55 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 24/05/2017 56 Multiscale properties of the approach • Infinite number of neurons • Identical dynamical behaviour 24/05/2017Modolo J., Mosekilde E., Beuter A., J Physiol Paris, 2007 57 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 58 Boundary conditions 24/05/2017 59