Presented by Sarah Hedayat. Supervised by Pr.Cappy and Dr.Hoel
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1 1 Presented by Sarah Hedayat Supervised by Pr.Cappy and Dr.Hoel
2 Outline 2 Project objectives Key elements Membrane models As simple as possible Phase plane analysis Review of important Concepts Conclusion and perspectives References
3 Project Objectives 3 Short term: Build and validate a membrane model Energy budget of one spiking neuron Long term: Design and fabrication of neuromorphic circuit This circuit must be simple and low power.
4 Key elements : Human Brain 4 The human brain have around : neurons synapses/neuron; 10 synapses billions connections in 1cm.
5 5 Key elements : Neuron Neuron: Soma Axon Synapses Dendrites Membrane Information : Action potential or Spike Regenerated (Ranvier node) Non attenuation
6 6 Key elements : Neuronal membrane Outside Neuronal membrane : 1) Na +, K + gated channels 2) Ion pump channels 3) Leaky channels Channels are selective Ion gradient => Built in potential Opposite sign (Ena Ek) Ena< Spike amplitude <Ek Inside
![mechanisms nerve cell membrane & Spike [1] 1963 : Nobel Prize](/docs-images/93/111796145/images/7-1.jpg "Medicine [1] Hodgkin and Huxley, 1952 The Journal of")
7 7 Membrane model 1945 : The first intracellular recording of an action potential 1952 : Discovered the relation between : Ionic mechanisms nerve cell membrane & Spike [1] 1963 : Nobel Prize Medicine [1] Hodgkin and Huxley, 1952 The Journal of Physiology,2012
8 Membrane model 8 Hodgkin Huxley Vs. Wei : Infinite Volume Vs. definite volume. Charge density conservation Vs. Individual charge conservation. Constant E Nernst Vs. Variable E Nernst Non Ipump Vs. Ipump Squid axon Vs. Human neuron [2]: Wei et al. 2014
9 MembraneModel : HH Vs. Wei 9 HH (1952) Wei (2014)
10 10 Membrane Model: Wei Model Wei model: Based on Hodgkin Huxley equations. Variable E Nernst Ipump Individual ions conservation
11 11 Membrane Model: Excitability of neuron Iex=7, 50 and 100µA/cm 2, Ts=7ms
12 12 Membrane Model: For Iext= 7µA/cm 2 Ts=7 ms, Ionics current (INa, IK, IL)
13 13 Membrane Model: For Iext= 7µA/cm 2 Ts=7ms, Power (PNa, PK, Pd)
14 14 Membrane Model: Energy Dissipation for Iext= 7µA/cm 2 Ts=7ms S=10-6 cm 2 Wei s Energy (pj) ENa = EK = ED = == 0.03 LF model energy by Cea-Leti (pj) ED = [3] Antoine Joubert, Thèse Neurone analogique robuste et technologies emergentes pour les architectures neuromorphiques, Cea Leti 2014.
15 15 Membrane Model The membrane model is a nonlinear four dimensional dynamical system (V, m, n, h). The understanding of nonlinear dynamic is difficult. To propose a simple neuromorphic circuit a simplified membrane model is suitable. Various simpler mathematical model, which capture the key features of the full system, have been proposed. The best known is the FitzHugh-Nagumo model.
16 As simple as possible 16 In the mid-1950 s, FitzHugh sought to reduce the Hodgkin- Huxley model to a two variable model for which phase plane analysis applies. Ø n and h have slow kinetics relative to m. => m = m steady state Ø n + h is approximately 0.8. [4] Richard FitzHugh at the National Institute of Health.
17 17 As simple as possible : Wei model simplified Wei model with 4 variables [2] Wei model with 2 variables Allow phase plane analysis. n w (V) : time constant [2] Y. Wei et al, Unification of Neuronal Spikes, Seizures, and Spreading Depression, The Journal of Neuroscience (August 27, 2014):
18 18 Phase plane analysis : Nullclines, Equilibrium point, Stability Nullclines: V Nullcline : dv/dt=0 N Nullcline : dn/dt=0 Equilibrium point : The intersection of nullclines is an equilibrium point. The equilibrium point may be unstable. Stability : Definition stable equilibrium point : (dv/dt). (dn/dt) < 0 Definition unstable equilibrium point : (dv/dt). (dn/dt) > 0
19 19 Phase plane analysis : Iext = 0 µa/cm 2 3 Equilibrium point : 1 stable 2 unstable
20 20 Phase plane analysis : A step of Iext = 7 µa/cm 2 1 Equilibrium point : 1 unstable
21 21 Phase plane analysis : A step of Iext = 0 µa/cm 2 Vs Iext = 7µA/cm 2 3 Equilibrium point for Iext=0 µa/cm 2 Stable 1 Unstable 2 1 Equilibrium point for Iext=7µA/cm 2 Stable 0 Unstable 1 N Nullcline remain the same for both Iext=0µA/cm 2 and Iex=7µA/cm 2.
22 22 Phase plane analysis : A step of Iext= 0 µa/cm 2 to 1.8µA/cm 2 Iext= 0 to 1.6 µa/cm 2 : Stable 1 Unstable 2 Iext= 1.7µA/cm 2 is the break point : Stable 1 Unstable 2 Iext = 1.8 µa/cm 2 : Stable 0 Unstable 1
23 23 Phase plane analysis Iex = 7µA/cm 2 N- N+ V- V+ Cycle : Counterclockwise 4 different zone s signs.
24 24 Review of important Concepts q Neurons are dynamical systems. q A good neuron model must reproduce not only electrophysiology but also the non linear dynamics of neurons. q A good neuron circuit has to be low power and as simple as possible.
25 25 Conclusion and perspectives Conclusion The HH and Wei publications has been coded with MATLAB and results show similar behavior. These models permit the estimation of the energy dissipated for one spiking neuron. Wei code was simplified for non linear analysis and remain our choice for cell membrane model. Perspectives Two inter-connected neurons. Matlab Spice Spice Modeling of MOS (EKV, BSIM) or other devices (TiFET, Memristors, ) Manufacturing of simple, ultra low power Neuoroinspired circuit.
26 26 References Publications Books & Journals [1]A.L. Hodgkin, and Huxley, A.F., A quantitative description of membrane current and its application to conduction and excitation in nerve, J.Physiol.1952; 117, [2] Y. Wei et al, Unification of Neuronal Spikes, Seizures, and Spreading Depression, The Journal of Neuroscience (August 27, 2014):
27 THANK YOU FOR LISTENING! Neuroinspired Project. Supervised by Pr Cappy and Dr Hoel. Presented by Sarah Hedayat.
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