Electronic Neuron Model

Chapter 10

Membrane Modeling

• Nernst & Goldman equation – Resting potential

• Cable model of axon: – General cable equation

– Subthreshold response & pulse propagation

• Parallel conductance model – Behavior during activation

– Conductance variation

• Strongly tied to the concepts of electronic circuits

Physical Realization

• Realize physically the equivalent circuits

1. Analysis to verify model

– Really behave as same as the excitable tissue

– Improve understanding

– Adjust properties of the model

2. Constructing electronic circuits

– Whose behavior similar with real tissue

– Information processing similar with nature • Neuro-computing

cf: computer simulation

Classification of Neuron Model

• Based on structure of model

– Mathematical, Imaginary construction by physical laws, Physical model

• In conceptual dimensions

– Structure, Function, Evolution, Position in hierarchy

• According to physiological level

– Intraneuronal, Single neuron, Synapse, Neural interaction, Psychophysiological

• According to model parameters

– Resting, Stimulus, Recovery, Adaptation

Membrane Model

• Electronic realization of membrane excitation mechanism

– Theoretical model of Hodgkin & Huxley model

• Circuit modeling for conductance

– Between two nodes: inside & outside

– By active filters with transistors

• Parameters modification by variable resistors

• Voltage multiplied by 100: (10mV 1V)

– Other quantities in original values

Lewis Membrane Model

Block diagram of the Lewis membrane model

Circuit for potassium conductance

Circuit for sodium conductance

Response with Lewis Model

Complete Lewis membrane model

Single action pulse

A series of action pulse

Roy Membrane Model

• Simplicity than accuracy

• Neurofet

– Simplified with FET for conductance simulation • Easy implementation of amplifier with FET

Response with Roy Model

• Reasonably close the experimental results

Lewis Neuron Model

• Inclusion of excitatory & inhibitory synapse

Responses

Sodium & potassium current

Lewis

H &H

Lewis

H &H

Peak Na+ current

Steady state K+ current

Action pulse & corresponding ion currents

• Very similar with H-H model • Approximate within a order

Harmon Neuron Model

• Too complex to simulate neural networks

– Internal construction is not important

• Simplified pulse generation with multivibrator – Excitatory/inhibitory

– Drive up to 100 neurons

• Investigated 7 properties of neuron

Properties of Harmon Model

Properties of Harmon Model

Pulse obeys all-or-none law Width varies with frequency in some degree

Time from stimulus onset to output Fn of integration & refractory period

Response to constant input voltage

Propagation Model

• Inclusion of axial resistance

– Electronic realization of linear core-conductor model

6-unit chain

10-unit ring

Simulate pulse propagation in squid axon 17m/s (14~23m/s in experiments)

IC Realization

• Electronic neuron model in large quantity

– Electronic neuron as processing elements

• Stefan Prange model(1988,1990)

– Neuron with 8 synapses, with 300 transistors

• Misa Mahowald model(1991)

– CMOS and VLSI technology

– Simulated spikes in neocortical neurons accurately

– 0.1mm2 with 60uW power dissipation

– 100~200 neurons in 1cm1cm die