Download Day 4 - EE Sharif

Biomedical engineering Group
School of Electrical Engineering
Sharif University of Technology
Single Neuron vs Neural
population
Strategy to discover the Brain
Functionality
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The Single Neuron
What kind of physical devices are neurons?
Neurons are electro-chemical devices.
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Synapse
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STRUCTURE
They have three distinct
parts:
 (1) Cell body,
 (2) Dendrites, and
 (3) the Axon
The particular type of
neuron that stimulates
muscle tissue is called a
motor neuron.
Dendrites receive impulses
and conduct them
toward the cell body.
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Myelinated Axons
The axon is a single long,
thin extension that
sends impulses to
another neuron.
They vary in length and
are surrounded by a
many-layered lipid and
protein covering called
the myelin sheath,
produced by the
schwann cells.
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Resting Potential
In a resting neuron
(one that is not
conducting an
impulse), there is a
difference in
electrical charges on the outside and inside of
the plasma membrane. The outside has a
positive charge and the inside has a negative
charge.
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Contribution of Active Transport
There are different numbers of potassium ions (K+)
and sodium ions (Na+) on either side of the
membrane. Even when a nerve cell is not
conducting an impulse, for each ATP molecule
that’s hydrolysed, it is actively transporting 3
molecules Na+ out of
the cell and 2 molecules
of K+ into the cell, at
the same time by
means of the
sodium-potassium pump.
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Contribution of facilitated diffusion
The sodium-potassium
pump creates a
concentration and
electrical gradient for
Na+ and K+, which
means that K+ tends to
diffuse (‘leak’) out of
the cell and Na+ tends
to diffuse in. BUT, the membrane is much more
permeable to K+, so K+ diffuses out along its
concentration gradient faster. Conversely, the electric field
causes both ions tend to come in.
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RESULTS IN:
a net positive charge
outside & a net negative charge
inside. Such a membrane is
POLARISED
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Action Potential
When the cell membranes
are stimulated, there is
a change in the
permeability of the
membrane to sodium
ions (Na+).
The membrane becomes
more permeable to Na+
and K+, therefore
sodium ions diffuse into the cell down a concentration
gradient. The entry of Na+ disturbs the resting
potential and causes the inside of the cell to become
more positive relative to the outside.
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All-or-None Principle
Throughout depolarisation, the Na+ continues
to rush inside until the action potential
reaches its peak and the sodium gates close.
If the depolarisation is not great enough to
reach threshold, then an action potential
and hence an impulse are not produced.
This is called the All-or-None Principle.
Neuron is a physical device that converts an ‘input’ voltage change on their
dendrites into an ‘output’ voltage spike train that travels down their axon.
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Speed of Nerve Impulses



Impulses travel very
rapidly
myelin sheath greatly
increases the velocity
In unmyelinated fibres,
the entire axon
membrane is exposed
and impulse conduction
is slower.
A low-precision electrical device
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Equivalent Model for Dendrites
and Axons
dx
Rdx
Cdx
i ( x, t )
v( x, t )
 C
x
t
v( x, t )
  Ri ( x, t )
x
 2 v ( x, t )
v( x, t )

RC
x 2
t
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Equivalent Model for an excited Neuron
dx
Rdx
v0(t)
Cdx
i ( x, t )
v( x, t )
 C
x
t
 2 v ( x, t )
v( x, t )

RC
x 2
t
v( x, t )
  Ri ( x, t )
x
v(0, t )  v0 (t )
The passive membrane time constant in the soma is on the order of about 10 ms.
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Transmission of Action
Potential/ Dendrite potential
 2v
v
 RC
2
x
t
 2V ( x, f )
 j 2fRCV ( x, f )
2
x
V ( x, f )  V0e
 2fRC x  j 2fRC x
e
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Neuron: Transistor







Electrical devices
Highly nonlinear
Signal/information processors
Short memories: Long Memories
Output voltage spikes: proportional
Heterogeneous : Homogeneous
Biological : Manufactured
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Beyond the single neuron
Ch2,3
Mainly
Population of Neurons
ch4
‘population-temporal’
representation
ch5
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Neural population Benefits




Varying degrees of detail.
Extract the information that was
nonlinearly encoded using a linear
decoder
Allows many of the tools of linear
signals and systems theory
Ability to better observation
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NEURAL
TRANSFORMATION


Neural representation paves the way for
a useful understanding of neural
transformation
Can be characterized using linear
decoding.
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