The Nervous System
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Introduction
Nerve fibre structure
Transmission Lines
Speed of propagation
Nerve fibre action
Measurement of potentials
Introduction
• A number of our modern concepts of
electrical activity in the body date back
many years.
• Luigi Galvani made the first contribution in
this field in 1786 when he discovered
animal electricity in a frog's leg.
• Basic research in this area is called
neurophysiology.
Introduction
• The electricity generated inside the body serves
for the control and operation of nerves, muscles,
and organs. Essentially all functions and activities
of the body involve electricity in some way. The
forces of muscles are caused by the attraction of
opposite electrical charges. The action of the brain
is basically electrical. All nerve signals to and
from the brain involve the flow of electrical
currents.
Introduction
• The nervous system plays a fundamental role in
nearly every body function.
• Basically, a central computer (the brain) receives
internal and external signals and (usually) makes
the proper response. The information is
transmitted as electrical signals along various
nerves.
• This efficient communication system can handle
many millions of pieces of information at one time
with great speed.
Introduction
• In carrying out the special functions of the body,
many electrical signals are generated. These
signals are the result of the electrochemical action
of certain types of cells.
• By selectively measuring the desired signals
(without disturbing the body) we can obtain useful
clinical information about particular body
functions, for example ECG (Electrocardiogram),
EEG (Electroencephalogram), EMG
(Electromyogram)
Introduction
• The nervous system can be divided into two partsthe central nervous system and the autonomic
nervous system.
• The central nervous system consists of the brain,
the spinal cord, and the peripheral nerves. Nerves
are made up of a bundle of nerve fibres (neurons)
which transmit in only one direction. Nerves that
transmit sensory information to the brain or spinal
cord are referred to as afferent nerves and nerves
that transmit information from the brain or spinal
cord to the appropriate muscles and glands are
referred to as efferent nerves.
Introduction
• The autonomic nervous system controls
various internal organs such as the heart,
intestines, and glands.
• The control of the autonomic nervous
system is essentially involuntary.
Nerve Fibre Structure
• The basic structural unit of the nervous system is the
neuron, a nerve cell specialized for the reception,
interpretation, and transmission of electrical messages.
There are many types of neurons. Basically, a neuron
consists of a cell body that receives electrical messages
from other neurons through contacts called synapses
located on the dendrites or on the cell body. The dendrites
are the parts of the neuron specialized for receiving
information from stimuli or from other cells. The dendrite
may be a transducer (stretch receptor, temperature receptor,
etc).
Nerve Fibre Structure
• If an applied stimulus is strong enough, the neuron
transmits an electrical signal outward along a fibre
called an axon.
• The axon or nerve fibre carries the electrical signal
to muscles, glands, or other neurons.
• It can be more than a metre in length, extending
for example from the brain to a synapse low in the
spinal cord or from the spinal cord to a finger or
toe.
Nerve Fibre Structure
• Efferent (or Motor) Neuron
Synapse
Myelin Sheath
Axon Node of Ranvier Motor Nerve Endings
~1 m
Dendrite
Cell Body
Nucleus
Muscle Fibres
Nerve Fibre Structure
• Axon Cross Section
Myelin Sheath
(~2mm dia)
(nb - absent at
Nodes of Ranvier)
Axon core
(~0.7-5 mm dia.)
Membrane
(5-10 nm)
Transmission of Signals
• Across the surface or membrane of every neuron
is an electrical potential (voltage) difference due to
the presence of more negative ions on the inside of
the membrane than on the outside. The neuron is
said to be polarized.
• The inside of the cell is typically 60 to 90 m V
more negative than the outside. This potential
difference is called the resting potential of the
neuron.
• When the neuron is stimulated, a large momentary
change in the resting potential occurs at the point
of stimulation.
Transmission of Signals
• The potential change resulting from a stimulus is
called the action potential.
• The action potential propagates along the axon.
• The action potential is the major method of
transmission of signals within the body. The
stimulation may be caused by various physical and
chemical stimuli such as heat, cold, light, sound,
and odours.
• If the stimulation is electrical, only about 20 mV
across the membrane is needed to initiate the
action potential.
Transmission of Signals
• Qualitatively, the resting potential of a
nerve exists because the membrane is
impermeable to the large A- (protein) ions
while it can be permeable to the K+, Na+,
and Cl- ions.
Transmission of Signals
• The axon can be thought of as an electrical
transmission line
– Consider a small element of such a line, dx,
with resistance Ra, and capacitance C per unit
length (also include a leakage resistance, RL)
Vin
Vout
Ra
RL
C
Transmission of Signals
Vin
Vout
Ra
RL
C
Ra = Rdx where R = resistance per unit length
1/RL = Gdx where G = leakage conductivity across axon
membrane per unit length
C = Cm.2p.ra.dx where Cm = capacitance per unit area, and a
cylindrical cross section is assumed:
r
a
Axon Membrane
dx
Transmission of Signals
• Assume capacitance is small, hence:
– Vout = Vin . RL /(Ra + RL)
– Can therefore obtain a characteristic
attenuation length for an axon
– For an element dx, carrying current ia
(writing Vin = V(x) and Vout = V(x+dx) ) :
V(x) – V(x+dx) = ia(x).R.dx ….(1)
Transmission of Signals
Now in lim dx→0 {(V(x+dx) – V(x))/dx} = dV/dx
Thus equation (1) becomes:
dV/dx = - ia(x).R ……(2)
Leakage current across the segment of axon is:
dil = Gdx.V
where V = potential across axon membrane
Transmission of Signals
The change in axon current = leakage current, so:
ia(x) - ia(x+dx) = dil = Gdx.V
Now lim dx→0 {(ia(x+dx) – ia(x))/dx} = dia/dx
dia
Hence,
 GV
dx
……. (3)
Transmission of Signals
– Eliminating ia from equations (2) and (3), we
obtain:
d 2V
2   RGV
dx
Solution of the form:
V  V0 exp( x /  )
with , the Space Parameter
 1
RG
Transmission of Signals
– For an unmyelinated neuron,
RG = 3.6x106 m-2
 = 0.5 mm
– For a myelinated neuron,
RG = 2.0x104 m-2
 = 7 mm
Transmission of Signals
• Nodes of Ranvier
– Essential to effective conduction of signals
down long axons
– Short (~2mm) regions without myelin, allowing
ion exchange and regeneration of signal
– Myelinated regions carry signal rapidly
between Nodes of Ranvier
Transmission of Signals
• Nodes of Ranvier
– A threshold potential of some 20 mV above a
resting potential is required to trigger ion
exchange, leading to a maximum signal of
about 110 mV
– What is the maximum distance between Nodes
of Ranvier?
Transmission of Signals
Vmax ~ 110 mV
V = Vthres (~20 mV)
l
Vthresh  Vmax exp(  l  )
Node of Ranvier
Hence,
l   ln(Vmax Vthresh )  12 mm
In practice, nodes are ~ 1-2 mm apart
Transmission of Signals
• Speed of Propagation
– A good estimate is to assume the time taken to
travel between nodes is the time constant of the
axon segment, t
l
R’
Assume equivalent circuit:
R’
C’
Transmission of Signals
– Time constant is that of a simple RC circuit,
t = R’C’
– In terms of axon parameters,
R’ = Rl/2 = ral/2pra2
C’= 2praCml
– Hence
t = ral2Cm/ra
v = l/t = ra/ lraCm
Transmission of Signals
The myelin sleeve is a very good insulator and
thus the myelinated segments of the axon
have very low capacitance (Cm very small)
thus v is large (~70 m/sec). This is very
important – high speed reflexes and rapid reactions.
The signal from toe to brain takes about 0.05 sec.
This is still quite a long time if the bath water is hot!
Typical Axon Parameters
Property
Myelinated
Unmyelinated
2
2
Capacitance of unit area
of membrane, Cm (Fm-2 )
5 x 10-5
10-2
Conductance of unit area
of membrane, G (Ω-1 m-2)
2.5 x 10-2
50
Axon Resistivity, ρa
(Ωm)
Myelin thickness (μm)
2
Distance between nodes
of Ranvier (mm)
1-2
Transmission of Signals
Myelinated nerves in man have high signal propagation
velocities ,v, even in axons with small diameter because
of small Cm.
Thus 10,000 myelinated fibres of 10μm diameter
can be contained in a bundle with a cross-sectional
area of 1-2 mm2.
However the same number of unmyelinated fibres with
the same v would need a bundle ~ 100 cm2
Transmission of Signals
v = l/t = ra/ lraCm
For a high v need large ra or small l, since ra & Cm
are fixed for a particular axon. However at each node
energy is expended to re-establish Action Potential,
hence large l preferable; hence there has to be a
compromise in the size of l.
Action of Nerve Fibres
• Normal (resting) state of an axon is
polarised
– Typically, interior is -86 mV with respect to
exterior of axon.
+ + + + +
- - - - -
~0.14 mol/l K+
~0.15 mol/l (protein)~0.01 mol/l Na+
~0.005 mol/l Cl-
+ + + + +
- - - - -
~0.01 mol/l K+
~0.04 mol/l (protein)~0.14 mol/l Na+
~0.1 mol/l Cl-
Origin of Resting Potential
Membrane permeable to K+ ions
+ -+ + - +-- + - +
+ - +-+- +
+
-
- +
+
+ + + +- - +
- +
- ++
-+ - - + +
+- -+
Initially:
At equilibrium:
High KCl concn. on left
Low KCl concn. on right
K+ diffuses through
membrane, setting up a
dipole field across the
membrane
Action of Nerve Fibres
– On application of a stimulus, the potential
difference rises towards zero
– If a threshold voltage of ~ -70 mV is reached,
sodium “gates” in the axon membrane open,
allowing Na+ ions into the axon.
Sodium gate
+ - - + +
- + + - -
Resting
Activated
Na+
+ + + ++
- - - - -
Action of Nerve Fibres
– After ~0.1 ms, the Na+ gate closes and K+ gates
open allowing flow of potassium ions out to
restore the resting potential
40
Potential (mV)
20
0
-20
0
0.1
0.2
-40
-60
-80
-100
Time (ms)
0.3
0.4
Action of Nerve Fibres
• Propagation of Action Potential
– Impulse flows away from cell body
– Length of pulse ~ few ms (~20-50 ms in the
heart)
K+ out Na+ in
+ - - + +
- + + - -
Direction of
propagation
+ + + ++
- - - - -
Origin of Action Potential
The graphs on the next slide show the potential at P.
(a) Axon Resting Potential ~ - 80 mV
(b) Stimulation on the left causes Na+ ions to move into
the cell and depolarize the membrane
(c) Current flow on leading edge (arrows) causes
neighbouring region to the right to depolarize and the
potential change propagates (d) & (e) . K+ ions move
out of the core of the axon and restore the Resting
Potential (repolarizes the membrane).
This is the Action Potential.
Origin of Potential Measured on Skin
The potential measured outside an axon arises
from an injection of current (leakage
current) into the interstitial fluid and/or
tissue that surrounds the axon.
Leakage current, il , from an axon is only
large enough to measure over the region of
the action potential.
As we have seen previously dil = - dia
Simplified Form of Axon Potential
Simplified Form of Axon Potential
The axon current ia only
occurs if a potential
gradient exists along the
axon. Consider the
depolarization alone
initially.
Between x=0 and x=d
ia = ΔVa /Rd
where R is the resistance per
unit length of axon
Simplified Form of Axon Potential
Since il = change in axon current, il is zero
except at the discontinuities in the action
potential (i.e at x=0 and x=d).
Thus ia = 0 for x<0 and x>d and il = i0 at x=0
and x=d. (i0 is the change in ia)
Thus have a current source at at x=d and a
current sink at x=0
This is called a Current Dipole
Summary of Origin of Potentials
– Potentials due to current leakage into a
conducting medium (surrounding tissue)
– Current leakage only occurs at potential
discontinuities
– Consider depolarisation end only:
• Current dipole, with source and sink a distance d
apart
d
- - - - +
+ + + + -
Measurement of Potentials
• Direct
– Insertion of microprobes into nerve.
– Impractical for routine monitoring
– Historically important
• Measurement of potential in 1mm dia, squid axon
• Indirect
– Monitoring of small signals at the skin surface
– High attenuation due to tissue resistance
– Typically 50 mV
Measurement of Potentials
– Consider a current i0 injected into an infinite
conducting medium (the interstitial fluid), and
flowing out with spherical symmetry
– Current density given by:
j = i0 / 4pr2
– Electric field strength, E, given by:
E = j/s
= i0 / 4p s r2
where s = conductivity of the interstitial fluid
Measurement of Potentials
– At point B at a distance r from a current source,
the potential is then given by:
1
VB    Edr 


4ps r
B
i0
B
r
Current Source
Measurement of Potentials
Potential at a point some distance outside an
axon due to current dipole:
i0  1 1 
VB 
  
4 ps  rd r0 
B
i0  r0  rd 
i0 d cos 




4 ps  r0rd  4 ps
r2
r0
r
rd

source
sink
Measurement of Potentials
– Fixed skin electrode, action potential moves
– Geometry:
B
Skin surface
a
r
Axon

0
|i0d|
x
Measurement of Potentials
Repolarisation
Depolarisation
Total
Further Reading
• Physics of the Body, Cameron, Skofronick
and Grant, Ch. 9,
• Electromyograms
– Section 9.3
• Electrocardiograms
– Section 9.4
• Electroencephlograms
– Section 9.5