The Nervous System Introduction Nerve fibre structure Transmission Lines Speed of propagation Nerve...

The Nervous System

• 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 parts-

the 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).


• 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.


• Efferent (or Motor) Neuron

Synapse

DendriteCell Body

Nucleus

Axon

Myelin Sheath

Node of Ranvier Motor Nerve Endings

Muscle Fibres

~1 m


• Axon Cross Section

Axon core(~0.7-5 m dia.)

Myelin Sheath (~2m dia)(nb - absent at Nodes of Ranvier)

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.


• 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.


• 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.


• 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)

Ra

RLC

Vin Vout


Ra

RLC

Vin Vout

Ra = Rdx where R = resistance per unit length

1/RL = Gdx where G = leakage conductivity across axon membrane per unit length

C = Cm.2ra.dx where Cm = capacitance per unit area, and a cylindrical cross section is assumed: ra

dx

Axon Membrane


• 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)


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


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

Hence,di

dxGVa ……. (3)

Transmission of Signals– Eliminating ia from equations (2) and (3), we obtain:

d V

dxRGV

2

2

V V x 0 exp( / )

1 RG

Solution of the form:

with , the Space Parameter


– For an unmyelinated neuron,RG = 3.6x106 m-2

= 0.5 mm– For a myelinated neuron,

RG = 2.0x104 m-2

= 7 mm


• Nodes of Ranvier– Essential to effective conduction of signals

down long axons– Short (~2m) regions without myelin, allowing

ion exchange and regeneration of signal– Myelinated regions carry signal rapidly

between Nodes of Ranvier


• 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?


lNode of Ranvier

Vmax ~ 110 mV V = Vthres (~20 mV)

V V l

l V V

thresh max

max thresh

exp( )

ln( )

Hence,

mm12

In practice, nodes are ~ 1-2 mm apart


• Speed of Propagation– A good estimate is to assume the time taken to

travel between nodes is the time constant of the axon segment,

l

Assume equivalent circuit: C’R’R’


– Time constant is that of a simple RC circuit, = R’C’

– In terms of axon parameters,R’ = Rl/2 = al/2ra

2

C’= 2raCml

– Hence= al2Cm/ra

v = l/ = ra/ laCm


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

Axon Resistivity, ρa (Ωm)

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

Myelin thickness (μm) 2

Distance between nodes of Ranvier (mm)

1-2


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


v = l/ = ra/ laCm

For a high v need large ra or small l, since a & 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

-

+ +

+++

+ +

+ ++

++

+

-

-

-- -

- --

- -

-

-

-

Initially:

High KCl concn. on leftLow KCl concn. on right

-+ +

+

+

+ ++

+

++

++

+--

-- - -

- -

-- - -

-

At equilibrium:

K+ diffuses through membrane, setting up a dipole field across the membrane

Membrane permeable to K+ ions


– 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.

Na+Activated

Resting

Sodium gate

+-

-+

-+

+-

+-

+- -

+-+ +

-+-


– After ~0.1 ms, the Na+ gate closes and K+ gates open allowing flow of potassium ions out to restore the resting potential

-100

-80

-60

-40

-20

0

20

40

0 0.1 0.2 0.3 0.4

Time (ms)

Pot

enti

al (

mV

)


• Propagation of Action Potential– Impulse flows away from cell body– Length of pulse ~ few ms (~20-50 ms in the

heart)

+-

-+

-+

+-

+-

+- -

+-+ +

-+-

Na+ inK+ out

Direction of propagation

Origin of Action PotentialThe 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 intothe cell and depolarize the membrane(c) Current flow on leading edge (arrows) causes neighbouring region to the right to depolarize and thepotential change propagates (d) & (e) . K+ ions move out of the core of the axon and restore the RestingPotential (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


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


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 V

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 / 4r2

– Electric field strength, E, given by:E = j/

= i0 / 4r2

where = 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:

Current Source

B

r

V Edri

rB

B

0

4

1

Measurement of PotentialsPotential at a point some distance outside an

axon due to current dipole:

Vi

r r

i r r

r r

i d

r

Bd

d

d

0

0

0 0

0

02

4

1 1

4 4

cos

source sink

r0 rdr

B


– Fixed skin electrode, action potential moves– Geometry:

r

|i0d|0

B

Axon

Skin surfacea

x


Depolarisation

Repolarisation

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

The Nervous System Introduction Nerve fibre structure Transmission Lines Speed of propagation Nerve...

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