Medical Physics Tutorial 6 - Non-Ionising Imaging 2 (Endoscopy and MRI Scanning)

Contents

Endoscopy

Image formation

The Endoscope

Lasers
Safety Issues with Lasers

Magnetic Resonance Scanner

Benefits and Drawbacks

Larmor Frequency

 

Endoscopy

Endoscopy is non-invasive in that the skin does not need to be broken.  However the endoscope has to be inserted through the nose, mouth, urinary tract, or anus.  None of these are pleasant experiences for the patient.

 

Endoscopes are based on Optical fibres are basically long thin glass rods which are surprisingly flexible.  They conduct light by total internal reflection

 

  

Question 1

What is the condition needed for total internal reflection?

Answer

 

The light is guided down a core surrounded by glass cladding of slightly lower refractive index.  This is to prevent the loss of light if the core were to come into contact with material of a higher refractive index.

 

 

Question 2

What would happen if the light ray in the core hit a boundary between the core and a material of higher refractive index? Would it matter?

Answer

 

When dealing with optic fibres we use the Snell's Law Equation:

 

You may wish to revise this from Waves Tutorial 6

 

Here is how light is conducted in a glass fibre:

 

 

Question 3 

An optical fibre has a core refractive index of 1.55, and the cladding refractive index is 1.42.  What is the critical angle?

Answer

Question 4

What is the angle of refraction that gives this critical angle? 

Answer

Question 5 

What is the angle of incidence that gives this angle of refraction, as the light crosses from air into the glass?  Refractive index of air is 1.00.

Answer

 

The maximum angle of incidence in the examples above was about 38o.  Anything above that angle, the refraction will make the light ray strike the side of the glass at less than the critical angle.  This maximum angle of incidence is called the half angle.

 

The analysis above works for straight fibres.  If the fibre is bent sharply, then light will escape.  However as long as the radius of the bend is about 20 times the diameter or more, the light loss will be insignificant.

 

 

Image formation

Optical fibres are bundled together into a fibre optic light guide and the whole bundle is held together by a sheath.  In the short length that is used in an endoscope, about 1 metre, the light loss is negligible.  Each fibre carries the light that is incident on it independently of the other fibres.  To transmit a picture, the fibres in a bundle have to be kept in the same relative positions with a smooth square surface so that each fibre is contributing to the formation of the image.  This is called a coherent bundle.

 

 

You can see how each fibre contributes to the picture.  Each fibre is about 10 mm across.  The more fibres there are, the more detailed picture that is possible.  A good quality endoscope will have about 40 000 fibres packed into a bundle about 3 mm across.

 

The endoscope has to have a light source for the doctor to see what's going on.  The fibres for this do not have to be coherent (hence non-coherent), and are somewhat wider, about 30 mm.  This ensures more efficient transfer of light.  Also it is cheaper to produce.

 

The Endoscope

The first endoscope was invented by a German doctor, Adolph Kassmaul (1822 - 1902), at the turn of the twentieth century, but being non-flexible, was not much use.  A flexible device was made by another German, Rudolf Schindler (1888 - 1968), but it was still not very flexible unless the patient was contorted to suit the instrument.  Schindler's wife did the manipulation of the patient in the early days.  The endoscope became a much more practical instrument in the 1960's with the invention of the optical fibre.

 

Picture by Kalumet (adapted), Wikimedia Commons

The modern endoscope has:

 

A range of special instruments can be inserted which enables doctors not only to see inside to make an accurate diagnosis, but also operate on the diseased area.  This might be to:

 

At the eye piece end, there can also be attached:

 

The endoscope has also enable doctors to carry out keyhole surgery where surgical treatments can be applied without having to make major incisions.  This leads to less complications and more rapid recovery of the patient.

 

The latest development is to have a video camera at the end of the endoscope.

 

Question 6

Write down and explain three ways in which a doctor might use an endoscope.

Answer

 

Attenuation of images in optical fibres is discussed in Waves 6.

 

 

Lasers

LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.  If a photon of the right wavelength hits an excited atom of certain materials, it can stimulate the emission of a second photon of exactly the same wavelength and phase as the first.  If enough atoms are excited, the photons can stimulate further emissions of further photons, all travelling in the same direction.  At one end of the material there is a mirror that totally reflects the photons, while at the other is a mirror that partially reflects the photons.

 

 

 

Question 7

If there were no mirror at all, more photons could get out.  Why should there be a partially reflecting mirror instead of no mirror at all?

Answer

 

The properties of laser light are:

Lasers can produce continuous light.  Pulsed light is achieved not by turning the laser on and off, but by placing a shutter between the two mirrors.

 

The table shows some of the continuous lasers that can be used in medicine:

 

Laser

Wavelength (nm)

Power (W)

Fibre Transmission

CO2

10600

0.5 - 50

No

Nd-YAG

1064

0.5 - 100

Yes

Argon

488 or 514

1 - 10

Yes

Dye

Tunable

0.05 - 5

Yes

 

This table shows some of the pulsed lasers:

 

Laser

Wavelength (nm)

Pulse duration

Energy per pulse (J)

Fibre Transmission

Nd-YAG (QS)

1064

nanoseconds

0.1 - 1 

No

Nd-YAG

1064

microseconds

0.1 - 1

Yes

Dye

tunable, visible

microseconds

0.01 - 0.1

Yes

Excimer

UV

nanoseconds

0.01 - 0.1

Yes

 

Skin will absorb laser light:

The black pigment melanin increases the absorption.  The pigment haemoglobin in blood absorbs the blue green light of an argon laser.  Tissue damage arises because the water in cells boils and proteins are denatured, just like when they are cooked.

 

Lasers are often used with optic fibres to guide the laser to the precise location it is needed.

 

Tissue damage is reduced by using a pulsed laser, but there are difficulties sending high powered laser pulses down glass fibres as they will shatter due to thermal shock.

 

Lasers are used to cut away diseased material.  The Carbon Dioxide laser can be used with very delicate tissues such as the brain.  However it cannot be used with optical fibres as the far infra red radiation is absorbed by the fibres.  The argon laser can be used to spot weld the retina if it becomes detached.  It also used to remove birthmarks.  Lasers can be used to seal up (cauterise) bleeding wounds and ulcers.

 

There is work being carried out in which a chemical is injected into a tumour and can be activated by laser light to become toxic to the tumour, but not to the rest of the body.  This is called phototherapy.

 

 

Question 8

Which laser would you use for the following procedures?  Give a reason for each one:

(a) removing a tumour from the brain;

(b) spot welding a detached retina.

Answer

 

Safety Issues with Lasers

Lasers are potentially dangerous.  Hazards arise from:

Therefore strict rules have to be enforced so that persons using lasers are fully trained and competent in their use.

 

 

Magnetic Resonance Scanner

This machine is used widely in hospitals to carry out magnetic resonance imaging (MRI).  The technique was invented by Peter Mansfield (1933 - 2017), Professor of Physics at the University of Nottingham, and Paul Lauterbur (1929 - 2007), an American chemist.  A picture of the machine is shown below:

 

Image from Ptrump16 - Wikimedia Commons

MRI scanning is a very safe technique, as no ionising radiation is used.  However it can be quite claustrophobic due to the large size of the magnet (on the right hand side of the picture).   The space within the magnet is about 60 cm in diameter.  You are not expected to know about the precise constructional details of the machine.  However it is worth saying that the machine produces a static magnetic field, the strength of which is up to 3 Tesla.  There is also an alternating magnetic field of about 60 MHz.  The magnets are superconducting, so have to be kept very cold.

 

The key to MRI is that the human body is, in effect, a bag of sea-water.  The MR scanner uses properties of the water molecule for it to work.  You will be familiar with the water molecule as:

 

 

The water molecule is polar.  That means that the electrons tend to move towards the oxygen atom, leaving the hydrogen atoms with a slight deficiency of negative charge.  Therefore it has a slight positive charge.  The MRI scanner does not interact with the oxygen atom, or the electrons around the hydrogen atom.   It does interact with the protons (hydrogen nuclei).  To distinguish the protons in the hydrogen and the oxygen, we will call the protons in the hydrogen the hydrogen nuclei.

 

Question 9

Why doesn't the magnetic field interact with the protons in the oxygen atom?

Answer

 

The hydrogen nuclei have the quantum property called spin.  This allows them to interact with magnetic fields.  Normally the hydrogen nuclei are randomly oriented, just like domains in a magnet.  So there is no magnetisation.  The MRI scanner uses a combination of strong magnetic fields and radiofrequency electromagnetic radiation to "irritate" them.

 

An Analogy

I will use an analogy to show the idea.  Consider a number of teenage students in a large tent.  They are asleep.  It is dark, so you can't see them.

 

 

Then someone comes round and shouts in a rasping voice, "Morning! Wakey Wakey! Rise and shine!" 

 

It is dark, so you can't see the students.  But you can hear them and locate them.  Not all the students reply, but you can see that these students have replied:

 

 

Because the hydrogen nuclei have spin, they orient themselves along the magnetic field lines, as iron filings do.  They act as little compasses.  Most will align with the magnetic field.  These are nuclei with low energy, marked with the letter, 'L'.  Unlike the compasses, however, which all align in direction of the magnetic field, a minority of nuclei orient themselves in the opposite direction to the magnetic field.  This requires more energy, so the nuclei are called high energy and are marked in the diagram with a letter 'H'.  Spin is a quantum phenomenon that works on probability.  Therefore there is a probability that any nucleus can achieve the higher energy level.

 

 

Question 10

What is the effect of one low energy nucleus combined with one high energy nucleus?

Answer

 

There are more low energy nuclei than high energy nuclei. So we see:

 

 

At the moment, all we have is a physics curiosity.  Now we have to do something to the unpaired low energy nuclei.  They will respond to an alternating magnetic field, which is provided by a coil that carries a radio frequency current.  The field coils that do this are sometimes called the gradient field coils.  The radiofrequency current is in pulses;  it NOT continuous. 

 

 

This makes the hydrogen nuclei oscillate like this:

 

 

Question 11

What happens to oscillators at a certain frequency?

Answer

 

At a certain frequency, the little magnets gain sufficient energy to flip over like this:

 

 

 

Then the radio frequency is turned off:

 

Immediately the little magnets flip back to where they were, and give off radio frequency energy:

 

The radiofrequency current is in pulses;  it NOT continuous.  This enables the receivers to pick up the waves emitted by the hydrogen nuclei.  The time taken for the hydrogen nuclei to flip back from the high to the low energy state is called the de-excitation relaxation time.  You will not be asked questions on this. 

 

The receiver coil picks up the radio waves from the hydrogen nuclei:

 

The signals picked up by the receiver are not displayed like this CRO trace.  They are processed using powerful computers to give out an image that can be looked at by the doctors.  Here are some images from an MRI scan:

Souce: KieranMaher, Wikimedia Commons

 

Often a fluid is injected to enhance the contrast to enable more detail to be seen in the pictures.  Normal and abnormal tissues respond slightly differently to the dyes, so different signals are given out.

 

If all the hydrogen nuclei in a particular area are made to resonate at the same time, the image could end up quite messy.  The way around this comes from the fact that the resonant frequency of the nuclei is linked to the magnetic field strength.  The higher the magnetic field strength, the higher the resonant frequency.  So we can adjust the magnetic field strength by have a flux density of 1.5 T in the area of interest, and reducing the magnetic field strength to 1.0 T in the adjacent areas.  The hydrogen nuclei will not resonate in the adjacent areas.  This enables pictures to be made of the body in the form of slices a few millimetres thick. The picture shows the idea:

 

 

Although the slices are normally perpendicular or transverse to the body, they can be at any angle the doctors want.  It's like slicing bread.  Usually bread is sliced at 90 degrees, but it doesn't have to be.

 

Here is a picture of a healthy 20-year-old man. The slice has been taken length-wise (or longitudinally):

 

Image from Cincinatti Children's Hospital

 

The data from the slices can be combined to make a three-dimensional image of a particular organ.

 

Image by Jccmoon, Wikimedia Commons

 

Benefits and Drawbacks

Benefits of MRI

 

Disadvantages of MRI

 

When a patient is about to have an MRI scan, it is very important that metal objects are removed from the room.  This includes keys, jewellery, and watches.  Injuries have occurred when metal objects have been attracted to the very powerful magnet.  Other injuries have been caused by metal implants, for example screws used to treat bad leg fractures.  Also shrapnel embedded from injuries sustained on active service can do a lot of damage.

 

Burns can happen from rings on fingers, since the ring can act as a perfectly good secondary coil to the radiofrequency coil.  Therefore eddy currents are induced, which would lead to a marked heating effect in the ring.

 

Careful management of the procedure will minimise such risks.

 

 

The Larmor Frequency  (Welsh and Eduqas)

The Larmor Frequency (strictly speaking the Larmor Constant), named after Joseph Larmor (1857 - 1942), an Irish physicist, is used as a constant of proportionality in NMR. 

 

It has the value of 42.6 10Hz T-1.  The units may be quoted as MHz T-1 (so watch out for this).

 

It is at this ratio that the hydrogen nuclei resonate in a magnetic field, which is the crucial part of NMR.    If the value of the magnetic field is 1.0 T, the frequency is 42.6 MHz.  We can use any value of magnetic field.

 

The resonant frequency for protons is worked out the equation:

 

f = 42.6 106 B

 

We can show the proportionality on the graph:

Other nuclei have a different ratio.  

 

Question 12

In the discussion on NMR above, we saw that the radio frequency was quoted as 60 MHz.

 

What is the magnetic field strength needed to get the hydrogen nuclei to resonate?

Answer

 

 

Derivation (Extension only)

You are NOT expected to derive the equation you have used to work out the resonant frequency.  I have included this argument to show how the constant of proportionality arises.  You need to be aware of the idea of angular momentum.  Like an object moving a straight line, spinning objects possess angular moment.  You can find out more about this in Engineering Physics Tutorial 2.

 

In the discussion on NMR above, we considered the hydrogen nuclei in two dimensions only, i.e. they waggled forwards and backwards.  In three dimensions, they spin round rather like a gyroscope or spinning top. 

 

Consider an electron of charge e in a magnetic field of flux density B.  The electron rotates on an axis of spin (just like the Earth rotates on an axis of spin).    If the electron is in a magnetic field of strength B, the axis of spin will trace a circular path as shown in the diagram:

 

 

The change in the orientation of the axis of spin is called the precession.  The proton can be considered to be a tiny magnetic dipole.  The orientation of the axis of spin is also the orientation of the magnetic dipole.  Therefore the axis is considered to undergo a magnetic moment.   As the moment is acting on an object with rotational moment, we can say that it has angular momentum, L, and is subject to a torque, t, from the external magnetic field, B.  (The symbol t is "tau", a Greek lower case letter 't', and is used as the Physics code for torque.)

 

These two quantities are related by a simple equation:

t = mB

 

The term m is the magnetic dipole moment.

 

The magnetic dipole moment is related to the angular momentum, L, and the magnetic field by:

 

t = gLB

 

Therefore:

 

mB = gLB

 

The term g (gamma) is called the gyromagnetic ratio.  The magnetic field term cancels out.  Therefore:

 

m = gL

 

The gyromagnetic ratio is the ratio of the magnetic moment to the angular momentum.

 

It can be shown that for any precessing particle:

Where:

 

Particle

g-factor

Electron

2.002

Neutron

3.826

Proton

5.586

 

 

Worked Example

What is the gyromagnetic ratio of a proton?

 

Mass of a proton = 1.673 10-27 kg.

g-factor = 5.586

Answer

Use:

g = (1.602 10-19 C 5.586) (2 1.673 10-27 kg) = 2.674 108 C kg-1

 

 

The angular momentum vector precesses at an angular velocity of w rad s-1.  This is often called the Larmor frequency.  It is an angular velocity.   It can be shown that the Larmor frequency is given by the relationship:

 

w = gB

 

So we can write:

 From circular motion, we know that:

Therefore:

 

Worked Example

What is the Larmor frequency of a proton at a magnetic field strength of 1.0 T?

 

Mass of a proton = 1.673 10-27 kg.

e = 1.602 10-19 C

g-factor = 5.586

Answer

Use:

 

f = (1.602 10-19 C 5.586 1.0 T) (4 p 1.673 10-27 kg) = 42.57 106 Hz

 

 

Therefore the Lamour frequency for protons gives the equation:

 

f = 42.6 106 B