Download Option I – Biomedical Physics

2. Medical Imaging
The uses of radiation in medicine dall into two
classes:
 Diagnostic imaging
 Radiation therapy
 The first radiation to be used in medicine was X-rays
– short wavelength radiation discovered by Röntgen
in 1895.
 Other ionizing radiations, such as alpha particles,
beta particles, gamma rays and radioactive isotopes
have uses in medicine or have an effect on living
organisms.
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β

Nature
He nucleus
Electron
Photon
Mass (u)
4
1/1840
0
Charge
+2e
-e
0
10 000
1000
1
A few cm of air
A few mm of Al
10 cm of Pb
Ions produced
per mm of path
Stopped by
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If we consider a point source of X-rays or gamma rays radiating
uniformly in all directions, the intensity at a distance r from the
source falls off according to the inverse square law.
Let P be the energy per unit time (the power) radiated by the
source.
The energy radiated can be thought to pas through an area of a
sphere of radius r and so the energy per unit area of the sphere is
P
I 
4r 2

This is the intensity of the source at a distance r from it.
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If, however, monochromatic radiation is directed into a medium
that can absorb radiation, the fall in intensity is exponential.
The degree to which X-rays can penetrate matter is called the
quality of the radiation.
It can be shown that the transmitted intensity decreases as
I  I 0 e  x

Here μ is a constant called the linear attenuation coefficient.
This coefficient can be determined from the slope of a plot of
the logarithm of the intensity versus distance.

It depends both on the material through which the radiation
passes and on the energy of the photons.
x
I0
Incident
intensity

I
Intensity is
reduced
This law is similar to the radioactive decay law and we
define by analogy the half-value thickness (HVT),
which is the length that must be travelled through in
order to reduce the intensity by a factor of 2.

Then,
HVT 
0.693


If x=x1/2 then I = ½ I0

Using I = I0 e-μx, we have ½ I0= I0 e-μx1/2 
1/2 = e-μx1/2  ln (0.5) = -μx1/2 
 - ln (0.5) = μx1/2  0.6931 = μx1/2 
 x1/2 = 0.6931/μ
The main methods by which X-rays are absorbed
are the photoelectric and Compton effects.
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In the photoelectric effect, the X-ray photon is absorbed by an
electron, which is then emitted from is atom or molecule.
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The importance of the photoelectric effect is mostly for lowenergy photons and increases sharply with increasing atomic
number of the specimen upon which the photons fall.
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In the Compton effect, the photon gives part of its energy to
a free electron and scatters it off with a reduced energy and
so increased wavelength.
The energy given to the electron appears as kinetic energy
for the electron.
The Compton effect, on the other hand, does not vary much
with energy and increases linearly with atomic number.
In both cases the electrons can ionize matter along their
paths.
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X-rays were the first radiation to be used for medical imaging.
X-ray machines used for taking an ordinary X-ray picture operate
at voltages around 15-30 kV for a mammogram and at about 50150 kV for a chest X-ray.
electrons
X-rays
At these voltages the dominant mechanism for
energy loss by the X-rays is the photoelectric effect.
 Since this effect is strongly dependent on atomic
number and there is a substantial difference
between the atomic numbers of the elements
present in bone (Z=14) and soft tissue (Z=7), it
follows that bone will absorb X-rays much more
strongly that soft tissue.
 Hence, the X-ray picture will show a contrast
between bone and soft tissue.
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The X-rays that are directed through a patient’s body will
penetrate the body and those that make it through the
other side fall on photographic film, which they expose.
In those cases where there is no substantial difference
between the Z of the area to be imaged and the
surrounding area, the image can be improved by giving the
patient a contrast medium.
Usually this consists of what is called a barium meal (barium
sulphate), which the patient swallows.
When this moves into the intestinal tract and an X-ray is
taken, the barium will absorb X-rays more strongly than the
surrounding tissue, resulting in a sharper image.
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The image created by the
X-ray on the film is actually
a shadow of the high-Z
material in the body (e.g.
bones) against the
surrounding low-Z tissue.
To increase the sharpness
of the shadow the source
of X-rays must be made as
point-like as possible.

The quality of the image is
improved is the film is as close to
the patient as possible, or if the
distance from the source to the
patient is large. (In the later case
the intensity of X-rays is
diminished, which implies a
longer exposure time).
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The image is also improved is as
many scattered rays as possible
are prevented from reaching the
film.
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This can be achieved with the use of a
grid of lead (i.e. X-ray opaque) strips,
which are placed between the patient
and the film.
The strips are oriented along the
direction of the incoming X-rays, and
so scattered rays are blocked and do
not make it to the film.
The strips are about 0.3 mm apart and create unwanted
images that can be eliminated by moving the grid sideways
back and forth during exposure so that the strip images are
blurred.
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Low energy X-rays will simply be absorbed by the skin of the
patient and cannot therefore penetrate the body.
So they are usually removed from the X-ray beam in a
process called filtering.
Because photographic film is much more sensitive to
ordinary visible light than X-rays, the exposure time must be
longer.
However, it can be reduced by using intensifying screens.
An intensifying screen is a piece of plastic containing
fluorescent crystals in the top and bottom surfaces and a
double-sided photographic film in between.
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X-rays that have gone through the patient enter this screen
and transfer some of their energy to the crystals.
The energy absorbed by the crystals is then emitted as visible
light that exposes the film.
In another technique called fluoroscopy, a real-time dynamic
image is created on a TV monitor.
X-rays that have passed through the patient fall on a
fluorescent screen and visible light is emitted.
The photons cause the emission of electrons from a
photosurface, which are then accelerated by a p.d. so that
they fall on a second fluorescent screen from which they cause
emission of light that is fed into the TV monitor.
The advantage of real-time is, however, out weighted by the
unusually high doses of radiation that the patient receives.
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One of the highest advances in the medical use of X-rays
has been the discovery in 1973 through work of
Hounsfield and Cormack, of a technique known as
computed (axial) tomography (CT) or computedassisted tomography (CAT).
This diagnostic method has made possible much more
accurate diagnosis with much less invasive action on the
patient.
It does use X-rays, however, and so its use does present
dangers to the patient.
A complete scan lasts about 2s and a whole-body scan
lasts about 6s.
The beam of X-rays are directed to the patient at right angles
to the long vertical axis of the patient.
 The CT scan creates an image of a horizontal slice through the
patient.

A movable source of X-rays
emits a beam that is
confined to a plane and
travels through the
patient’s body so that it is
received by detectors on
the other side.
 The source is then rotated
so that the beam enters the
body from a different angle.
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The use of many detectors as
opposed to just one cuts
down the time required for
the scan and the amount of
radiation deposited in the
patient.
Detectors record the
intensity of the X-rays
reaching them and the
information is then sent to a
computer, which analyses
the data and constructs the
image.
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Magnetic resonance imaging is bases on a nuclear physics
phenomenon known as nuclear magnetic resonance and is
a superior method to CT scans.
Unlike CT scans, the image is constructed without
dangerous radiation but it is significantly more expensive.
Electrons and protons have a property called spin.
Particles with electrical charge and spin behave as tiny
microscopic magnets – magnetic moment.
In the presence of a magnetic field, the magnetic moment
will align itself either parallel (spin-up) or anti-parallel (spindown) to the direction of the magnetic field.
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Protons inside nuclei belong to energy levels of specific
energy.
If the protons are put in a region of external magnetic field,
the energy of the level will change depending on how the
proton magnetic moment aligns itself with respect to the
magnetic field.
The difference in energy between the split levels is
proportional to the external magnetic field.
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The state with spin-up has the lower energy.
If a radio-frequency (RF) source provides energy to a
sample of hydrogen nuclei in a magnetic field, the protons
in the lower energy spin-up state may absorb photons a
make a transition to higher spin-down state.
This will happen if the frequency of the e.m. radiation
correspond to the energy difference between the spin-up
and the spin-down
Once the transition is made, it will be followed by a
transition down again with the accompanying emission of
a photon of the same frequency.
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Detectors can record these photons and techniques similar
to CT scans are used to create the magnetic resonance
image so that photons detected can be correlated with
specific points of emission.
Of great interest in MRI is the rate at which the transitions
take place, since the rate is related to the type of tissue in
which the transition occurs.
Thus, measuring the rate gives information about the type
of tissue.
The point of emission of the emitted photons can be located
by placing the patient in and additional magnetic field that
destroys the high degree of uniformity of the original
magnets.
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Suppose that the B now varies across the patient, so that it
becomes stronger as we move upwards.
Imagine that the variation of the B is the same along
horizontal planes though the patient.
The frequency that can be absorbed by the H nuclei
depends on the external B, so for a fixed RF only on plane
within the body will have the correct value of B for
absorption to take place.
To measure absorption in other planes through the body,
the frequency of the RF source can be varied.
The imaged so created shows the density of hydrogen
nuclei since it is H that is primarily responsible fro
absorption.
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More sophisticated
techniques measure the
rate at which excited nuclei
return to their ground state
(relaxation times) and there
produce images of
especially high resolution.
Different kinds of tissue
show different relaxation
times, thus allowing the
identification of tissue type.
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This technique is similar to the CT scan and involves the
annihilation of an electron and a positron and the
detection of the two photons so produced.
The patient is injected with a solution of radioactive
material containing isotopes that decay by positron
emission (β+)
As soon as the positron is emitted, it will collide with and
electron in the tissue of the patient.
The electron-positron pair will annihilate into two photons
each of energy 0.511 MeV.
e  e  2


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The electron-positron total momentum
is, essentially, zero, which means that
the two photons must move in opposite
directions with the same energy.
The detectors surrounding the patient
can therefore determine the line along
which the emissions took place and
eventually locate the point of emission.
PET scans have a resolution of about
1mm.
They are used mainly for biochemical
and metabolism related studies.
They produce superior brain images.
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A major tool in diagnostic medicine is ultrasound,
Ultrasound is sound that is not audible to the human ear –
its frequency is higher than about 20 kHz.
The ultrasound used in diagnostic medicine is in the range
of about 1 to 10 MHz.
Ultrasound has the advantage over X-rays in that it does
not deposit radiation in the body and no adverse side
effects of its use are known.
For certain organs, like the lungs, X-rays cannot produce
and image but ultrasound can.
One disadvantage of ultrasounds is that the images are not
as detailed as those from X-rays.
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The ultrasound is emitted towards the patient’s body in
short pulses, typically lasting 1 μs, and their reflections off
surfaces of various organs are detected.
The idea is thus similar to sonar.
The speed of sound in soft tissue is 1540 m/s, similar to that
in water. This means that the λ involved are 1.54mm for
1MHz waves and 1.54mm for 10MHz waves.
Thus, if we use 1MHz waves, the length of the pulse is
1.54mm and so contains just one full wave.
For 10MHz waves, the wavetrain contains 10 full waves.
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In general, diffraction considerations place a limit on the
size, d, that can be resolved by a wave of wavelength .
The constraint is that
<d
If a resolution of a couple of mm is required, the  used
must therefore be less than a few mm.
In view of the frequencies used, this is not a problem.
As we saw, a 10MHz ultrasound has a wavelength of about
0.15 mm, and so, in principle, such an ultrasound can ‘see’
objects of linear size of about 0.15mm.
On the other hand, in practice, the pulse used must contain
at least a few full waves for resolution to be possible.
Thus, in the case of the ultrasound frequencies used in
medicine, it is the pulse duration, and not diffraction, that
sets the limit on resolution
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The frequency used is usually determined by the organ to be
studied and the resolution desired. A rough rule is to use a
frequency given by
c
f  200
d
were c is the speed of sound in tissue and d is the depth of the
organ below the body surface
The source of ultrasound is a transducer that converts electrical
energy into sound energy.
 This is based on a phenomenon called piezoelectricity.
 An alternating voltage applied to opposite faces of a crystal such
as strontium titanate or quartz will force the crystal to vibrate,
emitting ultrasound.
 Similarly, ultrasound falling on such a crystal will produce an
alternating voltage at the faces of the crystal.
 This means that the source of ultrasound can also act as a
receiver.
 The sound energy must then be directed into the patient’s body.
 In general, when a wave encounters and interface between the
two different media, part of the wave will be reflected and part
will be transmitted into the other medium.
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The amount of transmission depend on the impedances of the
two media. Acoustic impedance is defined as
Z  v
where ρ is the density of the medium and v is the speed of sound
in that medium. The units of impedance are kg m-2 s-1.
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If I0 is the incident, It the transmitted and Ir the reflected intensity
then
It
4Z1Z 2

2
I 0 Z1  Z 2 
I r Z1  Z 2 

2
I 0 Z1  Z 2 
2
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This shows that for most of the energy to be transmitted , the
impedances of the two media must be as close to each other as
possible (impedances matching).
The impedance of soft tissues differs from that of air by a factor
of about 104, so most of the sound would be reflected by the
body.
This is why the area between the body and the transducer is filled
with a gel-like substance whose impedance matches that of the
body.
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In a type of ultrasound called the A scan, the ultrasound pulse is
directed into the body and the reflected pulse from various
interfaces in the body is recorded by the transducer.
This time it converts the sound energy into electrical energy.
The reflected signal is then displayed on a cathode-ray
oscilloscope. The CRO signal is, in fact, a graph of signal strength
versus time of travel from the transducer to the reflecting surface
and back.
transducer
organ
body surface
skeleton
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The dots in the
graph show another
way of representing
the results.
The dot brightness
is proportional to
the signal strength
(darker colours
representing
stronger signal).
signal strength
transducer
organ
body surface
skeleton
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The A scan provides a one-dimensional image.
Imagine a whole series of A scans performed by sending parallel
beams of ultrasound into the patient by a transducer that mover
up along the surface of a body or by a series of transducers:
transducer
organ
body surface
If the A scans are put together, the result is the dots on the right
of the diagram, which begin to form an outline of the surface of
the organ in a two-dimensional image.
 A series of transducers are put on the body and each sends one
short pulse after the other.
 Typically, the time delay between two consecutive signals is 1ms.
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transducer
body surface
organ
When the results are displayed on the CRO screen, the
image is a real-time, two-dimensional representation of the
object which is viewed as a movie. This is called a B scan.
Ultrasound can also be put to other uses. One is to measure
blood-flow velocities and foetal heart movement.
 Ultrasound is directed at the heart, say, and the reflected signal
detected.
 Because the heart moves, the reflected signal will have a slightly
different frequency because of the Doppler effect.
 Comparison of the emitted and received frequencies gives the
speed of the reflecting surface.
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Method
Resolution
Advantages
Disadvantages
X-rays
0.5 mm
Cheap
Presents radiation danger;
some images are obscured;
some organs are not
accessible
CT scans
0.5 mm
Can distinguish between
different types of tissue
Presents radiation dangers
MRI
1 mm
Presents no radiation
Expensive; difficult for
dangers; superior images; patients who are
can distinguish between
claustrophobic
different types of tissue
Ultrasound
2 mm
Presents no radiation
dangers
Some organs are not
accessible
PET scans
1 mm
Organ function studies;
superior brain images
Some organs are not
accessible
In ultrasound, the following events happen:
 The ultrasound machine transmits highfrequency (1 to 5 megahertz) sound pulses into
your body using a probe.
 The sound waves travel into your body and hit
a boundary between tissues (e.g. between
fluid and soft tissue, soft tissue and bone).
 Some of the sound waves get reflected back to
the probe, while some travel on further until
they reach another boundary and get
reflected.
 The reflected waves are picked up by the probe and relayed to the machine.
 The machine calculates the distance from the probe to the tissue or organ
(boundaries) using the speed of sound in tissue (1,540 m/s) and the time of the
each echo's return (usually on the order of millionths of a second).
 The machine displays the distances and intensities of the echoes on the screen,
forming a two dimensional image like the one shown below.
 In a typical ultrasound, millions of pulses and echoes are sent and received each
second. The probe can be moved along the surface of the body and angled to
obtain various views.
Photo courtesy Philips Research
3-D ultrasound images
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Radioisotopes are used for diagnosis and to monitor specific
body organs and their functions.
Uses include the monitoring of the thyroid gland using
radioactive iodine, measurement of body fluids, studies of how
food is digested, vitamin absorption, how amino acids are
synthesized, how ions can penetrate cell wall, etc.
m
Most commonly used is the radioisotope technetium-99 ( 9943
Tc ),
a metastable (i.e. long-lived) excited state of technetium-99.
It is produced in the decay of molybdenum-99:
99
42
Mo
Tc  e  e  
99 m
43
0
1
0
0
0
0

The produced technetium then decays by gamma emission:
Tc Tc  
99 m
43



99
43
0
0
The photon energies are about 140keV.
This is an advantage since any alpha or beta particles emitted
would be absorbed within the body and would not reach the
outside detector; also, photons of these energies are easily
detectable.
Technetium has a half-life of about 6h, which is conveniently
short, and can combine into a large number of compunds.
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Technetium is useful in diagnostic studies of most body organs ,
such as the heart, the lungs and the liver.
In investigations of calcium absorption by bones, technetium and
calcium-45 or calcium-47 are used.
Iodine-131 is another commonly used radioisotope. It is used in
blood volume measurements and in studies of the thyroid gland.
Thallium-201 is used in studies of muscle function and disease.
The compound to be tagged with technetium is chosen
according to what part or organ of the body needs to be imaged
– different compounds will accumulate in different parts of the
body.
The radioactive compound so formed is called a
radiopharmaceutical.
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This is given to the patient (orally or by injection) and the
radiation emitted by technetium can then be recorded by a
detector placed over the relevant part of the patient’s body.
The amount of radiation compared with the amount expected
from a healthy body then provides information about the
function of the particular body organ.