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.

β

Nature He nucleus Electron Photon

Mass (u) 4 1/1840 0

Charge +2e -e 0

Ions produced per mm of path

10 000 1000 1

Stopped by A few cm of air

A few mm of Al

10 cm of Pb

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

This is the intensity of the source at a distance r from it.

24 r

PI

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

xeII 0

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.

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.

x

Incident intensity

Intensity is reduced

I0 I

Then,693.0

HVT

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

In the photoelectric effect, the X-ray photon is absorbed by an electron, which is then emitted from is atom or molecule.

The importance of the photoelectric effect is mostly for low-energy photons and increases sharply with increasing atomic number of the specimen upon which the photons fall.

The main methods by which X-rays are absorbed are the photoelectric and

Compton effects.

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.

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 50-150 kV for a chest X-ray.

X-rays

electrons

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.

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.

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).

The image is also improved is as many scattered rays as possible are prevented from reaching the film.

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.

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.

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.

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 computed-assisted 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.

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.

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 (spin-down) to the direction of the magnetic field.

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.

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.

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.

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.

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.

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.

2 ee

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.

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.

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.

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

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

d

cf 200

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.

The amount of transmission depend on the impedances of the two media. Acoustic impedance is defined as

vZ

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.

If I0 is the incident, It the transmitted and Ir the reflected intensity then

221

21

0

4

ZZ

ZZ

I

I t

221

221

0 ZZ

ZZ

I

I r

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.

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

body surface

organ

skeleton

transducer

body surface

organ

skeleton

signal strength

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).

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

body surfaceorgan

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.

transducer

body surface

organ

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.

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.

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 dangers; superior images; can distinguish between different types of tissue

Expensive; difficult for patients who are claustrophobic

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

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.

In ultrasound, the following events happen:

The ultrasound machine transmits high-frequency (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.

Photo courtesy Philips Research3-D ultrasound images

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.

Most commonly used is the radioisotope technetium-99 ( ), a metastable (i.e. long-lived) excited state of technetium-99.

It is produced in the decay of molybdenum-99:

Tcm9943

00

00

01

9943

9942 e

m eTcMo

The produced technetium then decays by gamma emission:

009943

9943 TcTcm

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.

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.

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.