X-Rays
In the exam you are expected to know about:
- X-ray imaging
- The physics of diagnostic X-rays
- Physical principles of the production of X-rays
- Rotating-anode X-ray tube; methods of controlling the beam intensity, the photon energy, the image sharpness and contrast and the patient dose
- Differential tissue absorption of X-rays
- Exponential attenuation, Linear coefficient m, mass attenuation coefficient, mm and half-value thickness;
- Image contrast enhancement
- Use of X-ray opaque material as illustrated by the barium meal technique
- Radiographic image detection
- Photographic detection with intensifying screen and fluoroscopic image intensification;
- reasons for using these.
The use of X-rays for making shadow pictures of bones has been around for over a century. The first X-ray machine was built by a German, Wilhelm Röntgen in the late nineteenth century. Within a few months, the machines were becoming widespread in hospitals. They were also used for amusement as there was little knowledge about the risks involved. Nowadays X-rays are used for:
- looking at fractures in bones;
- looking at teeth to diagnose any decay;
- looking for the shadows caused by tumours and other disease in soft tissue;
- treatment of tumours by radiotherapy.
Production of X-Rays
X-rays are photons of electromagnetic radiation produced when a target of heavy metal is struck by electrons travelling at high speed. Only about 1 % of the electrons produce an X-ray photon; the rest is lost in heating up the target. X-rays are produced by:
- slowing the electron down, called bremsestrahlung (German for "braking radiation")
- by removing an inner electron. As electrons replace the inner electron, photons are emitted as the electrons undergo transitions from energy level to energy level.
Bremsestrahlung is summarised in the diagram:
In bremsestrahlung the spectrum of photons is continuous.
When the atom is ionised by the removal of an inner electron, other electrons fill the space by dropping down the quantum ladder. The photons have a particular energy. This mechanism is shown below:
The maximum energy that can be obtained is when all the energy from the electron is converted into the energy of the photon. So we can say:
Kinetic energy = photon energy
Kinetic energy = charge of electron × voltage
Therefore:
eV= hf
Then we can link this with the wave equation c = fl to give us:
Question 1 Rearrange this expression and use it to give you a rule that will give you the wavelength if you know the voltage. ANSWER
Rearranging:
Question 2 What is the minimum wavelength gained from electrons accelerated by a p.d. of 50 000 V? ANSWER
Use
l = 2.48 x 10-11 m.
Ionisation results in a characteristic or line spectrum. Each line is named by the shell in which the electrons end up. So if the electron were removed from the K shell, the innermost shell, electrons would fall down the energy ladder giving out a photon of energy consistent with a fall into the K shell. These are called K-lines. For tungstenas a target material, the accelerating voltage needs to be about 70 kV.
A characteristic is shown below:
If we plot the voltage on the horizontal axis we get:
If we reduce the current we see a graph like this:
We should note the following:
- If we halve the current, we get half the intensity. This is reasonable. Halve the number of electrons and we will get half the number of photons.
- The K-lines are not affected, nor is the maximum energy of the photons. This is because of the quantum nature of photon emission.
If we reduce the voltage we would see:
Notice that the K-lines are visible until the maximum energy is less than the energy of the photon energy of the K-lines. If we increase the voltage we may well see more characteristic lines.
If we change the target material, keeping the voltage the same, we will see a completely different characteristic. As the proton number is increased:
- E max remains constant, as it's a function of the voltage;
- the total intensity (the area under the graph) will change because there is a greater probability of a collision between the incoming electron and the electron shells. The more protons, the more electrons;
- The characteristic lines are shifted to higher photon energies.
Low energy X-ray photons are called "soft X-rays", while high energy photons are called "hard X-rays".
A filter can be made of a sheet of material that will selectively absorb lower energy photons, so that the beam consists of harder X-rays. The beam is more penetrating.
Question 3 An X-ray tube is operated at a peak voltage of 100 kV and the beam current is 40 mA.
(a) What is the power of the machine?
(b) How many electrons reach the machine every second?
(c) How many photons are released every second?
(d) What is the maximum energy of each photon? What is its wavelength?
[Data: e = 1.6 × 10-19 C; h = 6.63 × 10-34 Js; c = 3 × 108 m/s]
ANSWER
ANSWER
(a) Power = VI = 100 000 V × 0.04 A = 4000 W
(b) Number of electrons per sec = 0.04 ÷ 1.6 × 10-19 = 2.5 x 1017 s-1
- How many electrons are there in a charge of -1 C?
- We know the charge of one electron is
- 1 e = 1.6 x 10 - 19 C
- Divide both sides of that equation by 1.6 x 10 - 19 to get
- 1 C = 6.25 x 10 + 18 e
- or 0.04 A x 6.25 x 10 + 18 e = 2.5 x 1017 s-1
- Only about 1 % of the electrons produce an X-ray photon; the rest is lost in heating up the target.
Wavelength = hc/E = (6.63 x 10-34 x 3 x 108) ÷ 1.6 x 10-14 = 1.24 x 10-11 m
= 0.0124 nm
- Photon energy = QV
- Wavelength = hc/E
The most common X-ray generator is the rotating anode tube. It is an evacuated glass envelope, immersed in oil to cool it and surrounded by lead.
- Electrons are boiled off the hot filament which glows just like a light bulb.
- They are accelerated by the anode voltage.
- They hit the target, giving off energy mostly as heat, but 1 % is given off as X-rays.
- The target would rapidly melt, so it is turned by an AC induction motor. The rotor is in the evacuated glass bulb, while the stator (the coils of wire) is on the outside. The cathode spins at 3000 rpm.
Question 4 An X-ray machine is accelerating electrons through a p.d. of 200 kV. The current is 25 mA. The target is a black of heavy metal mass 1.0 kg, and specific heat capacity 300 J kg K-1 and melting point 3000 K. The machine is at 300 K when it is turned on. While the machine is being turned on the cooling fails. The machine is being run for 3 minutes to sterilise some instruments and the operator has gone off somewhere. What do think the operator will come back to? ANSWER
Power is 200 000 V x 0.025 A = 5000 W
99% is heat.
Therefore heating effect is 4950 Js
Anode has a mass of 1 kg.
Temperature change = 4950 J s-1 ÷ (300 J kg-1K-1 x 1 kg) = 16.5 K s-1
Temperature rise to melting point = 3000 K - 300 K = 2700 K
Time taken to get to melting point = 2700 K ÷ 16.5 K s-1 = 164 s
The anode will have melted. Whoops!
The answer to the last question should show how vital the cooling system of an X-ray machine is. Actually if the cooling system were to fail, the machine would be turned off automatically. The X-ray bulbs are precision pieces of kit and extremely expensive. Even a jolt may well break the filament and lead to a massive bill.
Controlling the X-ray Beam
Unlike light or electron beams, X-rays cannot be focused. So they can only make shadow images. If you use a small point source of light, you get sharp shadows. If it's a wide source of light, the shadows become fuzzy. Obviously the doctor wants a sharp shadow.
There are various ways in which an X-ray source can be made into a point source:
- The beam is made narrow by the geometry of the anode to about 17o.
- The beam can be limited by using apertures. This can be a simple diaphragm or a cone made from lead.
- Scattering in the tissues can make the picture fuzzy. A grid made of strips of lead will absorb any scattered X-rays.
The diagram shows how the X-ray beam can be directed:
Absorption of X-Rays by Tissues
When X-rays pass through materials the energy of the beam is reduced or attenuated:
- by scattering; the X-ray photons are reradiated as lower energy photons;
- Photoelectric effect where an electron gets ejected. Photons of visible light are given off as the atom comes out of the excited state;
- Compton scattering where both an electron and a lower energy X-ray photon are emitted;
- Pair production where a very high energy photon interacts with the nucleus of an atom. An electron and a positron emerge, losing their energy by ionisation until the positron is annihilated by an electron, generating two identical photons.
Any of these can do immense damage to biological material:
- Water is ionised to form free radicals that are highly reactive. Free radicals can combine to make hydrogen peroxide H2O2 which is a powerful oxidising agent and can damage the DNA of the chromosomes;
- At the molecular level, enzymes, RNA and DNA are damaged, and metabolic pathways are interfered with.
- At the sub-cellular level cell membranes are damaged, along with the nucleus, chromosomes, and mitochrondria.
- Cellular level, cell division is damaged. Cells can die, or be transformed to malignant growth.
- Tissue and organ damage. There can be disruption to the central nervous system, death of bone marrow and the lining to the gastro-intestinal system, leading to sickness and death. Cancers may arise.
- Whole animal can die; or life is shortened;
- Populations: mutations can alter the genetic characteristics of populations.
X-ray doses are very carefully controlled and maximum limits are set to minimise the risks to patients. These limits are well below the doses that would cause the least harm. However the procedures, although very safe, always run a very slight risk of long term harm. So does watching the TV all day.
Bones absorb X-rays which means that good shadow pictures are easy to get. Soft tissue pictures are harder to obtain. They tend to be fuzzy, but there are differences in the absorption by soft tissues. A lung cancer can show up as a shadow on a chest X-ray. The detection of diseased lung tissue is done by X-ray because it's impossible to do with ultrasound.
Question 5 Why can lung disease not be detected by ultrasound? ANSWER
99.9% of ultrasound waves are reflected at the lung-air boundary. There is so little transmission and even less reflection at the other side that getting images is impossible.
Attenuation of X-rays
In a vacuum (and nearly so in air) the attenuation of X rays follows the inverse square law. Double the distance and the intensity reduces by a factor of 4.
In a material there are various different absorption processes going on and the intensity goes down by a constant fraction per unit distance. The calculus process of integration gives us a quantitative relationship:
[Io - Intensity at source (W/m2); I - intensity at a certain point (W/m2); m (mu - a Greek letter 'm')- total linear attenuation coefficient (m-1); x - distance (m); e - exponential number = 2.718...]
This means that the intensity goes down exponentially, as shown in the graph:
Notice the half value thickness of the material. It is the thickness of the material that makes the X-ray intensity 50 % of its original value. Double it, and the intensity goes down to 25 %. Treble it and it goes down to 1/8 or 12.5 % or the original value.
For copper the half value thickness is 1 mm, which means that I = 0.5 Io behind 1 mm copper.
Therefore:
Worked example
What is the linear attenuation coefficient for copper, if its half value is 1 mm? |
| Use x1/2 = 0.693/m |
| 1.0 × 10-3 = 0.693/m |
| m = 693 m-1 |
Radiographers use another term, the mass attenuation coefficient, mm, which is the attenuation per unit mass of material. The equation is:
Units are m2 kg-1.
Question 6 What is the mass attenuation coefficient of copper? Density of copper is 8930 kg m-3. ANSWER
mm for copper = 693 m-1 ÷ 8930 kg m-3 = 0.0776 m2 kg-1
mm for copper = 693 m-1 ÷ 8930 kg m-3 = 0.0776 m2 kg-1
Bear Trap:
- It is very easy to confuse the total linear attenuation coefficient with the mass attenuation coefficient. Be careful. If you are given the mass attenuation coefficient and you have to use the exponential attenuation equation, you must convert by multiplying by the density.
- That said, I have only ever seen the half value thickness of a material given in all the past papers I have looked at. I have never seen a figure for the mass attenuation coefficient.
Question 7 The half value thickness of aluminium is 3.2 mm. What is the total linear attenuation coefficient? ANSWER
m for Aluminium = 0.693 ÷ 3.2 x 10-3 m = 217 m-1
m for Aluminium = 0.693 ÷ 3.2 x 10-3 m = 217 m-1
Question 8 An X ray tube operates at a voltage of 80 kV and a tube current of 50 mA. As the X-rays leave the tube the area of the beam is 10 mm2. The efficiency of the tube at producing X rays is 1 %. What is the intensity of the X-rays as they leave the tube? ANSWER
Power of the X-ray tube = 80 000 V x 0.050 A = 4000 W
The Power converted to X-rays = 4000 W x 0.01 = 40 W
Intensity = 40 W ÷ (10 x 10-6 m2) = 4 x 106 W m-2
Question 9 Assume that the intensity you worked out in Question 8 occurred 0.01 m away from the anode. What is the intensity 1.5 m away from the X-ray tube? [Hint: it's in air]. ANSWER
Use the inverse square law:
Distance goes from 0.01 m to 1.5 m which is 150 times
Intensity reduces by 1502 = 22500
Intensity now is 4 x 106 W m-2 ÷ 22500 = 178 W m-2
Question 10 What is the intensity of the beam behind a sheet of aluminium 5 mm thick placed 1.5 m away from the tube? ANSWER
Use I = Ioe-mx
I = 177 x e-217 x 0.005 = 177 x e-1.085 = 177 x 0.338
I = 60 W m-2
Making X-Ray Images
The commonest way of getting an image from the X-ray machine is a simple photographic film. The films used vary in size according to the investigation. For a dental X ray, the film would be about 3 x 4 cm; for a chest X-ray it would be 40 x 50 cm. Unlike a film in a camera, these films are double sided, i.e. they have the emulsion on both sides. The films are developed in the usual way in a photographic dark room. The films produce a negative image, so that the shadows of bones appear light. There is no reason, other than its being a waste of time and money, that the positive image could not be printed. Doctors examine the developed films on light boxes. With a broken bone, the problem is easy to see; looking for small cancers is not so easy.
To reduce the exposure of a patient, the film is placed in an image intensifier. If you have had an X-ray in hospital, you will have seen these as the metal cases that contain the film. The intensifier screen is a layer of zinc sulphide, a fluorescent material, that glows (fluoresces) when exposed to X-rays. It absorbs the X-rays and retransmits them as visible light. The light then deposits the silver grains on the film as well as the X-ray photons. These devices can intensify the image by about 40 times, although the resolution is decreased a little. The best resolution is about 0.1 mm.
The use of a fluorescent screen (without a film) can allow doctors to view events in real time. This diagnostic method is called fluoroscopy. To get a decent image, though, you need quite a high intensity. In the old days machines with fluorescent screens were available as an amusement in shops or fun-fairs. Nobody knew or cared about the risks then.
Image intensifier tubes can be used to avoid an increased dose of X-rays. The fluorescent screen is connected to a photocathode. Electrons are accelerated onto a second zinc sulphide screen, intensifying the original image by a factor of 1000.
Light from the second zinc sulphide screen passes to a TV camera for recording or direct viewing.
Question 11 Why should an observer not view the viewing screen directly? ANSWER
The photomultiplier tube is in the X-ray beam, which would expose the viewer to a high dose of X-rays. In particular, the head would be in the beam, which is not a good idea
The photomultiplier tube is in the X-ray beam, which would expose the viewer to a high dose of X-rays. In particular, the head would be in the beam, which is not a good idea
X-ray shadows are clearest where there is greatest difference in density of the tissues. For example bones are quite opaque to X rays. Soft tissues are slightly opaque while air is transparent. Lungs full of air show readily. The contrast can be increased by using a material that is opaque to X-rays. Studies of the function of the gastro-intestinal tract are carried out in real time, using the X-ray opaque material barium in the form of a barium meal. This shows up readily on X-rays.
Uses for X rays
X-rays are a common diagnostic tool. It is non-invasive, but there are risks due to the energetic radiation. As well as the normal shadow pictures, X-ray tomography makes images of cross sections of the whole body. This can be useful if there are a number of diseased sites in the body.
Energetic X-rays are used to treat cancer in a process called radiotherapy. The tumour is exposed to high energy X-rays and killed. However there can be side effects. Also the dose has to be worked out carefully. 10 percent less dose can leave a tumour unaffected, while ten percent more can damage the patient.
People working with X-rays have to take care as they could accumulate a high dose as they work:
- They wear a film badge to check the amount of radiation they get;
- They wear lead aprons while the machine is turned on.
- The machine is in an enclosed room and the controls are in a separate room.
- Interlocks are arranged so that nobody can walk into the X-ray room while the machine is turned on. If that were to happen, the machine would be turned off immediately.
Summary
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