MEDICAL PHYSICS: Imaging with X-Rays

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PRODUCTION OF X-RAYS

X-rays are ionizing electromagnetic radiations (photons) with short wavelengths (of about 10^-8 to 10^-12 m) and correspondingly high photon energies (of about 100 eV to 1 MeV). Diagnostic X-rays give best result at energies of about 30 keV, and are produced by bombarding a tungsten anode with electrons accelerated through potential differences of 60 to 125 kV.

X-rays are produced when electrons are rapidly decelerated as they strike the anode, It becomes very hot, so the usual material is tungsten which has a very high melting point. The electrons also disturb (excite) tungsten atoms which then emit more high-frequency photons at particular wavelengths. These photons add a line spectrum of K and L lines to the continuous spectrum produced decelerating electrons.

The spectra show that the distribution of photon energies depend on the target anode and the tube voltage and current.

X-ray examination.

Pixabay

Tube voltage

The higher the potential difference through which the electrons move, the more kinetic energy E_k they gain, and so the higher the frequency f of the X-ray photons produced:

Maximum energy of photon hf = E_k = eV

Where h is the Planck constant, e is the electronic charge and V is the accelerating voltage. Most electrons lose energy in heating the anode, and only a few have this maximum energy.

Tube current

Increasing the tube current, which means increasing the number of electrons moving from cathode to anode, increases the number of X-ray photons produced:

i.e the beam intensity is directly proportional to the tube current

Target anode material

Increasing the proton number Z of the anode material increases the likelihood that electrons produce X-ray photons:

Output beam intensity is directly proportional to Z, the proton number.

A change in Z also changes the frequency (energy) of the line spectra, which are characteristic of the target atoms.

RADIOGRAPHY: HOW X-RAYS PRODUCE IMAGES

X-rays interact with matter in various ways. In all of them, the material removes photons (absorbs energy) from the direct beam and so causes attenuation, meaning that the energy of the beam is diminished.

Radiography, the term given to producing images with X-rays, relies on the fact that different types of tissue cause differing attenuations. An X-ray image is really a shadowgraph and the darkest shadows are cast by the strongest absorbers (attenuators) of the X-rays. There are four main processes that can reduce the intensity of an X-ray beam:

· Simple scattering occurs when X-ray photons bounce elastically off the nuclei of atoms. They do not lose energy but change direction so that they do not reach the detector.

· A photon may instead ionize an atom, transferring all or most of its energy in doing so. This is essentially the photoelectric effect in which the photon energy liberates an electron from an atom. X-rays have high energy and tend to knock out inner orbital electrons in this ionizing process. (Ions usually result from loss of outer orbital electrons.)

· Sometimes a photon will collide with an outer electron in an atom. The photon acts as a particle with a particular momentum, which it shares with the electron. The photon goes off at an angle after losing energy to the electron. This process is called the Compton effect.

· A photon with very high energy that travels very close to the nucleus of an atom may disappear completely. Its energy is enough to produce a pair of particles – an electron and a positive electron (a positron). The photon’s energy has been converted to matter in a process called pair production. The energy has to be high enough to satisfy Einstein’s relationship E = mc², where m is the sum of the masses of the two particles produced.

Measuring the total attenuation

Each of the four processes produces attenuation which depends on the mass of matter interacted with, and this is measured in terms of the mass attenuation coefficient, μ_m.

As a general rule, attenuation gets less as photon energy increases, so the higher the X-ray energy, the more the photons penetrate matter. In diagnostic radiography, an optimum photon energy of about 30 keV produces the best contrast between different types of tissue. This is because at 30 keV energy the main attenuation process is the photoelectric effect, with absorption proportional to the cube of the proton number Z. This means that bones, which are mainly calcium with Z = 20, produce significantly more attenuation per unit mass than soft tissue (mostly water with hydrogen: Z = 1 and oxygen: Z = 16).

X-Ray.

BruceBlaus - Own work, CC BY-SA 4.0

HOMOGENEOUS BEAMS

It is not easy to obtain an intense beam of X-rays containing photons of just one energy a – homogeneous or monoenergetic beam. A near-monoenergetic beam can be obtained by filtering it: the beam passes through a metal sheet which absorbs some X-ray photons, more of the low-energy photons than the high-energy ones. This means that when an X-ray beam is filtered, the beam becomes more penetrating.

In the ideal case, a near-monoenergetic beam is attenuated in matter to give the percentage transmission curve. The shape of the graph is familiar: it is an exponential fall. This is because each small distance Δx in the material produces a small attenuation - ΔI, which is proportional both to Δx and to the beam intensity I:

-ΔI = μIΔx [1]

μ is a constant for a given X-ray wavelength in a given attenuating material, and is called the linear attenuation coefficient.

In any situation where the change in a quantity is proportional to the (varying) quantity itself, the result is an exponential change. We can rewrite equation [1] as:

ΔI/I = -μΔx

or, in calculus notation:

dI/I = -μdx [2]

where integrating equation [2] gives:

ln I = -μx + C [3]

where I is the intensity at a depth of penetration x. C is a constant which we can identify by the fact that when x is zero, the beam has its starting unattenuated value I₀, so:

ln I₀= C

Putting this value for C in equation 3 gives:

ln I – ln I₀ = - μx

ln I/I₀ = - μx

which we can write as:

I/I₀ = e^-^μx [4]

Note that filtering the beam makes it harder, that is, more penetrating. For a filtered, monoenergetic beam we can define a half-value thickness (compare half-life in radioactivity) which is the thickness of a material that cuts the X-ray intensity by a half. We can use equation [4] to state the half-value thickness x_1/2 in terms of the linear attenuation coefficient μ as follows:

I = ½ I₀

so:

e^-^μx1/2 = ½

or:

e^μx1/2 = 2

giving:

x_½ = ln2/μ

The inverse square law

As with light., in a vacuum the energy of X-rays spreads out from the source according to the inverse square law. This means that the intensity decreases as 1/r² where r is the distance from the source.

X-RAY IMAGE QUALITY

The X-ray image or shadowgraph is usually produced on special photographic film. The sharpness of the image is affected by the size of the X-ray source, known as the focal spot, and the scattering effect as photons pass through the object.

A point source produces perfectly sharp shadows. But X-rays originate in a small spot of finite size on the tungsten anode. And so the shadow contains an edge effect – a penumbra. The penumbra can be reduced by placing the film as close to the object (part of the patient) as possible.

Photons scattered by nuclei in the object carry no information and merely blur the final image, reducing contrast between the darker and lighter areas. To minimize this effect, a filter grid is used. Only unscattered photons can reach the film.

Clearer pictures would be produced if higher energy (harder) beams were used and the exposure time increased. But this would increase the risk of damage to the patient because atoms in living cells would be ionized, and that increases the risk of cancer.

Improvements in detection systems allow better images with quite low beam intensities. For example, a fluorescent (phosphor-coated) screen placed in front of and behind light-sensitive film will absorb X-rays and re-emit the energy as light in a pattern matching the X-ray image. In the arrangement of the phosphors and light sensitive film; the film is much more sensitive than ordinary X-ray film, so images can be produced using low-intensity X-ray beams.

When an X-ray image of the digestive system is required, the patient swallows a harmless suspension of barium sulphate (a ‘barium meal’). This enhances image contrast since barium atoms have a high Z value. Similarly, harmless high-Z dyes can be injected into blood.

COMPUTERIZED TOMOGRAPHY (CT)

This technique for X-ray imaging was developed in the 1970s, and is a great improvement on traditional X-ray imaging techniques. A narrow beam of X-rays is rotated around the patient and after passing through the body is detected electronically. The body is surrounded by several hundred photon detectors, whose outputs are fed to a computer. This analyses the data and forms an image of a narrow slice of the body on a monitor screen: a CT scan. This method produces images with good resolution and does so very quickly – so that changes in ‘real time’ can be observed. The technique is particularly useful for diagnosing damage (e.g. lesions) in the brain, where exploratory surgery is not usually possible.

GE LightSpeed CT scanner at Open House, Monroeville, Pennsylvania.

Daveynin from United States, CC BY 2.0

MAGNETIC RESONANCE IMAGING (MRI)

This technique gives images of tissues deep in the body by using radio waves and a rather obscure property of nuclei, their nuclear magnetic resonance, or NMR. The process is now generally called magnetic resonance imaging. MRI, and targets the hydrogen nuclei which form such a large component of living tissue.

The nucleus of an atom spins. It is also charged, and a spinning charge generates a magnetic field. Just as one magnet becomes aligned in the presence of another (e.g. compass needle in the Earth’s magnetic field), so hydrogen atoms are aligned in a magnetic field. The field has to be very strong, and a hydrogen nucleus can align itself in one of two ways, which correspond to two different quantized energy states.

The magnetic field of the nucleus is along its axis of spin. When an external field is applied, the spin axis itself rotates in an effect known as precession. The earth’s axis, for example, precesses in a period of 23,000 years or so about a line perpendicular to the plane of its orbit. The rate of precession of the hydrogen nucleus, the Larmor precession, is a lot quicker; in a field of strength 1.5 Tesla, the frequency is about 63.8 MHz, which is in the radio frequency (RF) range at 42.57 MHz. When an extra, weaker magnetic field is applied which is made to oscillate at this frequency, the direction of the nucleus’ magnetic axis reverses. Most of the nuclei align in the direction of the field, but some align in the opposite direction, giving rise to two different quantized energy states.

The frequency of the applied RF signal is chosen to match the precession frequency of the hydrogen nuclei so that resonance can occur. The magnetic component of the electromagnetic wave supplies the energy to cause the reversal of the spin alignment of many nuclei. The energy taken from the radio wave depends on the number and distribution of the nuclei in the sample: molecules of biological tissue contain plenty of hydrogen nuclei in water and carbohydrates. In simple absorption MRI this loss is measured and used to build up the image.

A better method is to send the RF signal as a short pulse. This realigns the nuclei as before, but after a time the nuclei return to the normal arrangements of their alignment in the steady magnetic field. The effect due to the pulse decays in a way similar to the decay of charge in a capacitor or of radioactive nuclei. This is characterized by a time constant called the relaxation time, typically about 1 second. As the precession rearrangements decay, the nuclei emit a radio signal at the same frequency as the original pulse. The character of the signal is decided by the number and distribution of the hydrogen nuclei in the tissue and is used to create the final image. The relaxation time depends on the molecule of which the hydrogen is a part – in water the relaxation time is longer than in more complex molecules, for example. This means that the decay signal is complex and carries information about the different molecules in the tissue – hence providing contrast. By changing the timing of the pulses, the signal can be better matched to the relaxation times of the different components of the tissue. In practice, the pulsing is repeated many times, and in more complex ways, so building more detail in the final image. Further improvement is produced by injecting chemicals with magnetic properties that enhance contrast.

Magnetic resonance angiography.

Ofirglazer at English Wikipedia, CC BY-SA 3.0

MRI can produce images of slices of tissue. This is done by making the steady magnetic field graded in strength from strong to weak. The strength of this field decides the resonance frequency of the precession of the nuclei, so by choosing the appropriate frequency, the system can target a slice of the tissue that has that particular field strength.

Magnetic resonance imaging needs expensive equipment, but it is a particularly useful technology for probing delicate areas of the body such as the brain. This is because the energy carried by the radio signal is very small and at a frequency far from the frequencies at which molecules of the body vibrate, so it does no damage. Lower frequencies (such as those in microwave ovens) might provide information – but at the expense of cooked tissue!