Cyberphysics - X-rays

Medical Physics Option : X-rays

For details on the production of X-rays click here

An ideal X-ray examination would produce a film that showed sufficient contrast between the features that the doctor wanted to examine while putting the patient at minimal risk from the ionizing effect of the radiation.

An X-ray tube does not produce a monochromatic beam, it produces a spectrum of X-ray energies limited at the high energy end by the accelerating voltage applied.

Click on graphic to enlarge

Attenuation (reduction of the beam strength) occurs as the X-rays pass through matter. This attenuation is exponential.

Let

I_o = Intensity of the incident beam
I = Intensity of emerging beam
x = the thickness of the material the beam travels through
m = linear attenuation coefficient

then (in data book)

Click on graphic to enlarge

I = I_oe^-m x
I/I_o = e^-m x
natural log of (I/I_o) = -m x
ln ¹/₂= -m x_0.5
but natural log of (I_o/I) = m x
ln 2 = m x_0.5

So:-

Ensure you can calculate half thicknesses as well as find them off graphs. In a similar way you can find out the thickness needed to reduce penetration to a tenth etc. ( put I = 0.1 I_ointo the equation).

Values for the mass attenuation coefficient m_mcan be changed into m by using the equation

m_{m
=}m / r

The lower energy rays are more likely to be attenuated by the body than the high energy ones. Attenuation occurs as the radiation passes through the body of the patient by two principal mechanisms: photoelectric absorption and Compton scattering.

Photoelectric absorption occurs when a photon of energy is absorbed by an orbital electron and this electron is then promoted to a higher energy level (more outer orbit) or leaves the influence of the nucleus completely (ionization).

A.H. Compton discovered that if he bombarded graphite with monochromatic X-rays, the scattered X-rays had lower energies (longer wavelengths) than the undeflected ones: the greater the deflection the bigger the energy loss. The bombarding X-ray photon has a lot of energy - the force binding the electron to the atom is insignificant compared to the force exerted by the photon on impact. When the photon 'bounces off' the electron, the electron recoils and thereby picks up some of the photon's energy. This is called Compton Scattering.

Photoelectric absorption is the dominant mechanism for low energy X-ray photons (used in soft tissue) whereas Compton Scattering becomes more significant for higher energy photons (bone).

Low energy photon energies produce a better contrast between media of similar density but overall absorption is greater. This means that a higher anode current (resulting in a more intense beam) has to be used the lower the accelerating potential employed across the tube.

Click on graphic to enlarge

In a mammogram a typical range of X-ray energies would need to be in the region of 20-30 keV in order to get an image of sufficient contrast as the breast is composed primarily of fatty tissue.

Click on graphic to enlarge

In a chest X-ray the densities of tissue to be investigated is much more diverse (bone/lung/heart) and 'harder' X-rays can be employed. These still give the contrast required in the image but absorption is reduced by using high energy rays and filtering out the lower energy ones (soft X-rays) produced by the tube. This can be done using an aluminium filter. Suitable energy for a chest X-ray would be 60-100 keV depending upon the exact nature of the detail required to make the diagnosis.

Patient doses

When calculating the collective dose to the population the average dose received per person is multiplied by the number of persons.

To calculate the average dose received because of X-ray examinations the number of each type of investigation would be found and then the typical dose given for each procedure would become the multiplying factor.

X-ray examinations of

limbs, joints and teeth involve a typical effective dose of about 0.01 mSv whereas a
chest CT scan involves 8.0 mSv. and a
barium enema 7.2 mSv.

Hence one CT scan is equivalent in dose to about 800 knee X-rays!!

This is why although many more low dose X-rays are carried out, they do not contribute very much to the population dose. The much lower number of major scans make a significant contribution to population dose because they individually are equivalent to a vast number of low dose investigations.

Type of X-Ray investigation	Typical EFFECTIVE Dose (mSv)
Extremities X-ray (limb, joint, teeth)	0.01
Chest X-ray	0.017
Lumbar Spine X-ray AP	0.69
Abdominal X-ray	0.7
CT Scan to head	2.0
IVU	2.4
Barium Meal	2.6
Barium Enema	7.2
CT Scan to chest/abdomen	8.0

The effective dose of each procedure varies because dose depends on:

X-ray intensity,
energy and
application time.

A real time investigation such as Barium meal involves the patient being bathed in X-rays as the doctor watches an image on a TV monitor. The dose is minimized by pulse application and image freezing but necessarily involves a much bigger dose than a simple 'snapshot' method as used in a chest X-ray. The dose varies in its effect on tissue too as this is dependent upon the quantity of cell division taking place and summed absorption of layers of tissue (see variation in CT Scan doses for head and chest).

LOJ (October 2000) revised December 2002

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