X-ray penetration describes how the ability of x-rays to pass through material such as the human body. The x-rays that either pass through the body (i.e. penetrate), scatter or become absorbed. If the x-rays are scattered or become absorbed that is referred to as attenuated (as those x-rays are no longer in the beam). The penetration depends on the thickness of the material, the density of the material and the mass attenuation coefficient.
For a useful calculator on x-ray penetration checkout our site:
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Chapters:
00:00. Introduction to X-ray Penetration
00:19. Projectiles traveling in matter
01:05. Charged particles in matter
01:35. X-rays traveling in matter
03:10. What is x-ray Penetration?
03:40. Thickness dependence of Penetration
04:04. X-ray attenuation
04:48 Mass Attenuation Coefficient dependence of penetration
05:20 Density dependence of Penetration
06:20 Penetration matters for Imaging
07:12 Beers Law
Credit for Buckshot Photo: Thanks so much to Lucky Gunner at LuckyGunner.com for sharing this still frame from a video they produced on gun ammo.
Two terms “X-Ray Transmission” and “X-Ray Attenuation” are different ways to describe the same thing - how x-rays pass through the body of patient. While X-Ray Transmission quantifies the x-rays that pass through the body, X-Ray Attenuation describes x-rays stopped in the body. Transmission and Attenuation can be expressed as a number from 0 to 1. (Transmission=1-Attenuation, or if percentage values are being used [% Transmission=100% - % Attenuation]).
Let’s imagine a simple model: x-rays of a single energy (i.e. monoenergetic) passing through one single material and the x-rays are parallel as they go through the material. One important parameter in this model is how thick is the material.
These x-rays have an intensity which is the number of x-rays incident on the material (over a given area and a given time).
In real x-ray systems it is slightly more complex as there are many energies in an x-ray spectrum, but this exercise will help provide us with the basic intuition on x-ray attenuation.
If intensity of the incoming x-rays is I0 and output intensity is I. The transmission will be: I/ I0.
The question that we ask here is how does the transmission change depending on the type of material. Some materials of interest in the human body are: water, air, fat, and bone.
Next we’re going to talk about Beer’s Law. Do you think it has anything to do with this nice sampling arrangement of brews here? Unfortunately, it’s not related to this kind of beer. Beer’s Law has several names including Beer-Lambert and Beer-Lambert-Bouguer law. The additional names come from different individuals who made contributions to the discovery of this basic physic behavior. It was discovered first in chemistry for optical photons (i.e. regular light), but the same behavior applies for x-rays as well. We’ll just call it Beer’s Law for simplification in this post.
Beer’s Law relates to two variables - input intensity, I0, and output intensity - I. The multiplying term here will always be a number between 0 and 1. This is just saying that the output intensity will be the same or lower compared with the input intensity.This coefficient in the exponential function µ (pronounced mu) is dependent on the material and the energy of the x-rays.
The intensity of output x-rays depends on the thickness of material as well. The µ and thickness are both in the exponent. Higher µ means that more x-rays are absorbed by the material and larger thickness, x, also means more x-rays absorbed.
The linear attenuation coefficient, µ, can be separated in two pieces in order to see how x-ray absorption depends on density of material. The linear attenuation coefficientis separated into the mass attenuation coefficient µ/ρ and the density ρ.
The mass attenuation coefficient depends on material and the x-ray energy. The density depends on material and is simply mass/volume. More dense materials stop x-rays at a higher rate.
When there is sufficient flux of x-rays through the patient, there is more contrast at the lower energies and that’s especially true for materials like bone and calcium. This is because the x-ray attenuation coefficient is higher at lower energies ( Link to description of photoelectric effect).
Another fact that we wanted to note here is that fat is less dense than water (e.g. oil floats in water), and for that reason it has a lower x-ray attenuation. Other important materials of interest in the body are water and muscle. Muscle has a little bit higher x-ray attenuation than water.