About

 

Translations

Code	Language		Translator	Run
es	es	es

Credits

Michael R. Gallis; lookang

http://iwant2study.org/lookangejss/06QuantumPhysics/ejss_model_DifferentialXRayAbsorbtionwee/DifferentialXRayAbsorbtionwee_Simulation.xhtml

Briefing Document: X-Ray Differential Absorption Simulation Applet

1. Overview

This document reviews a resource focused on an interactive JavaScript HTML5 applet simulating X-ray differential absorption. The applet, developed by Michael R. Gallis and hosted by Open Educational Resources / Open Source Physics @ Singapore, is designed to help students understand how different materials interact with X-rays and how this interaction leads to contrast in X-ray images. It is intended for use across multiple platforms including computers, tablets, and smartphones.

2. Core Concept: Differential Absorption

The central idea revolves around the principle of differential absorption of X-rays. This means that different materials absorb X-rays to varying degrees, and these differences create the contrast necessary for diagnostic imaging. This is accomplished by examining how X-rays interact with materials via two main mechanisms: the photoelectric effect and Compton scattering. The simulation visually demonstrates these effects and allows users to manipulate several parameters for better understanding.

3. Key Concepts and Mechanisms

• Photoelectric Effect: This is a primary interaction mechanism for X-rays in the diagnostic energy range. The source states that "τm is proportional to the cube of atomic number Z and inversely proportional to the cube of the X-ray photon energy E." This effect is more prominent for materials with higher atomic numbers and at lower photon energies.
• Compton Scattering: Another key interaction that also affects how X-rays are absorbed. The source explains that "σCm is independent of atomic number...[and] decreases with increasing energy."
• Attenuation Coefficient (μ): This is the probability of an X-ray photon interacting with the material. It’s directly related to the photoelectric effect and Compton scattering. A higher attenuation coefficient means that more photons are likely to be absorbed or scattered.
• Mass Attenuation Coefficient (μm): This is the attenuation coefficient divided by the density of the material. It is denoted by μm = μ/ρ
• Transmission: This represents the fraction of X-rays that pass through a material without being absorbed or scattered. The transmission graph ranges from 0 (no transmission) to 1 (full transmission), and it is affected by both the material properties and the material thickness.

4. Simulation Functionality

The applet allows users to manipulate the following variables:

• Material Properties:Atomic Number (Z): Users can alter the atomic number of each of two material slabs, noting its effect on X-ray absorption.
• Density (ρ): The simulation allows for changes to the density of each material.
• Material Mixtures: Notes that the effective atomic number for mixed materials is calculated using an averaging process.
• X-Ray Properties:Photon Energy: The simulation lets the user adjust the X-ray photon energy. It explains that diagnostic X-rays are typically in the few keV to 150 keV range.
• Exposure: This simulates mAs (milliampere-seconds), controlling the number of photons incident on the material.
• Material Thickness: While users can adjust thickness, they will always have the same thickness for both slabs.

5. Student Activities & Exploration

The applet provides a set of guiding questions to encourage active learning, including:

• Impact of Atomic Number (Z): How does increasing Z affect the attenuation and transmission of X-rays?
• Impact of Density (ρ): How does increasing density affect attenuation and transmission?
• Impact of Photon Energy: Does changing the photon energy change the attenuation or transmission graphs? Does it affect the contrast in the simulated X-ray image?
• Impact of Exposure: How does adjusting exposure change the simulated X-ray film?
• Differential Absorption with Different Materials: The students are instructed to use presets like lung tissue and soft tissue, then bone and barium, and to analyze the transmission curves to predict ranges of energy that will penetrate the different materials differently, thereby creating contrast.

6. Mathematical Model

The simulation uses a simplified model for the mass attenuation coefficient:

μm = (τ0(Z/Z0)3(E0/E)3+σ0(E0/E))

Where:

• τ0 and σ0 are constants representing the photoelectric and Compton effects at reference values.
• Z0 is the reference atomic number (set to 20).
• E0 is the reference photon energy (set to 100 keV).
• E is the X-ray photon energy.
• Z is the atomic number.

It is important to note that this is a simplified model which "will over estimate the photoelectric absorption of X-rays for higher Z materials at low to intermediate energies." This is mainly due to neglecting absorption edge effects. Despite the simplification, the model accurately represents the general behavior and is sufficient for the educational goals of the applet.

7. Other Key Information:

• Exponential Decay: The reduction of X-ray intensity due to absorption follows the equation: I = I0 exp(-μt) Where I is the transmitted intensity and I0 is the incident intensity. μ is the absorption coefficient, and t is the thickness of the material.
• Mass Thickness: The applet also references use of mass thickness x=ρt

8. Purpose The simulation’s main objective is to provide students with a practical, qualitative understanding of how X-rays interact with different materials and how those differences are utilized to generate contrast in X-ray images. It encourages exploration, prediction, and comparison of results with graphical representations.

9. Links & Resources:

• The provided text offers links to the applet itself, as well as supplementary materials. There is a blog post associated with it as well as links to the original simulation by Michael R. Gallis.
• The document also links to Stanford's material on properties and safety of X-rays

10. Conclusion

This simulation applet is a valuable tool for teaching the core concepts of differential X-ray absorption. Its interactive nature and manipulation of various parameters offer a hands-on approach for students to grasp the underlying physics of diagnostic X-ray imaging. The simplified model is adequate for qualitative exploration of these principles.

 

X-Ray Differential Absorption Study Guide

Quiz

1. What are the two primary ways X-rays interact with matter in medical imaging, and how does their strength relate to photon energy?
2. How does an increase in a material's atomic number affect its attenuation coefficient and what does this mean for x-ray absorption?
3. Explain the relationship between a material's density and x-ray transmission.
4. How does photon energy influence the contrast seen in an x-ray image when using different materials?
5. Describe the exponential relationship between x-ray intensity, absorption coefficient, and material thickness.
6. What are the photoelectric effect and the Compton effect, and what are their respective influences on the mass absorption coefficient?
7. According to the simplified model, how does the photoelectric effect contribution to the mass absorption coefficient change with photon energy and atomic number?
8. How is the "exposure" control in the applet similar to mAs in real X-ray imaging, and what does adjusting either change?
9. In the applet, if lung tissue has a lower attenuation coefficient than soft tissue, what does this indicate about how X-rays travel through these materials?
10. Why does the applet over estimate the photoelectric absorption of X-rays for higher Z materials at low to intermediate energies?

Quiz Answer Key

1. The two primary ways X-rays interact with matter are the photoelectric effect and Compton scattering. The strength of these mechanisms depends on the energy of the X-ray photons, with the photoelectric effect being dominant at lower energies and Compton scattering at higher energies.
2. Increasing the atomic number of a material increases its attenuation coefficient. This means that X-rays are more likely to interact with and be absorbed by the material.
3. Increasing a material's density decreases X-ray transmission. Higher density materials absorb more X-rays, allowing fewer to pass through.
4. Photon energy affects the contrast in an x-ray image by changing the degree to which different materials attenuate the X-ray beam, creating variations in intensity on the detector. Some materials show more dramatic differences in absorption at different photon energies.
5. The intensity of X-rays decreases exponentially as they pass through material. The degree of decrease is determined by the product of the material's absorption coefficient and its thickness, where a higher coefficient or greater thickness results in greater attenuation.
6. The photoelectric effect involves the absorption of an x-ray photon by an electron, leading to the emission of the electron. The Compton effect involves a photon scattering off of an electron. The mass absorption coefficient is the sum of these effects, with the photoelectric effect dominating at lower energies and the Compton effect at higher.
7. The photoelectric effect contribution to the mass absorption coefficient is proportional to the cube of the atomic number (Z^3) and inversely proportional to the cube of the photon energy (1/E^3).
8. The exposure control in the applet simulates mAs (milliampere-seconds) in real x-ray imaging. Increasing either results in a greater number of photons which increases the intensity of the exposure and affects the simulated film, but not the attenuation and transmission graphs.
9. Because lung tissue has a lower attenuation coefficient, x-ray photons are more likely to pass through it than soft tissue. As a result, more of the x-ray beam transmits through the lung tissue.
10. The applet overestimates the photoelectric absorption at low to intermediate energies because it does not account for the reduced interaction of the x-ray photons at low energies due to the insufficient energy of the photon to overcome the binding energy of the electrons (which produce the absorption edge features).

Essay Questions

1. Discuss the role of atomic number, density, and photon energy in creating differential absorption in diagnostic x-ray imaging. Include an analysis of how these factors interact to produce contrast in a radiographic image.
2. Explain the simplified model of the mass absorption coefficient used in the applet, including the contributions from the photoelectric and Compton effects. Why is this model considered adequate for the qualitative behavior observed in the simulation, but not for accurate quantitative modeling?
3. Using the applet, analyze how changes in photon energy affect the contrast between two different materials and how this can be interpreted using the attenuation and transmission graphs. Explain why certain photon energies are better than others for imaging certain tissues.
4. Discuss the interplay between material properties (atomic number and density), x-ray photon energy, and the resulting x-ray attenuation and transmission. Use examples from the simulation to support your analysis.
5. Describe how the simulated x-ray applet can be used as a tool for teaching and understanding the physical principles underlying x-ray imaging. Discuss both the strengths and limitations of such a tool.

Glossary

• Attenuation Coefficient (μ): A measure of how easily a material absorbs X-rays at a given energy without accounting for the thickness of the sample of material. A higher coefficient means that X-rays are more likely to be absorbed.
• Differential Absorption: The variation in the amount of X-rays absorbed by different materials, which produces the contrast seen in X-ray images.
• Photoelectric Effect: An interaction where an X-ray photon is absorbed by an electron, leading to the electron's emission. This effect is dominant at lower X-ray energies.
• Compton Scattering: An interaction where an X-ray photon collides with an electron, causing the photon to scatter and lose some energy. This effect is dominant at higher X-ray energies.
• Atomic Number (Z): The number of protons in an atom's nucleus, which influences how strongly the atom interacts with X-rays (particularly through the photoelectric effect).
• Density (ρ): The mass per unit volume of a material, affecting how many atoms are present to interact with X-rays.
• Photon Energy (E): The energy of an individual X-ray particle, impacting how the photon interacts with matter through photoelectric and Compton interactions.
• Transmission: The amount of X-rays that pass through a material without being absorbed.
• Mass Absorption Coefficient (μm): The absorption coefficient of a material normalized by its density, often used to compare the interaction of X-rays with different materials.
• mAs (milliampere-seconds): A measure of the quantity of X-rays produced by an X-ray machine, directly related to the number of X-ray photons. Higher mAs increases the intensity of the exposure.

Physics Explained Differential Absorption and Diagnostic X-Rays

Differential Absorption and Diagnostic X-Rays

X-ray images are created when X-rays from a source penetrate an object and then expose a film. The difference in how different materials absorb the X-rays in the beam produces the contrast that generates the detail of the image.

For a typical medical diagnostic image, the X-ray interaction with matter is primarily through the Photoelectric effect and Compton scattering.

The strength of these two mechanisms depends upon the energy of the X-ray photons, the atomic number of the material as well as the density of the material.

This simulation provides a qualitative exploration of the difference of how X-rays interact with varying material properties and how this difference can produce contrast in the x-ray image. 

Student Activities: Questions to explore:

The probability that an X-Ray photon will interact with the material depens upon the properties of the material as well as the properties of the photon. For diagnostic X-rays, the photon energies lie between a few keV and 150 keV. These X-rays interact with matter primarily through the Photoelectric Effect and Comptonb Scattering.

This applet simulates the interaction of X-rays 0f a particular energy going through slabs of material. For the purposes of comparison, two slabs are placed side by side, and a simulated X-Ray image is shown. Graphs are provided of the attenuation cofficients at different X-Ray photon energies. The attenuation coefficient is essentially the probability that the X-ray photon will interact with the material (withought taking into account the thickness of the sample of material). Graphs are also provided for the transmission of X-rays at different energies. The transmission graphs go from 0 (no X-Rays at that energy are transmitted) to 1 (all of the X-Rays at that energy are transmitted). The transmission graphs do include the effects of the thickness of the sample.

Experiment with different material settings. You can change the atomic number and the density of the two slabs separately. You can also change the thickness of the slides, but they will always have the same thickness. You can also control the photon energy1 and exposure (think of this as setting mAs). Mixtures of materials (such as bone, soft tissue and other materials) use an averaging process to determine an effective atomic number.

• How does increasing the atomic number (Z) affect the attenuation coefficient graph?
• How does increasing the atomic number affect the transmission graph?
• How does increasing the density (ρ) affect the attenuation coefficient graph?
• How does increasing the density affect the transmission graph?

Changing the photon energy just changes the energy for the simulated exposure, and is indicated by the markers on the graph. 

• Verify that changing the photon energy does not change the graphs.
• Does changing the photon energy change the simulated film?

The exposure control is essentially an uncalibrated version of mAs for the radiation technologist.

• Does increasing or decreasing exposure affect any of the graphs?
• Does increasing or decreasing exposure affect the simulated film the way a similar increase in mAs would affect a real X-Ray image?

Use the preselected material properties for lung tissue for the left slab of material and soft tissue for the right slab of material. Make sure to set the other parameters to their defaults (Photon Energy = 50 keV, thickness = 1.0 cm, exposure = 1.0). The attenuation coefficient curve (in blue) for lung tissue is less than that for soft tissue (in red) at all X-ray photon energies. This means that the photons are more likely to interact with the material if they pass through soft tissue than if they were to pass through lung tissue.

• Which material will the X-Ray photons be more likely to pass through? Do the respective transmission curves show what you expect? Explain.
• With these two materials, vary the Photon Energy but leave the thickness set to 1 cm and the exposure set to 1. Is there an energy or range of energies that give a "best" contrast between the two sides in the simulated X-Ray film? Is there some feature of the transmission graphs that could explain this "best" contrast?
• Set the thickness to 10 cm. Can you predict what range of Photon Energy would give better contrast?
• Reset the thickness to 1 cm, and now select the left side material as bone and the right side material as Barium. Using the transmission graphs, make a prediction for a range of energies which will penetrate each slab.

1 Remember that real diagnostic X-Ray machines produce photons at a variety of efferent energies. The amount of photons at a particular energy is called the X-Ray spectrum and will depend upon kVp, tube current and the xray target material (usually Tungsten).

 Description

The reduction of X-ray intensity due to absorbtion follows the following exponential decay:

I = I0 exp(-μt)

where I is the incident intensity, I0 is the transmitted intensity, μ is the absorption coefficient, and t is the thickness of the matterial. the mass absorption coefficient

μ_m = μ/ρ

is usually used in place of μ and a mass thickness

x=ρt

used in place of the physical thickness of the attenuating material.

Over the range of X-ray energies found in a typical diagnostic X-rays, μ_m is dominated by contributions from the phtoelectric effect (τm) and the Compton effect (σ_Cm):

μ_m = τ_m+σC_m

According to both reference 2 and 3, τ_m is proportional to the cube of atomic number Z and inversely proportional to the cube of the X-ray photon energy E. The behavior of σCm is less well defined. Both reference 2 and 3 note that σ_Cm is independent of atomic number. Reference 2 only states that σCm decreases with increasing energy while reference 3 suggests that it is inversely proportional to photon energy.

The simplified model for μ used in the applet is given by

μm=(τ₀(Z/Z0)³(E0/E)³+σ₀(E₀/E))

where τ0 and σ0 are the contributions of the photoelectric effect and the Compton effect at the reference atomic number Z0 and reference photon energy E0. The following values are used

Z0	20
E0	100 keV
τ0	0.085 cm2/g
σ0	0.2 cm2/g

This discussion does not take into acount reduced interaction at lower energies due to insufficient X-ray photon enery to overcome the binding energy of the electrons (which produce the absorption edge features). As a result, the simple model used here will over estimate the photoelectric absorption of X-rays for higher Z materials at low to intermediate energies. While this model is inadequate for accurate modeling of X-ray interaction with matter, is is sufficiently accurate to provide the qualitative behaviour students will be exploring with this applet.

The graph below compares the simple model of μm with the experimental data from reference 1:

 

Other Resources

1. http://web.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/01_Properties%20&%20Safety.pdf 

 

Version: 

1. http://weelookang.blogspot.sg/2016/04/x-ray-differential-xray-absorption-by.html Blogpost by Loo Kang Wee
2. http://www.compadre.org/osp/items/detail.cfm?ID=13390 original simulation by Michael R. Gallis

 

Frequently Asked Questions: X-Ray Differential Absorption Simulation

1. What is differential absorption in the context of X-ray imaging, and why is it important?
2. Differential absorption refers to the varying degrees to which different materials absorb X-rays. This difference in absorption is what creates contrast in an X-ray image. Materials with higher atomic numbers and densities tend to absorb more X-rays, leading to lighter areas on the film, while materials that absorb fewer X-rays allow more to pass through, resulting in darker areas on the film. This contrast allows us to visualize the internal structures of objects and is crucial for diagnostic medical imaging.
3. What are the primary mechanisms of X-ray interaction with matter in the diagnostic energy range?
4. For diagnostic X-rays, the primary interactions are the photoelectric effect and Compton scattering. The photoelectric effect involves an X-ray photon being completely absorbed by an atom, resulting in the ejection of an electron. Compton scattering occurs when an X-ray photon collides with an electron, transferring some of its energy and changing direction. The relative strength of each mechanism depends on the X-ray energy and the material's atomic number and density.
5. How do atomic number (Z) and density (ρ) of a material affect X-ray absorption?
6. Increasing the atomic number of a material significantly increases its X-ray absorption. This is primarily due to the photoelectric effect, which is proportional to the cube of the atomic number. Similarly, increasing the density of the material also increases absorption because there are more atoms in the path of the X-rays. In essence, both higher atomic number and higher density leads to greater likelihood of X-ray photons being absorbed or scattered.
7. How does the energy of an X-ray photon affect its interaction with matter, and what is the diagnostic range of X-ray energies?
8. The energy of an X-ray photon plays a critical role in its interaction with matter. Diagnostic X-ray energies typically range from a few keV (kilo-electronvolts) to 150 keV. The probability of both photoelectric and Compton interactions decreases as photon energy increases. However, photoelectric effect is more sensitive to energy, decreasing more rapidly as energy increases when compared to compton effect. This is why the energy range chosen in an X-ray is important to achieve optimal contrast.
9. What is an attenuation coefficient, and how is it related to X-ray transmission?
10. The attenuation coefficient is a measure of the probability that an X-ray photon will interact with a material, effectively removing it from the beam. A higher attenuation coefficient means that more photons are absorbed or scattered, resulting in lower transmission. Transmission, on the other hand, refers to the fraction of X-ray photons that pass through a material without interacting. Materials with higher attenuation coefficients will have lower transmission. In the applet, the attenuation coefficient does not consider thickness of the material while transmission graphs include the thickness of the sample.
11. How is the intensity of an X-ray beam reduced as it passes through a material, and what is the role of thickness?

The reduction of X-ray intensity due to absorption follows an exponential decay as given by the equation: I = I₀ exp(-μt), where I is the transmitted intensity, I₀ is the incident intensity, μ is the absorption coefficient, and t is the thickness of the material. As X-rays pass through the material, the intensity decreases exponentially, with a greater decrease if the material has a higher absorption coefficient or a greater thickness.

1. How does the applet simulate the relationship between material properties, photon energy, and resulting contrast in an X-ray image?
2. The applet allows users to adjust material properties, such as atomic number, density, and thickness, as well as the photon energy and "exposure," to observe their effect on the attenuation coefficient, transmission, and contrast in a simulated X-ray image. It does this by using a simplified model to calculate mass absorption coefficient as a combination of photoelectric and compton effect. It graphically shows how the probability of interaction changes with energy, and demonstrates how these changes impact the brightness/darkness of the simulated X-Ray. This provides an intuitive way to understand how these factors interplay to influence the final X-ray image. The “exposure” setting controls the number of simulated photons, acting similarly to mAs (milliampere-seconds) in real X-ray machines.
3. What is the simplified model used in the applet for the mass absorption coefficient, and what are its limitations?

The applet uses a simplified model for the mass absorption coefficient (μm) given by μm=(τ0(Z/Z0)3(E0/E)3+σ0(E0/E)), which combines the photoelectric effect and the Compton effect at reference values for atomic number (Z0) and photon energy (E0). While this simplified model accurately describes the general trends, it does not take into account the more complex interactions like the absorption edge features, and will therefore overestimate the photoelectric absorption for high Z materials at low to intermediate energies. However, despite its limitations it is still sufficient to demonstrate the qualitative behavior of X-ray absorption for educational purposes.