Muon tomography for medical imaging
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Muon tomography for medical imaging
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[ID] => 559968
[post_author] => 12815
[post_date] => 2025-01-09 21:53:53
[post_date_gmt] => 2025-01-10 02:53:53
[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
Muons are elementary, charged particles that undergo the same interactions as electrons, but which have much greater masses. For this reason, muons could be used as an alternative to electrons in transmission microscopy, in which the pattern formed by scattered, charged particles after passing through a sample may be used to infer the structure of biological tissues. Such methods are useful for probing structural details of biological materials that are smaller than the optical diffraction limit, which determines the smallest feature sizes that can be observed using a traditional, light-based microscope.
A simple muon detector (Figure 1) consists of an array of diodes. Each diode emits an electric signal when a muon passes through it, and so the specific diode in the array that emits a signal after a muon strike indicates the two-dimensional location of the strike. A beam of muons with known energy passes through the sample, and at each beam location, the location on the detector plate at which muons arrive after passing through the sample is recorded. Locations at which the beam was most strongly deflected indicate the presence of internal structures, resulting in a two-dimensional image of the tissue. The total deflection of the incident beam by the sample is, at most, a few degrees for the densest parts of the sample.
This technique has recently been generalized to provide three-dimensional information about samples in a method known as muon tomography. In order to gain information about the three-dimensional scattering field with which the muon interacts before it reaches the detector, the direction that each muon is traveling after it exits the tissue sample must be known. This method requires at least two detector arrays, since the velocity vector of the muon can be calculated from the 2D location on each detector array where the muon struck, the distance between the two arrays, and the time between the two detection events. Assume that the muons are heavy enough to be treated as point masses subject to classical electromagnetism and Newton’s laws. Additionally, assume that the detectors themselves barely affect the muons’ trajectories.
Figure 1: The elements of a muon measurement assembly. Muons exit the source and are deflected as they pass through the sample. The deflected muons pass through one of the diodes in the diode array, which indicates their position in the plane of the array.
[post_title] => Muon tomography for medical imaging
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[questions] => Array
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[question] => Which of the following best describes the cause of the small-angle deflections of the incident muon beam?
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[answer] => 4
[description] => Reason for the Correct Answer:
A deflection (rather than reflection or emission) implies that the muons retain some of their original momentum as they pass through the material.
Particles may not exchange spin, which is an intrinsic property distinct from angular momentum.
The strong force holds the nucleus together, but it is not responsible for the deflection of a beam of charged particles. Moreover, the questions states that muons are like electrons, which do not interact via the strong force.
Muons are charged particles and thus deflected electromagnetically predominantly by the electron cloud within the tissue.
)
[answers] => Array
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[0] => Array
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[each_answer] => A. The muons exchange their spin with the molecules in the tissue, causing their trajectories to become curved due to exchange of angular momentum.
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[1] => Array
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[each_answer] => B. The muons are repelled by the strong nuclear force arising in the nuclei of the tissue.
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[2] => Array
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[each_answer] => C. The muons are captured by unfilled valence orbitals within the tissue, and then re-emitted.
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[3] => Array
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[each_answer] => D. The muons are electromagnetically repelled by the electrons in the tissue.
)
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => Which of the following would DECREASE the resolution of the three-dimensional structure of a tissue sample in the transmission microscope?
[value] => Array
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[answer] => 4
[description] => Reason for the Correct Answer:
There is an inverse relationship between the energy of a particle and its characteristic wavelength.
Thicker samples, or samples with significant structural variation along their vertical axis, may scatter muons multiple times, making it more difficult to distinguish single, large scattering events from multiple small scattering events. Two of the answer choices would actually help improve vertical resolution for this reason.
A metal coating would absorb or reflect charged particles in a transmission microscope, reducing the resolution of the apparatus.
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[answers] => Array
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[0] => Array
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[each_answer] => A. Applying the beam from multiple incident angles and recording changes in the scattering field.
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[1] => Array
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[each_answer] => B. Increasing the energy of the beam of muons directed at the sample.
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[2] => Array
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[each_answer] => C. Slicing the sample into thin slices, and imaging each slice separately.
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[3] => Array
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[each_answer] => D. Covering the sample in a conductive coating or foil.
)
)
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => In order to reconstruct the three-dimensional structure of a tissue during muon tomography, which of the following quantities must be measured during the experiment?
I. The total charges of the atoms within the tissue sample
II. The velocity of muons entering the sample
III. The velocity of muons exiting the sample
[value] => Array
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[answer] => 4
[description] => Reason for the Correct Answer:
The biological sample is essentially a “black box”—the purpose of the measurement is to determine its internal structures.
The velocities (speeds and directions) of exiting muons are sufficient to create a two-dimensional image of the sample
Three-dimensional information is encoded in the changes in all three coordinates of the momentum vector before and after the particle interacts with the sample.
The total scattering of a muon is given by the difference in its velocity before and after interacting with the sample.
In order to use Newton’s laws in three dimensions, the velocity (speed and direction) must be known before and after the particle interacts with the tissue.
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[answers] => Array
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[0] => Array
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[each_answer] => A. I, II, and III
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[1] => Array
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[each_answer] => B. I and II
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[2] => Array
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[each_answer] => C. I and III
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[3] => Array
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[each_answer] => D. II and III
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[3] => Array
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[quiz_unique_key] => 2377279144
[question] => If muons are travelling towards the first detector along a direction normal to the plane of the diode array, where should a second detector array be placed so as to allow the most precise determination of the three-dimensional structure of the sample?
[value] => Array
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[answer] => 2
[description] => Reason for the Correct Answer:
Three-dimensional information requires knowledge of the velocity of the exiting muons: both their speeds and directions.
The position of the muons must be measured at least twice to find their velocity: The difference in the positions of the two detection locations, as well as the time interval between detections, allows the velocity to be determined.
Larger intervals in both space and time can be measured with greater precision.
Two of the options do not guarantee that the muon will strike both plates.
Two parallel plates spaced distantly apart allow the three-dimensional coordinates of the muon to be measured at two separate times, and with greater precision because the muon travels farther between measurement events.
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[answers] => Array
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[0] => Array
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[each_answer] => A. 
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[1] => Array
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[each_answer] => B. 
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[2] => Array
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[each_answer] => C. 
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[3] => Array
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[each_answer] => D. 
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[4] => Array
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[quiz_unique_key] => 2261298308
[question] => In practice, muon-based measurements are rarely used on living tissues. Which of the following would NOT be a problem with using muons instead of electrons?
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
Heavier particles tend to decay faster because they have more possible decay products
Muons are not one of the dominant particles that comprise matter, suggesting that they are both scarce and that they decay quickly.
The energy of a beam 
, and so 
Muons are elementary particles, and their charge is an intrinsic property that they cannot shed.
Remember to read the question closely! The question asks for which listed property would NOT be a problem with using muons instead of electrons. Since muons have an intrinsic charge that cannot be shed, the answer choice “Muons are more likely to lose their charge as they pass through the sample” is not true, and would thus be the correct answer.
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[answers] => Array
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[0] => Array
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[each_answer] => A. Muons are more difficult to generate
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[1] => Array
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[each_answer] => B. Muons require a greater beam energy to achieve a given incident momentum
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[2] => Array
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[each_answer] => C. Muons are more likely to lose their charge as they pass through the sample
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[3] => Array
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[each_answer] => D. Muons are heavier and thus decay faster
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[559968|1] => D
[559968|2] => D
[559968|3] => D
[559968|4] => B
[559968|5] => C
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