Atomic Structure of Magnets - Revision history

N at 14:01, 14 April 2025

2025-04-14T14:01:37Z

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	'''Claimed by Stepan Shabalin (Spring 2025). ~~Undergoing editing, please check back later~~		'''Claimed by Stepan Shabalin (Spring 2025).

	Sarah Ghalayini (Fall 2017)		Sarah Ghalayini (Fall 2017)

N: /* Magnetic Resonance Imaging */

2025-04-14T13:57:59Z

Magnetic Resonance Imaging

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	<math>\tau = \mu \times B</math>		<math>\tau = \mu \times B</math>

	Where <math>\mu</math> is the current spin and B is the external magnetic field. So, what this means is that the spin will rotate along a ring offset along the B axis, because the velocity at every point is orthogonal to both the current spin and B.		Where <math>\mu</math> is the current spin and B is the external magnetic field. So, what this means is that the spin will rotate along a ring offset along the B axis, because the velocity at every point is orthogonal to both the current spin and B. It can easily be seen that the velocity and thus the frequency of the precession is proportional to B (this will be important later!).

	But then why do compasses work? I found two explanations online: it's either because the motion is restricted to a plane (two axes) or because the fluid in a compass creates drag that dampens the motions of the arrow:		But then why do compasses work? I found two explanations online: it's either because the motion is restricted to a plane (two axes) or because the fluid in a compass creates drag that dampens the motions of the arrow:
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	The explanation above is incomplete. In addition to the precession, the spin of protons is affected by random thermal motion of the molecules; this thermal motion walks around the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution], which means the spin is more likely to switch to a lower energy state tan a higher energy one. Overall, the spin will lose energy, which makes it point either to or away from the external magnetic field. In the end, the spins are '''somewhat more likely to align with the magnetic field than oppose it.''' This creates a net magnetization pointed in the direction of the magnetic field.		The explanation above is incomplete. In addition to the precession, the spin of protons is affected by random thermal motion of the molecules; this thermal motion walks around the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution], which means the spin is more likely to switch to a lower energy state tan a higher energy one. Overall, the spin will lose energy, which makes it point either to or away from the external magnetic field. In the end, the spins are '''somewhat more likely to align with the magnetic field than oppose it.''' This creates a net magnetization pointed in the direction of the magnetic field.

	What are the radio frequency pulses mentioned in the explanation of spin in the presence of a magnetic field? Recall that there are two coils in the MRI machine. Taking an image requires creating an electromagnetic wave at a frequency that matches the one that all the nuclei are precessing over. A magnetic field that travels in space and changes direction over time at the same frequency the precessing is rotating (see the "Pulsed Magnetic Fields" section of [https://www.cis.rit.edu/htbooks/mri/inside.htm The Basics of MRI]) will resonate with the precession in a way that lets us rotate ''all'' nuclei by 90 or 180 degrees. I haven't managed to get this to work in a Trinket, but the math seems persuasive.		What are the radio frequency pulses mentioned in the explanation of spin in the presence of a magnetic field? Recall that there are two coils in the MRI machine. Taking an image requires creating an electromagnetic wave at a frequency that matches the one that all the nuclei are precessing over. A magnetic field that travels in space and changes direction over time at the same frequency the precessing is rotating (see the "Pulsed Magnetic Fields" section of [https://www.cis.rit.edu/htbooks/mri/inside.htm The Basics of MRI]) will resonate with the precession in a way that lets us rotate ''all'' nuclei at a constant rate. If we are very precise with our timing and stop the pulse after a few microseconds, we can rotate the nuclei by exactly 90 or 180 degrees. I haven't managed to get this to work in a Trinket, but the math seems persuasive.

			So, we have nuclei with a small average bias in the direction of the external magnetic field, we can rotate them by 90 degrees. What do we do next? Nothing. Once we stop the magnetic pulse, the nuclei will continue precessing and eventually regain the original distribution with the barely-noticeable orientation towards the external magnetic field. We can model the rate at which the situation becomes normal using variables called T1 and T2. What is important is that for a brief time, the net magnetic field is rotated by 90 degrees and is entirely in the plane orthogonal to the external magnetic field (the transverse plane). The precession in the transverse plane will produce magnetic waves and can be captured with the receiver. But what is the use of the received signal? It seems like there's no way to localize where the nuclei are just from the sum of the signals they emit.

			And you are right! This is where the second coil comes in. While the first produces an RF pulse, the second creates a slight magnetic field gradient which makes the external magnetic field vary slightly at different points in space. This variance means that the ''precession frequencies'' also vary slightly (remember the frequency is proportional to field strength!). This means that they will precess at different frequencies inside the transverse plane and relay signals of different frequencies to the receiver. If we can find the intensity of the received signal at all frequencies, we can find the density at all slices along one axis. We can find the intensity with a Fourier transform, which is complicated to explain but is the perfect algorithm for this. [https://www.cis.rit.edu/htbooks/mri/inside.htm See Basics of MRI for more.] Once we can find the density along one axis, we can make 2D scans by rotating the axis in a plane and combining observations along all axes using the [https://en.wikipedia.org/wiki/Radon_transform Radon transform]. These details aren't as interesting because they're more CS than physics and you can learn how they work in a few minutes.

			These are the basics. There are a lot of improvements to be made upon this including a way to scan in 3D, more details of the quantum mechanics of why this works, and you can look at the sources for information on that.

			This section doesn't have as many illustrations as I'd like because I failed to replicate some of the experiments and image uploading doesn't seem to work at this time. It is short, but I spent more than 5 hours on research. Feel free to extend this.

	== See also ==		== See also ==

N: /* Magnetic Resonance Imaging */

2025-04-14T13:36:52Z

Magnetic Resonance Imaging

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	An MRI machine has a large superconducting magnet that creates a magnetic field, two coils that produce radio waves and a receiver. MRI works by producing two magnetic pulses which affect (in a way I will explain below) hydrogen atoms and recording the echo radio waves the atoms' nuclei emit afterwards.		An MRI machine has a large superconducting magnet that creates a magnetic field, two coils that produce radio waves and a receiver. MRI works by producing two magnetic pulses which affect (in a way I will explain below) hydrogen atoms and recording the echo radio waves the atoms' nuclei emit afterwards.

	There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding Magnetic Resonance? (IQMNFUMR)"). The inaccuracies begin with the first step of the process: applying the constant magnetic field. It is typically claimed that the field makes protons, the thing that we care about, can be approximated as small magnets, and that they align with the magnetic field in the same way that magnets align with the Earth's magnetic field.		There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding Magnetic Resonance?" (IQMNFUMR)). The inaccuracies begin with the first step of the process: applying the constant magnetic field. It is typically claimed that the field makes protons, the thing that we care about, can be approximated as small magnets, and that they align with the magnetic field in the same way that magnets align with the Earth's magnetic field.

	Firstly, are hydrogen atoms small magnets? You may have heard the explanation in lecture that atoms are magnets because they have electrons orbiting nuclei, which is a constant flow of current going in a loop, which obviously produces a dipole. However, if you think about it, it stops making sense: we rarely see hydrogen atoms (H) on their own; they will be part of H2O or H2, which doesn't intuitively seem to have those properties. What actually gives hydrogen atoms magnetic properties is an inherent quantity called '''spin''' that elementary particles like protons have. [https://www.cis.rit.edu/htbooks/mri/inside.htm See this resource for a detailed explanation of spin in the context of MRI.] Hydrogen is the one element with a nucleus whose spin is not cancelled out on the net that is abundant in the human body. Spin is similar to classical angular momentum, and its magnitude can change depending on the energy level of the particle. The previous sentence is incorrect: spin isn't a 3D vector like angular momentum, but instead is a probability distribution on those 3D vectors parametrized by two complex numbers. IQMNFUMR doesn't explain the specifics, and you should take a QM course if you want to learn them. We will try to give a classical explanation of spin in the rest of this section.		Firstly, are hydrogen atoms small magnets? You may have heard the explanation in lecture that atoms are magnets because they have electrons orbiting nuclei, which is a constant flow of current going in a loop, which obviously produces a dipole. However, if you think about it, it stops making sense: we rarely see hydrogen atoms (H) on their own; they will be part of H2O or H2, which doesn't intuitively seem to have those properties. What actually gives hydrogen atoms magnetic properties is an inherent quantity called '''spin''' that elementary particles like protons have. [https://www.cis.rit.edu/htbooks/mri/inside.htm See this resource for a detailed explanation of spin in the context of MRI.] Hydrogen is the one element with a nucleus whose spin is not cancelled out on the net that is abundant in the human body. Spin is similar to classical angular momentum, and its magnitude can change depending on the energy level of the particle.

			The previous sentence is incorrect: spin isn't a 3D vector like angular momentum, but instead is a probability distribution on those 3D vectors parametrized by two complex numbers. IQMNFUMR doesn't explain the specifics, and you should take a QM course if you want to learn them. We will try to give a classical explanation of spin in the rest of this section.

	Secondly, do magnets align with the Earth's magnetic field? Actually, by all means, they shouldn't: if you place a bar magnet into a uniform magnetic field and keep its position fixed, it will keep spinning around the axis of the direction of the external magnetic field. [https://trinket.io/glowscript/ec83c99d4dcb See this trinket for a visualization.] This happens because the magnetic torque can be expressed as:		Secondly, do magnets align with the Earth's magnetic field? Actually, by all means, they shouldn't: if you place a bar magnet into a uniform magnetic field and keep its position fixed, it will keep spinning around the axis of the direction of the external magnetic field. [https://trinket.io/glowscript/ec83c99d4dcb See this trinket for a visualization.] This happens because the magnetic torque can be expressed as:
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	The explanation above is incomplete. In addition to the precession, the spin of protons is affected by random thermal motion of the molecules; this thermal motion walks around the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution], which means the spin is more likely to switch to a lower energy state tan a higher energy one. Overall, the spin will lose energy, which makes it point either to or away from the external magnetic field. In the end, the spins are '''somewhat more likely to align with the magnetic field than oppose it.''' This creates a net magnetization pointed in the direction of the magnetic field.		The explanation above is incomplete. In addition to the precession, the spin of protons is affected by random thermal motion of the molecules; this thermal motion walks around the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution], which means the spin is more likely to switch to a lower energy state tan a higher energy one. Overall, the spin will lose energy, which makes it point either to or away from the external magnetic field. In the end, the spins are '''somewhat more likely to align with the magnetic field than oppose it.''' This creates a net magnetization pointed in the direction of the magnetic field.

	What are the radio frequency pulses mentioned in the explanation of spin in the presence of a magnetic field? Recall that there are two coils in the MRI machine. Taking an image requires		What are the radio frequency pulses mentioned in the explanation of spin in the presence of a magnetic field? Recall that there are two coils in the MRI machine. Taking an image requires creating an electromagnetic wave at a frequency that matches the one that all the nuclei are precessing over. A magnetic field that travels in space and changes direction over time at the same frequency the precessing is rotating (see the "Pulsed Magnetic Fields" section of [https://www.cis.rit.edu/htbooks/mri/inside.htm The Basics of MRI]) will resonate with the precession in a way that lets us rotate ''all'' nuclei by 90 or 180 degrees. I haven't managed to get this to work in a Trinket, but the math seems persuasive.

	== See also ==		== See also ==

N: /* Magnetic Resonance Imaging */

2025-04-14T09:12:41Z

Magnetic Resonance Imaging

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	This explanation sounds good and introduces the important principle of precession, but it is utterly irrelevant to protons because they don't experience damping like compasses are designed to. The real explanation of what happens to protons in a magnetic field requires quite a bit of quantum mechanics and thermodynamics. We explained before that spin is probabilistic; what this means is that until you sample it, all of the possibilities for its values evolve together. Once you sample it, it points either in the direction of or against the external magnetic field. This has been confused with the compass metaphor to create the picture that the protons all point in the direction of or against the magnet when that is simply untrue. '''Before the radio frequency pulses are applied, the spins are precessing while pointing in random directions.'''		This explanation sounds good and introduces the important principle of precession, but it is utterly irrelevant to protons because they don't experience damping like compasses are designed to. The real explanation of what happens to protons in a magnetic field requires quite a bit of quantum mechanics and thermodynamics. We explained before that spin is probabilistic; what this means is that until you sample it, all of the possibilities for its values evolve together. Once you sample it, it points either in the direction of or against the external magnetic field. This has been confused with the compass metaphor to create the picture that the protons all point in the direction of or against the magnet when that is simply untrue. '''Before the radio frequency pulses are applied, the spins are precessing while pointing in random directions.'''

	The explanation above is incomplete. In addition to the precession, the spin of protons is affected by random thermal motion of the molecules; this thermal motion walks around the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution] ~~(analogously to [https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo HMC])~~, which means the spin is more likely to switch to a lower energy state tan a higher energy one. Overall, the spin will lose energy, which makes it point either to or away from the external magnetic field. In the end, the spins are '''somewhat more likely to align with the magnetic field than oppose it.'''		The explanation above is incomplete. In addition to the precession, the spin of protons is affected by random thermal motion of the molecules; this thermal motion walks around the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution], which means the spin is more likely to switch to a lower energy state tan a higher energy one. Overall, the spin will lose energy, which makes it point either to or away from the external magnetic field. In the end, the spins are '''somewhat more likely to align with the magnetic field than oppose it.''' This creates a net magnetization pointed in the direction of the magnetic field.

	What are the radio frequency pulses mentioned in the explanation of spin in the presence of a magnetic field? Recall that there are two coils in the MRI machine. Taking an image requires		What are the radio frequency pulses mentioned in the explanation of spin in the presence of a magnetic field? Recall that there are two coils in the MRI machine. Taking an image requires

N: /* Magnetic Resonance Imaging */

2025-04-14T09:06:31Z

Magnetic Resonance Imaging

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	<math>\tau_{drag} = \mu \times \frac{d \mu}{dt}</math>		<math>\tau_{drag} = \mu \times \frac{d \mu}{dt}</math>

	[https://trinket.io/library/trinkets/0e75b85205b9 I tested the drag explanation here.] It works really well, probably because the drag direction is pointed down away from B by the right hand rule.		[https://trinket.io/library/trinkets/0e75b85205b9 I tested the drag explanation here.] It works really well, probably because the drag direction is pointed down away from B by the right hand rule. [https://trinket.io/glowscript/1a995b667d70 The axis restriction one doesn't work as well.]

	This explanation sounds good and introduces the important principle of precession, but it is utterly irrelevant to protons because they don't experience damping like compasses are designed to. The real explanation of what happens to protons in a magnetic field requires quite a bit of quantum mechanics and thermodynamics. We explained before that spin is probabilistic; what this means is that until you sample it, all of the possibilities for its values evolve together. Once you sample it, it points either in the direction of or against the external magnetic field. This has been confused with the compass metaphor to create the picture that the protons all point in the direction of or against the magnet when that is simply untrue. '''Before the radio frequency pulses are applied, the spins are precessing while pointing in random directions.'''		This explanation sounds good and introduces the important principle of precession, but it is utterly irrelevant to protons because they don't experience damping like compasses are designed to. The real explanation of what happens to protons in a magnetic field requires quite a bit of quantum mechanics and thermodynamics. We explained before that spin is probabilistic; what this means is that until you sample it, all of the possibilities for its values evolve together. Once you sample it, it points either in the direction of or against the external magnetic field. This has been confused with the compass metaphor to create the picture that the protons all point in the direction of or against the magnet when that is simply untrue. '''Before the radio frequency pulses are applied, the spins are precessing while pointing in random directions.'''

			The explanation above is incomplete. In addition to the precession, the spin of protons is affected by random thermal motion of the molecules; this thermal motion walks around the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution] (analogously to [https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo HMC]), which means the spin is more likely to switch to a lower energy state tan a higher energy one. Overall, the spin will lose energy, which makes it point either to or away from the external magnetic field. In the end, the spins are '''somewhat more likely to align with the magnetic field than oppose it.'''

			What are the radio frequency pulses mentioned in the explanation of spin in the presence of a magnetic field? Recall that there are two coils in the MRI machine. Taking an image requires

	== See also ==		== See also ==

N: /* Magnetic Resonance Imaging */

2025-04-14T08:59:21Z

Magnetic Resonance Imaging

← Older revision		Revision as of 04:59, 14 April 2025
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	An MRI machine has a large superconducting magnet that creates a magnetic field, two coils that produce radio waves and a receiver. MRI works by producing two magnetic pulses which affect (in a way I will explain below) hydrogen atoms and recording the echo radio waves the atoms' nuclei emit afterwards.		An MRI machine has a large superconducting magnet that creates a magnetic field, two coils that produce radio waves and a receiver. MRI works by producing two magnetic pulses which affect (in a way I will explain below) hydrogen atoms and recording the echo radio waves the atoms' nuclei emit afterwards.

	There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding		There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding Magnetic Resonance? (IQMNFUMR)"). The inaccuracies begin with the first step of the process: applying the constant magnetic field. It is typically claimed that the field makes protons, the thing that we care about, can be approximated as small magnets, and that they align with the magnetic field in the same way that magnets align with the Earth's magnetic field.
	Magnetic Resonance?"). The inaccuracies begin with the first step of the process: applying the constant magnetic field. It is typically claimed that the field makes protons, the thing that we care about, can be approximated as small magnets, and that they align with the magnetic field in the same way that magnets align with the Earth's magnetic field.

	Firstly, are hydrogen atoms small magnets? You may have heard the explanation in lecture that atoms are magnets because they have electrons orbiting nuclei, which is a constant flow of current going in a loop, which obviously produces a dipole. However, if you think about it, it stops making sense: we rarely see hydrogen atoms (H) on their own; they will be part of H2O or H2, which doesn't intuitively seem to have those properties. What actually gives hydrogen atoms magnetic properties is an inherent quantity called '''spin''' that elementary particles like protons have. [https://www.cis.rit.edu/htbooks/mri/inside.htm See this resource for a detailed explanation of spin in the context of MRI.] Hydrogen is the one element with a nucleus whose spin is not cancelled out on the net that is abundant in the human body.		Firstly, are hydrogen atoms small magnets? You may have heard the explanation in lecture that atoms are magnets because they have electrons orbiting nuclei, which is a constant flow of current going in a loop, which obviously produces a dipole. However, if you think about it, it stops making sense: we rarely see hydrogen atoms (H) on their own; they will be part of H2O or H2, which doesn't intuitively seem to have those properties. What actually gives hydrogen atoms magnetic properties is an inherent quantity called '''spin''' that elementary particles like protons have. [https://www.cis.rit.edu/htbooks/mri/inside.htm See this resource for a detailed explanation of spin in the context of MRI.] Hydrogen is the one element with a nucleus whose spin is not cancelled out on the net that is abundant in the human body. Spin is similar to classical angular momentum, and its magnitude can change depending on the energy level of the particle. The previous sentence is incorrect: spin isn't a 3D vector like angular momentum, but instead is a probability distribution on those 3D vectors parametrized by two complex numbers. IQMNFUMR doesn't explain the specifics, and you should take a QM course if you want to learn them. We will try to give a classical explanation of spin in the rest of this section.

	Secondly, do magnets align with the Earth's magnetic field? Actually, by all means, they shouldn't: if you place a bar magnet into a uniform magnetic field and keep its position fixed, it will keep spinning around the axis of the direction of the external magnetic field. [https://trinket.io/glowscript/ec83c99d4dcb See this trinket for a visualization.]		Secondly, do magnets align with the Earth's magnetic field? Actually, by all means, they shouldn't: if you place a bar magnet into a uniform magnetic field and keep its position fixed, it will keep spinning around the axis of the direction of the external magnetic field. [https://trinket.io/glowscript/ec83c99d4dcb See this trinket for a visualization.] This happens because the magnetic torque can be expressed as:

	This explanation sounds good and introduces the important principle of precession, but it is utterly irrelevant to protons because they don't experience damping like compasses are designed to. The real explanation of what happens to protons in a magnetic field requires quite a bit of quantum mechanics and thermodynamics. ~~Here~~ it is, in ~~short:~~ in ~~addition to~~ the ~~precession~~, the ~~spin of protons~~		<math>\tau = \mu \times B</math>

			Where <math>\mu</math> is the current spin and B is the external magnetic field. So, what this means is that the spin will rotate along a ring offset along the B axis, because the velocity at every point is orthogonal to both the current spin and B.

			But then why do compasses work? I found two explanations online: it's either because the motion is restricted to a plane (two axes) or because the fluid in a compass creates drag that dampens the motions of the arrow:

			<math>\tau_{drag} = \mu \times \frac{d \mu}{dt}</math>

			[https://trinket.io/library/trinkets/0e75b85205b9 I tested the drag explanation here.] It works really well, probably because the drag direction is pointed down away from B by the right hand rule.

			This explanation sounds good and introduces the important principle of precession, but it is utterly irrelevant to protons because they don't experience damping like compasses are designed to. The real explanation of what happens to protons in a magnetic field requires quite a bit of quantum mechanics and thermodynamics. We explained before that spin is probabilistic; what this means is that until you sample it, all of the possibilities for its values evolve together. Once you sample it, it points either in the direction of or against the external magnetic field. This has been confused with the compass metaphor to create the picture that the protons all point in the direction of or against the magnet when that is simply untrue. '''Before the radio frequency pulses are applied, the spins are precessing while pointing in random directions.'''

	== See also ==		== See also ==

N: /* Magnetic Resonance Imaging */

2025-04-14T08:37:04Z

Magnetic Resonance Imaging

← Older revision		Revision as of 04:37, 14 April 2025
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	===Magnetic Resonance Imaging===		===Magnetic Resonance Imaging===


			[[File:FMRI_coronal_scan_of_Nathanial_Bradford.png\|thumb\|An example of structural brain MRI image.]]


	'''MRI (Magnetic Resonance Imaging)''', as you all probably know, is a medical imaging technology that works by putting some really strong magnets near your body. It is safer than '''CT (Computational Tomography)''' because it doesn't need to shoot high-energy high-frequency rays into your body. Unlike CT, it doesn't image dense (''high attenuation'') objects, but ''hydrogen atoms''. It can be used to take 3D volumetric images of various parts of your body, and, more interestingly, the brain. Depending on the parameters (more on this later), MRI can diagnose various diseases such as strokes and tumors. It has non-clinical applications in psychology, too: ''functional MRI'', the type that looks at blood flow in various vessels of the brain, can even be used to [https://arxiv.org/abs/2305.18274 read minds]!		'''MRI (Magnetic Resonance Imaging)''', as you all probably know, is a medical imaging technology that works by putting some really strong magnets near your body. It is safer than '''CT (Computational Tomography)''' because it doesn't need to shoot high-energy high-frequency rays into your body. Unlike CT, it doesn't image dense (''high attenuation'') objects, but ''hydrogen atoms''. It can be used to take 3D volumetric images of various parts of your body, and, more interestingly, the brain. Depending on the parameters (more on this later), MRI can diagnose various diseases such as strokes and tumors. It has non-clinical applications in psychology, too: ''functional MRI'', the type that looks at blood flow in various vessels of the brain, can even be used to [https://arxiv.org/abs/2305.18274 read minds]!

	MRI is a specialized application of '''Nuclear Magnetic Resonance (NMR)''. This is a different technology from the one that was used to detect submarines during WWII, and is based on advances in quantum physics. The exact explanation for how it works is a few years above the level of this course, but I will try to ~~explain~~ it ~~accurately~~. MRI works by producing two magnetic pulses which affect (in a way I will explain below) hydrogen atoms ~~(hydrogen is the one element with a nucleus that has a spin [see https://www.cis.rit.edu/htbooks/mri/inside.htm] that is abundant in the human body)~~ and recording the echo radio waves the atoms' nuclei emit afterwards.		MRI is a specialized application of '''Nuclear Magnetic Resonance (NMR)''. This is a different technology from the one that was used to detect submarines during WWII, and is based on advances in quantum physics. The exact explanation for how it works is a few years above the level of this course, but I will try to summarize it without wild inaccuracies.

			An MRI machine has a large superconducting magnet that creates a magnetic field, two coils that produce radio waves and a receiver. MRI works by producing two magnetic pulses which affect (in a way I will explain below) hydrogen atoms and recording the echo radio waves the atoms' nuclei emit afterwards.

	There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding		There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding
	Magnetic Resonance?"). The inaccuracies begin with the first step of the process: applying the ~~first radio frequency (RF) pulse~~. It is typically claimed that the ~~first pulse is applied so~~ that ~~protons~~, ~~which~~ can be ~~(incorrectly)~~ approximated as small magnets, align with the magnetic field, in the same way that magnets align with the Earth's magnetic field. ~~This happens for two reasons~~, ~~both~~ of which ~~I visualized with~~ a ~~Trinket~~: [https://~~trinket~~.~~io/glowscript~~/~~0e75b85205b9 damping of magnetic moment] and [https:~~//~~trinket~~.~~io/glowscript/1a995b667d70 being restricted to one axis (~~this ~~one doesn't actually offer~~ a ~~full~~ explanation)]. ~~Without damping~~, ~~a compass~~'s magnet ~~would instead infinitely~~ [https://trinket.io/glowscript/ec83c99d4dcb ~~precess~~] ~~around the axis of the magnetic field, or rotate around it. So, this~~ explanation sounds good, but is utterly irrelevant~~, and the~~ real explanation requires quite a bit of quantum mechanics and thermodynamics.		Magnetic Resonance?"). The inaccuracies begin with the first step of the process: applying the constant magnetic field. It is typically claimed that the field makes protons, the thing that we care about, can be approximated as small magnets, and that they align with the magnetic field in the same way that magnets align with the Earth's magnetic field.

			Firstly, are hydrogen atoms small magnets? You may have heard the explanation in lecture that atoms are magnets because they have electrons orbiting nuclei, which is a constant flow of current going in a loop, which obviously produces a dipole. However, if you think about it, it stops making sense: we rarely see hydrogen atoms (H) on their own; they will be part of H2O or H2, which doesn't intuitively seem to have those properties. What actually gives hydrogen atoms magnetic properties is an inherent quantity called '''spin''' that elementary particles like protons have. [https://www.cis.rit.edu/htbooks/mri/inside.htm See this resource for a detailed explanation of spin in the context of MRI.] Hydrogen is the one element with a nucleus whose spin is not cancelled out on the net that is abundant in the human body.

			Secondly, do magnets align with the Earth's magnetic field? Actually, by all means, they shouldn't: if you place a bar magnet into a uniform magnetic field and keep its position fixed, it will keep spinning around the axis of the direction of the external magnetic field. [https://trinket.io/glowscript/ec83c99d4dcb See this trinket for a visualization.]

			This explanation sounds good and introduces the important principle of precession, but it is utterly irrelevant to protons because they don't experience damping like compasses are designed to. The real explanation of what happens to protons in a magnetic field requires quite a bit of quantum mechanics and thermodynamics. Here it is, in short: in addition to the precession, the spin of protons

	== See also ==		== See also ==

N at 07:45, 14 April 2025

2025-04-14T07:45:27Z

← Older revision		Revision as of 03:45, 14 April 2025
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	'''Claimed by Stepan Shabalin (Spring 2025)		'''Claimed by Stepan Shabalin (Spring 2025). Undergoing editing, please check back later

	Sarah Ghalayini (Fall 2017)		Sarah Ghalayini (Fall 2017)

N: /* Magnetic Resonance Imaging */

2025-04-13T23:42:00Z

Magnetic Resonance Imaging

← Older revision		Revision as of 19:42, 13 April 2025
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	There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding		There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding
	Magnetic Resonance?"). The inaccuracies begin with the first step of the process: applying the first radio frequency (RF) pulse. It is typically claimed that the first pulse is applied so that protons, which can be (incorrectly) approximated as small magnets, align with the magnetic field, in the same way that magnets align with the Earth's magnetic field. This happens for two reasons, both of which I visualized with a Trinket: [https://trinket.io/glowscript/0e75b85205b9 damping of magnetic moment] and [https://trinket.io/glowscript/1a995b667d70 being restricted to one axis (this one doesn't actually offer a full explanation)]. Without damping, a compass's magnet would instead infinitely [~~precess~~ https://trinket.io/glowscript/ec83c99d4dcb] around the axis of the magnetic field, or rotate around it. ~~This is~~ explanation sounds good, but is utterly irrelevant, and the real explanation requires quite a bit of quantum mechanics and thermodynamics.		Magnetic Resonance?"). The inaccuracies begin with the first step of the process: applying the first radio frequency (RF) pulse. It is typically claimed that the first pulse is applied so that protons, which can be (incorrectly) approximated as small magnets, align with the magnetic field, in the same way that magnets align with the Earth's magnetic field. This happens for two reasons, both of which I visualized with a Trinket: [https://trinket.io/glowscript/0e75b85205b9 damping of magnetic moment] and [https://trinket.io/glowscript/1a995b667d70 being restricted to one axis (this one doesn't actually offer a full explanation)]. Without damping, a compass's magnet would instead infinitely [https://trinket.io/glowscript/ec83c99d4dcb precess] around the axis of the magnetic field, or rotate around it. So, this explanation sounds good, but is utterly irrelevant, and the real explanation requires quite a bit of quantum mechanics and thermodynamics.

	== See also ==		== See also ==

N: /* Magnetic Resonance Imaging */

2025-04-13T23:41:11Z

Magnetic Resonance Imaging

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	'''MRI (Magnetic Resonance Imaging)''', as you all probably know, is a medical imaging technology that works by putting some really strong magnets near your body. It is safer than '''CT (Computational Tomography)''' because it doesn't need to shoot high-energy high-frequency rays into your body. Unlike CT, it doesn't image dense (''high attenuation'') objects, but ''hydrogen atoms''. It can be used to take 3D volumetric images of various parts of your body, and, more interestingly, the brain. Depending on the parameters (more on this later), MRI can diagnose various diseases such as strokes and tumors. It has non-clinical applications in psychology, too: ''functional MRI'', the type that looks at blood flow in various vessels of the brain, can even be used to [https://arxiv.org/abs/2305.18274 read minds]!		'''MRI (Magnetic Resonance Imaging)''', as you all probably know, is a medical imaging technology that works by putting some really strong magnets near your body. It is safer than '''CT (Computational Tomography)''' because it doesn't need to shoot high-energy high-frequency rays into your body. Unlike CT, it doesn't image dense (''high attenuation'') objects, but ''hydrogen atoms''. It can be used to take 3D volumetric images of various parts of your body, and, more interestingly, the brain. Depending on the parameters (more on this later), MRI can diagnose various diseases such as strokes and tumors. It has non-clinical applications in psychology, too: ''functional MRI'', the type that looks at blood flow in various vessels of the brain, can even be used to [https://arxiv.org/abs/2305.18274 read minds]!

	MRI is a specialized application of '''Nuclear Magnetic Resonance (NMR)''. This is a different technology from the one that was used to detect submarines during WWII, and is based on advances in quantum physics. The exact explanation for how it works is a few years above the level of this course, but I will try to explain it accurately. MRI works by producing two magnetic pulses which affect ~~hydrogen atoms~~ (in a way I will explain below) and recording the echo radio waves the atoms emit afterwards.		MRI is a specialized application of '''Nuclear Magnetic Resonance (NMR)''. This is a different technology from the one that was used to detect submarines during WWII, and is based on advances in quantum physics. The exact explanation for how it works is a few years above the level of this course, but I will try to explain it accurately. MRI works by producing two magnetic pulses which affect (in a way I will explain below) hydrogen atoms (hydrogen is the one element with a nucleus that has a spin [see https://www.cis.rit.edu/htbooks/mri/inside.htm] that is abundant in the human body) and recording the echo radio waves the atoms' nuclei emit afterwards.

	There are many incorrect explanations of MRI online. ~~Even~~ the first step of the process is ~~often explained~~ in a ~~very inaccurate way~~.		There are many incorrect explanations of MRI online (see "Is Quantum Mechanics necessary for understanding
			Magnetic Resonance?"). The inaccuracies begin with the first step of the process: applying the first radio frequency (RF) pulse. It is typically claimed that the first pulse is applied so that protons, which can be (incorrectly) approximated as small magnets, align with the magnetic field, in the same way that magnets align with the Earth's magnetic field. This happens for two reasons, both of which I visualized with a Trinket: [https://trinket.io/glowscript/0e75b85205b9 damping of magnetic moment] and [https://trinket.io/glowscript/1a995b667d70 being restricted to one axis (this one doesn't actually offer a full explanation)]. Without damping, a compass's magnet would instead infinitely [precess https://trinket.io/glowscript/ec83c99d4dcb] around the axis of the magnetic field, or rotate around it. This is explanation sounds good, but is utterly irrelevant, and the real explanation requires quite a bit of quantum mechanics and thermodynamics.

	== See also ==		== See also ==