Physics of Medical Scans
Magnetic Resonance Imaging
Introduction
Magnetic resonance imaging (MRI) is a medical imaging technique that employs a strong magnetic field, generally of the magnitude 0.5-3 Tesla. Compared to other imaging techniques, MRI produces more detailed images of soft tissues and organs, making it an invaluable tool for doctors to diagnose a wide range of health problems, such as brain tumours, injuries to the spinal cord, and heart problems (by imaging the heart valves).
The physics behind MRI is fascinating. It relies on an understanding of quantum spins and employs state-of-the-art superconducting technology.
The Science behind the MRI Scan
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The protons that make up the molecules in our body have an intrinsic property called spin. Usually, spins align in random directions. However, when protons are placed under the influence of an external magnetic field, protons align themselves either parallel (spin up) or anti-parallel (spin down) to the direction of the magnetic field.
Spin up protons have energy and spin down protons have energy , where is the dipole moment of the proton and is the external magnetic field strength.
When a spin-up proton absorbs a photon with an energy of , it becomes excited to a spin-down state. A frequency corresponding to this energy is known as the resonant frequency.
When the magnetic field is turned off, the proton de-excites to its spin-up state, emitting a photon with the same energy, which can be detected by the detectors around the scanner.
Proton Spins
Magnetic Dipole Moment
Magnetic dipole moment is a measure of the tendency of an object to interact with an external magnetic field, defined as:
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A dipole moment has potential energy:
Chemical Shifts
Different molecular environments have different resonant frequencies. For example, protons in fat are shielded by the electron clouds of the long carbon chains and so do not respond to the magnetic field as strongly, whereas protons in water are less shielded because the electron cloud is pulled towards the more electronegative oxygen atom.
Electrons that are more shielded will have a lower resonant frequency. A computer can detect these photons of different frequencies and map them to the spatial location at which they were created.
Chemical shifts are expressed in arbitrary units known as "parts per million" (ppm), and these values are independent of the magnetic field strength. [1]
Proton Precession
When a magnetic dipole moment is placed in an external magnetic field, it experiences a torque, and the torque tends to align the dipole moment to the direction of the field. However, when the dipole moment is at some angle to the field, i.e. it does not align perfectly, the torque causes it to precess about the direction of the field.
The frequency of precession is known as the Lamor frequency.
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Circular Coils and a Static Magnetic Field
An MRI scanner uses coils (loops of conducting wires) to create a uniform magnetic field,
Inside the main coil, there exists a gradient coil, which is another set of coils that create magnetic fields which superimpose with the main magnetic field to create variations. These variations allow the detectors to position the locations at which photons were emitted. [2]
If you want to learn about how to generate a uniform magnetic field using different configurations of coils, click the link below to learn about the Biot-Savart Law.
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Radio-frequency Coils
The Lamor frequency is in the range of radio frequency. It has the same frequency as the electromagnetism that is used to transmit radio signals.
In an MRI scanner, another set of coils, known as the radio-frequency coils, or the RF coils, generates a magnetic field perpendicular to the main field. The magnetic field, is delivered in pulses – it is constantly being switched on and off. When the frequency of these pulses corresponds to the Lamor frequency, it causes the proton spins to flip, releasing photons in the process.
Superconducting Magnets
The magnetic field used in an MRI scanner is typically between 0.5 - 3.0 Tesla. (A bar magnet is typically 0.001 Tesla.)
In order to generate such a strong magnetic field, a large current is required, and this means there is significant heat loss when passing a large current through the coils.
The solution to this problem is to use superconducting magnets - materials that have zero resistance below their critical temperature. [3]
A common material used in these MRI scanners is Niobium-Titanium, which has a critical temperature of 10 Kelvins (-263.15 Celsius) .[4] To keep the magnets at such a low temperature, the wires must be bathed in liquid helium.
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Contrast Medium
Gadolinium complexes – molecules containing gadolinium – are paramagnetic, which means they consist of unpaired electrons that induce an internal magnetic field when placed under the influence of an external magnetic field.
The electronic configuration of Gadolinium is [Xe] 4f7 5d1 6s2. [7] It has seven unpaired electrons in the f-orbitals. When an orbital is partially filled – having only one electron – it has a net spin, which can respond to an external magnetic field.
The paramagnetic property shortens the relaxation time of the nearby protons. This increases the signal intensity. [8]
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Electronegativity
Electronegativity: A measure of how strongly atoms attract bonding electrons to themselves.
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Mulikan electronegativity=1/2(electron affinity + ionisation energy),
where electron affinity is the energy required when adding an electron to an atom, and ionisation energy is the
energy required to remove an electron
from an atom. [9]
Why does the scan room have metal strips on the ceiling?
The scan room is actually a Faraday cage.
A Faraday cage is enclosed by conducting materials, and is able to shield electromagnetic field. This means, anyone outside of the scan room won't be exposed to the strong magnetic field generated by the scanner. [2]
Did you know...
over 60% of superconducting wires are used in MRI scanners?
Over the last decade, more than 60% of the superconducting materials worldwide are used in MRI scanners.
MRI scanners also use 40% of Niobium-Titanium (NbTi) alloy, which is what the superconducting wires are made of. [5]
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References:
[1] Dwyer A et al,1985 "Frequency Shift Artefacts in MR Imaging", Journal of Computer Assisted Tomography, vol 9, no.1.
[2] Ansorge R and Graves M, "The Physics and Mathematics of MRI", Morgan and Claypool Publishers, Bristol, (2016)​
[3] Aarnink R and Overweg J, 2012, "Magnetic Resonance Imaging: A Success Story for Superconductivity", Europhysics News, vol 43, no.4, pp.26-29
[4] Muller J H, "The Upper Critical Field of Niobium Titanium", University of Wisconsin-Madison, Madison(1989)
[5] Cosmus T and Parizh M, "Advances in Whole Body MRI Magnets", IEEE/CSC & ESAS European Superconductivity News Forum, Issue 14 (2010)
[6] Butikov E, "Precession and Nutation of a Gyroscope", St. Petersburg State University, St. Petersburg (2016)
[7] Griffiths D J, "Introduction to Quantum Mechanics: Second Edition", Cambridge University Press, Cambridge (2017), p.217
[8] Hao D, “MRI Contrast Agents: Basic Chemistry and Safety”, Journal of Magnetic Resonance Imaging, vol 36 (2012)
[9] Simon SH, "The Oxford Solid State Basics", Oxford University Press, Oxford (2013), p.49.