MR 1 Flashcards
Matter is composed of atoms, which are made of ________ and ______ (containing _______ and ________).
Electrons
Nuclei
Protons
Neutrons
What are the 4 fundamental properties of nuclei?
- Spin
- Charge
- Mass
- Magnetic moment
Give the equation for the mass number
A = mass number
N = number of protons/neutrons
Give the equation for the atomic number
Z = atomic number
N = number of protons
What type of nuclei have spin?
Nuclei with an odd number of protons or neutrons.
Give 7 examples of elements with spin
C-13
F-19
Na-23
P-31
K-39
H-1
H-2
What nuclei are used for magnetic resonance imaging?
Hydrogen nuclei
Nuclei with spin possess ____ _______ _______ (J) and a _______ ______ (µ)
Spin angular momentum
Magnetic moment
Give the equation for magnetic moment
µ = magnetic moment
γ = Gyromagnetic ratio
J = spin angular momentum
Nuclear spin and charge give rise to a _______ ______.
Magnetic moment
What is the longitudinal direction in NMR?
The direction that the B₀ field (the static magnetic field) is aligned with. This is normally the z-axis.
What is the transverse plane in NMR?
The xy-plane, perpendicular to the static magnetic field.
What property causes a bar magnet to align with an applied magnetic field?
Torque (τ)
How do nuclear magnetic moments respond when they experience torque?
The nuclei precess because they have a spin.
Give the equation for the torque on a magnetic dipole in a magnetic field
τ = torque
µ = magnetic moment
B = magnetic field
Give the equation for precession
µ = magnetic moment
t = time
γ = Gyromagnetic ratio
B = magnetic field
Describe the shape of precessional motion for a magnetic dipole in a magnetic field
It exhibits gyroscopic motion.
- Pression occurs about B₀
- Spin occurs about µ, J
Give the equation for precession frequency
ω = Larmor frequency (frequency of precession)
γ = Gyromagnetic ratio
B = magnetic field
What is the name for the frequency of precession
Larmor frequency
What direction is the precession of H-1?
Clockwise
Define spin angular momentum
An intrinsic property of atoms with spin, described by a vector quantity (J).
It is the product of the nuclear spin quantum number, I, and reduced Planck’s constant, ħ.
Define the nuclear spin quantum number
A characteristic property of the nucleus that can take on integer and half-integer values. It is represented by the letter I.
Give the equation for the magnitude of spin angular momentum
J = spin angular momentum
I = nuclear spin quantum number
How many eigenstates (spin states) does spin angular momentum, J, have?
2I + 1
What is the name for the spin states of spin angular momentum?
The azimuthal spin quantum number, mₗ
What is the range for the azimuthal spin quantum number?
mₗ = I, (I - 1), (I - 2), …, -I
What are the spin states for a proton?
I = 1/2 so mₗ = ±1/2
Give the equation for the z-component of spin angular momentum
Jz = z-component
mₗ = spin quantum number
What are the z-component values of spin angular momentum for protons?
Is spin angular momentum quantised?
Yes
The potential energy of a magnetic moment is the ____ _____ to rotate the magnetic moment in a magnetic field.
Work done
Give the equation for the energy of a spin magnetic field
E = energy
µ = magnetic moment
B = applied magnetic field
γ = Gyromagnetic ratio
J = spin angular momentum
When is potential energy lowest for a magnetic moment in a magnetic field?
When the magnetic moment is parallel to the magnetic field.
What do spin states correspond to energetically?
Zeeman energy levels
How many Zeeman energy levels do H-1 atoms occupy?
2
Why is electromagnetic radiation applied in NMR?
To cause a transition between the Zeeman energy levels.
What frequency is the applied electromagnetic radiation for NMR equal to?
The Larmor precession frequency
Spins are distributed amongst energy levels according to the _______ ________, depending on the ______ ______ in the system.
Boltzmann distribution
Thermal energy
Give the equation for the Boltzmann distribution
∆E = difference between energy levels
kB = Boltzmann constant
T = temperature
γ = Gyromagnetic ratio
B = applied magnetic field
What two factors determine how many protons there are in each energy state?
- Magnetic field
- Temperature
Is the spin-up state high or low energy?
Low
Is the spin-down state high or low energy?
High
When are spins detectable with MR?
When there are more protons in the spin-up than the spin-down state, generating a net nuclear equilibrium magnetisation (M₀) that is detectable.
Give the equation for the number of excess spins in the spin-up state
n = spin-up - spin-down (excess spins)
kB = Boltzmann constant
T = temperature
γ = Gyromagnetic ratio
B = applied magnetic field
N = spin-up + spin-down (total number of spins)
How many spins will be in the high energy state (spin-down) if the temperature is reduced to 0?
Zero spins
How many spins would be aligned in the absence of an external magnetic field?
There would be no net alignment as the spins are randomly oriented.
What is the level of spin alignment in a 1T magnetic field at 310K?
~3 ppm aligned
Give the equation for the fractional difference in the population of up and down spin states
n = spin-up - spin-down (excess spins)
N = spin-up + spin-down (total number of spins)
T = temperature
γ = Gyromagnetic ratio
B = applied magnetic field
What is the impact of spins precessing incoherently in an applied magnetic field?
There is no net magnetisation in the xy-plane as the spins aren’t in phase and cancel one another out.
Give the equation for the net magnetisation vector in the longitudinal direction
M₀ = net magnetisation
Σµ = sum of magnetic moments
n = excess up spins
N = total number of spins
Give the equation of motion for magnetisation
M = magnetisation
t = time
γ = Gyromagnetic ratio
B = applied magnetic field
What does the equation of motion for magnetisation represent?
A net magnetisation that precesses about B (the direction of the applied magnetic field).
Give 4 safety precautions that have to be followed around MRI scanners
- Don’t bring metals close to the scanner
- No pacemakers
- No metallic implants (e.g. stents)
- No neurostimulators
Give 4 effects of a static magnetic field
- Sensory effects (e.g. dizziness)
- Reaction to the noise from generation of the magnetic field
- Minor changes to chemical reaction rates
- Peripheral nerve stimulation (PNS)
