Nuclear Magnetic Resonance Flashcards
What is MRI used for and why?
To clinically detect:
* tumours and other abnormalities
* regions of stroke
* bleeding in the brain
* brain injuries
due to its good soft tissue contrast and high spatial resolution
Where does MRI signal come from?
Primarily from protons in water: hydrogen which is highly abundant in the body
What is put in the walls of MRI scanner rooms?
Iron plates
What does NMR focus on and what is used?
NMR focuses on the properties of atomic nuclei
For MRI, our favourite nucleus is 1H (a proton)
Nuclei possess an intrinsic quantum mechanical property called spin
What is the angular momentum of a point object of mass m?
L = mv x r
v = linear momentum
r = radius
What do elementary particles with angular momentum have and what is the equation for it?
Spin:
S = ħ √ (I (I +1))
I = spin quantum number (either zero, integer or half integer)
ħ = reduced Planck’s constant (h/2π)
When will a nucleus have non-zero spin?
If its number of protons and/or neutrons is odd and it will exhibit NMR
What are examples of nuclei with non-zero spin?
1H: I = 1/2
2H: I = 1 (odd number of protons and neutrons)
3H: I = 1/2 (odd atomic number)
4He: I = 0 (spins cancel as even)
What happens in the absence of an external magnetic field, according to quantum theory?
Knowledge of the magnitude but no knowledge of the direction of the vector at the same time
When a magnetic field is applied in z direction, how is the projection of S quantised?
S_z = m_z ħ
m_z = spin projection or magnetic quantum number = 2I + 1
What are the possible spin angular momentum projection states for protons?
As I = 1/2 so m_z = (2(1/2) +1) = 2, only 2 possible states: -1/2 ħ (spin down) and 1/2 ħ (spin up)
Which spin is less energetically favourable?
spin down as it requires more energy
What does a magnetic moment experience?
A magnetic moment in an applied magnetic field experiences a rotating force “torque”:
τ = m x B
also happens when a current loop I enclosing an area
What is the magnetic moment of a rotating sphere?
A rotating sphere with uniformly distributed charge and mass will have a magnetic moment given by:
μ = q/2m L
L = angular momentum
What is the gyromagnetic ratio γ?
How rotation relates to magnetism for given nucleus (known constant for each nuclear species)
γ = q/2m
What is the magnetic moment associated with spin?
μ = γS = γħ √(I(I+1))
(gives size of magnet)
What is the projection of μ in the direction z?
μ_z = γS_z = γ m_z ħ
What is the direction of the field and what do the other two axis form?
Z axis (magnetic field moves up and down)
Transverse plane: Y and X axis (magnetic field moves side to side)
What happens when an external field is applied to a magnetic moment?
A torque is produced:
dμ / dt = μ x γ B
What is the solution to the torque produced when an external field is applied to a magnetic moment?
Precession frequency: ω = γ B
Angular frequency which defines MR system
What is the energy of a magnetic moment in a static magnetic field of strength B?
E = - μ . B
Along the axis:
E = - μ _z . B = - γ S_z B
What do transitions between the two energy levels involve?
The release of a photon at frequency of ΔE = γ ħ B = hf
What happens as B increases?
ΔE increases and spin up becomes more preferable as it is at a lower energy level and moves in direction of field (unlike spin down)
What is the energy of spin up and spin down in a static field?
Spin down: E = 1/2 γ ħ B
Spin up: E = - 1/2 γ ħ B
What is the frequency (equation) that will cause transitions between two energy levels?
f = γB / 2π
or (Lamor) angular frequency: ω = γ B (ω = 2π f)
What causes transitions between energy levels?
Radio frequency (body is transparent at this frequency)
How are the units of gyromagnetic ratios converted?
(γ / 2π = MHz/T)
MHz/T divided by 2π = MHz
What happens in the absence of an external field to nuclear magnetic moments?
They are aligned randomly and their vector sum is zero
How do nuclear magnetic moments get aligned or anti-aligned?
With an external field B
Alignment with B is less energy-costly than anti-alignment
More nuclei will align parallel with B than anti-parallel
What is macroscopic magnetisation?
Once nuclei are aligned with B, a magnetisation is parallel to B
this leads to bulk magnetisation which leads to individual spins getting cancelled out (including x and y components)
What describes
The distribution of nuclei between energy states in thermal equilibrium
N_u / N_d = e^(ΔE/kT)
N_u = Number of spin up nuclei
N_d = Number of spin down nuclei
T = temperature (K)
Are there more spin up nuclei or spin down nuclei? What does this lead to?
There is a small excess of N_u spins as they require less energy to align with field
This leads to a net macroscopic magnetisation which is the source of the MRI signal
What happens to the population energy levels, N_u and N_d when B is increased?
Difference in population increases and the net magnetisation signal increases
Why does MRI require large magnetic fields?
To get large population difference and increase net magnetisation
How can a response be excited?
If energy is put in at a resonant frequency into the oscillating system
What are radio frequency (RF) coils used for?
To transmit signals at the Larmor frequency in the transverse plane
How can magnetisation be detected at thermal equilibrium?
Magnetisation can only be detected in transverse (xy) plane, (perp to B_0)
Are magnetic moments aligned in the z-direction?
No, they are precessing in the xy plane at the Lamor frequency
What does a rotating frame do?
xy plane are continually rotating so net magnetization will appear static and magnetic moment doesn’t appear to rotate about z axis
After radio frequency is applied, what happens to the rotating frame?
RF magnetic field, B1 is produces which appears static in rotating y direction and the net magnetic field also still appears static in z direction
How is the motion of a net magnetic field M in the presence of an applied magnet field described?
By Bloch equations”
dM/dt = M x γB
With time, the net magnetic field M will drop towards x -axis due to perpendicular force imposed
