M1L1 - Radio Messages, Spin, Resonance, NMR

RADTH 305 - MRI Physics. University of Alberta

Describe the basic idea of how MRI works

An MRI machine sends an Rf signal to the protons in body tissue, which causes them to resonate and emit a response signal which is picked up by an NMR receiver

Are protons (aka spins & hydrogen atoms) magnetic?

Yes, protons are magnetic due to their spin.

what is the name of the signal protons send out after they are affected by an Rf pulse?

Nuclear Magenetic Resonance signal

Charge + angular momentum =

magnetic moemnt

Do protons have direction, and what is this direction in the absence of an external magnetic field?

Yes, protons do have a direction, which is random in the absence of an external magnetic field.

What is the B₀ Magnet?

The main static uniform and STRONG magnetic field produced by the superconducting magnet in an NMR system.

What direction is B₀ coventially drawn along

The Z-axis, also know as the longitudinal direction

What is the XY plane called?

The transverse plane

Three rules for a single spin (proton) in a B₀ field

1. Each proton has a magnetic direction (in ANY 3D Direction) represented by a vector

2. The transverse component (xy plane) of a spin precesses about the Z-axis at the Larmour frequency

3. The Z component of a spin dies not spin

   • if a spin is pointing along ± Z, it will remain pointing in the same direction with no rotation

What is the Larmor frequency

The frequency at which a magnetic moment precesses around the direction of an external magnetic field, related to the strength of the field and the specific properties of the nucleus.

what is the formula for Larmor frequency

How is frequency impacted by magnetic field

The frequency of the Larmor precession increases linearly with the strength of the magnetic field; as the magnetic field strength increases, the precession frequency also increases.

When is spin precession detectable? When is it not detectable?

Spin precession is detectable when the transverse component of the spin vector is non-zero, typically during resonance with an external radiofrequency field. It is not detectable when the spin is aligned along the Z-axis, as in this case, there is no transverse component to observe.

Spin is affected by it’s ….

environment

• electrons, other spins, fields we apply, etc.

Excited spins precess within which plane?

the transverse (xy) plane away from the equilibrium state

what is phase?

Phase refers to the position of a spin system in its precession cycle, represented as an angle in radians or degrees. It describes the timing of spin behavior relative to an external reference point.

• phase = rotation angle

Formula for phase

Does an exicted spin have phase?

Yes, an excited spin has phase, indicating its position in the precession cycle.

What does the saying “spin phase accumulates over time, like a memory” mean in MRI physics?

It means that the phase of spins in an MRI system builds up over time, affecting the overall signal strength and coherence, which reflects previous interactions and influences the imaging results.

• Phase reflects the history of a spin’s precession. Differences in local magnetic fields or applied gradients cause spins to gradually drift apart in phase. This accumulated phase shift is not lost — it “remembers” the effects of the magnetic environment and can be manipulated (e.g., refocused in spin echo, used in phase encoding) to generate MRI signal and spatial information.

Spin phase in MRI

Phase refers to the instantaneous direction that the precessing spins are pointing in. If many spins point in the same direction (‘in -phase’ with eachother), then the fields they produce add, and we can detect the signal

What happens to the MRI signal if the spins are in phase

if many spins point in the same direction (in phase), the fields they produce have an additive effect, and we can detect a signal

what happens to the MRI signal if the spins are out of phase

if the spins are pointing in many different directions, we get a weak signal or none.

What is resonance

Resonance is the phenomenon that occurs when the frequency of the applied radiofrequency pulse matches the natural frequency of the precessing protons, allowing for maximum energy absorption and enhanced MRI signal.

will a resonant system accept energy at a different frequency?

No, a resonant system will not efficiently accept energy at a different frequency.

four factors of a resonant system

1. has it’s own natural frequency

2. accepts energy at a resonant frequency

3. vibrates/oscillates at it’s resonant frequency

4. radiates energy at the resonant frequency

What is the resonant frequency range in NMR

radiofrequency = Rf = B₁ , is in the MHz range

spins accept energy at at specific …

frequency, the resonant frequency

once the system is excited, it emits energy at what frequency?

its resonant frequency (the same resonant frequency)

resonant frequency depends on what two factors

1. type of nucleus

2. magnetic field strength

Calculate the linear resonant frequency for a 1.5 T magnet

What conditions must be met for resonance in an MRI machine

The frequency of the RF (B₁ field) is set to match the B₀ field strength

which component precesses about the Z-axis at the larmor frequency?

the transverse component

spin frequency is proportional to …

the applied magnetic field

spins have to be excited in the ____ plane

XY plane

M__ precesses, M__ does not

Mxy precesses, Mz does not

What is FID

Free induction decay

• the decaying signal detected by the RF coil after a single RF excitation pulse

why is it called free induction decay

it’s called “free” because no further RF or gradient pulses are applied; the spins are just left to evolve on their own.

• It’s called “induction” because the changing transverse magnetization induces a current in the receiver coil (Faraday’s law).

• It’s called “decay” because the signal strength decreases over time due to relaxation.

Step-by-step process of FID

1. RF pulse applied

   • tips magnetization (usually 90 into the xy plane)

2. Spins in phase

   • net transverse magnetization is at maximum —> strong signal

3. As time passes

   • spins dephase due to T2 effects, transverse magnetization decreases

4. The decaying oscillation is recorded by the coil —> this is the FID

the decay constant of FID decay is

T2*

what are the two mechanisms of T2* decay

1. B0 inhomogeneities

2. T2 decay

short T2 means …

rapid decay

describe T2 decay

T2 decay refers to the time it takes for the transverse magnetization to decrease to 37% of its original value due to interactions between spin states and dephasing caused by local magnetic field inhomogeneities.

What is TR

TR stands for Time of Repetition, which is the time interval between successive RF pulsations in MRI. It is crucial for determining image contrast and influences the signal received during imaging.

What does T1 relaxation govern

the return of Mz back to equilibrium

T1 recovery is 95% completed after ____ T1 times

three T1 times

T1 relaxation vs T2 relaxation

 T1 (longitudinal) relaxation

• Protons give energy back to the surrounding lattice → recover along z-axis.

• Fat (short T1) recovers fast, water (long T1) recovers slow.

b) T2 (transverse) relaxation

• Spins lose phase coherence in the xy-plane due to spin–spin interactions.

• Signal decays as they dephase.

• Fat (short T2) dephases fast, water (long T2) dephases slow.