Relaxation Theory & Measurement - T1 & T2 Flashcards
What is the NMR recap?
- Nuclei have ‘spin’
- Quantum mechanical quantity
- Relates to the angular momentum of the nucleus
- Restricted to nuclei with odd no. of protons or neutrons or both
- Mostly use the hydrogen nucleus (single proton) for MRI
What is highly abundant in human tissue?
Hydrogen 1H
What is a proton?
A spinning sphere with charge and mass
What does spin give the proton?
- Magnetic moment
2. Angular momentum
When will spins align?
When placed in an external magnetic field (B0)
Where does the spin not ‘snap to’?
To the B0 axis, due to its angular momentum, but precesses around it
Where does precession occurs at?
Larmor frequency
w= yB0
Y= gyromagnetic ratio = 42.57 MHz/T (protons)
What is established in the presence of a magnetic field for hydrogen?
Two energy levels
E= -mHyB-
m=1/2 or -1/2, spin up or spin down
What orientation is spins most likely to be found in and what does it represent?
Parallel than anti-parallel (~1 in 100,000 protons, B0=1.5T, 37)
This represents ‘net magnetisation’ of the system M0
What does M0 precess at?
Frequency w=yB0
64 MHz at 1.5T, 128 MHz at 3.0T (radiofrequency)
What is the orientation of Mz?
Stays the same
Changing the field in XY (transverse) plane
How do you detect M0?
Place Receive coils on X and Y axis
Change Flux
Induced EMF
NMR Signal
What is the RF Excitation pulse?
Expose spins to alternating magnetic field (B1)
B1 frequency must match the Larmor frequency, and is applied in the transverse plane
Spins absorb energy, and nutate away from longitudinal axis, creating time-varying transverse component
What can be determined by using two coils?
The direction of the rotation of the magnetisation, and the phase of the spins
What do parallel state have?
Slightly lower energy level than the anti-parallel state
What is M0 used to generate?
the MR signal
What is net magnetisation?
When more of the spins are aligned with the magnetic field than anti-parallel
What is frame of reference?
- B0 is the main magnetic field [direction in which the main magnetic field is pointing]
- The spins are spinning around main field
- X/Y plane is perpendicular to the main magnetic field
- In the presence of main magnetic field and the spins is precessing around it, there is a change in signal in X/Y plane – place coil and measure as it will induce the change in magnetic field going through a coil induces a voltage – measure it as a voltage
What is the basis of magnetic resonance imaging?
RF frequency pulse are placed into the system that is of the same frequency as the Larmor frequency
What happens when you hit the resonance frequency and put RF energy in?
it transfers energy into the system and tips the magnetisation down into transverse plane and continues to sweep around the Larmor frequency and get more signal in the coils that are placed to detect the signal from transverse axes
What is the benefit of using more coils?
- Detects more antenna [get more signal]
2. Get the phase of the signal
What is rotating frame of reference?
- Z is the main magnetic field
- X/Y are the transverse plane
- The angle in which we flip is the flip angle
What is T1 relaxation also known as and what does it describe?
Spin-lattice relaxation
It describes the process of M0 gradually returning to equilibrium [Regrowth of the magnetisation back in the Z direction]
What is the recovery of Mz given by?
Mz = M0 . (1-e-t/T1)
What is the T1 relaxation time?
Time needed to reach (1-e-1) or 63% of M0
How does T1 relaxation work?
- Transfer of energy from nuclear spin system to neighbouring molecules (the lattice)
- Leads to restoration of Boltzmann equilibrium
- Most common source of local fluctuating field is direct dipolar interaction
What are the requirement for energy transfer?
- Motion in the lattice must cause fluctuating magntic field (tiny, local B1 pulse)
- Local fluctuating field must have a components at the Larmor frequency)
- Only X and Y compontents of local field can cause T1 relaxation
What is dipole interaction?
Fluctuating source of magnetic field that can transfer energy into and out of the system
- Interactions between their spins and their lattice
What is the function of correlation time?
Characterise the motion of these molecules around the spins in the system
What is the correlation time?
- How rapidly are the molecules around the spin system fluctuating
- It’s the fluctuating movement that causes changes in magnetic field that transfers energy in and out
3.time taken for (spherical) molecule to rotate by ~ 1 radian
Tc ~ 10-12 Mw (Mw = molecular mass in Daltons)
What is 1/correlation time?
- Frequency
2. We want the frequency to be same around the Larmor frequency
What does the system have?
Resonance Larmor frequency which is omega 0
What is the rapid reorientation of the dipolar interaction due to?
Molecular motions provides fluctuating field
- T1 relaxation is temperature dependent
What do we need to induce spin transition?
1/ Tc ~~ W0
What is the characteristic of solid state?
- Cannot tumble around very quickly
- Much lower than the Larmor frequnecy - inefficient at exchanging energy
- End up with a long T1 relxatiom time
What is the characteristic of intermediate state?
They are free but get stuck to hydrogenation layer around large molecules
- Tend to tumble around the right level of frequency for the system [Larmor frequency]
- Efficient in getting energy back out the system and therefore give a short T1
Solid-state/large molecules
Hindered molecular motion
Large Tc –> 1/Tc «_space;W0 –> long T1
Fluid/small molecules
Rapid motion
Short Tc–> 1/Tc»W0 –> long T1
Intermediate
1/Tc ~~ W0 –> short T1
What do Free water, solid-state and bound water have?
- Free water = long T1
- Solid-state = Long T1
- Bound water (water bound in hydration layers around macromolecules) –> short T1
What do short Tc have?
Low viscosity/small molecules
What do long Tc have?
High viscosity/large molecules
What are the 3 pools of spectral density function?
- Marcomolecules
- Bound water
- Free water
What do free water cover?
A whole range of tumbling frequency
What is the bound water?
Where the NMR signal comes from
- Tend to tumble about the Larmor frequency
When does the Larmor frequency go up?
If we go up in field strength from 1.5T or 3.0T
What does increasing B0 decrease?
The fraction of bound protons able to interact at the new (higher) Larmor frequency
- Less efficient T1 relaxation
- T1 will increase with the field strength
What do different tissues have?
Different T1 relaxation times
depending on the structures of the molecules
How are different curves achieved?
Flip magnetisation into the transverse plane and wait for it to recover
What is CSF?
- Free water
- High frequency
- Not very efficient in exchanging energy in the system
- long T1 recovery
What is fat?
- Bound to large structures
- They are in the right spot for exchanging energy in the system
- Efficient T1 recovery
- Signal recovers much more quickly
What is the order of T1 relaxation time from short to long?
- Fat
- White matter
- Grey matter
- CSF
What should be done when creating an MR image?
Make it a T1 weighted image
Define Repetition time (TR)
Refers to amount of time for magnetisation to recover back to equilibrium before next excitation
What happens at the repetition time (TR)?
The longitudinal magnetization that has recovered provides the M0 for the next excitation
What can TR be used for?
provide contrast between tissue types
What is the process of measuring T1: inversion recovery pulse sequence?
- 180 degree pulse to invert M0
- Wait for a short time period (Inversion time, TI)
- Apply 90 degree pulse
- Measure signal
- Repeat over a range of inversion times
What is the T1 relaxation time of the tissue?
The rate at which the curve recovers
What is TI?
Time we waited between 180 degrees pulse and start of our experiment
What is acquired along T1 recovery curve after an inversion pulse?
Multiple single-shot images
What is the Look-Locker?
- Initial inversion pulse followed by a series of low flip angle alpha pulses
- Each alpha pulses tip Mz slightly away from the z axis, giving signal of Mz . sin (alpha) in the transverse plane
- As Mz relaxes from -M0 back to equilibrium, the alpha pulses give a series of imags showing the changing magnetisation
- Alpha pulses interfere with ‘true’ relaxation –> faster recovery of M0 –> artificially short T1
Where is T1 weighted image seen in?
Clinical scan
What is T1 map?
measured the relaxation time in every voxel and the values do mean something
What is CSF in T1 map?
- High value of T1
- Takes a long time for the signal to recover
- It is therefore dark in the T1-weighted image
What is T2 relaxation also known as?
Spin-spin relaxation
What is phase coherence in T2 relaxation?
After 90 degree pulse, spins are all precessing in concert
How are spins gradually de-phased?
Due to number of processes
What is spin-spin interaction?
- W0 = YB0
- Two spins meet –> Blocal increases –> W increases locally –> precessional frequencies change –> spins dephase relative to W0
- Spins move apart –> both return to Larmor frequency –> phase angle remains
- Many 1000s of these interactions –> eventually all spins out of phase with each other: vector sum of M0 goes to 0
What does random spin motion lead to?
Exponential decay in transverse net magnetisation
- MXY = M0e-t/T2
What is T2?
Time for signal to drop by 1/e, or 37% of M0
Due to random motion of spins, this process is irreversible
What happens the longer we wait after we flipped the magnetisation onto the transverse plane?
Less signal
the spins are dephased
Dephasing is T2 relaxation
What influences T2 relaxation?
Fluids (free spins) → rapid motion → Blocal constantly changing → net dephasing averages out over a few ms (motional averaging) → long T2
Bound protons → less rapid motion of spins →relatively static Blocal → more rapid dephasing → short T2
What are the free water, bound water and solids in T2 relaxation?
- Free water = Long T2
- Bound water = Intermediate T2
- Solids = v.short T2 (‘MR invisible’
Why is B0 not homogenous in reality?
Due to the design of the magnet itself – scanner dependent
Due to different magnetic susceptibilities with tissue:
Most body tissues are diamagnetic (slightly oppose B0)
Air / dense bone have almost zero susceptibility
De-oxyhaemoglobin is paramagnetic (slightly enhance B0)
What do local B0 inhomogeneities cause?
Additional de-phasing of spins
- Adds to the decay of coherence in transverse magnetisation
- These effects are constant in time
What are the static (T2’) and dynamic (T2) effects combine to form?
T2*
1/T2*=1/T2’ + 1/T2
What is T2*?
Always shorter than T2
What is the free induction decay?
The initial signal, after flipping M0 into the transverse plane
Do not measure this due to technical limitations
What is measured instead of FID?
Induced echo:
- Gradient echo sequences have T2* weighting
- Spin echo sequences hav T2 weighting
What is gradient echo?
Echo of the original signal
That is due to rephasing and dephasing of spins
What is T2* weighted sequence?
Combined influence of the freely diffusing spins that all cancel out their magnetic field and spatially dependent change in magnetic field which we apply with rephasing and dephasing gradient
What is spin echo?
- Applies 180-degree pulse
- Spatially variant magnetic field
- Reverses the direction in which the dephasing happens
- 180 degrees ‘un-do’ the dephasing due to B0 in-homogeneities
- The refocusing pulses can undo static B0 in-homogeneities (T2’) but not dynamic spin dephasing (T2)
- So, spin echo has T2 decay only
- It isn’t as strong as the original signal
- T2 weighted
What is echo time?
Time we flip the magnetisation onto transverse plane and creating an image
Why it crucial to make echo time shorter?
Capture more signal
What is the consequence of making echo time too short?
All the tissues will look the same
What is required for T2 weighting image?
Long TE
What is Car-Purcell multi-echo sequence?
- Sequence where you get a lot of echoes
- Train of echoes
- Get all the echoes over time
- Magnitude at which the echoes decay is T2 relaxation time
- Measure that signal as a function of echo time and it will decay
- Keep TR as long as possible – as much signal in each acquisition
What are the disadvantages of Car-Purcell-Meiboom-Gill (CPMG)?
- 180 degree pulses are not perfect
2. Cumulative phase errors occur in the echo train
What is the modification for CPMG?
- Shift 180 pulse 90 to the initial excitation pulse
e. g. initial 90 in X,alternate subsequent 180 pulse in +/-Y
What do T1 and T2 relaxation describe?
The return to equilibrium within a system of spins
Occurs over different time scales
What do T1 relate to?
recovery of longitudinal magnetization, via loss of energy back into the ‘lattice’
What does T2 relate to?
loss of coherence of spins in the transverse plane
Influenced by irreversible (T2) and reversible (T2’) processes
What are the workhorses of MRI?
T1 and T2 weighted imaging
What is possible in vivo?
Quantitative measurement of T1 and T2
