MRI Physics Flashcards
T1 in different tissues
Spin-Lattice
Water (slowest)
Muscle
Fat (fastest due to long chains have complex thermally-induced flexions and rotations)
T2 in different tissues
Spin-Spin - density related:
Water (slowest)
Fat
Muscle (fastest)
How TE affects T2 contrast
T1 Weighted sequence
TR - weight long enough the spins have dephased and the transverse vector is net zero
If you apply an RF pulse AGAIN
- The net longitudinal vector that was T1 recovery will be flipped 90 degrees
So fat would have :
- relaxed more, have a higher net longitudinal vector
- when flipped 90 degrees, have a higher magnitude transverse vector
- Use a short TE to negate T2 so now you’re measuring T1 differences in the transverse plane!
T1 weighted scan
Negate T2 differences: SHORT TE
Maximise T1 contrast: SHORT TR
Proton density scan
Negates
T1 differences - LONG TR
T2 differences - VERY SHORT TE (before they begin dephasing)
(Water + Fat have a higher proton density)
T2 Weighted Scan
Negate T1 differences - LONG TR
Maximise T2 contrast - Short TE (but allowing some dephasement)
T1 and T2 recovery
T2 Decay Vs T1 signal gain
T2 happens A LOT FASTER
Long TR value range
1500-2000’s
Long TE value range
80-160ms
Short is 10’s
Lamour Frequency = B0 x Gyromagnetic ratio
Slice selection using RF
- Apply a gradient along B0 creating a gradient of precessional frequencies
- Apply an RF pulse of a bandwidth for your slice
Slice selection by changing the strength of Bo
Increase slice thickness by increasing bandwidth
Decrease slice thickness by increasing field strength
Higher max Bo - greater range, so a set bandwidth of RF would resonate with a narrower plane.
With a slice thickness, there’s a gradient of B0, which creates a slice phase.
So after RF pulse, apply a rephasing gradient.
Equal and opposite gradient to Z axis
Slice is now completely in phase
Slice selection sequence
- 90 degree flip
- Rephasing flip/dip
- 180 flip to account for T2* (free induction decay)
You need multiple TEs to infer what’s happening to net magnetisation over time.
And receiver coil has a bandwidth as well.
Visualising T2* correction
So you need to factor this in when using multiple TEs
Frequency encoding gradient applied along x-axis AT THE TIME OF READ OUT
So frequency differs depending on x-axis location
But if you apply frequency encoding gradient, they would lose phase and transverse magnetisation vector / signal.
So you apply an equal and opposite frequency encoding gradient prior to read out.
So more IN PHASE despite DIFFERENT FREQUENCIES during readout.
You can now sample at multiple TEs during frequency-encoded readout.
Every read-out is a numerical number for the whole image. Frequencies and their amplitudes can be teased out to give you x.
The Fourier transformation converts this time-based based data set into a frequency-based data set.
Also the more you sample, the more frequencies you can tease out.
You do a one dimension inverse Fourier transformation
Phase encoding gradient:
Apply a gradient between the 90 and 180 degree RF pulses
Only applied for a short period to cause a phase change, but then stopped so frequency is still with larmour frequency Bo
Phase encoding gradient:
Loss of transverse magnetisation because of phase differences
So each coloumn has the same frequency but in the y axis there is phase variability but with null in the middle in terms of phase change
Phase encoding gradient:
Increasing phase encoding gradients and also in opposite direction
Calculate amplitude without and then applying each.
Do a one dimensional inverse Fourier transform for each
Once you have enough phase encoding spaces you have k space
No. rows = No. phase encoding steps
Each line of k space is the net magnetisation vector over a period of time
Do a one dimensional inverse Fourier transform for each and transform it into frequency based or x axis location based data
K space data = TIME based data
EACH POINT along x axis in k space
represents net magnetisation vector of the ENTIRE SLICE at a given period of time.
You can convert that to x axis location based data
Do a one dimensional inverse Fourier transform for each and transform it into
Signal gets weaker at the start and end because of the phasing and dephasing
Signal weaker at the periphery because the signal is weaker when you apply stronger phase encoding steps
You can use k space and the one dimension fourier transform data to create your image
The specific net magnisation of the
Entire slice: From K Space
Entire data acquisition period from frequency based data
This is the 2D Fourier transformation where you combine these two data points that give you the axis data
Use simultaneous equations to work you the y contributions
K Space: Net magnetisation vector of the whole space over time
Spin echo sequence: Flipping 180 and measuring at TE when they come back into phase. So you’re measuring T2 rather than T2*
Central region of K space:
- Lose phase encoding and time acquisitions around it.
- Strong signal - able to see differences in signal easily
SO GIVES CONTRAST
- Lose spatial encoding
Any bright signal in T1 weight - likely come from FAT
Lower signal from H20
If you isolate the periphery of K space
- Multiple frequency and phase encoding steps
- GIVES SPATIAL RESOLUTION AND EDGES
Periphery of k space contains higher frequency info - the rate of phase change is much higher with the stronger gradients
The two halves of k space have conjugate symmetry
You use a mathematic formula to work out other half
However
- Not a perfect machine
- Magnetic field inhomogeneities
MRI Field of View
By narrowing field of view you have the same matrix size but pixel size is smaller
So better spatial resolution over a smaller field of view
Bandwidth
Range of frequencies within FOV in the frequency encoding plane
In the middle - its just B0 so they will have the Lamour frequency
Reducing FOV will also reduce the bandwidth
Reducing frequency encoding gradient increases the bandwidth for a particular thickness
So bandwidth is a function of both gradient and field of view
Rotational frame of reference. You’re looking at the differences in frequenecy
Processional frequency from null or centre will be different by half the bandwidth to either end
Aliasing
If you don’t sample high enough for a frequency
Nyquist limit = Sampling rate / 2
So you need to sample double the frequency you’re measuring
Sampling rate = bandwidth
Sampling interval is the inverse of this:
1/ sampling rate
aka DWELL TIME
Summary
Laboratory frame - when you look at the absolute value in terms of precessional frequency
Rotating frame - relative differences in precessional frequency relative to the centre
This is what it looks like when it is the RELATIVE difference in spins.
Frequency encoding gradient is then inverted so it comes back into phase as you record
If you pick a larger bandwidth by applying a stronger gradient
Stronger gradients will mean the dephasing and rephasing will happen much quicker.
So higher sampling frequency.
30Hz Bandwidth
Vs…
60Hz Bandwidth
Narrower bandwidth = Longer to acquire as sampling rate does not have to be as high
So narrower bandwidth = BETTER SNR
Weaker gradient = more time to acquire data
Higher bandwidth = POORER SNR
SNR = 1 / squareroot of BW
Benefits and drawbacks of narrow bandwith
Pros: Better SNR
Cons:
- More metal artefact
- More chemical shift artefact
- Can’t use short TE sequences
Aliasing - wrap around - when you are not sampling high enough
This can happen when you pick a smaller field of view from things outside of your range.
With phase encoding gradients, you could flip them 370 degrees - but it will only look like 10!
Ideally you should not be applying more than 180 degrees because adjacent spins could be completely out of phase.
This will cause aliasing in the phase encoding gradient.
The smaller you make the difference in phase encoding steps = greater you can make your FOV
Larger phase steps = smaller possible FOV as you’ll reach you phase shift limit quicker and risk aliasing.
Higher risk of aliasing at the edges
Soo….
You reduced your FOV with the same matrix size for better resolution
But now you get more aliasing from everything outside of your FOV
So reduce aliasing by…
- Remove tissue or arms outside FOV!
- Increase FOV but you lose resolution if you keep same matrix size
- Oversampling - taking more samples so frequencies or phase steps outside the FOV but don’t include it in the image.
Machines will often oversample 2-4x anyway in the frequency encoding direction because it doesn’t add any additional time to the sequence.
So reduce aliasing by…
However, over sampling in Y requires MORE phase encoding steps.
OR you can change the direct of your frequency and phase directions but you can’t as chemical shift only affects frequency encoding direction
So reduce aliasing by…
Parallel imaging
In parallel imaging you can have TWO RECEIVER COILS.
Different signal intensities depending on proximity to coils
Removing phase encoding aliasing though parallel imaging
So the aliased portions of the image will be the ones differing in intensity between the two coils, can be calculated and removed.
So no need for additional phase encoding steps!
Chemical shift….
Water and Fat precess differently despite the same Bo
Electron shielding is stronger in fat
In a water molecule, P() of the electron orbiting near oxygen instead of hydrogen is HIGHER
So water hydrogen is LESS SHIELDED
So precessional frequency is a function of the LOCAL magnetic field
Which is Bo + magnetic field from electrons that can oppose Bo
Chemical shift delta =
d= 3.5 ppm = parts per million.
For every million / megahertz, there will be a difference of 3.5Hz
By increasing the bandwidth, the range of frequencies per pixel has increased.
Increase the frequency encoding gradient field strength, you can reduce the chemical shift artefact.
Increasing the matrix size so each pixel is representing a wider range of frequency.
Increasing BW
= Reduces Chem Shift Artefact
= But increases SNR
Spin Echo Pulse Sequence
- Slice selecting RF 90 degrees to give transverse
- Phase encoding gradient
- 180 degree RF pulse
- Sample at TE - time to echo - when spin echo occurs WHILST applying frequency encoding gradient
- Wait time TR = Time to repetition.
Rephasing 180 - regaining signal - just slightly less than T2 - so no it is only due to spin-spin interactions
Differing transverse decay. T2 time constant is the time to LOSE 63% of signal.
Free induction decay T2* actually happens a lot faster
Gyromagnetic ratio for hydrogen is 42.58 MHz per Tesla
Total Scan Time
Rephasing frequency encoding gradient, can be made positive but put before the 180
IF after the 180 it would need to be positive.
Multiecho Spin Echo: Repeat 180 flips allows repeat TEs
So you read out more along the True T2 decay.
Short TE sequences: V. short in Proton Density Imaging + T1 (you don’t want T2 differences in your image)
Longer TE: T2 images - you get rid of T2 contrast.
So you can acquire a more T2 weight image with the second echo making use of the downtime.
Multiecho Spin Echo: Same slice different weightings
Multislice spine echo imaging:
Apply a DIFFERENT RF slice selection gradient
Multislice spine echo imaging: Same weighting different slices
FAST Spin echo imaging:
Apply an equal and opposite phase encoding gradient.
You can then use a different phase encoding for a different part of k space.
Number of echoes = Echo train length (ETL)
Scan time reduce by the factor of ETL
FAST Spin echo imaging:
Downsides:
Reduced SNR
Less contrast with each echo.
Each echo will have less transverse magnetisation so better for T2 weighting / fluid sensitive sequences such as MRCP.
As K Space has conjugate symmetry.
Filling only half of k space reducing scan time by a factor of 2.
Spin Vs Gradient Echo sequence
Gradient Echo sequence:
- Slice selection at angle α.
- Dephasing + rebound frequency enocoding gradient along x axis.
Spins have kept orientation but speeds have inversed so now the slow ones can catch up.
So you’ve corrected for phase change by the FEG.
Gives you signal equal to T2* / free induction decay.
Gradient Echo sequence:
Not using the 180 degree flip saves time, so the T2* measures is a stronger signal
Smaller flip angles allows shorter TRs
ALL RF Pulses are equally spaced
If you constantly flip at 90, you’re only putting the longitudinal recovery back it the transverse plane
If you flip at a smaller angle e.g. 15. You get a smaller transverse magnetisation (as they’re in phase) but you don’t fully loose the longitudinal like you do with 90 flips.
Flipping at a smaller angle allows FASTER longitudinal recovery.
So you can repeatedly flip with a smaller angle getting similar transverse magnitudes each time with short TRs
You can plot the steady state signal for a set TR for a tissue of a particular T1 at different flip angles.
ERNST ANGLE = Optimum angle for highest signal
Different tissues with different T1s will have different Ernst Angles.
How changing TR affects different flip angles
For short TRs higher flip angles do not neccessarily equate to the highest signal for specific tissues.
Smaller angles have a higher proportion of longitudinal recovery for shorter TRs e.g. 20 vs 60 degrees
with 20 vs 60 degrees
Stimulated gradient echo:
at TR, residual transverse magnetisation is flipped further and will relax more into the transverse plane
This is the stimulated echo
Tissues with SHORT T2 (shorter than TR) will not contribute
Tissues with a LONGER T2 wont have relaxed and can flip further - so stimulated gradient echo gives T2 weighting.
Coherent gradient echo:
The spins are IN PHASE at the next TR
The PEGs are applied in equal and opposite direct to allow for rephasing
Gives T1 AND T2 contrast:
Gradient echo / free induction decay is T1 weighting (short TR and short TE)
Stimulated echo from residual transverse magnetisation - gives T2 weighting
TR, TE, flip angle, T1 and T2 Tissue time constants
For purely T1 weighting…
To get ride of RESIDUAL transverse magnetisation
- Don’t apply a rephasing PEG
- Apply a spoiler gradient causing spins to become completely out of phase
“SPOILED GRADIENT ECHO”
- No residual magnetisation as its spoiled
- Longitudinal recovery is flipped and measured in transverse - T1 weighting!
For pure T2 weighting:
Sample stimulated echo in isolation from free induction decay
Rewinder gradients: Decouples the stimulated echo
Rewinder gradients: Accelerates the stimulated echo rephasing before the next TR, so TE can me moved and it can be measured in isolation.
Steady state free precession gradient echo (SSFP)
Inversion recovery sequences
Suppressing signal from tissues
- Start with basic spin echo sequence
- BUT START with 180 RF pulse, more spins in antiparallel
When all are anti-parallel you have -100% of B0. Slowly they start relaxing until you have 0 (50% parallel / antiparallel))
Fat has more spin-lattice interactions has a shorter T1, gains 63% of signal faster than water
So you can predict how longitudinal magnetisation will recover at these time points
What it would look like if you didn’t invert the spins:
The TI time is when you flip 90 from the initial 180
STIR - Short TI (TAU) Inversion Recovery
- SUPRESSES FAT
- Blood and water is brighter
Phased Recovery Graph:
Can also be shown as a magnitude sequence
FLAIR: Fluid attenuated inversion recovery
Use the water bounce time (net zero longitudinal after 180 flip)
FLUID SUPPRESSED
Higher signal fat
Intermediate from muscle
PARTIAL SATURATION
TR BEFORE T1 recovery.
Applying a regular RF pulse BEFORE tissues have made their T1 recovery.
You reach a steady stage where same degree of T1 recovery is flipped into transverse plane.
The signal is less than the original 90 degree = partial saturation difference.
SATURATION
- Tissue targeted 90 RF - no longitudinal
- Apply SPOILER FEG and PEG to completely dephase - no transverse plane
- Do a pulse or gradient echo pulse sequence, only whats left along B0 will flip.
Water and Fat have chemical shift
Oxygen in H20 - DESHIELDS by keeping the electron away from H+
Fat: MORE SHIELDING.
Precessional frequency is different in B0
CHEMICAL SHIFT selective RF pulse will matching precessional frequency of e.g. FAT. Spoiler gradients then applied.
Gadolinium shortens T1 but doesn’t change precessional frequency.
So YOU CAN combine with Gado (UNLIKE STIR)
Metal - will introduce inhomogeneities
FAST SPIN ECHO IMAGING
LONG TRs
Each RF = Multiple echos / lines of k space
No. echoes = Echo train length ETL
AKA
Turbo spin echo
- Using rewinder PEGs
- Apply another 180 to get another spin echo
- Signal decays at rate of T2 at each echo.
- You need a longer TR but fill multiple lines of k space each time
Most contrast near centre due to little PEG
Edge definition due to edge of k space due to steeper PEG
SHORT TR (<50ms) Gradient echo
The dephasing and rephasing Frequency encoding GRADIENT is why it is called a “GRADIENT ECHO”
Signal decay at a rate of T2*
Short TR BUT Each RF = Single line of k space
More consistent contrast throughout whole image
Gradient Echo, Echo Planar Imaging GE-EPI
- Gradient echo WITH 90 RF, with dephasing and rephasing FEG
- Apply an opposite FEG to rephase and get another gradient echo but the read out in opposite direction due to inversed FEG
- Add in successive PEG blips to fill each line
Multishot echo planar imaging = multiple lines of k space at a time
Spin Echo, Echo Planar imaging SP-EPI
Start with Spin echo instead
- 90 RF
- LARGE Dephasing PEG + FEG
- 180 flip
- Alternating FEG with PEG blips
So your FEG and PEG are in optimal phase around the centre of your echo
Due to the large dephasing PEG, space is filled from a higher point down.
- You can RAPIDLY reduce motion artefact
- At peripheries - very little signal amplitude.
D = diffusion
KB = Boltzmann Constant
T = Temperature
Size of particle
n = viscosity
Movement by Brownian motion
Isotropic diffusion
In e.g. pure liquid = random particle movement in any direction = net movement = 0
Anisotropic diffusion
Brownian diffusion along membranes / borders
A diffusion tensor (DT) is a 3x3 matrix that describes how water molecules diffuse
A DT can be visualized as an ellipsoid
Restricted diffusion in cells
ADC = Apparent Diffusion co-efficient
(Proxy for actual diffusion)
Represent hydrogen atom movement with a grey scale.
More restricted = lower value
b0 + DWI are used to create an ADC map
bo image
Spin-Echo Echoplanar image
T2 weighted image due to long TE
DIFFUSION GRADIENTS
- 90 RF, T2* decay
- Strong gradient applied, water movement will result in further lose of phase
- 180 RF for spin echo
- Rephasing diffusion gradient applied.
Restricted diffusion will be closer in position to first diffusion gradient
Movement will result in significant signal loss
b value = strength, duration and time in between diffusion gradients = the higher the valyue the more signal loss with diffusion
Repeated for all 3 cartesian planes
DWI:
- T2* spin echo planar sequence
- b value
- ADC
You get multiple source images in different images and amalgamate this into your DWI image
High signal in DWI =
Inherent T2 characteristics
OR
Restricted diffusion
b0 image = same sequence but with no diffusion gradient e^0= 1 = represented by T2*
DWI = Signal averaged image from the sources for a particular b
ADC = (-1/b) ln (DWI/b0)
T2 weighting has been negated
High signal in DWI =
Inherent T2 characteristics
OR
Restricted diffusion
High signal on B0 = T2*
High signal on DWI and low on ADC = you confirm its restricted diffusion
When the lesion itself has a long T2 = T2 Shine through
If b0 = low signal
DWI = you can’t see anything
ADC = Low signal
If b0 = Low signal = Short T2
DWI = Low signal because you had no T2 signal to do the echo planar imaging
So no idea about diffusion characteristics
T2 Blackout
Signals affecting blood vessels
Large vessel e.g. aorta or IVC: High velocity signal loss
IN SPINE ECHO PULSE SEQUENCE (has RF 180)
- Blood velocity high enough to move out of slight between RF 90 and RF 180 = TOF
- New blood within the slice will get the RF 180 , so will be antiparallel to B0 and have NO transverse magnetisation.
TOF = Time of flight effect
TURBULENCE
- Blood velocity is high enough
- Stenosis
- Bifurcation
Loss of laminar / plug flow: varying velocity and direction = causes rapid dephasing = lower signal.
Flow enhancement:
Background has Partial Saturation
Gradient echo
1. Use a short TR to fill k space faster preventing full T1 relaxation
2. To prevent recovery of B0 magnetisation
Partial saturation = tissues are not leaving the slice, unable to recover the longitudinal magnetisation
Eventually you reach a steady state where same amount of longitudinal recovery with each TR.
Stationary tissue will lose signal
FLOW RATE ENHANCEMENT
New blood entering the slice = not been partially saturated
Undergoes RF pulse for the first time, has full longitudinal magnetisation = high signal = “tagged”
No idea of what direction blood is coming from - you need saturation bands.
MRI Spectroscopy
- Looking at a specific region within a slice
- Fourier transform - to look at what frequencies contribute to the signal at that specific location - generating a spectrum of frequencies
MIP
- Take slices where background is partially saturated and blood vessels give high signal
- Create 3D imaging using only the highest signal
Key points about Time of flight effects:
- Fresh blood enters between the TRs - blood too slow will partially saturate
- Best when vessels are perpendicular to transverse plane i.e. not ALONG the slice
- You can confuse signal loss - occlusion vs turbulence. 3D helps get around this.
- Tissue with very short T1 will also be bright
- Larger flip angles leads to more saturation
Spin Phase Effects
- FEG normally causes loss of phase based on location (thats why you apply the pre-dephasing)
- PEG temporarily induces different frequencies to introduce a phase difference.
Spins MOVING cross a gradient, will ACCUMULATE MORE PHASE in a non-linear fashion
Can be calculated:
k = constant velocity
t = time applied gradient
Same for dephasing and rephasing gradients.
Loss of phase coherence = loss of signal for non-stationary spins
Gradient moment nulling - compensates for phase loss of spins moving a long a gradient
Allows rephasing of both stationary and moving spins
- Initial gradient
- Second opposite gradient 2x strength
- Apple initial gradient again
Phase contrast MRA
- Apply gradient
- Faster spins will gain more phase per unit time
- The gradient in the equal opposite direction
- Faster spin will lose more phase - tell you velocity of flow
- Spins moving in a direction will have a net negative or positive phase
- Apply in all three cartesian planes or more
Phase contrast angiography
- DOES NOT RELY ON T1 like partial saturation where tissues with short T1 will give a high signal in addition to blood moving in.
- But takes long because you have to apply it in so many directions.
Velocity encoding gradients
- IF YOU apply a higher amplitude gradient - higher degree of phase change for moving spins
- When reversed - more phase change
- BUT You pass the 180 degree of phase change - lose ability to know which direction of movement - use a gradient just shallower to this.
- Tell MRI machine the flow of blood you’re interested in and it adjusts
- gradient field strength
- time of gradient
Gadolinium
- Toxic so needs to be bound to a ligand
- Shortens T1 times
- Stays in extracellular / intravascular space
Hund’s rules for filling electron shells
Gadolinium has the maximum SEVEN UNPAIRED electrons in its shells with non-zero spin (because they’re unapaired can’t be spin up/down)
Gadolinium
1. INCREASES SPIN LATTICE INTERACTION = T1 time
- Higher doses will also shorten T2
Which sequences?
- Short TR will prevent soft tissue from regaining longitudinal magnetisation and catching up with Blood + Gd
- Gd also shortens T2 so you need a short TE
Gadolinium
1. Best with short TE TR
2. INCOHORENT Gradient echo - because of the spoiler gradients
3. You need to go FAST whilst its still in arterial
Risks
1. Risk of nephrogenic systemic fibrosis
2. Allergy
- Most things are made of water and fat, with different precessional frequencies due to local magnetic field differences (relative electron shielding) causing chemical shift
- Other molecules also have hydrogen BUT H20 + Fat have single stronger 10,000x
- Different metabolites will have different peaks and you can compare this for different areas of interest
- Water and fat signals need to be suppressed in order to measure
- CHESS - Chemical shift selective pulse with spoiler gradient - can be use to suppress WATER
- STIR - to suppress fat
- Saturation bands -
Or over entire image
- MRS - Looks at a specific voxel / region of interest
- Signal localisation - still need for it to have transverse magnetisation - basically use three slice selection gradients that are orthogonal.
11b. Apply a slice selective gradient RF 90 ZG
11c. Apply a 180 to YG to select a column within the slice generating a SPIN ECHO WHERE THERES OVERLAP
11d. Apply another 180 in the x axis (XG)
PRESS - Point resolved spectroscopy
- Echo will come from the voxel only. No need to further gradients just measure echo.
Very good SNR at the level of T2 not T2*
