MRI Physics

ACVR Theoretical

How does magnetic field strength affect the precessional frequency of hydrogen atoms?

Precess faster with stronger magnetic field

What is the role of the gradient coil?

To apply a gradient along the magnetic field

• can manipulate the field strength (and thus precessional frequencies) along B0

What does the radiofrequency coil do?

Generates an alternating magnetic field that’s perpendicular to the main magnetic field

• only the H+ atoms precessing at the exact same frequency as the radiofrequency pulse will gain more and more energy

Why is H+ the chosen isotope for MRI?

• largest magnetic moment

• most abundant isotope

• predominately in water and fat

What does the Larmour frequency calculate?

the precessional frequency of the atom of interest

Signal strength is proportional to what type of magnetization?

Transverse magnetization

• strongest signal at 90deg

What is T2 magnetization?

Loss of transverse magnetization

• aka spin spin relaxation

What is T1 magnetization?

Regaining of longitudinal magnetization

What causes dephasing in T2 relaxation?

Spins interacting with each other

Why is there a * added to T2*?

Because it’s not only the interactions of the spins (spin-spin relaxation) but also magnetic field inhomogeneities that cause the relaxation

At what percent loss of transverse magnetization does T2* happen?

63% - this is a time constant

List 3 reasons there could be field inhomogeneities

1) Scanner can’t make an equal strength magnetic field all the way through the transverse plane

2) Could be a substance in the patient that causes a local disruption of the magnetic field

3) When spins start to dephase, the magnetic vectors are becoming out of phase with one another and they can disrupt the local magnetic field

How can you compensate for T2* decay?

• administer a 180deg RF pulse

• same frequency as 90deg but twice as long

• now slow spin is leading and fast spin will catch up and they will be in-phase with eachother

• sample when at the max

• sample at same time between 90 and 180 pulse

• allows you to compensate for field inhomogeneities

How will the contrast of the tissue be affected by a long TE time in T2 relaxation?

Prolonging TE time will create more contrast between tissues in T2 relaxation

Define TE

Time to/of echo = time from RF pulse to the time we measure the signal given off by the tissue

What is T1 relaxation?

Longitudinal recovery - spin lattice relaxation

What is T1 time?

Time it takes to gain/regain 63% of magnetization (longitudinal)

How do we highlight T1 differences?

• RF pulse to 90deg

• thus losing all longitudinal and gaining all transverse

• then sample at TE and wait for a given period of time

• repeat 90deg RF pulse (TR pulse)

• if you do a second 90deg RF pulse the vectors stay the same and become y-axis values which can be measured

What do a short TE and short TR highlight?

T1 relaxation differences and negates T2 differences

Which is faster? Loss of transverse magnetization or gain of longitudinal magnetization?

Loss of transverse magnetization is much faster

e.g.) CSF T1 time = 2200ms, T2 time = 160ms

Define TR

Time of repetition = time b/w 1st and 2nd RF pulse

What do TE and TR time highlight?

TE time highlights T2 differences

TR time highlights T1 differences

What is an example TE and TR time for T1W, T2W, and PD sequences?

T1W

• Short TE (10-30ms)

• Short TR (300-600ms)

T2W

• Long TE (80-140ms)

• Long TR (2000ms)

PD

• Short TE

• Long TR

What does a PD sequence highlight?

Differences only b/c of the # of protons available for nuclear magnetic resonance

• contrast is fully from contrasting density

• fat and synovial fluid bright b/c highest density of protons

What are examples of short and long TEs and TRs?

Short TE - 10-30ms

Long TE - 60-80ms

Short TR - hundreds

Long TR - 1000-2000ms

Which plane does the slice selection occur in?

z plane/axis

List 3 ways to change the slice selection

1) Change RF pulse

2) Change the gradient field

3) move the patient

List 2 ways to change slice thickness

1) Change bandwidth of RF pulses

2) Change angle of the gradient

• make the difference bigger vs. smaller

• make gradient steeper → larger bandwidth

What happens to resolution and signal when we increase slice thickness?

Lose some resolution but increase signal

Why must we apply a rephasing gradient?

Due to slice thickness having some width there is a slight variation in RF pulse applied so spins are slightly out of phase with each other w/in a slice

• apply a rephasing gradient to counter the slice phase

• this applies an equal and opposite gradient in the opposite direction along the z-axis and allows spins to all spin together

• Entire slice has the same amount of external magnetic field

In which plane does the frequency encoding gradient occur?

x-axis

When is the frequency encoding gradient applied?

During TE - only when reading out the signal

What is applied immediately prior to TE?

Equal and opposite FEG

In regards to the FEG what determines the frequency we can measure?

The number of times we sample

• Take a time based data set and convert it to a frequency based data set = 1 dimensional Fourier Transformation

In which plane does the PEG act upon?

Y-axis

Describe the PEG

Phase encoding gradient

• changes phase but not frequency

• can’t change frequency b/c FEG is already doing that

• So induce a magnetic gradient change at a different time

  • change b/w 90 and 180 pulse

  • this allows the gradient to go back to normal but keep the phase different for the TE

With PEG describe the changes in magnetic field from top to bottom

• increased magnetic field at the top

• no change in the middle (only B0)

• decreased magnetic field in the bottom

Leads to more dephasing at the outer ends compared to the null point (middle)

How is K space created?

• Applying PEG for a specific amount of time causes the vectors to de-phase in relation to their y-axis location

• Can switch the direction of the phase and obtain multiple data lines with varying strengths and ± aspect of PEG

• overall creates a grayscale value which represents a data point

• these values get plugged into formulas and become images ultimately creating k-space

What determines y-axis resolution?

The number of PEG steps

What does fourier transformation converts K space data into?

Converts k space data (time based) into x-axis location (frequency based)

• do this for each phase encoding step

• ultimately combine k-space data set and 1D fourier transformation data → picture image

What determines the x-axis resolution?

Number of columns in K-space (time points)

What does each row in k-space represent?

A specific data acquisition period that we used in a specific pulse sequence

• these points are acquired at TE when the FEG is applied

• each sequential row represents a different PEG that we’ve used to introduce phase difference along the y-axis of our slice

• Each k-space pixel represents signal from the entire slice

Where in k-space do you get the best contrast? And spatial resolution?

• Middle of k-space has the most signal and thus contrast

• periphery of k-space adds spatial resolution

How does the rate of dephasing change as you move towards the periphery of k-space

Rate of dephasing increases as you head to the periphery

Even though 2 halves of k-space have conjugate symmetry, why can’t you create an image with just ½ k-space?

Local field inhomogeneities and noise make this not possible

How can you change the FOV to get better resolution?

Decrease FOV to improve resolution

Define resolution

The dimension of individual pixels along the x-y axis within the image we’re generating

Define matrix size

Number of pixels within a picture

If 2 pictures have the same matrix size (8×8) but different FOV, which FOV will have better resolution?

The one with smaller FOV

How can a smaller FOV also be faster?

Smaller matrix size (4×4 vs. 8×8) will require fewer phase encoding steps, and thus be faster

Define bandwidth

Range of frequencies w/in the designated FOV in the frequency encoding plane (x-axis)

What is the Larmour frequency in a 1 Tesla MRI?

64 MHz

If a range is 50,000Hz positive and negative, what is the bandwidth (range of frequencies)

100,000Hz

How does reducing the FOV change the FEG and bandwidth?

Reducing FOV can decrease FEG → decreased bandwidth

How does reducing the gradient affect the bandwidth?

Reducing the gradient → more gradual slope and thus decreased bandwidth

How does bandwidth influence sampling rate?

The bandwidth determines the frequency we have to calculate and thus the sampling rate

What causes aliasing?

True precessional frequency and sampling of the frequency don’t match up = misrepresentation due to incorrect sampling

How often do we need to sample in order to accurately sample a specific frequency?

Need to sample at least twice during one wavelength

• Nyquist limit = sampling rate / 2

• sampling rate = bandwidth

What is another term for sampling interval?

Dwell time = the amount of time the FEG needs to be applied to get all of our samples

What is your sampling interval if your bandwidth is 50,000?

• Since bandwidth = sampling rate then sampling rate =50,000

• Then sampling interval = 1/sampling rate

• So 1/50,000 = 20

• Sampling interval = 20 microseconds

Overall how do we get from FOV to sampling time?

1) determine FOV

• Pick resolution (matrix size) - this will determine how many PEG we need and how many samples we need to take during the FEG

2) Set bandwidth

3) MRI machine will calculate gradient needed

4) Calculate sampling rate (Nyquist limit x 2 = sampling rate)

5) Can calculate sampling interval = (1/sampling rate)

6) Can get sampling time = sampling interval x number of samples

• number of samples = matrix = number of pixels we want (e.g 256)

• e.g. 33microseconds x 256 = 8448 microseconds or 8.448 ms

As bandwidth increases what happens to sampling time?

sampling time decreases

• because sampling interval = 1/sampling rate

• and sampling rate = bandwidth

Does a narrow or wide bandwidth have better SNR?

Narrow bandwidth has a better SNR

• more noise = mottling

• SNR = 1/(square root of bandwidth)

With a shorter TE, what kind of bandwidth is needed?

With a shorter TE, need a shorter sampling time, thus may need a wide bandwidth

If you decrease bandwidth by 1/2, how much does SNR change?

40% increase in SNR

What happens to image quality when SNR decreases?

Image quality gets worse with decreasing SNR

List 3 reasons having a narrow bandwidth all the time is not beneficial.

1) Too long - especially for short TEs

2) Lower frequency means greater gradient difference across each pixel

3) Metal artifact is worse with lower bandwidth

List 1 pro and 3 cons of a decreased bandwidth

Pro = better SNR

Cons = more metal artifact, more chemical shift, can’t use with short TE sequences

Describe aliasing

When frequencies are measured outside of the bandwidth

• misrepresent an analog signal with a falsely calculated digital signal

Happens b/c too high frequency with too low sampling rate

In what direction does aliasing occur?

Phase encoding direction

List 4 ways to decrease aliasing

1) Prevent tissue from being outside of the FOV or increase FOV

2) Oversampling (keeps resolution)

• increase the number of sampling points and then get rid of areas outside image wanted

• oversampling in the FE direction (doesn’t add time)

• oversampling in the PE direction (adds time)

3) Change PE and FE direction

• want shortest axis to be PE (since it takes more time)

4) Parallel imaging

• use 2 coild to calculate aliasing

• only PE ½

• only sampled ½ area

Why does chemical shift occur?

Slight differences b/w the precessional frequencies of fat and water

How does increasing magnetic field strength impact chemical shift?

Chemical shift artifact is increased in higher magnetic field strengths

How does chemical shift artifact look on MRI?

Bright band on one side and dark band on the other

In what direction is chemical shift predominately?

Frequency encoding direction

How does increasing bandwidth impact chemical shift?

Increasing bandwidth → decreases chemical shift

• b/c each pixel represents more frequencies

How does increasing the number of pixels impact chemical shift?

Increasing the pixel number (changing matrix size) → decrease in the range of frequencies covered by each pixel → increased chemical shift

Without doing FSE or GRE, what is the equation for scan time?

Total scan time = TR x #PE x NEx x # of slices

• NEx = number of excitations

What is different with FSE?

Fast spin echo = records multiple echoes after each 90 deg RF pulse

• the number of echoes = ETL

• So new equation for total scan time = (TR x #PE steps x NEx x #slices)/ETL

List 2 pros and 2 cons of FSE.

Pros:

• since multiple echoes within one TR you are filling different lines of K-space at the same time and thus it is very fast

• It has a decreased sensitivity to magnetic susceptibility and magnetic field inhomogeneities

Cons:

• decreased SNR

• change of contrast with T2 relaxation over time. Echoes near TR have very low signal but water retains signal for a long time

  • can’t get short TE to get T1 sequences

What is the main difference between a FSE and GRE?

• In FSE an RF pulse flips the orientation and allows the fast to then catch up with the slower spins

• In GRE an opposite gradient (FEG) is then applied which allows the slow spins to catch up (think headwind vs. tailwind) and then measure peak value at TE

What’s different about the RF pulse in GRE sequences?

There’s just one, no 180 deg, and it doesn’t have to be 90, sometimes it’s less

In GRE sequences you don’t get to T2 like in FSE but how do get to T2* at least?

Need equal and opposite FEG right before the readout gradient

Why can you get really short TEs in GRE sequences?

Can move TE closer to the RF pulse because there’s no 180deg RF pulse in the way

Why is GRE only able to get to T2* levels?

Because it doesn’t account for local field inhomogeneities like spin echo does

Why would you use GRE over spin echo?

• Since you’re only using one RF pulse you can bring TE closer to RF pulse making it faster

What is the Ernst angle?

Angle at which the greatest signal is given

How can GRE’s sensitivity to T2* effects be used as a benefit?

Can be used to look for hemorrhage

What do we manipulate in inversion recovery sequences?

Manipulate T1 relaxation time to prevent signal from a specific tissue type

• Make T1 time equal to the time where fat has zero longitudinal magnetization

In regards to STIR;

• which artifact is it useful with?

• which contrast can’t it be used with?

• which tissues are bright?

• good for metal artifact

• can’t be used with gadolinium

• muscle and CSF/fluid will be bright, not fat

In regards to FLAIR;

• how is TE time different than STIR?

• what tissue is bright?

• longer TE than STIR

• fat and muscle are bright, fluid is dark