fMRI Methods
Lecture2 – MRI Physics
Magnetic fields
magnetized materials and moving electric charges.
Electric induction
Similarly a moving magnetic field can be used to create
electric current (moving charge).
Electric induction
Or you could use an electric current to move a magnet…
Right hand rule
Force and field directions
Nuclear spins
Protons are positively charged atomic particles that
spin about themselves because of thermal energy.
Magnetic moment
μ (magnetic moment) = the torque (turning force) felt by
a moving electrical charge as it is put in a magnet field.
The size of a magnetic
moment depends on how
much electrical charge is
moving and the strength of
the magnetic field it is in.
A Hydrogen proton has a
constant electrical charge.
Spin alignment
Earth’s magnetic field is relatively small (0.00005 Tesla), so the
spins happen in different directions and cancel out.
Spin alignment
But when in a strong external magnetic field (e.g. 1.5 Tesla).
Net magnetization (M)
Sum of magnetic moments in a sample with a particular
volume at a given time.
Precession
Magnetic field direction
Hydrogen protons not only spin. They also precess around
the axis of the magnetic field.
True for all atoms with an odd number of protons
Precession speed
Two factors govern the speed of precession (Larmor
frequency): magnetic field strength & gyromagnetic ratio
Larmor frequency = Bo *
/2π
Gyromagnetic ratio
Gyromagnetic ratio (
)
Magnetic moment / Angular momentum
Combination of electromagnetic and mechanical forces.
Angular momentum is dependant on the mass of the atom.
Gyromagnetic ratio
Different atoms have different gyromagnetic ratios:
Nucleus
Gyromagnetic ratio (γ)
1H
267.513
7Li
103.962
13C
67.262
19F
251.662
23Na
70.761
31P
108.291
Larmor frequency
Different atoms placed in the same magnetic field have
different Larmor frequencies:
Nucleus
Larmor Frequency at 1 Tesla
1H
42.576 MGHz
7Li
16.546 MGHz
13C
10.705 MGHz
19F
40.053 MGHz
23Na
11.262 MGHz
31P
17.235 MGHz
“Tune in” to the Hydrogen frequency.
Longitudinal & transverse directions
The hydrogen atoms are precessing around z (direction of B0)
Steady state
Net magnetization is all pointing in the z direction
Excitation pulses
Applying a perpendicular magnetic field “flips” the protons
Excitation & Relaxation
Excite the sample in a perpendicular direction and let it relax.
Net magnetization of the sample changes as it relaxes,
inducing current to move in a near by coil.
Larmor
frequency
Flip angle
Defined by the strength of B1 pulse and how long it lasts (T)
θ = *B1*T
This is one of the parameters we set during a scan
It defines how far we “flip” the protons…
y
<900 pulse
z
z
z
x
y
900 pulse
x
y
>900 pulse
z
x
y
1800 pulse
x
T1 and T2/T2*
T1: relaxation in the longitudinal direction
T2*: relaxation in the transverse plane
Changes in the direction of the sample’s net magnetization
T1
Realignment of net magnetization with main magnetic field
direction
Before excitation
At excitation
Relaxation
Net magnetization along the longitudinal direction
T1
T1 = 63% recovery of original magnetization value M0
What influences T1?
Has something to do with the surroundings of the
excited atom. The excited hydrogen needs to “pass on”
its energy to its surroundings (the lattice) in order to
relax.
Different tissues offer different surroundings and have
different T1 relaxation times…
We can also introduce external molecules to a
particular tissue and change its relaxation time. These
are called “contrast agents”…
T2*/T2
Loss of net magnetization phase in the transverse plain
Before excitation
At excitation
Relaxation
Net magnetization in the transverse plain
T2/T2*
T2 = 63% decay of magnetization in transverse plain
T2* = T2 - T2’
Two main factors effect transverse relaxation:
1. Intrinsic (T2): spin-spin interactions. Mechanical
and electromagnetic interactions.
2. Extrinsic (T2’): Magnetic field inhomogeneity. Local
fluctuations in the strength of the magnetic field
experienced by different spins.
T2’
Magnetic field inhomogeneities
Examples of causes:
Transition to air filled cavities (sinusoids)
Paramagnetic materials like cavity fillings
Most importantly – Deoxygenated hemoglobin
What influences T2?
Again, has to do with the molecular neighborhood
affecting the amount and quality of spin-spin interactions.
Different tissues will have different T2 relaxation times.
The stronger the static magnetic field, the more
interactions there are, quicker T2 decay.
MR signal
We only have one measurement:
Measurement of the net magnetization in the transverse
plain as the sample relaxes.
Once T2* relaxation is complete
Protons precess out of phase in the transverse plain
Net magnetization in transverse plain = 0
TR and TE
Two important scanning parameters:
TR – repetition time between excitation pulses.
TE – time between excitation pulse and data acquisition
(“read out”).
Creating scanning protocols with different TR and TE lengths
will allow us to derive T1 and T2/T2* relaxation times.
TR length & MR signal strength
Short TR = weaker MR signal on consecutive pulses.
With short TRs relaxation in the longitudinal direction will not
be complete. So there will be fewer relaxed protons to excite.
TE: when to measure MR signal
We can measure the amplitude of net magnetization
immediately after excitation or we can wait a bit.
Longer TEs will allow more transverse relaxation to happen
and the MR signal will be weaker.
Different image contrasts
We can scan the brain using different pulse sequences by
choosing particular TR and TE values to create images
with different contrasts.
TR length will determine how much time the sample has
had to relax in the longitudinal direction.
TE will determine how much time the sample has had to
relax (loose phase) in the transverse plain.
Proton density contrast
Measuring the amount of hydrogen in the voxels
regardless of their T1 or T2 relaxation constants.
This is done using a very long TR and very short TE
Proton density
Higher intensity in voxels containing more hydrogen protons
T1 contrast
Measuring how T1 relaxation differs between voxels.
This is done using a medium TR and very short TE
You need to know when largest difference between the
tissues will take place…
T1 contrast
Images have high intensity in voxels with shorter T1 constants
(faster relaxation/recovery = release of more energy)
CSF:
Gray matter:
White matter:
Muscle:
Fat:
1800 ms
650 ms
500 ms
400 ms
200 ms
T2/T2* contrast
Measuring how T2 relaxation differs between voxels.
This is done using a long TR and medium TE
We can combine a T2 acquisition with proton density…
T2 contrast
Images have high intensity in voxels with longer T2 constants
(slower relaxation = more detectable energy)
CSF:
Gray Matter:
White Matter:
Muscle:
Fat:
200 ms
80 ms
60 ms
50 ms
50 ms
T2* contrast
Same as T2 only smaller numbers (faster relaxation)
CSF:
Gray Matter:
White Matter:
Fat:
100 ms
40 ms
30 ms
25 ms
T2* and BOLD fMRI
T2* = T2 +T2’
T2: Spin-spin interactions
T2’: field inhomogeneities
Exposed iron (heme)
molecules create local
magnetic inhomogeneities
BOLD – blood oxygen level dependant
Assuming everything else stays constant during a
scan one can measure BOLD changes across time…
T2* and BOLD
More deoxygenated blood = more inhomogeneity
more inhomogeneity = faster relaxation (shorter T2*)
Shorter T2* = weaker energy/signal (image intensity)
So what would increased neural activity cause?
T2* and BOLD
So what happened in particular time points of this scan?
Bloch equation
MR images
So far we’ve talked about a bunch of forces and energies
changing in a sample across time…
How can we differentiate locations in space and create an
image?
2004 Nobel prize
in Medicine
Paul Lauterbur
Peter Mansfield
Spatial gradients
Create magnetic fields in each direction (x,y,z) that move
from stronger to weaker (hence gradient).
Spatial gradients
Different magnetic fields at different points in space.
Hydrogen will precess at a different speed in each spatial
location.
By “tunning in” on the specific precession speed we can
separate different spatial locations.
Similarly to how we “tunned in” on hydrogen atoms…
Spatial gradients
(-)
62 MHz
63 MHz
64 MHz
G
65 MHz
66 MHz
(+)
Spatial gradients
Lot’s of Fourier transforms.
Work in k-space (a vectorial
space that keeps track of the
spin phase & frequency
variation across magnet
space).
It’s possible to turn gradients
on and off very quickly (ms).
Image reconstruction
Pulse sequences
The magnet
Main static field
Extremely large electric
charge spinning on a
helium cooled (-271o c)
super conducting coil.
Earth’s magnetic field 30-60
microtesla.
MRI magnets suitable for
scanning humans 1.5-7 T.
Main coils
The bulk of the structure
contains the coils generating
the static magnetic field and
the gradient magnetic fields.
RF coil
Transmit and receive RF coils
located close to the sample
do the actual excitation and
“read out”.
Homework!
Read Chapters 3-5 of Huettel et. al.
Explain how a spin-echo pulse does the magic of
separating T2 relaxation from T2* relaxation. You can
include figures/drawings if you like.