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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, so the spins happen
in different directions and cancel out.
Spin alignment
But when applying a very strong external magnetic field.
Precession
Magnetic field direction
Putting the hydrogen into an external magnetic field
generates the magnetic moment and causes the hydrogen
to precess around the axis of the magnetic field.
Energy states
The hydrogen aligns in parallel (low energy) and antiparallel (high energy – less stable) states.
Energy states
Energy states change with excitation and relaxation
fMRI measurements = energy release during relaxation!
Proportions
For every million hydrogen atoms 500,001 will position in
the parallel state and 499,999 will position in anti-parallel
state.
Luckily we have 1023 hydrogen atoms in every gram of
tissue…
Net magnetization (M)
Sum of magnetic moments in a sample with a particular
volume at a given time.
Gyromagnetic ratio ( )
A spinning hydrogen atom within an external magnetic field
has a particular magnetic moment.
It also has a particular angular momentum because it has
mass. Angular momentum is a rotation force pulling
perpendicular to the rotation plane according to the right
hand rule.
Magnetic moment / angular momentum = gyromagnetic
ratio
Combination of mechanical and electromagnetic forces.
Larmor frequency
The gyromagnetic ratio ( ) will determine how fast (v) the
hydrogen will spin around the axis of a magnetic field with a
given strength (Bo).
v = Bo *
/2π
The spin velocity of an atom/molecule is called its Larmor
frequency (for hydrogen 42.58 MHz/Tesla)
B = 1.0 T
B = 2.0 T
B = 3.0 T
TIME
Larmor frequency
Because different atoms/molecules have different Larmor
frequencies, we can “tune into” the Hydrogen frequency and
isolate it from other atoms/molecules in the scanned tissue.
We’ll do this by exciting and “reading out” relaxation within a
small window around the Hydrogen Larmor frequency.
This is also how spectroscopy methods determine the
molecular composition of a sample…
Lab/Rotating frame
The hydrogen atoms are precessing around z (direction of B0)
Excitation pulses: B1
Excite the sample into a less stable perpendicular direction
Before excitation
Low Energy
External
Magnetic
Field (B0)
High Energy
M0
At excitation
Low Energy
External
Magnetic
Field (B0)
High Energy
M0
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 much we excite our sample…
y
<900 pulse
z
z
z
x
y
900 pulse
x
y
>900 pulse
z
x
y
1800 pulse
x
Relaxation
Once the sample has been excited, it relaxes into a more
stable (lower energy state) and emits energy in the process
Relaxation
Magnetization
What frequency is the hydrogen energy at?
time
T1 and T2/T2*
T1: relaxation in the longitudinal plane
T2: relaxation in the transverse plane
Analogous to amplitude and phase…
T1
Realignment with main magnetic field direction
M0
M0
Static main field
M0
Excitation pulse
M0
Longitudinal relaxation
M0
T1
T1 = 63% recovery of
original magnetization
value M0
Magnetization
vector
Longitudinal
magnetization
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*
De-phasing in the transverse plane
M0
Static main field
Transverse relaxation
Excitation pulse
T2/T2*
Spin phase
Transverse
magnetization
What influences T2/T2*?
Again has to do with the molecular neighborhood of
the excited spinning atom.
The more spin-spin interactions there are the quicker
the decay and the shorter the T2.
The higher the static magnetic field, the more
interactions there are, quicker T2 decay.
Different tissues have different molecular
neighborhoods and different T2 constants…
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
Source of MR signal
The energy source driving the MR signal used to
determine T1 and T2 is identical!
The only thing we can measure is the energy released
by hydrogen atoms moving from excited to relaxed state.
But we can derive T1, T2, T2’, and T2* relaxation
properties by exciting the sample and measuring its
“resonating” energy release in clever ways (i.e. using
different pulse sequences).
Image contrast
Using different MRI sequences we can contrast different
features of the tissues like their T1/T2/T2* relaxation
times. Since neighboring tissues will have different
relaxation times this will enable us to visualize particular
tissues (e.g. gray & white matter):
T2*
40ms
TR and TE
Two important time constants are defined for each sequence:
TR – repetition time between excitation pulses.
TE – time between excitation pulse and data acquisition
(“read out”).
Contrasting different attributes of the tissue depends on the
choice of these two variables.
The TR length will determine the contribution of T1
relaxation to the contrast and the TE length will determine
the contribution of T2 relaxation to the contrast.
T1 and TR length
The amount of post-excitation
signal depends on how
relaxed the sample was during
the excitation time.
M0
Static main field
M0
M0
M0
Think about exciting a sample at different stages of longitudinal relaxation.
T1 and TR length
Choosing a short TR means less energy release (MR signal)
on consecutive scans.
T2/T2* and TE length
M0
Static main field
Transverse relaxation
Excitation pulse
TE: When to acquire the data
The relaxing hydrogen atoms emit a decaying amount of
energy. The question is how soon after excitation to measure
the energy?
For a T2 contrast you would want to wait a bit and let the
energy decay.
Only one signal source!
Remember that the only thing we can measure is in phase
energy release of the precessing hydrogen atoms.
To generate an electric current in the receiving magnet coil we
need a “large” number of hydrogen atoms to spin together
(remember electric induction – moving magnetic fields
generate an electric current).
Measuring T1/T2/T2* relaxation properties is only a
consequence of the order in which we excite, relax, and
acquire the energy released by the sample.
Proton density
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 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
Having the gradients in place changes the local magnetic
field experienced by hydrogen at different spatial points
inside the magnet.
This means the hydrogen will have different magnetic
moments and will precess at slightly different speeds at
each spatial location.
By “focusing in” on the precession speed (larmor
frequency) at each location we can achieve spatial
resolution.
Similarly to how we “focused in” on hydrogen atoms…
Fourier Transform
+
+
Intensity
Determining power in particular frequencies
Frequency
Fourier Transform
time
time
Intensity
time
Magnetization
Magnetization
Magnetization
Separates a complex signal into its sinusoidal components
Frequency
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
Main magnet field is
generated by a 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.