Basics of Magnetic Resonance Imaging

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Basics of Magnetic Resonance Imaging
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Angular Momentum
Orbital Angular Momentum
Principles of Medical Imaging Shung, Smith and
Tsui
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Angular Momentum
Spin Angular Momentum
Spin is an intrinsic property of the nucleons
(protons and neutrons) in a nucleus HOWEVER
The name doesnt mean that spin results from
the nucleons rotating about an axis!!!
http//svs.gsfc.nasa.gov/vis/a000000/a001300/a0013
19/
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Spin Angular Momentum
Spin is quantized it can only take certain
values
Here I is the total spin quantum number of the
nucleus. The proton has I ½. Lz is the
angular momentum due to that spin.
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Spin Angular Momentum
To get the total spin of a nucleus we add up
(separately) the spins of the protons and
neutrons
15N has spin ½ .
We do pairwise addition
7 protons
8 neutrons
Only nuclei with an odd number of protons or
neutrons will be visible to MRI
Note 14N has spin 1.
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Alignment of Spins in a Magnetic Field, B0
The spin angular momentum yields a magnetic
moment
Principles of Medical Imaging Shung, Smith and
Tsui
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Energy Levels of Spins and B0
Principles of Medical Imaging Shung, Smith and
Tsui
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Energy Levels and Spin
E1 ?B0
E2 -?B0
?E E1 - E2 2 ?B0 ?(h/2?) B0 for
spin-1/2 particles
B0 is the main magnetic field
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Energy Level Population and Field Strength
Spins are distributed according to the Boltzmann
distribution
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Larmor Frequency
Principles of Medical Imaging Shung, Smith and
Tsui
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Excitation Energy and Frames of Reference
B0 main magnetic field B1 applied field
(pulse) Beff vector sum B0B1
z?
z
?
?
y?
y
lab frame
rotating frame
x?
x
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Net Magnetization, M, and the Rotating Frame
While B1 ? 0, M precesses around B1
z?
z?
M
M
y?
y?
B1
x?
x?
B0 ? 0 B1 ? 0
B0 ? 0 B1 0
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Net Magnetization, M, and the Rotating Frame
We turn B1 on by a applying radiofrequency (RF)
to the sample at the Larmor frequency. This is a
resonant absorption of energy. If we leave B1 on
just long enough for M to rotate into the x? - y?
plane, then we have applied a 90? pulse. In
this case, Nupper Nlower. If we leave B1 on
just long enough for M to rotate along the -z?
axis, then we have applied a 180? pulse
(inversion). In this case, Nupper Nlower M.
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Free Induction Decay
What is the effect of applying a 90 ? pulse?
?/2
RF
time
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Free Induction Decay
The effect of a 90? pulse is to rotate M into the
x? - y? (transverse) plane. If we place a
detection coil (a loop of wire) perpendicular to
the transverse place, we will detect an
induced current in the loop as M precesses by (in
the lab frame).
Principles of Medical Imaging Shung, Smith and
Tsui
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Signal Processing of Free Induction Decay
Principles of Medical Imaging Shung, Smith and
Tsui

• We can characterize the signal by its
• Amplitude
• Phase
• Frequency

Fourier Transform
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Signal Processing of Free Induction Decay
We see that after a 90? pulse, we get a
cosinusoidal signal. To quantitatively describe
the signal we calculate its Fourier transform.
(think Larmor frequency)
Principles of Medical Imaging Shung, Smith and
Tsui
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Fourier Transform of Time Domain Data
http//www.med.harvard.edu/JPNM/physics/didactics/
improc/intro/fourier3.html
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Image Contrast (I)
We can detect the signal from water molecules in
the body. Can we make an image? Will it be a
useful image?
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Relaxation Processes
Fortunately for us, the signal we get from water
molecules in the body depends on their local
environment. Spins can interact by exchanging or
losing energy (or both). As in all spectroscopy
methods, we put energy into the system and we
then detect the emitted energy to learn about
the composition of the sample. We then use some
variables to characterize the emission of energy
which (indirectly) tell us about the environment
of the spins. Image Contrast!
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Relaxation Processes (T2)
1. Spin-spin relaxation time (T2) when spins
interact With each others magnetic field, they
can exchange energy (perform a spin flip). They
can lose phase coherence, however. Only affects
Mxy.
Signal without T2 interaction between spins
T2
Signal including T2 interactions between spins
T2???
http//irm-francophone.com/htm/signal.htm
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T2 and T2
T2 is an intrinsic property of the sample. This
is what we are interested in to use for contrast
generation. T2 is the time constant of the
decay of the free induction decay. It is related
to the intrinsic T2 in the following way
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T2 and T2
Not a random process
random process
Inhomogeneity term - dephasing due to magnet (B0)
imperfections depends upon position Susceptib
ility term - dephasing due to the interaction of
different sample regions with B0 (depends
upon position)
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Relaxation Processes (T2)
?/2 pulse
? (delay)
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Effect of Spin Coherence on Signal
T2
http//irm-francophone.com/htm/signal.htm
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Irreversible versus Reversible
http//www.cchem.berkeley.edu/demolab/images/HahnE
choSpinRes.htm
Start
Reverse
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Hahn Spin Echo Pulse Sequence
http//www.esr.ethz.ch/intro/spinecho.html
http//www.chem.queensu.ca/FACILITIES/NMR/nmr/webc
ourse/t2.htm
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Hahn Spin Echo and T2
We can calculate T2 by changing the echo spacing,
?, and recording the signal at 2?.
http//spiff.rit.edu/classes/phys273/exponential/e
xponential.html
Signal
Echo spacing , ?
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Spin-Lattice Relaxation, T1
To look at the behavior of the longitudinal
component of M (Mz), we start by putting M along
the -z axis and then read it out with a 90? pulse.
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Spin-Lattice Relaxation, T1 Energy levels and
Inversion
Equilibrium
After Inversion
Net Magnetization


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Relaxation Processes (T1)
? pulse
long TI
short TI
?/2 pulse
?/2 pulse
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Image Contrast and T1
In (a) the TI is chosen to null the signal from
curve ii, while the TI in (b) nulls out i
http//www.fmrib.ox.ac.uk/stuart/thesis/chapter_2
/section2_4.html
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Now Can We Make A Useful Image?
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Magnetic Resonance Imaging
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Magnetic Resonance Image Formation

• What do we need?
• Ability to image thin slices
• 2. No projections - image slices with arbitrary
  orientation
• 3. Way to control the spatial resolution
• 4. Way to carry over the spectroscopic contrast
  mechanisms
• to imaging.

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Magnetic Resonance Image Formation
How can we spatially encode this signal?
Principles of Medical Imaging Shung, Smith and
Tsui
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Magnetic Resonance Image Formation - Slice
Selection
Magnetic field gradients B B(position)
precessional frequency is now a function of
position
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Magnetic Resonance Image Formation - Slice
Selection
?? frequency bandwidth ?z slice thickness
MRI Basic Principles and Applications - Brown,
Semelka
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Magnetic Resonance Image Formation - Slice
Selection
How do we excite only a slice of spins?
Fourier Pairs!
sinc
rect
FT
time
frequency
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Magnetic Resonance Image Formation - Phase
Encoding
So far we have a slab of tissue whose spins are
excited. The next step is to place a grid over
the slab and define pixels.
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Magnetic Resonance Image Formation - Phase
Encoding
?eff lt ?0
Gy
?eff gt ?0
Center of magnet
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Magnetic Resonance Image Formation - Phase
Encoding
Apply gradient for a finite duration ? ?
?(y) (the phase of M over each region of the
sample depends upon its position) This is
because the gradient makes each spin precess
with an angular frequency that depends on its
position. For the duration of the gradient, t,
spins move faster or slower than ?0 depending
upon where they are. After the gradient is
turned off, all spins again precess at ?0.
The phase accumulated during time, t, is
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Magnetic Resonance Image Formation - Phase
Encoding
M after a 90? pulse
Turn on the phase encoding gradient
Gy 0
Gy lt 0
Gy gt 0
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Magnetic Resonance Image Formation Frequency
Encoding (Readout)
Now we need to encode the x-direction...
How do we spatially encode the frequency of the
signal? Can we turn on another gradient? When?
And for how long?
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Magnetic Resonance Image Formation Frequency
Encoding (Readout)
We apply a gradient while the signal is being
acquired as the spin-echo is being formed.
?
?/2
RF
Signal
Gx
time
Therefore, the precessional frequency is a
function of position
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Magnetic Resonance Image Formation Spin-echo
Pulse Sequence
?(3)
? (1)
?(2)
http//spl.harvard.edu8000/pages/papers/zientara/
fast/fastimaging.html
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(1)
Phase Encoding Each acquisition is separately
encoded with a different phase. The sum total of
the N acquisitions is called the k-space data.
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The Effect of Frequency Encoding on the Signal
(dephasing gradient)
(2)
MRI Basic Principles and Applications - Brown,
Semelka
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(3)
Slice-select refocusing gradient
The effect of having the gradient on during the
time that the magnetization is moving from the
z-axis to the y-axis is to curve the path. In
general, one needs to apply a slice refocussing
gradient of opposite magnitude after the RF
pulse so that the spins are in phase at the end
of the pulse. The area of the negative gradient
must be one half the area of the slice selection
gradient pulse.
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Structure of MRI Data k-space
http//www.indyrad.iupui.edu/public/lectures/mri/i
u_lectures/mri_homepage.htm
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Structure of MRI Data k-space
What is k-space? The time-domain signal that we
collect from each spatially encoded spin echo
gets put in a matrix. This data is called
k-space data and is a space of spatial
frequencies in an image. To get from spatial
frequencies to image space we perform a 2-D
Fourier Transform of the k-space data. General
intensity level is represented by low spatial
frequencies detail is represented by high
spatial freqs.
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low spatial frequencies
high spatial frequencies
all frequencies
http//www.indyrad.iupui.edu/public/lectures/mri/i
u_lectures/mri_homepage.htm
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Structure of MRI Data k-space
FT
k-space data
image data
http//www.jsdi.or.jp/fumipon/mri/K-space.htm