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MR Signal Generation
FMRI Undergraduate Course (PSY 181F)
FMRI Graduate Course (NBIO 381, PSY 362)
Dr. Scott Huettel, Course Director
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Housekeeping Clarifications
• Updated Syllabus (on BlackBoard)
– Minor changes to the orders of labs and
project planning later in the month
• Please complete self-assessment
questions weekly
– Email to me (with “SAQ”, “Ch1” in the title)
– These are not graded except for completion
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Outline for Today
• Lecture: MR Signal Generation
–
–
–
–
Protons and the NMR property
Protons in a magnetic field: Alignment, Precession
Excitation and resonance
Reception and relaxation
• Laboratory: Introducing MRI / fMRI data
– Basic MATLAB use
– Properties of MRI data
– Basic neuroanatomy
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Synopsis of MRI
M: Put subject in strong magnetic field
R: Transmit radio waves into subject, turn off
transmitter, receive radio waves emitted by
subject’s brain. This is the MR signal.
I: Modulate the strength of the magnetic field
slightly over space (next week).
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
1. Protons and the NMR property
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Properties of Atomic Nuclei
• Nuclei have two properties:
– Spin (incompletely understood)
– Charge (property of protons)
• Nuclei are made of protons and
neutrons
– Both have spin values of ½
– Protons give charge
• Pairs of spins tend to cancel, so
only atoms with an odd number
of protons or neutrons have spin
A nucleus has the NMR Property if it has both angular momentum and a magnetic
moment. Such nuclei have an odd number of protons or an odd number of neutrons.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
The spinning mass of the
proton generates an
angular momentum J.
The electric charge on the
surface of the proton
creates a small current
loop, which generates
magnetic moment μ.
Both μ and J are vectors that
point along the spin axis and
whose direction is given by
the right hand rule.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
What nuclei can we measure?
• Most common in our bodies:
–
–
–
–
12C
16O
1H
14N
• Of these, only Hydrogen has
the NMR property.
• But, Hydrogen is the most
abundant atom in the body
– Mostly in water (H2O)
This means that nearly all forms of MRI are measuring properties of Hydrogen.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
2. Protons in a magnetic field
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Protons in no magnetic field
In the absence of a strong
magnetic field, the spins are
oriented randomly.
Thus, there is no
net magnetization (M).
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Introduction of a Magnetic Field (B)
Bo
Image from G.A. Glatzmaier
Computer simulation of Earth’s
magnetic field
(~0.3-0.6 Gauss, or 0.00006T)
Helmholtz Pair
FMRI – Week 2 – MR Signal
Solenoid
Scott Huettel, Duke University
Some Terminology
Bo
B is used for magnetic fields.
B0 is the scanner’s main field.
FMRI – Week 2 – MR Signal
Bo
Longitudinal Axis
(z direction)
Transverse Plane
(xy plane)
Scott Huettel, Duke University
Alignment with a magnetic field
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Protons align with a magnetic field…
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
… but move around the field axis in a
motion known as precession.
Precession axis
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
In a magnetic field, protons can take
high- or low-energy states
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
The difference between the numbers of protons in the high-energy and
low-energy states results in a net magnetization (M).
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Energy states: Temperature effects
Low-energy protons at room
temperature in Earth’s B:
~50.000000001%
High-energy protons at room
temperature in Earth’s B:
~49.999999999%
Protons move back and forth between states because of thermal energy.
As temperature decreases to near absolute zero, all protons move to lower-energy state.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Energy states: Magnetic field effects
When the magnetic field is
weak, little energy is required
for a proton to change
between high and low states
(ΔE is small).
FMRI – Week 2 – MR Signal
But, when the magnetic field is
strong, much more energy is
required (ΔE is large).
Thus, protons in the lower-energy
state tend to stay in that state
Scott Huettel, Duke University
B0
Mk
T
The net magnetization (M) increases with increasing field strength (B0),
but decreases with increasing temperature (T).
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
3. Excitation and Resonance
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Excitation: Conceptual Overview
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Key Concept: To measure
magnetization we must perturb it
• Protons must absorb energy to change between states
– Parallel (aligned with) to B0 is lowest-energy state
– Anti-parallel (aligned against) to B0 is highest-energy state
• We can apply energy as electromagnetic radiation
– Higher frequency radiation  more energy
• How can we calculate how much energy (i.e., at what
frequency) to apply?
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
θ
(net magnetization)
M
(main field of scanner)
B0
Let’s try adding another magnetic field…
B1
(another very strong field)
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
So, we could reorient some of the protons (i.e., change the net
magnetization) by introducing a second, very strong magnetic field.
Why is this impractical?
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
J  mvr
The angular momentum (J) is the product of the proton’s
mass (m), it’s velocity (v), and its radius (r).
Cool Fact #1:
The current flow (I) and velocity (v) are vectors in the same
direction (i.e., the charge is spinning just like the mass).
μ
 max
B
Cool Fact #2:
The rotation radius (r) and area (A) are proportional.
 IA
The magnetic moment (μ) is given by the rotational force
experienced by the proton (torque, or τmax) divided by the
strength of the magnetic field. These are proportional to
the moving charge of the proton (I) times the area around
which its charge moves (A).
FMRI – Week 2 – MR Signal
μ  J
Magnetic Moment and Angular
Momentum have a constant relation!
Scott Huettel, Duke University
The constant γ (gamma) is known
as the gyromagnetic ratio. It is
fixed for any given atomic nucleus.
If we assume that the proton is a
point charge spinning in a circle,
then the gyromagnetic ratio is
given by a very simple equation
(see book for derivation).
The gyromagnetic ratio (γ)
depends on only two things:
charge (q) and mass (m).
That’s it.
FMRI – Week 2 – MR Signal
q
μ J
2m
Magnetic Moment and Angular
Momentum have a constant relation!
Scott Huettel, Duke University
The gyromagnetic ratio (γ) is critical for MRI.
It allows us to calculate the energy
(expressed in electromagnetic frequency, v)
needed to change an atomic nucleus from the low- to high-energy states
in a given magnetic field (B0).

v
B0
2
This frequency (v) is known as the Larmor Frequency.
It is the same as the precession frequency of the nucleus!
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
The Canonical Analogytm for resonance: a swing set
• Option #1
– A single, strong push to lift
the person off the ground
– Requires an enormous
amount of exertion,
delivered very rapidly
• Option #2
This is a random illustrative photo. The internet is great.
FMRI – Week 2 – MR Signal
– Many small pushes at the
resonant frequency of the
swing set
– Allows distribution of the
energy over time!
Scott Huettel, Duke University
… moving from happy kids to atomic nuclei
• Option #1
– Using a very strong
perpendicular field
– Impractical (perhaps
impossible) to do quickly
in a real device
• Option #2
– Many small pushes at the
resonant frequency of the
atomic nucleus of interest
– Allows distribution of the
energy over time!
Giving energy for a longer time period increases the flip angle.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
“Tipping” in a rotating frame of reference
The RF energy is called B1 because it is, in essence, a second magnetic field.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Resonance Frequencies of Common Nuclei
Remember, the resonant
frequency is constant for a given
atomic nucleus and proportional to
magnetic field strength.

v
B0
2
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
What are the consequences of electromagnetic
energy at this frequency?
X-Ray, CT
MRI (e.g., 6 x 107Hz)
MRI uses electromagnetic energy in the radio wave portion of the
electromagnetic spectrum. It can cause heating of biological tissue, but
does not break molecular bonds.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Radiofrequency Coils for Excitation
(and Reception)
• Defined by their function:
Transmit / receive coil (most common)
Transmit only coil (can only excite the system)
Receive only coil (can only receive MR signal)
• Defined by geometry
Volume coil (low sensitivity but uniform coverage)
Surface coil (High sensitivity but limited coverage)
Phased-array coil (High sensitivity, near-uniform coverage)
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
4. Reception and relaxation
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Tipping the net magnetization provides
measurable MR signal!
Before
Excitation
During
Excitation (to)
After
Excitation
During
Excitation (t1)
Excitation tips the net magnetization (M) down
into the transverse plane, where it can generate
current in detector coils (i.e., via induction).
FMRI – Week 2 – MR Signal
The amount of current oscillates at the (Larmor)
frequency of the net magnetization.
Scott Huettel, Duke University
Relaxation: Nothing Lasts Forever
• Once we stop applying energy, M will go back to being
aligned with static field B0
• This process is called relaxation
• The part of M perpendicular to B0 shrinks [Mxy]
–
–
•
This part of M is called transverse magnetization
It provides the detectable RF signal
Part of M parallel to B0 grows back [Mz]
– This part of M is called longitudinal magnetization
– Mz is not directly detectable, but can be again converted
into transverse magnetization by energy (e.g., B1)
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
T1
FMRI – Week 2 – MR Signal
T2
Scott Huettel, Duke University
Relaxation Times and Rates
•
Net magnetization changes in an exponential fashion
– Constant rate (R) for a given tissue type in a given magnetic field
– R = 1/T, leading to equations like e–Rt
•
T1 (recovery): Relaxation of M back to alignment with B0
–
•
T2 (decay): Loss of transverse magnetization over a microscopic region
( 5-10 micron size)
–
•
Usually 500-1000 ms in the brain (lengthens with bigger B0)
Usually 50-100 ms in the brain (shortens with bigger B0)
T2*: Overall decay of the observable RF signal over a macroscopic
region (millimeter size)
–
Usually about half of T2 in the brain (i.e., faster relaxation)
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
T1 and T2 parameters
By selecting appropriate pulse sequence
parameters (Week 4’s lecture), images
can be made sensitive to tissue
differences in T1, T2, or a combination.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
T1 and T2 values at 1.5T
Tissue
FMRI – Week 2 – MR Signal
T1 (s)
T2 (ms)
CSF
2-6
~200
White matter
~0.6
~80
Gray matter
~0.9
~100
Meninges
0.5 - 2.2
50 - 165
Muscle
0.95 - 1.82
20 - 67
Scott Huettel, Duke University
What about “I”?
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
We just have signal,
so far. We need
spatial gradients to
generate images.
Next week.
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
MR Signal Generation
• Scanners use very strong static fields (Tesla range) to generate net
magnetization (M)
• Protons in magnetic fields precess around the longitudinal axis of a
field at the Larmor Frequency
• Electromagnetic energy, when supplied at the Larmor frequency
(radio waves) by head coils, is absorbed by the protons
• This tips the net magnetization down into the transverse plane
• As the net magnetization rotates through the transverse plane, it
induces a changing current in the head coils.
• This current is the MR signal
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University
Laboratory #1
• Computers will be brought to our room
• Form groups of 2
– Try to identify what other days/times work
for your lab group
– We need to coordinate on a couple of
sessions
• All lab exercises available on BlackBoard
– You can print using EPrint
FMRI – Week 2 – MR Signal
Scott Huettel, Duke University