Transcript Variability of HRF

Introduction to fMRI physics for dummies (like
me!).
Outline
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History of NMR to MRI to fMRI
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Physics of protons (1H in particular)
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Creating MRI images
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From MRI to fMRI
History of Nuclear Magnetic Resonance
NMR = nuclear magnetic resonance
Felix Block and Edward Purcell
1946: atomic nuclei absorb and reemit radio frequency energy
1952: Nobel prize in physics
nuclear: properties of nuclei of atoms
magnetic: magnetic field required
resonance: interaction between
magnetic field and radio frequency
Bloch
NMR  MRI
Source: Jody Culham’s web slides
Purcell
History of fMRI
MRI
-1973: Lauterbur suggests NMR could be used to form images
-1977: clinical MRI scanner patented
-1977: Mansfield proposes echo-planar imaging (EPI) to acquire images faster
fMRI
-1990: Ogawa observes BOLD effect with T2*
blood vessels became more visible as blood oxygen decreased
-1991: Belliveau observes first functional images using a contrast agent
-1992: Ogawa & Kwong publish first functional images using BOLD signal
Source: Jody Culham’s web slides
Some terms to know
B0 – this is used to denote the main magnetic field – also known as longitudinal
magnetization
objects placed within B0 will gradually align to this field (longitudinal
relaxation)
M0 – this is used to denote the net magnetization of an object within B0
it is the M0 which is ‘tipped’ out of alignment with B0 to create the MR
image – so M0 is now measured as transverse magnetization
RF pulse – radio frequency pulse – not to be confused with ‘resonant frequency’
to read M0 it must be tipped out of alignment with B0 – this is achieved
by sending an RF pulse at certain resonant frequencies and gradients
Some more terms to know
Magnet – the big magnet that we allocate the Tesla value to that creates B0
Gradient Coil – smaller magnets that are used to tip the net magnetization of the
subject (M0) out of alignment with B0
There are actually three gradient coils orthogonal to one another so
that gradients can be applied in the x, y and z planes
RF coil – radio frequency coil – these are typically receive only coils and are
used to measure M0 at some time after the RF pulses have been applied.
Send/receive coils are also available
Physics of protons.
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motion of electrically charged particles results in a magnetic force
orthogonal to the direction of motion
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protons (nuclear constituent of atom) have a property of angular
momentum known as spin
Angular momentum (spin) of a proton.
Protons aligning within a magnetic field
In “field free” space
Inside magnetic field
Applied Magnetic
Field (B0)
M
randomly oriented
oriented with or against B0
M = net magnetization
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when placed in a magnetic field (B0; e.g., our MRI machines) protons will either align
with the magnetic field or orthogonal to it (process of reaching magnetic equilibrium)
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there is a small difference (10:1 million) in the number of protons in the low and high
energy states – with more in the low state leading to a net magnetization (M)
Source: Mark Cohen’s web slides
Source: Robert Cox’s web slides
Source: Jody Culham’s web slides
Precession – the spinning top analogy.
What is actually aligned with the B0 is the axis around which the proton
precesses – the decay of precession (i.e., it is the rate of precession out of
alignment with B0 together with the proton density of the tissue concerned
that is crucial in MRI)
Source: Cohen and Bookheimer article
Larmor Frequency
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the energy difference between the high (oriented with B0) and low (oriented against B0)
energy protons is measurable and is expressed in the Larmor equation
Larmor equation
f = B0
 = 42.58 MHz/T
At 1.5T, f = 63.76 MHz
At 4T, f = 170.3 MHz
170.3
Resonance
Frequency for 1H
63.8
1.5
4.0
Field Strength (Tesla)
RF Excitation
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protons can flip between low and high energy states (i.e., flip between
being aligned with or against B0)
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to do so the energy transfer must be of a precise amount and must be
facilitated by another force (e.g., other protons or molecules)
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in MRI, RF (radio frequency) pulses are used to excite the RF field – the
Swing analogy – tipping the net magnetization out of alignment with B0
Cox’s Swing Analogy
Source: Robert Cox’s web slides
RF Excitation
Excite Radio Frequency (RF) field
• transmission coil: apply magnetic field along B1
(perpendicular to B0) for ~3 ms
• oscillating field at Larmor frequency
• frequencies in range of radio transmissions
• B1 is small: ~1/10,000 T
• tips M to transverse plane – spirals down
• analogies: guitar string (Noll), swing (Cox)
• final angle between B0 and B1 is the flip angle
B0
B1
Source: Robert Cox’s web slides
Longitudinal relaxation and T1.
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temperature influences the number of collisions (and hence the rate at
which protons flip between low and high energy states)
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so magnetic equilibrium (M0), or the rate at which a body placed inside B0
becomes magnetized depends on temperature – this is known as
longitudinal relaxation
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the T1-weighted image (usually used for anatomical images) measures
the rate at which the object placed in B0 (the unsuspecting subject in our
case) goes from a non-magnetized to a magnetized state – the
longitudinal relaxation
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different types of molecules (and by extension tissue) approach M0 at
different rates allowing us to differentiate things like white and grey matter
– we creep close towards the image!!!
T1 and T2
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T1 measures the longitudinal relaxation (along B0) – or the rate at which
the subject (and the various different constituents of that subject) reaches
magnetic equilibrium
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T2 measures the transverse relaxation (along B1) – or the rate of decay of
the signal after an RF pulse is delivered
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T1 – recovery to state of magnetic equilibrium
T2 – rate of decay after excitation
Tissue
T2 decay times (in 1.5 T magnet)
white matter
70 msec
grey matter
90 msec
CSF
400 msec
Reading M0
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RF coils receive the net magnetization from the object placed within the
coil (e.g., a subject’s head)
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can also have send / receive RF coils that also deliver the RF pulse (to
get the swing going) – usually the pulse is delivered by gradient coils
Proton density, recovery (T1) and decay (T2 and T2*) times.
T1 weighted
Density weighted
T2 weighted
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By ‘weighting’ the pulse sequence (and point at which data is collected)
different images of the brain are obtained
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Weighting is achieved by manipulating TE (time to echo) and TR (time to
repetition of the pulse sequence)
Precession In and Out of Phase
all nuclei aligned and precessing
in the same direction.
nuclei not aligned but still precessing
in the same direction.
So MR signal will start off strong but as protons begin to precess out of phase the signal will decay.
Source: Mark Cohen’s web slides
T1 and TR
T1 = recovery of longitudinal (B0) magnetization after the RF pulse
• used in anatomical images
• ~500-1000 msec (longer with bigger B0)
TR (repetition time) = time to wait after excitation before sampling T1
Source: Mark Cohen’s web slides
T2 and TE
T2 = decay of transverse magnetization after RF pulse
TE (time to echo) = time to wait to measure T2 or T2* (after re-focusing
with spin echo)
Source: Mark Cohen’s web slides
T1 vs. T2
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effectively, T1 and T2 images are the inverse of one another, with T1
typically used to form anatomical images and T2* used in fMRI
T1 and TR
T2*
T2: intrinsic decay of transverse magnetization over microscopic region
(~5-10 microns)
~50-100 msec (shorter with bigger B0)
T2*: overall decay of transverse magnetization over macroscopic region
(~mm)
decays more quickly than T2 (by factor of ~2)
Source: Robert Cox’s web slides
T1 vs. T2
Source: Mark Cohen’s web slides
Repetition and echo time dependence.
Source: Buxton book Ch. 8
Spatial localisation of the signal – creating the 1D image.
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A spatially variant B1 leads to a spatially variant distribution of RFs.
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Frequency analysis is used to discriminate different spatial locations.
PULSE SEQUENCE
RF pulse
Gx (x – gradient)
data acquisition
time
add a gradient to
the main magnetic
field
Gradient magnetic field = applied in the
slice plane (i.e., the x direction) thus Gx
Freq
excite only
frequencies
corresponding to
slice plane
Spatial Coding
Field Strength (T) ~ z position
Gradient coil
Spatial localisation of the signal – creating the 2D image.
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Can’t simply turn on 2 gradients.
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Instead the 2 gradients need a precise sequence.
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The 1D sequence already shown is known as frequency encoding.
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A different pulse sequence can be used in the y-direction to create the 2D
image – phase encoding.
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This method is known as echo-planar imaging or EPI and is the most
common method used in fMRI.
Spatial localisation of the signal – creating the 3D image
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The RF field must be at the same resonant frequency as the nucleus
being scanned.
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For the 2D image we have selected only one resonant frequency in one
particular z-plane (and used EPI to sequences to obtain the x and yplanes).
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So we simply apply a gradient at different levels (slices) in the z-plane to
create the 3D image.
slices in the z-plane
Spatial localisation of the signal – creating the 3D image
frequ.
encode
phase
encode
Source: Buxton book Ch. 10
Echos
All RF pulses create an ‘echo’ of the M0 signal obtained by the pulse.
T2* signals decay more rapidly than T2
A refocusing pulse is used to create a transient echo of the signal – a spin echo
Multiple refocussing pulses create multiple echoes
Source: Buxton book
Echos
pulse sequence: series of excitations, gradient triggers and readouts
Echos – refocussing of signal
Spin echo: when “fast” regions get
ahead in phase, make them go to the
back and catch up
-measure T2
-ideally TE = average T2
Gradient echo: make “fast” regions
become “slow” and vice-versa
-measure T2*
-ideally TE ~ average T2*
Source: Mark Cohen’s web slides
EPI imaging and k-space
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Any net signal produced by proton spins can be expressed as a sum of
the sine and cosine waves of different wavelengths
The different spatial frequencies of these wavelengths are denoted as kspace – the inverse of the wavelengths
small k value = low spatial frequency / long wavelength
large k value = high spatial frequency / short wavelength
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k-space is what is actually measured in MRI (i.e., the signal from M0 is
transformed into x and y values via k-space)
EPI imaging and k-space
x = frequency and y = phase or angle
Source: Traveler’s Guide to K-space (C.A. Mistretta)
Fourier transformation.
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k-space is magically
transformed into our image via a
Fourier transformation.
Source: Buxton book Ch 5
EPI imaging and k-space
Source: Buxton book Ch 10
EPI imaging and k-space
Source: Buxton book Ch 10
k-space and sampling methods.
The EPI pulse sequence zig-zags across
k-space, slowly in the x-direction and
rapidly in the y-direction.
The Gz gradient shifts this process to the
next slice to be imaged.
Source: Buxton book Ch 11
A Walk Through K-space
single shot
two shot
Note: The above is k-space, not slices
k-space can be sampled in many “shots”
2 shot or 4 shot
•less time between samples of slices
•allows interpolation
•more shots = increased spatial resolution
vs.
both halves of k-space
in 1 sec
1st half of k-space
in 0.5 sec
2nd half of k-space 1st half of k-space
in 0.5 sec
in 0.5 sec
1st volume in 1 sec
interpolated
image
2nd half of k-space
in 0.5 sec
2nd volume in 1 sec
Voila! The MRI!
But what about activation?
Vascular Network
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Arterioles
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Venules
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Y=95% at rest.
Y=100% during activation.
25 mm diameter.
<15% blood volume of cortical tissue.
Y=60% at rest.
Y=90% during activation.
25-50 mm diameter.
40% blood volume of cortical tissue.
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Capillaries
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Y=80% at rest.
Y=90% during activation.
8 mm diameter.
40% blood volume of cortical tissue.
Primary site of O2 exchange with tissue.
Red blood cell
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6 mm wide and 1-2 mm thick.
Delivers O2 in form of oxyhemoglobin.
Neurons
Artery
Vein
Art erioles
Veneoles
Capillaries
1 - 2 cm
Source: Chris Thomas’ Slides
Transit Time = 2-3 s
Vascular network and BOLD
Source: Buxton book Ch 2
Susceptibility and Susceptibility Artifacts
Adding a nonuniform object (like a person) to B0 will make the total
magnetic field B nonuniform
This is due to susceptibility: generation of extra magnetic fields in
materials that are immersed in an external field
For large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform
magnetic fields can be adjusted to “even out” the ripples in B — this is
called shimming
Susceptibility Artifact
-occurs near junctions between air and tissue
• sinuses, ear canals
sinuses
ear
canals
Source: Robert Cox’s web slides
How Susceptibility Affects Signal
Susceptibility  nonuniform precession frequencies
RF signals from different regions that are at different frequencies will get
out of phase and thus tend to cancel out
Sum of 500 Cosines with Random
Frequencies
Starts off large when all phases are about equal
Decays away as different
components get different phases
Source: Robert Cox’s web slides
Susceptibility and BOLD fMRI
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Magnetic susceptibility (c) refers to magnetic response of a material when
placed in B0.
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Red blood cells exhibit a change in c during ‘activation’
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Basically, oxyhaemoglobin in the RBC (HbO2) becomes deoxyhaemoglobin
(Hb):
– Becomes paramagnetic.
– Susceptibility difference between venous vasculature and surroundings
(susceptibility induced field shifts).
BOLD signal
Blood Oxygen Level Dependent signal
Source: Buxton book Ch 17
BOLD signal
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CBF, CBV, and CMRO2 have different effects on HbO2 concentration:
Blood Oxygen Level Dependent signal
CBF
Local Hb
Content
(delivery of more HbO2 ->
less Hb on venous side if
excess O2 not used)
CMRO2
Local Hb
Content
(extraction of O2-> HbO2
becomes Hb)
CBV
Local Hb
Content
(more Hb in a given
imaging voxel)
Interaction of these 3 produce BOLD response
– They change [Hb] which affects magnetic environment.
BOLD signal
Source: Doug Noll’s primer
First Functional Images
Source: Kwong et al., 1992
Hemodynamic Response Function
% signal change
= (point – baseline)/baseline
usually 0.5-3%
time to rise
signal begins to rise soon after stimulus begins
time to peak
initial dip
-more focal
-somewhat elusive so far
signal peaks 4-6 sec after stimulus begins
post stimulus undershoot
signal suppressed after stimulation ends
And now we can all get some sleep!