“genteel” introduction to mri physics - ii: k-space ... · “genteel” introduction to mri...
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“Genteel” Introduction to MRI Physics - II: k-space, timing, and
contrasts
Rudolph Pienaar, M.Eng, D.EngAssistant in Medical Imaging
Dept of Radiology Massachusetts General Hospital
Boston MA, USA
Magnetic Resonance Imaging:Deconstructing Timing Diagrams
Andrew J. M. Kiruluta, Ph.D.Dept of Radiology, MGH,
Dept of Physics, Harvard UniversityBoston MA, USA
“Throw physic to the dogs; I’ll none of it.”Shakespeare, Macbeth
Organization
• Quick recap• More on k-space• MR Sequence Timing diagrams• Imaging practicalities: echoes
– Spin – Gradient
• Image Contrasts– Relaxation effects– T1, T2, and proton density
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Magnetic Resonance• Protons and Neutrons have intrinsic angular momentum.• Atoms with an odd number of proton and/or odd number of
neutrons have a net magnetic moment=> MR active• For example, 1H exhibit nuclear magnetic resonance.
-
-
-
-
--
- -
--
-+
+
+
+ ++
+ +
+
Neutrons + protons
1H
in selected slice: select ywith phase encoding
x
y
Imaging
xy
zslice select: define z position
in selected slice: select xwith freq encoding
• Some of the following images are copyright: DM Higgins
• http://www.revisemri.com/tutorials/what_is_k_space/
k-space
Imaging
xy
zslice select: define z position
in selected slice: select xwith freq encoding
in selected slice: select ywith phase encoding
x
y
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Timing Diagram
RF
G
G
G
A/D
slice
freq
phase
echo
TR
excitation phase
Phase encodephase
frequency encode& data acquisition
Analog signal
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Constructive InterferenceSame wavelength, phase difference = 0°Amplitude larger: Higher intensity
Sum
( ) cos( ) 0.5cos( ) 1.5cos( )E x kx kx kx= + =
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Destructive InterferenceSame wavelength, phase difference = 180° (1/2 λ)Amplitude smaller: Lower intensity
Sum
( ) cos( ) 0.5cos( ) 0.5cos( )E x kx kx kxπ= + + =
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Selective Excitation
Frequency
Mag
nitu
de
Time
RF
Am
plitu
de
(a)(b)
Pos
ition
(d)(c)
Slope = 1γ G
Frequency
)(
ˆ)(
0
0
zGB
zzGBB
z
z
+=⇒+=
γω
• Slice Encoding Gradient field
• Slice Location & Width:– Gradient strength – Center frequency – Bandwidth (BW) of RF
pulse
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Phase Encoding Step
RF
G
G
slice
phase
TR
phase encodingstep
kx
ky
phase encodingdirecion
0.5c
m1.
13cm
1.5c
m
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Frequency Encoding and Data AcquisitionGE
RF
G
G
G
A/D
slice
freq
phase
echo
TR
excitation phase
Phase encodephase
frequency encode& data acquisition
Analog signal
kx
ky
phase encodingdirecion
8.13cm
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If the spins are brought into phase, a net transverse magnetization is created.
RF Spin Phasing
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Measuring the MR Signal
RF signals from precessing protons
RF antenna/Rx coil
B0
Starts off large when all phases are about equal
High frequency curve is at the average frequency
Decays away as different
components get different phases
The pros and cons of gradients
in selected slice: select xwith freq encoding
in selected slice: select ywith phase encoding
x
y
• Gradients, though useful in manipulating frequencies, also add dephasing, resulting in signal loss.
As we perform readout, wealso dephase (disturb the phaserelationship) along the readout
The pros and cons of gradients
• The most important k-space signal is at the center of k-space
• By adding additional gradients (and possibly another RF pulse), we can mitigate against gradient induced phase (and signal loss) and refocus our signal close to the center of k-space
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Spin Echo versus Gradient Echo
Gradient Echo
F I D gradient recalledecho
αR F p u l s e
rephase
dephase
signal
gradient
Spin Echo
FID spinecho
9 0 RF pulse
readoutfrequency encode
signal
gradient
18 00 RF pulse
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Spin & Gradient Echoes
Ref. Schering
• RF (spin) echo: flip the track (direction) so that they come back to the starting point.• Gradient echo: flip speeds (i.e. frequencies) so that the rabbit is slower than the turtle.
t < T2
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Spin Echo Timing Sequence
12
3 4
ky
kx
phase encoding direcion
K-space trajectory
RF
G
G
G
A/D
slice
freq
phase
echo
TR
excitation phase
Phase encodephase
frequency encode& data acquisition
Analog signal
TE/2 TE/2
1 2 3 4
Only 1 line of k-spaceis read per TR!
TR = 1s / 256 samples= 256s for whole slice= 4.2 minutes / slice
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A word about Contrast and Relaxation Effects
• ρ – Spin (Hydrogen/proton) density results in contrast between tissues
“water/fat content in tissue”
• T1 – due to energy exchange between spins and “lattice” ”time for sample to magnetize”
• T2 – dephasing time due to spin-spin energy exchange”time to loss of phase coherence”
• T2* - dephasing due to B0 inhomogenitiesgradients and inhomogeneous field increase
phase accumulation and reduce T2
10
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Contrast - T1 Decay
• Longitudinal relaxation due to spin-lattice interaction
• Mz grows back towards its equilibrium value, M0
)1()( 1/0
Ttz eMtM −−=
0 1 2 3 4 5-1.0
-0.5
0.0
0.5
1.0
t/T1M
z/M
0
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Some sample tissue time constants - T1
Image, caption: Nishimura, Fig. 4.2
fat
liver
kidney
Approximate T1 values as a function of Bo
white matter
gray matter muscle
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Contrast - T2 Decay• Transverse relaxation
due to spin dephasing
• T2 irreversible dephasing
• T2/ reversible dephasing
• Combined effect:
*2/
/22
*2
)0()(
111
TteMtM
TTT−
⊥⊥ =
+=0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
t/T2*
Mx(
t)/M
x(0)
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41
Some sample tissue time constants: T2
Table: Nishimura, Table 4.2
T2 of some normal tissue types
47muscle
92white matter
100gray matter
43liver
58kidney
85fat
T2 (ms)Tissue
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T1 Contrast
Sig
nal
Time
Sig
nal
Time
Short Repetition Long Repetition
CSF
White/Gray Matter
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MRI of the Brain - Sagittal
T1 ContrastTE = 14 msTR = 400 ms
T2 ContrastTE = 100 msTR = 1500 ms
Proton DensityTE = 14 msTR = 1500 ms
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Useful links...
• MR Technology Information Portal Database:
• http://www.mr-tip.comhttp://www.mr-tip.com/serv1.php?type=db
• Basics of MRI (online book):
• http://www.cis.rit.edu/htbooks/mri/
• Revise MRI:
• http://www.revisemri.com/