AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Overview
• Excitation & Signal Collection Process
• Gradients for Spatial Localization
The Principles of Quantitative MRI
• Measuring Tissue Volumes
• Measuring NMR Properties of Tissues
Geoffrey D. Clarke
Dept. of Radiology
• Tissue Physiology Measurements
University of Texas Health Science Center at
San Antonio
• Tissue Biochemistry Measurements
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2
B1 TX Field
RF Nonuniformities
• Directly related to current in TX coil
• RF Nonuniformities are the
Single Biggest Cause of Errors
in qMRI
– Depends on Q of coil & coil loading
• Depends on TX Coil Geomtry
• TX power auto-adjusted (pre-scan)
• RF Nonuniformities Increase as
the Bo-Field Increases
– Values should be know to 1%
– 1% = 0.086 dB
• Dielectric Resonance Effects
Become Pronounced at High Bo
• TX nonlinearities
• RF pulse droop
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4
The B1 RF Magnetic Field
NMR Signal
z
δv(t ) = ωo B1x,y M x, yδVs cos(ωot )
N
S
x
y
Principle of
Reciprocity
B1
ξ =−
G
∂ G G
( m ⋅ B 1) where m is the (nuclear)
∂t
magnetic dipole moment and
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G.D. Clarke, UTHSCSA
G
G
G
B 1 = ( B x iˆ + B y ˆj )
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
FT Approximation
RF Pulse Bandwidth (BW)
BW is inversely proportional to RF pulse duration:
TX
sin x
A sinc function ( x ) envelope on the r.f.
pulse produces a nearly square excitation
profile of the phantom…
phantom…..
FT
time
frequency
TX
FT
time
frequency
time
Slice select gradient is scaled based on BW & Gss:
slice thickness =
FT
BW
2π BW
⋅
γ
G
frequency
tp
ss
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8
Resonant Frequency Offset
M
M
B = Bo+ΔΩ/γ
Beff = B1x’y’+ΔΩz/γ
B1
X’
Y’
Y’
Beff
Mz
Mx
After 90o,
Magnetization
IS NOT on y’
X’
axis
Magnetization
X’
1
My’ = real
Mx’ = imaginary
Mz does not
contribute to
signal
1
My
Magnetization
Beff ΔΩ/γ
ΔΩ/γ
90o Sinc Pulse Profile
0.5
0
Mx
-0.5
-1
-5
-2.5
0
2.5
5
0.5
Mz
0
-0.5
-1
-5
-2.5
0
2.5
My
X’
2 ms, 5-lobe, chemical shift refocused
Y’
Y’
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Slice Selection
180o Sinc Pulse
rf1
TX
1
My
Magnetization
Magnetization
1
0.5
0
Mx
-0.5
-1
-5
-2.5
0
2.5
Frequency (kHz)
5
RX
0.5
Gsl
0
-2.5
0
2.5
Spin
Echo
time
time
time
– Larmor frequency of spins varies with position
– The flip angle depends on the local Larmor frequency
and the frequency content of the RF field pulse
– the RF pulse can be “crafted” to contain frequencies in
only a specified range
5
Frequency (kHz)
2 ms, 5-lobe, chemical shift refocused
11
G.D. Clarke, UTHSCSA
rf2
• If constant gradient field is on during the rf
pulse:
Mz
-0.5
-1
-5
5
Frequency (kHz)
Frequency (kHz)
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Slice Profile Variations
Bloch Equations
• Flip Angle varies with location
• A set of simultaneous differential equations that
describe the behavior of the magnetization under
any conditions.
– Due to B1, B0 nonuniformities
• Non-linearity of Excitation (Bloch Eqns)
– FT approximation invalid for big flip angles
– Bloch simulator software
http://www-mrsrl.stanford.edu/~brian/mritools.html
• T1-weighting of excitation profile
M (t)−M0
dMz (t)
=γ[Mx(t)By (t)−MyBx(t)]− z
dt
T1
Magnetization
along the z-axis
dMx (t)
M (t)
=γ[My (t)Bz (t) − Mz By (t)]− x
dt
T2
Magnetization
along the x-axis
dMy (t)
Magnetization
along the y-axis
dt
= γ [Mz (t)Bx (t) − Mx Bz (t)]−
M y (t)
T2
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Brain Hargreaves
Poor RF Pulse Calibration
B1 Field Mapping - Purpose
a. Needed for accurate measurement of
many NMR parameters, i.e. relaxation
times
b. Enables estimation of systematic
errors in parameter measurement
c. Enable correction of spatial
sensitivity variation using reciprocity
180o
Miscalibration of FSE
rf pulses (left
image) is corrected (right image)
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B1 Field Mapping
B1 Field Mapping - Methods
• One-pulse Mx,y
method
a. One-pulse read Mx,y
• Hard 1800o pulse
preceding 2D field
echo sequence
Venkatsen et al. Magn Reson Med 1998; 40:592
b. Spin Echo (both pulses altered)
• Bright center is
maximum B1
Barker et al. BJR 1998; 71: 59-67
c. One-pulse read Mz
• Ring pattern occurs
at every 5%
change in B1-field
Vaughn et al. Mgn Reson Med 2001; 46: 24
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Deichmann R et al. Magn Reson Med 2002; 47: 398
G.D. Clarke, UTHSCSA
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Dielectric Resonance Effect
Image Uniformity at 3 Tesla
1.5T
• Fields inside a sample of diameter, d,
can be resonant when d = nλ
• This can make the B1 field at the
center of the sample larger than at the
edges
3T
• This effect is dampened as the
conductivity of the sample increases
• B1 field maps in a saline phantom (18 cm diameter)
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RL Greenman et al. JMRI 2003, 17(6): 648-655
Dielectric Resonance
Spin-Echo Sequence
rf1
rf2
TX
Spin
Echo
RX
time
Gsl
time
Gro
Gpe
time
time
Symbolizes gradient increment
from excitation to excitation
21
Hoult DI, J Magn Reson Imag, 2000; 12:46-67
Gradient Subsystems
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One Dimensional FT
Bo(x)
x
Mag
FT
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G.D. Clarke, UTHSCSA
ν
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AAPM 2006 - MRI Physics &
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8/1/2006 08:00
MRI Gradient Fields
MRI Geometric Distortions
ωo = γ (Bo + xGx )
Sources of Error:
• Gradient Amplitude Calibration
• Machine dependent
–Best about 1% error
• PatientPatient-dependent
• Gradient Non-linearities
• Accessory device dependent
• Eddy Currents
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Eddy Currents
Eddy Currents
• The magnetic field produced by Eddy
Currents have two time-dependent
components:
• Accelerating current in gradient
coils (gradient pulse) causes
induced currents in nearby metallic
structures.
– An offset of the Bo field
– An additional gradient field
• These currents produce magnetic
fields which, in turn, oppose the
magnetic fields of the gradient coils
G
G
Bec (r , t ) = Δg (r , t ) + ΔBo (t )
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Eddy Current Pre-emphasis
Gradient Waveforms
Gradient to Magnet Ratio
Gradient Current
Eddy Current
Actual Gradient Field
G/R=0.8
G/R=0.6
In free space
In magnet
In magnet
A. Whole body system.
In magnet
Gradient Current
with Pre-Emphasis
Actual Gradient Field
0
10 ms
A. Microscopy system.
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G.D. Clarke, UTHSCSA
In
free
space
In
free
space
B. Whole body, G/R=0.6
In magnet
0
In
free
space
10ms
B. Microscopy system
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Actively Screened Gradients
Measuring Eddy Currents
•Reduce gradient field strength outside
of gradient coil former
- Current in shield is opposite polarity
•Reduces gradient field in imaging
volume also
- Improves magnet homogeneity
•Each gradient coil is associated with a
screen coil
- Twice as many amplifiers required
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De Deene Y et a. Phys Med Biol 2000; 45:1807-1823
MRI Gradient Fields
Eddy Currents
Gradient Nonlinearities
are often tolerated as part
of trade-offs with gradient
field strength or coil size
Time course
of eddy
current field
offset
following
different
numbers of
gradient pulse
units
Manufacturers often apply
gradient distortion
corrections in order to
make images appear to
be distortion free
Influences image quality
parameters (SNR, spatial
resolution, etc.)
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http://www.nbirn.net
De Deene Y et a. Phys Med Biol 2000; 45:1807-1823
Brain Volume Measurement
Brain Volume Relationships
White Matter
“Basal” Gray
Cerebellum
• High agreement between qMRI volumetry and physical sections
• qMRI volumetry is susceptible to high inter-observer variability
• Problems greatest in those regions where tissue margins are
poorly defined
35
Jelsing J NeuroImage 2005; 26: 57-65
G.D. Clarke, UTHSCSA
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Jelsing J NeuroImage 2005; 26: 57-65
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Cartilage MRI
Relaxation Times
• T1: longitudinal relaxation time defines recovery
of potential for next signal (T1=1/R1)
• T2: transverse relaxation time defines rate of
dephasing of MRI signal due to microscopic
processes (T2=1/R2)
• T2*: transverse relaxation time with Bo
inhomogeneity effects added; defines rate of
dephasing of MRI signal due to macroscopic
and microscopic processes (T2*=1/R2*)
Accuracy of 3T high and tends to be more reproducible than 1.5 T
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Eckstein F et al. Arth & Rheum 2005; 52: 3132-3136
Longitudinal Relaxation
Transverse Magnetization
M = Mo (1- exp(-TR/T1)
T2* Decay
Mo
T1
2T1
3T1
4T1
τ
39
Applications for T1 Images
Factors Influencing T1
• Macromolecular concentration
in cytosol
• Tissue characterization
• Contrast agent uptake studies
• Water binding
• Measurement of Tissue Perfusion
• Measurement of Blood Volume
• Water content
• Gd and Fermoxide Contrast
Agents
41
G.D. Clarke, UTHSCSA
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Inversion Recovery
T1 Measurement Sequences
90o
180o
• Inversion Recovery
180o
180o
Spin Echo
– 180o-90o-180o; the gold standard
TI
• Saturation Recovery – 90o-180o
TE
TR
Inversion
• Stimulated Echo – 90o-90o-90o
Excitation Refocusing
+Mo
M = Mo (2 - exp[-TI/T1])
• Look-Locker Sequence (see below)
TI
-Mo
43
Look-Locker Sequence
44
Saturation Recovery for CMRI
180o
αo
αo
αo
αo
αo
Encode Encode Encode Encode Encode
τ
τ
τ
τ
τ
• Very sensitive to RF pulse errors
• Magnetization recovery rate, T1* :
T1* =
τ
⎛ τ ⎞ − ln(cosα )
⎜ T⎟
⎝ 1⎠
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Higgins DM, Med Phys 2005; 32(6):1738-1746
T1 Parametric Maps
For Accurate & Precise T1
• Never Assume RF Flip Angle is Correct
– Varies over imaged slice due to slice profile
– Flip angle must be calibrated across slice
• Be careful in assuming magnetization has
reached steady state between acquisitions
(a) T1 Map of tubes of
gel doped with Gd-DTPA
(b) T1-weighted image
of heart in short axis
(c) T1 parametric map
image of heart in (b)
• T1’s calculated from short-acquisition period T1
sequence (SAP-T1) with varying delay times
• Optimize sequence acquisition parameters to
ensure maximal SNR
• Always check that fitted conforms to
assumed model
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Higgins DM, Med Phys 2005; 32(6):1738-1746
G.D. Clarke, UTHSCSA
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Multi-Echo with 180o Pulses
Multi-Echo Acquisitions
Mo exp(-TE/T2)
Mo exp (-TE/T2*)
Mo exp(-TE/T2)
Signal
Strength
Signal Strength
Mo exp (-TE/T2*)
90o
180o
SE3
o
SE2 180
time
3*TE
SE3
180o
o
SE2 180
Gslice
SE1
TE
180o
SE1
2*TE
TE
time
90o
180o
TE >>
2*TE
T2*
Gread
3*TE
Gphase
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Longitudinal
Magnetization
Time Scale of Relaxation
Calculation of T2
M xy = M o e − t / T2
'
Mo
1- exp (-TR / T1)
ln M xy = − 1 / T2 t + ln M o
Transverse
Magnetization
100’s of ms
'
ln( M xy / M o ) = slope = − 1 / T2
'
exp (-TE/T2*)
T2 = − 1 / slope
10’s of ms
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Eddy Current Effects on Slice
Gel Dosimeters
• Used for 3D Radiation Dosimetry QC
a
c
b
• Relies on direct relationship between
relaxation rate, R2 (R2=1/T2) of gel following
exposure and dose
Ideal – no eddy currents
worst case
pre-gradient train
RF pulse profiles used for T2-relaxometry a) Ideal profile
calculated from Bloch equations b) profile showing the
influence of eddy currents; c) pre-gradient pulse train
establishes steady-state which regularizes the RF pulse profile
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www.mgsresearch.com
G.D. Clarke, UTHSCSA
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De Deene Y et a. Phys Med Biol 2000; 45:1807-1823
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Effective Flip Angles
B1 Changes with Slice Position
Average
transverse
magnetization
within a slice as
a fraction of Mo
for various slice
positions for flip
angles ranging
from 0o to 360o
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De Deene Y et a. Phys Med Biol 2000; 45:1825-1839
R2 Calibration
De Deene Y et a. Phys Med Biol 2000; 45:1825-1839
T2* Parametric Imaging
M xy = M o e−t / T2
'
*
• Similar to T2 measurements but use
gradient echo imaging with varying
TE
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Magnetization Transfer Contrast
Contrast Agent Maps
Multislice
FSE:
T1-weighted image
Magnetization
Transfer
Contrast
Enhances T2Weighted
Appearance
Parametric map of R2*
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http://www.research.philips.com/
G.D. Clarke, UTHSCSA
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Magnetization Transfer
Magnetization Transfer Ratio
PROTON SPECTRUM
MTR =
0
Frequency (Hertz)
Magnetization Transfer Ratio (MTR)
“Free” Water
Lipids
Mo − Ms
Mo
“Bound” Water
217 Hz
Frequency (Hertz)
• the difference of the saturated versus non-saturate
images relative to the signal in the normal (nonsaturated images)
1500 Hz
0
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MTR and Aging
62
Physiological Measurements
Gray matter and white matter MTR images reveal a quadratic
change with age that is primarily attributed to normal
demylenation
• Flow – bulk motion of blood and other
fluids within body
• Perfusion – amount of blood traveling
through capillaries in ml/s/gm of tissue
• Diffusion – random motion of spins in a
homogeneous solution
– Apparent Diffusion Coefficient – measured
diffusion rate of water through tissue
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Inglese & Ge, Top Magn Reson Imag 2004; 15:355-363
Attenuation Due to Diffusion
DWI Basic Pulse Sequence
δ
A(TE ) = A(0) exp[−γ 2G 2 Dappδ 2α 2 (Δ − )]
4
Where: α=π/2;
G is amplitude of diffusion sensitive gradient
pulse;
δ is duration of diffusion sensitive gradient;
Δ is time between diffusion sensitive gradient
pulses;
Dapp is the apparent diffusion coefficient
65
90o
180o
time
G
G
δ
δ
Δ
(
b = γ 2G 2δ 2 Δ − δ
3
)
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Stejskal EO & Tanner JE, J Chem Phys 1965. 42: 288-292
G.D. Clarke, UTHSCSA
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AAPM 2006 - MRI Physics &
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8/1/2006 08:00
The b-value
Anisotropic Diffusion
• Controls amount of diffusion
weighting in image
• The greater the b-value the greater
the area under the diffusion-weighted
gradient pulses
H2O
– longer TE
– stronger and faster ramping the
gradients
H2O
Restricted diffusion along neural fibers
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Diffusion-Weighted MRI
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Hemispherical Hypoperfusion
Images
acquired 55
minutes after
onset of
aphasia,
hemiplegia,
and
hemiparesis.
Top. Conventional 1-shot EPI DWI B. SENSE EPI-DWI with R=3
shows reduced susceptibility artifacts in frontal brain
b = 1000 s/mm2
T2-weighted Diffusion Time-to-peak
Weighted
Perfusion
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Sunshine JL et al. Radiology 1999; 212: 325-332.
Bammer R, Schoenberg SO. Top Magn Reson Imag 2004; 15: 129-158
Diffusion Fiber Tracking
Diffusion-Weighted Breast MRI
Diffusion tracks
(red and blue) in
the splenium of
the corpus
callosum selected
with ellipsoid
filtering volumes
(black)
Parametric maps calculated from
biomodal exponential decay model:
(
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Conturo et al. PNAS 1999; 96:10442.
G.D. Clarke, UTHSCSA
)
(
I
= P1' exp − bD1' + P2' exp − bD2'
Io
)
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Paran Y et al. NMR Biomed 2004; 17:170-180
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AAPM 2006 - MRI Physics &
Technology
8/1/2006 08:00
Dephasing Due to Motion
Diffusion Tensor Imaging
• In anisotropic tissues
(neural fibers, muscle
fibers) scalar ADC depends
on direction of diffusion
sensitizing gradient
Gslice
time
o
+180
PHASE
BLOOD: phase not zero
• Diffusive transport of water
can be characterized by an
effective diffusion tensor
TISSUE: phase equals zero
time
Phase Shift
Due to Motion
in a
Gradient Field
-180o
• Direction of diffusion can
be used to create a map
showing orientation of
myocardial fibers.
t=0
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Tseng et al. , Radiology 2000; 216: 128-139.
Phase Contrast Imaging
Phase Contrast Images
Velocity
Encoded Image
PHASE
+180o
Two Signals:
S1 = Ss + Sm ;S2 = Ss + Sm e(iϕm)
where ϕm= γ ΔM1 υ (υ = velocity)
Phase Difference
time
Velocity
Compensated
Image
-180o
PHASE
+180o
Motion
Compensation
Gradient
(Bipolar)
Applied
TISSUE: phase equals zero
in BOTH images
ΔS =S2-S1 =Sm[e(iϕm)-1] =2iSmsin(ϕm/2)
Phase difference -
Δϕ = arg S2 - arg S1, then
υ = Δϕ / (γ ΔM1)
time
Velocity
Encoded Image
-180o
Complex difference -
BLOOD: phase is
DIFFERENT in each image
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Phase Contrast Velocity
Phase Contrast
+Venc
Stationary
In
Out
In
Out
Phase Difference
(degrees)
No Flow
Flow
Velocity
29 cm/s
180o
MRI Velocity (cm/s)
Magnitude
Velocity Encoding (Venc)
-180o
-Venc
True Flow Velocity (cm/s)
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G.D. Clarke, UTHSCSA
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AAPM 2006 - MRI Physics &
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8/1/2006 08:00
Cardiac Output
Partial Volume Effect
Asc. Aorta Flow (l/min)
25
Stotal
Stotal
Smoving
Smoving
φmoving
φ
15
10
5
0
-5
0
4
8
12
φmoving
Cardiac Output = 4.01 L/min
Stroke Volume = 68 ml
Sstatic
79
Coronary Artery Flow
A
B
C
D
16
Cine Frame Number
φ
Sstatic
20
80
Gadolinium Uptake
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Max Upslope Parametric Map
Nonuniformity Correction
Real-time TrueFISP cine study with GRAPPA ×2 was performed
between two perfusion scans
SInormalization= SIperf/SIcine
Correct for overall
effects
Correct for baseline
signal
SIcorrection= SInormalization-SIbase
50
50
45
Anterior
45
Anterior
Anteroseptal
40
Anteroseptal
40
Inferoseptal
Inferoseptal
Inferior
35
Inferior
35
Inferolateral
Inferolateral
SI (A.U.)
SI (A.U.)
Anterolateral
30
25
Anterolateral
30
25
20
20
15
15
10
10
5
5
MRI perfusion image
0
0
0
5
10
15
20
25
Tim e (s ec)
30
0
5
10
15
20
25
30
Tim e (sec)
83
G.D. Clarke, UTHSCSA
Maximum upslope
parametric map
84
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AAPM 2006 - MRI Physics &
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8/1/2006 08:00
SUMMARY
Data Analysis Results
3
Before undertaking qMRI:
MPRI
2
1
in
fe
ri
or
in
fe
ro
la
te
ra
an
l
te
ro
la
te
ra
l
an
te
ri
or
an
te
ro
se
pt
al
in
fe
ro
se
pt
al
0
Myocardial perfusion reserve index (MPRI) is
not significantly different between segments in
asymptomatic individuals after corrections
Bullseye display depicts segmental
MPRI from most apical slice (center
ring) to most basal slice (outer ring)
•
•
•
•
•
Check gradient calibrations
Understand gradient non-linearities
Evaluate eddy currents
Measure RF pulse changes in space
Determine RF receive nonuniformities
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Quantitative MRI Methods
86
Learn More Details …
• Measuring things with MRI:
–Diffusion Coefficients
–Frequency of a signal
–Relaxation rates (T1, T2 , MTC)
–Velocity of motion
–Volumes of tissues
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G.D. Clarke, UTHSCSA
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