Overview
• Sources of Error in qMRI
The Principles
of Quantitative MRI
• Volume Measurements with MRI
Perspectives for Imaging Cancers
• Relaxation Time Measurements
•
•
•
Geoffrey D. Clarke, Ph.D.
San Antonio, TX
T1 Measurements
T2 Measurements
Magnetization Transfer Contrast
• Motion Measurements with MRI
• Diffusion
• Tissue Perfusion
MR Images are Produced
Using ⊥ Gradient Fields
Spin-Echo Sequence
rf1
TX
RX
Gsl
Gro
Gpe
rf2
Spin Echo
y
time
time
time
x
z
time
Symbolizes gradient increment
from excitation to excitation
Courtesy C. Keener
• Image must be defined in 3 dimensions
• z - slice selection
• x - frequencyfrequency-encoded
• y - phasephase-encoded
1
Gradient Coils are Typically
Wound on Cylindrical Former
MRI Gradient Fields
Gradient Nonlinearities
are often tolerated as
part of trade-offs with
gradient field strength or
coil size
Manufacturers often
apply gradient distortion
corrections in order to
make images appear to
be distortion free
Influences image quality
parameters (SNR,
spatial resolution, etc.)
http://www.nbirn.net
Eddy Currents
• Accelerating
current in gradient
coils (gradient
pulse) causes
induced currents in
nearby metallic
structures.
• These currents
produce magnetic
fields which, in
turn, oppose the
magnetic fields of
the gradient coils
Eddy Currents
• The magnetic field produced by
Eddy Currents have two timetimedependent components:
• An offset of the Bo field
• An additional gradient field
r
r
Bec (r , t ) = ∆g (r , t ) + ∆Bo (t )
2
Eddy Current Pre-emphasis
Gradient Current
Eddy Current
Actual Gradient Field
Actively Screened Gradients
•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
Gradient Current
with PrePre-Emphasis
Actual Gradient Field
For details see:
Morich et al, IEEE Trans Med Imag 1988; 7:247-254.
Eddy Current Effects on Slice
b
a
Ideal – no eddy currents
•Each gradient coil is associated with a
screen coil
- Twice as many amplifiers required
Tumor Volume Measurement
c
worst case
prepre-gradient train
RF pulse profiles used for T2T2-relaxometry a) Ideal
profile calculated from Bloch equations b) profile
showing the influence of eddy currents; c) prepregradient pulse train establishes steadysteady-state which
regularizes the RF pulse profile
De Deene Y et a. Phys Med Biol 2000; 45:1807-1823
Invasive ductal carcinoma Grade III in a 59 y.o.
y.o.
woman, studied while undergoing neoadjuvant
chemotherapy. MRI was 3D fast GRE sequence.
Partridge S et al. AJR 2005; 184: 1774-1781
3
Kaplan-Meier Curves
Patients divided based on initial MRI volume of their
tumors showed significant differences in recurrencerecurrencefree survival (p
(p = 0.042, Wilcoxon’
Wilcoxon’s test).
1. A source of error in the
prescribed gradient fields
used in MRI include:
0%
1. B1 magnetic field inhomogeneities.
inhomogeneities.
0%
2. Eddy currents.
0%
3. RF pulse timing instabilities
0%
4. Stimulated echoes
0%
5. Gradient coils coupling with the RF
coils
10
Partridge S et al. AJR 2005; 184: 1774-1781
1. A source of error in the
prescribed gradient fields
used in MRI include:
1. B1 magnetic field inhomogeneities.
inhomogeneities.
Slice Selection
rf1
TX
RX
Gsl
rf2
Spin
Echo
time
time
time
2. Eddy currents.
currents.
3. RF pulse timing instabilities
4. Stimulated echoes
5. Gradient coils coupling with the RF
coils
• If constant gradient field is on during the rf
pulse:
• 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”
crafted” to contain frequencies
in only a specified range
4
FT Approximation
B1 Transmission Field
sin x
• Proportional to current in TX coil
A sinc function
envelope on the r.f.
x
pulse produces a nearly square excitation
profile of the phantom…
phantom…..
• Depends on Q of coil & coil loading
• Depends on TX Coil Geometry
• TX power autoauto-adjusted (pre(pre-scan)
time
FT
• Values should be known to within 1%
• 1% = 0.086 dB
BW
• TX nonlinearities
• RF pulse droop
frequency
tp
Resonant Frequency Offset
RF Nonuniformities
• Radio Frequency Field
Nonuniformities are the Single
Biggest Cause of Errors in
qMRI
• RF Nonuniformities Increase as
the Bo-Field Increases
M
∆Ω/γ
X’
B=
Bo+∆Ω/γ
Y’
M
Beff =
B1x’y’+∆Ωz/γ
Beff ∆Ω/γ
X’
My’ = real
Mx’ = imaginary
Mz does not
contribute to
Y’
signal
B1
90o,
After
Magnetization
IS NOT on y’
axis
Beff
Mz
Mx
X’
X’
My
Y’
Y’
5
90o Sinc Pulse Profile
0
Mx
-0.5
-1
-5
-2.5
0
2.5
5
1
0.5
Magnetization
0.5
Mz
0
-0.5
-1
-5
Frequency (kHz)
-2.5
0
2.5
5
Frequency (kHz)
1
My
Magnetization
1
My
Magnetization
Magnetization
1
180o Sinc Inversion Pulse
0.5
0
Mx
-0.5
-1
-5
-2.5
0
2.5
Frequency (kHz)
5
0.5
0
Mz
-0.5
-1
-5
-2.5
0
2.5
5
Frequency (kHz)
2 ms, 5-lobe, chemical shift refocused
2 ms, 5-lobe, chemical shift refocused
Slice Profile Variations
Poor RF Pulse Calibration
• Flip Angle varies with location
• Due to B1, B0 field nonuniformities
• NonNon-linearity of Excitation (Bloch Eqns)
Eqns)
• FT approximation invalid for big flip angles
• Bloch simulator software
http://wwwhttp://www-mrsrl.stanford.edu/~brian/mritools.html *
• T1T1-weighting of excitation profile
*Brain Hargreaves
Miscalibration of phase between 90o and
180o RF pulses in FSE (left image) is
corrected (right image)
6
B1 Field Mapping - Purpose
B1 Field Mapping - Methods
a. Needed for accurate measurement
of many NMR parameters, i.e.
relaxation times
a. OneOne-pulse read Mx,y
b. Enables estimation of systematic
errors in parameter measurement
c. Enable correction of spatial
sensitivity variation using
reciprocity
B1 Field Mapping
• OneOne-pulse Mx,y
method
Venkatsen et al. Magn Reson Med 1998;
40:592
b. Spin Echo (both pulses altered)
Barker et al. BJR 1998; 71: 5959-67
c. OneOne-pulse read Mz
Vaughn et al. Magn Reson Med 2001; 46: 24
2. During the MRI excitation
process, B1-field inhomoinhomogeneities will be manifest as:
• Hard 1800o pulse
preceding 2D field
echo sequence
0%
1. an increase in MRI signal.
0%
• Bright center is
maximum B1
0%
2. distortion in the phasephase-encoding
direction.
3. reduction of contrastcontrast-toto-noise ratio.
ratio
4. spatial variation of the prescribed
flip angle.
5. changes in the gyromagnetic ratio.10
• Ring pattern occurs
at every 5%
change in B1-field
0%
0%
Deichmann R et al. Magn Reson Med 2002; 47: 398
7
2. During the MRI excitation
process, B1-field inhomoinhomogeneities will be manifest as:
1. an increase in MRI signal.
2. distortion in the phasephase-encoding
direction.
3. reduction of contrastcontrast-toto-noise ratio.
ratio
4. spatial variation of the prescribed
flip angle.
5. changes in the gyromagnetic ratio.
Longitudinal Relaxation
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*)
Applications for T1 Images
M = Mo (1- exp(-TR/T1)
• Tissue characterization
Mo
• Contrast agent uptake studies
• Measurement of Tissue Perfusion
τ
T1
2T1
3T1
• Measurement of Blood Volume
4T1
8
Multi-Echo Acquisitions
For Accurate & Precise T1
Mo exp(exp(-TE/T2)
Mo exp ((-TE/T2*)
• Varies over imaged slice due to slice profile
• Flip angle must be calibrated across slice
Signal
Strength
• Never Assume RF Flip Angle is Correct
90o
• Be careful in assuming magnetization has
reached steady state between acquisitions
• Optimize sequence acquisition parameters
to ensure maximal SNR
• Always check that fitted data conforms to
assumed model
Gel Dosimeters
• Used for 3D Radiation Dosimetry QC
180o
TE
180o
SE1
2*TE
o
SE2 180
SE3
time
3*TE
Gslice
Gread
Gphase
B1-Field Changes
with Slice Position
• Relies on direct relationship between
relaxation rate, R2 (R2=1/T2) of gel
following exposure and dose
www.mgsresearch.com
De Deene Y et a. Phys Med Biol 2000; 45:1825-1839
9
Effective Flip Angles
R2 Calibration
Average
transverse
magnetization
within a slice
as a fraction of
Mo for various
slice positions
for flip angles
ranging from
0o to 360o
De Deene Y et a. Phys Med Biol 2000; 45:1825-1839
For Accurate & Precise T2
• Never Assume RF Flip Angle is Correct
T2* Parametric Imaging
• Varies over imaged slice due to slice profile
• 180o flip angle must be calibrated across
slice
• Use multimulti-echo (vs. dual echo) approach and
big TX coils whenever possible
• Analyze and understand eddy current effects
on T2 measurement
M xy = M o e −t / T2
'
*
• Similar to T2 measurements but
use gradient echo imaging with
varying TE
• In tissues, beware of multimulti-exponential
decay
10
Calculation of T2
Contrast Agent Maps
M xy = M o e−t / T2
*
'
ln M xy = −1/ T2*t + ln Mo
'
ln(M xy / M o ) = slope= −1/ T2*
'
T2* = −1/ slope
T1-weighted image
Parametric map of R2*
http://www.research.philips.com/
Magnetization Transfer
MTC in Liver Tumors
PROTON SPECTRUM
0
Frequency (Hertz)
Post-Contrast T1W SE
Axial T2W SE
Post-Contrast MTC
Non-Contrast MTC
“Free” Water
Lipids
“Bound” Water
217 Hz
Frequency (Hertz)
1500 Hz
Mahfouz M et al. J Egypt Nat’l Cancer Inst 2000;12(3):191–198
11
0
Magnetization Transfer Ratio
MTR =
Mo − Ms
Mo
Magnetization Transfer Ratio (MTR)
• the difference of the saturated versus nonnonsaturate images relative to the signal in
the normal (non(non-saturated images)
MTR in Parotid Cancer
• MR images obtained without (Left) and with
(Right) magnetization transfer pulse.
• Lesion toto-muscle MTR = 0.92.
• Tumor diagnosed as malignant using
combined criteria of poorly defined margins
and lesionlesion-toto-muscle MTR > 0.71.
Takashima et al. AJR 2001;176:1577–1584
3. Using magnetization
transfer contrast effectively
changes what?
3. Using magnetization
transfer contrast effectively
changes what?
0%
1. The T1 of tissue.
tissue.
1. The T1 of tissue.
tissue.
0%
2. The T2 of tissue.
2. The T2 of tissue.
0%
3. The T2* of tissue.
3. The T2* of tissue.
0%
4. The eddy currents.
currents
4. The eddy currents.
currents
0%
5. The rate of contrast uptake.
5. The rate of contrast uptake.
10
12
Physiological Measurements
• Diffusion – random motion of spins
in a homogeneous solution
Diffusion Trajectory
MRI exploits
xploits phase losses in the signal due to
diffusion of spins in a magnetic field gradient
• Perfusion – amount of blood
traveling through capillaries in
ml/s/gm of tissue
• Flow – bulk motion of blood and
other fluids within body
Hagmann, P. et al. Radiographics 2006;26:S205-S223
Crick Model
Apparent Diffusion Coefficient
ADC
• Time must large enough
so there is time for
particles to interact with
barriers
• Do > ADC
One dimensional model.
• κ ≡ permeability of
membrane barriers
• a ≡ distance between
barriers
• ADC ≡ diffusion
coefficient of molecules
in presence of barriers
• Do ≡ diffusion
coefficient of bulk fluid
Sotak C. Neurochem Internat’l
2004; 45(4): 569-582.
The b-value
• Controls amount of diffusion
weighting in image
• The greater the bb-value the greater
the area under the diffusiondiffusionweighted gradient pulses
• longer TE
• stronger and faster ramping the
gradients
13
Attenuation Due to Diffusion
δ
A(TE ) = A(0) exp[−γ 2G 2 Dappδ 2α 2 ( ∆ − )]
4
Where: α=π/2;
G is amplitude of diffusion sensitive
gradient pulse;
δ is duration of diffusion sensitive
gradient;
∆ is time between diffusion sensitive
gradient pulses;
Dapp is the apparent diffusion coefficient
Diffusion Weighted Images
Taylor WD et al. Biological
Psychiatry. 55(3):20155(3):201-7, 2004
• Brighter regions indicate
reduced diffusion values
• Different effect for
different directions of the
diffusion sensitizing
gradients
• Splenium of the corpus
callosum is aligned mainly
with the x direction and
has a large Deff
• Splenium is dark when the
gradients are in the x
direction (upper left).
DWI Basic Pulse Sequence
90o
180o
time
G
G
δ
δ
∆
(
b = γ 2G 2δ 2 ∆ − δ
3
)
Stejskal EO & Tanner JE, J Chem Phys 1965. 42: 288-292
Changes in Tissue Cellularity are
Related to Molecular Water Mobility
Hall, D. E. et al. Clin Cancer Res 2004;10:7852-7859
Copyright ©2004 American Association for Cancer Research
14
MRI of Patients with
Oligodendrogliomas
DWDW-MRI of Glioblastoma Multiforme
7-week course of radiation therapy
7-week course of radiation therapy
Moffat, Bradford A. et al. (2005) Proc. Natl. Acad. Sci. USA 102,
102, 55245524-5529
Hamstra, Daniel A. et al. (2005) Proc. Natl. Acad. Sci. USA 102, 1675916759-16764
DW MRI on Breast Tumor
Parametric maps calculated from
biomodal exponential decay model:
(
)
(
I
= P1' exp − bD1' + P2' exp − bD2'
Io
)
Paran Y et al. NMR Biomed 2004; 17:170-180
4. The degree of diffusiondiffusionweighting applied to a given
pulse sequence is
parameterized by the:
0%
1. b-value
0%
2. diffusion tensor
0%
3. ADC
0%
4. MTR
0%
5. effective RF flip angle
10
15
4. The degree of diffusiondiffusionweighting applied to a given
pulse sequence is
parameterized by the:
Tissue Perfusion
arteries
Grey
Matter
1. b-value
vein
2. diffusion tensor
3. ADC
White
Matter
4. MTR
5. effective RF flip angle
500µ
500µm
http://www.fmrib.ox.ac.uk/~patricia/web_talk/index.htm
Compartmental Modeling
Clinically available
MRI contrast
agents do not leak
into the
intracellular
space.
(Interstitial Space)
Ktrans = volume
transfer constant
of contrast agent
leakage into the
interstitial spaces
Jackson A et al. Clin. Cancer Res. 2007, 13(2): 3449 - 3459
Phases of Contrast
Enhancement
Uptake Phase:
Phase: signal intensity rises above
baseline and there is a net leakage of
contrast from the blood vessels into the
interstitial space.
Zahra MA et al. Lancet Oncology 2007; 8: 6363-74.
16
Phases of Contrast
Enhancement
Phases of Contrast
Enhancement
Plateau Phase:
Phase: maximum enhancement with an
equilibrium in the movement of contrast between
the plasma and extracellularextracellular-extravascular space.
Washout Phase:
Phase: contrast starts to leave tissue
and goes back into blood vessels. Red part of
graphs refer to phase in corresponding diagram
showing movement of contrast.
Zahra MA et al. Lancet Oncology 2007; 8: 6363-74.
Zahra MA et al. Lancet Oncology 2007; 8: 6363-74.
Dynamic Contrast Enhancement
Angiogenesis
• Angiogenesis is new blood vessel
development, which can occur in the
development of pathological states
• Angiogenesis plays an important role in
the growth and metastasis of tumors
• Curves denote difference between uptake of
normal glandular tissue (green
(green)) & lesion
(blue)
blue)
• High rate of uptake is linked to larger micromicrovessel size and density
• Expanding tumors become hypoxic and
express transcription factors, which
induce the release of proangiogenic
growth factors such as vascular
endothelial growth factor
Vlaardingerbroek & den Boer, 1999
17
DCEDCE-MRI In a Patient with Partial
Response to Monoclonal Antibody Rx
Angiogenesis
Inflammatory Breast Cancer
• A wide range of novel tumor
therapies directed against
angiogenesis have been developed
Baseline
Post Cycle 1
Bevacizumab (inhibits VEGFVEGF-A)
+ doxorubicin (chemo agent)
Post Cycle 4
Post Cycle 7
• Perfusion MRI can assess
hemodynamic parameters of tumors
• Angiogenesis can be inferred from
perfusion measurements from MRI
s
s
DCE-MRI: tumor enhancement outlined in red; contrast kinetics (black line)
Wedam, S. B. et al. J Clin Oncol; 24:769-777 2006
5. Dynamic Contrast Enhanced
(DEC) MRI can be used to
evaluate which physiological
characteristic of tumors?
0% a. Diffusion
5. Dynamic Contrast Enhanced
(DEC) MRI can be used to
evaluate which physiological
characteristic of tumors?
a.
b.
c.
d.
e.
0% b. Apoptosis
0% c. Angiogenesis
0% d. Tumor growth
0% e. Tumor oxygenation
Diffusion
Apoptosis
Angiogenesis
Tumor growth
Tumor oxygenation
10
18
Quantitative MRI Precautions
Before undertaking qMRI:
•
•
•
•
•
Check gradient calibrations
Understand gradient nonnon-linearities
Evaluate eddy currents
Measure RF pulse changes in space
Determine RF receive
nonuniformities
References for SAMS
1. De Deene Y et al. Phys Med Biol.
45:1825–
45:1825–1839 (2000)
2. Jezzard P, Barnett AS & Pierpaoli C.
Magn Reson Med. 39:80139:801-812 (1998)
3. Look DC, Locker DR. Rev Sci Instrum.
Instrum.
41: 250250-251 (1970)
4. Le Bihan D et al. J Magn Reson Imag.
Imag.
13: 534534-546 (2001)
5. Collins CM et al. J. Magn Reson Imag.
Imag.
21:192–
21:192–196 (2005)
Suggested Reading
• Quantitative MRI of the Brain,Tofts
Brain,Tofts,, P.
ed. (2003, John Wiley & Sons,
Southern Gate, Chichester,
Chichester, UK)
• Clarke GD, Lee Y. The Principles of
Quantitative MRI. In Advances in
Medical Physics 2008.
2008. AB Wolbarst,
KL Mossman & WR Hendee, eds.
(Medical Physics Publishing, Madison,
WI) 2008.
19