Transcript Document

Center for Magnetic Resonance and Optical Imaging
Department of Radiology
School of Medicine
University of Pennsylvania
T MR imaging: Techniques and
basis for image contrast
Ravinder Reddy
Center for Magnetic Resonance and Optical Imaging
Department of Radiology
University of Pennsylvania
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Outline
• Nuclear spin relaxation
• T1 and T2
• Spectral density
– Defining equations, Frequency dependence
• T relaxation
– Definition and pictorial illustration
• Defining equation, Frequency dependences
– Methods of measurement
– Contributing mechanisms and image contrast
» Chemical exchange, D-D interaction, relaxation
» Applications in the study of collagen rich tissues
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Thermal equilibrium?
• How is the thermal equilibrium established?
dMz/dt = -(Mz-Mo)/T1

dMxy/dt = -(Mxy)/T2
Bo =0
Bo = 1.5T
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
T1 and T2
wo
60 MHz
1
T
 w 2 J(w 0)
1

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T2 Process
•
Fluctuating fields (Hz) which perturb the energy
levels of the spin states cause transverse
magnetization to dephase
E=Bo
Observed line =  1/2 = 1/T2*
1/T2* =Center
1/T
+ Bo/2 and Optical Imaging, UPENN , NCRR
for 2
Magnetic Resonance
Relaxation Mechanisms
Motion of nuclear magnetic moments generates
fluctuating magnetic fields
H= iHx +jHy+kHz
M= iMx + jMy +kMz
(magnetization vector)
Interaction between them
(H x M)= i(HyMz-HzMy)+j(HzMx-Hx Mz) +k(HxMy-HyMx)
Hx,y ----> T1 and T2 relaxation
Hz ----> T2 relaxation
-----> T1>T2
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Fluctuating fields and spectral
densities
z
• Fluctuating fields have
zero average:
• <Bx(t)> = 0
• Mean square fluctuating
field <Bx2(t)> ≠0
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x
Bo
Bx
My
y
Correlation time
Comparison of field at any one time point t with its value at
t+
•
If ‘’ is small compared to the
timescale of the fluctuations,
then the values of the field at
the two time points tend to be
similar.
•
If ‘’ is long, then the system
loses its memory.
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Fluctuating fields
• How rapidly do the fields fluctuate?
• Autocorrelation function of the field (convolution
of a function with itself) defined as
• G(t) = <Bx(t) Bx(t+)>≠ 0
• It tells us how self similar a function is
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Autocorrelation function G(t)
•
•
•
An exponential form is assumed:
G(t)= <Bx2> exp(-|t|/tc)
G(t) is large for small values of t, and
tends to zero for large values of t.
•
‘c’ is known as correlation time of the
fluctuations.
It indicates how long it takes before the
random field changes sign.
•
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Spectral density J( )
•
•
Spectral density function(SDF) is
defined as the 2 FT of G(t):
J( ) = 2 ∫o∞ G(t) exp{-i t}
•
For G(t)= <Bx2> exp(-|t|/c)
•
•
•
The spectral density is given
J( ) = 2 <Bx2> c/(1+ 2 c 2)
Normalized SDF,
J( o) = c/(1+ 2 c 2)
If tc is short then the SDF is broad
and vice versa
•
•
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Levitt, Spin dynamics
Spectral density
•
•
•
•
As the solution gets more
viscous the number of
molecules with high frequency
components decreases.
Viscosity of Tissues vary
significantly.
Biological tissues have different
T1s.
SDF also varies with temp.
J( )
o
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log( )
Rotational Motion
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Dipole-dipole relaxation
• For spins-1/2, the important relaxation
mechanism is through space dipolar coupling:
• Rotational correlation time c
– 1/T1= (3/10)b2{J( o)+ 4J(2 o)}
– 1/T2= (3/20)b2{3J(0)+ 5J( o)+ 2J(2 o)}
• b= ( oh2/4r3)
– J( o)= c/{1+ ( oc)2}
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
T1 and T2
• Variation of relaxation
time of protons in water
as a function of
correlation time at a
resonance frequency of
100 MHz (1/ o = 10-8 s)

 o c < 1, T1=T2

 o c ≥ 1, T1>T2
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Frequency range probed
• T1 probes molecular motional processes in MHz range
• To measure the processes in <MHz to KHz
– experiments at Bo fields corresponding to <MHz
– Implies low SNR and compromised contrast
• T measures low frequency processes while
performing the measurements at high Bo
– T dispersion can be measured at the constant Bo
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
What is T ?
Z
X
Y
1
o
60 MHz
1
T
 w 2 J(w 0)
1
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
~kHz
T
: Spin-locking
/2
TSL
1
Rot, CE, DD
•
•
Redfield, Phys Rev. 98 (1955)
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time
Spin locking RF pulse prevents normal
T2 relaxation process due to dipolar
interaction etc.
T is primarily determined by the
presence of low frequency motions
T relaxation and dispersion
For a fixed  1, collect an image (or FID) as a
function of TSL
Sig (TSL)= A exp(-TSL/T )+c
(/2)x
T variation as a function of  1 is
known as T dispersion
(/2)x
(/2)-x
(TSL)y
(/2)-x
R
e
R
e
a
d
a
d
Relaxation
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
(TSL)y
Dispersion
Mechanisms that contribute to T dispersion
• Rotational motion of a fraction of water bound
to proteins
• Exchange of protons on macromolecules with
bulk water
– Scalar relaxation
– Exchange of -OH, -NH, NH2 with bulk water
• Non averaged residual dipolar interaction (RDI)
• Diffusion through field gradients
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Mechanisms for T1ρ Relaxation
Bo
θ
A
Molecular Rotation
Chemical Exchange
B
r
Residual dipole-dipole
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Diffusion through Magnetic
Field Gradients
Relaxation rates in biological tissues
+RDI
+RDI
b= fraction of bound water, C= diffusion contribution
e= water proton exchange time, r= rotational correlation time
B= ( oh2/4r3)2
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
T and chemical exchange
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Chemical Exchange
Solute Pool (with
exchangeable
proton)
Water Pool
O
H
O
ksw
kws
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
H
H
O
H
H H
O
O
H H
O
H H
H
H
O
H
H
H
O
H
H
Chemical exchange and T1ρ
• GABA amine protons
• Exchange rate ~1.5kHz
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Quantification of spin exchange from T1ρ Images
Readout
Readout
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GABA: Exchange of Amine protons and T1ρ
• A. Low B1
• B. High B1
GABA
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GABA CEST and T1ρ
• ~18%
• ~36%
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Spin exchange in cartilage and T
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Aggrecan and Proteoglycans
HA
Core protein
Glycosaminoglycans (GAG)
G1 G2
Keratan sulfate
rich sections
G3
Chondroitin sulfate
rich sections
G1 G2
Fixed Negative Charge (FCD)
G3
COO-
CH2OSO3 HO
O
O
O
NHCOCH3
O
OH
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
OH
Chondroitin Sulfates
Chondroitin-4-sulfate
H
CH2OH
COO-
-
O3SO
O
H
O
O
O
OH
O
NHCOCH3
OH
H
O
H
H
H
Chondroitin-6-sulfate
O
CH2OSO3 COO-
HO
O
O
O
OH
O
OH
H
H
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NHCOCH3
H
H
O
CS phantom images
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Regatte et al, JMRI, 17(2003)
T Maps of Cartilage Specimen
256 ms
Articular Surface
Subchondral
Bone
0ms
Normal
1
Enzymatically Degraded
T
1
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR

1
T
0
 f [ R1  ]
1
Akella et al, MRM,46(2004)
T imaging of chondromalacia
Preliminary results from an osteoarthritic subject diagnosed (arthroscopically) with grade I
chondromalacia in the lateral facet of the patella. The left hand side figure shows the 3D T
relaxation map of the patellar cartilage. The color scale shows a volume rendered
representation of T relaxation times.
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
T and dipolar interaction
Bo
θ
A
B
r
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Static dipolar interaction
Spins with no D-D interaction
Without spin-lock
During spin-lock
ωD
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Dipolar interaction
H= A(1-3 cos2 )[3Iz2-I(I+1)]

‘ ’ is the angle between the
main Bo field and the dipolar
vector

Dipolar interaction broadens
the resonance lines

Variation in orientation and
content of collagen leads to

different degree of line
broadening in cartilage
zones

Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR

B0
Arrangement of collagen in cartilage
Superficial
Middle
Radial
Calcified
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Effect of RDI on MRI of cartilage
T2
• Signal is insensitive to small
changes in PG
• Produces “laminar” appearance
– Difficult to interpret image contrast
and maps
• How do we reduce its effect?
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Parallel to B0 - Images
T2
250 Hz
500 Hz
B0
Akella et al, MRM,46(2004)
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
1 KHz
2 KHz
Effect of spin-lock pulse on RDI
T2
250 Hz
T2 = 32 ms T = 62
500 Hz
T = 76
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1 KHz
T = 86
2 KHz
T = 109
Profile plots (|| to B0)
T1 -2 kHz
T2
T1 -500
T1 -250
Articular
surface
Bone
0
5
10
15
20
25
30
35
Pixel Number
T2
250
Hz
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500
Hz
2
KHz
Profile plots (magic angle)
T1 -2 kHz
T2
T  -500Hz
Articular
surface
0
5
10
Bone
15
20
Pixel number
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
25
30
35
T1ρ dispersion
parallel
54.7o
Akella et al, MRM,46(2004)
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Reducing laminar appearance
T2 weighted image
T1ρ weighted image (500Hz)
1/T = (1/T )ex+ (1/T )rot + (1/T )RDI+..
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
T1ρ and Sodium MRI of Inter vertebral Disc
Symptomatic 24 yo male
Healthy 26 yo male
T map
Sodium map
T1rho
scale bar
in ms
Sodium
scale bar
in mM
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
T map
Sodium map
T1ρ dispersion in Miocardial Infarction
ν1 = 0 Hz
ν1 = 2 kHz
Field Artifacts
Proton Dipole-Dipole Coupling in Collagen
Chemical Exchange On/Off Amide and Hydroxyl
Molecular Rotation of Water Protons
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
B1-dependent relaxation times
T2-weighted
infarction scar
T1ρ-weighted
0
1
B1 (kHz)
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2
T1ρ Dispersion
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T1ρ dispersion and Tumor
A and B: T2 and T1ρ weighted
C and D: T2 and T1ρ maps
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Comparison of the T2 and T1 relaxation time
constants (in ms) between MDA-MB-468 (N=2, open
symbols and dashed lines) and more metastatic MDAMB-231 tumors (N=3, solid symbols
and solid lines).
T1ρ pulse sequence developments
• We begun with a T1ρ pulse cluster preencoded to a 2D single slice readout
• We developed 3D SLIPS sequence
– Enable 3D T1ρ map in about 10 minutes
• Addressed issues of Bo and B1
inhomogeneity compensations
• Sl SSFP New sequence with reduced SAR,
which can be implemented at 7T
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
T Imaging- Pulse Sequence
FREQ
PHASE
SLICE
(/2)
(/2)x
(/2)
(/2)-x
SLP
1H
RF
TSL
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
SLIPS pulse sequence
Enables Rapid T1 mapping
3D T1 mapping (30 slices) in about 10 min
Newer version ----> ~5 min
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B1 and Bo insensitive spin-lock cluster
Witchey et al, JMR 186 (2007)
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
slSSFP pulse sequence
Witschey et al, MRM, 2009
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
T Characteristics
• Sensitive to processes at or around the time scale ~
1/ 1.
• Low frequency (Hz-KHz) molecular motions can be
probed at high Bo.
• By manipulating  1:
– B0 inhomogeneities, susceptibility and diffusion-related signal loss
– Has higher dynamic range
– Ability to measure and minimize
• spin-exchange
– exchange dependent pH changes
• dipolar coupling effects
– sensitive to small changes in macromolecular content
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
Acknowledgements
Work was supported by
NIH grants
R01-AR045242 (RR)
R01-AR045404 (RR)
R01-AR051041 (RR)
RR02305 (RR)
and
Arthritis Foundation (RR)
Wyeth Research (RR)
OA Spine (AB)
NIH/NCRR
NCRR
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR
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Arijitt Borthakur
Walter Witschey
Andy Wheaton
Dharmesh Tailor
Erik Shapiro
Eric Mellon
Michael Wang
Feliks Kogan
David Pilkinton
Anup Singh
Victor Babu
Harris Mohammad
Kejia Cai
Hari Haran
Mark Elliott
•H. Ralph Schumacher
•J. Bruce Kneeland
•Jess H. Lonner
•Jesse Khurana
•Jay Udupa
Thanks for your patience
Thank You
Center for Magnetic Resonance and Optical Imaging, UPENN , NCRR