ravinder reddy, phd professor of radiology & director of cmroi, department of radiology,...
TRANSCRIPT
Ravinder Reddy, PhDProfessor of Radiology & Director of CMROI,
Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia,
PA
CMROICMROI Slide Slide 22
Outline
CMROICMROI Slide Slide 33
Thermal equilibrium?
How is the thermal equilibrium established?
ν
Bo =0 Bo = 1.5T
dMz/dt = -(Mz-Mo)/T1
dMxy/dt = -(Mxy)/T2
CMROICMROI Slide Slide 44
T1 and T2
o
60 MHz
CMROICMROI Slide Slide 55
T2 Process
Fluctuating fields (Hz) which perturb the energy levels of the spin states cause transverse magnetization to dephase
ΔE=γBo
Observed line = ν1/2 = 1/πT2*
1/T2* = 1/T2 + γΔBo/2
CMROICMROI Slide Slide 66
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
CMROICMROI Slide Slide 77
Fluctuating fields and spectral densities
Fluctuating fields have zero average:
<Bx(t)> = 0 Mean square
fluctuating field <Bx
2(t)> ≠0
z
y
x
Bx My
Bo
CMROICMROI Slide Slide 88
Correlation time
If ‘τ’ 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 ‘τ’ is long, then the system loses its memory.
Comparison of field at any one time point t with its value at t+τ
CMROICMROI Slide Slide 99
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+τ)>≠ 0
It tells us how self similar a function is
CMROICMROI Slide Slide 1010
Autocorrelation function G(t)
An exponential form is assumed: G(t)= <Bx
2> exp(-|τ|/τc) G(τ) is large for small values of τ,
and tends to zero for large values of τ.
‘τc’ is known as correlation time of the fluctuations.
It indicates how long it takes before the random field changes sign.
CMROICMROI Slide Slide 1111
Spectral density J(ω)
Spectral density function(SDF) is defined as the 2 FT of G(t): J() = 2 ∫o
∞ G(τ) exp{-iτ}
For G(t)= <Bx2> exp(-|τ|/τc)
The spectral density is given J() = 2 <Bx
2> τc/(1+2 τc 2) Normalized SDF:
J(0) = τc/(1+2 τc 2) If τc is short then the SDF is
broad and vice versa
Levitt, Spin dynamics
CMROICMROI Slide Slide 1212
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. o
J()
log()
CMROICMROI Slide Slide 1313
Rotational Motion
CMROICMROI Slide Slide 1414
Dipole-dipole relaxation
For spins-1/2, the important relaxation mechanism is through space dipolar coupling:
Rotational correlation time τc 1/T1= (3/10)b2{J(ωo)+ 4J(2ωo)} 1/T2= (3/20)b2{3J(0)+ 5J(ωo)+ 2J(2ωo)}
▪ b= (μohγ2/4πr3) J(ωo)= τc/{1+ (ωoτc)2}
CMROICMROI Slide Slide 1515
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 τc < 1, T1=T2 o τc ≥ 1, T1>T2
CMROICMROI Slide Slide 1616
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
T1ρ measures low frequency processes while performing the measurements at high Bo T1ρ dispersion can be measured at the
constant B0
CMROICMROI Slide Slide 1717
What is T1ρ?
1~kHz
o
60 MHz
Z
YX
CMROICMROI Slide Slide 1818
T1ρ : Spin-locking
• Spin locking RF pulse prevents normal T2 relaxation process due to dipolar interaction etc.
• Tρ is primarily determined by the presence of low frequency motions
π/2
time
1
TSL
Redfield, Phys Rev. 98 (1955)
Rot, CE, DD
CMROICMROI Slide Slide 1919
T1ρ relaxation and dispersion
(π/2)x (π/2)-x
(TSL)y
Re
ad
Relaxation
(π/2)x (π/2)-x
(TSL)y
Re
ad
Dispersion
For a fixed 1, collect an image (or FID) as a function of TSL
Sig (TSL)= A exp(-TSL/Tρ)+c
Tρ variation as a function of 1 is known as Tρ dispersion
CMROICMROI Slide Slide 2020
Mechanisms that contribute to T1ρ 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
CMROICMROI Slide Slide 2121
Mechanisms for T1ρ Relaxation
Molecular Rotation Diffusion through Magnetic Field Gradients
Chemical Exchange
A
B
Bo
θ
r
Residual dipole-dipole
CMROICMROI Slide Slide 2222
Relaxation rates in biological tissues
b= fraction of bound water, C= diffusion contribution
τe= water proton exchange time, τr= rotational correlation time
B= (μohγ2/4πr
+RDI
+RDI
CMROICMROI Slide Slide 2323
T1ρ and chemical exchange
CMROICMROI Slide Slide 2424
H
ksw
kws H HO
H HO
H HO
H HO
H HO
H HO
H HO
H HO
Solute Pool (with exchangeable proton)
Water Pool
Chemical Exchange
H
CMROICMROI Slide Slide 2525
Chemical exchange and T1ρ
GABA amine protonsExchange rate ~1.5kHz
CMROICMROI Slide Slide 2626
Readout
Readout
Quantify spin-exchange from T1ρ MRI
CMROICMROI Slide Slide 2727
GABA: Exchange of Amine protons and T1ρ
GABA
CMROICMROI Slide Slide 2828
GABA CEST and T1ρ
~18%
~36%
CMROICMROI Slide Slide 2929
Spin exchange in cartilage and T1ρ
CMROICMROI Slide Slide 3030
Aggrecan and Proteoglycans
G1 G3G2
G1 G3G2
Chondroitin sulfaterich sections
Keratan sulfaterich sections
HACore protein Glycosaminoglycans (GAG)
O
O
O
COO-
CH2OSO3 -
OH
OH
NHCOCH3
O
HOFixed Negative Charge (FCD)
CMROICMROI Slide Slide 3131
Chondroitin SulfatesH H
O
H HO
H H
O
H H
OH H
O
CMROICMROI Slide Slide 3232
CS phantom images
Regatte et al, JMRI, 17(2003)
CMROICMROI Slide Slide 3333
T1ρ Maps of Cartilage Specimen
SubchondralBone
Articular Surface
256 ms
0ms
Normal
Enzymatically Degraded
Akella et al, MRM,46(2004)
CMROICMROI Slide Slide 3434
T1r 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 Tρ relaxation map of the patellar cartilage. The color scale shows a volume rendered representation of Tρ relaxation times.
CMROICMROI Slide Slide 3535
T1ρ and dipolar interaction
A
B
Bo
θ
r
CMROICMROI Slide Slide 3636
Static dipolar interaction
During spin-lock
ωD
Spins with no D-D interactionWithout spin-lock
CMROICMROI Slide Slide 3737
Dipolar interaction
H= A(1-3 cos2θ)[3Iz2-I(I+1)]
‘θ’ 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
B0
CMROICMROI Slide Slide 3838
Superficial
Middle
Radial
Calcified
Arrangement of collagen in cartilage
CMROICMROI Slide Slide 3939
Effect of RDI on MRI of cartilage
Signal is insensitive to small changes in PG
Produces “laminar” appearance Difficult to interpret image
contrast and maps
How do we reduce its effect?
T2
CMROICMROI Slide Slide 4040
250 Hz 500 Hz 1 KHz 2 KHzT2
B0Akella et al, MRM,46(2004)
Parallel to B0 - Images
CMROICMROI Slide Slide 4141
T2 = 32 ms
T2250 Hz 500 Hz 1 KHz 2 KHz
Tρ = 62 Tρ = 76 Tρ= 86 Tρ = 109
Effect of spin-lock pulse on RDI
CMROICMROI Slide Slide 4242
T2
T2
Pixel Number
0 5 10 15 20 25 30 35
T1ρ-2 kHz
T1ρ-500
T1ρ-250
Articular surface
Bone
250 Hz
500 Hz
2 KHz
Profile plots (|| to B0)
CMROICMROI Slide Slide 4343
Profile plots (magic angle)
T2
Articular surface
Bone
T1ρ-2 kHz
T ρ-500Hz
Pixel number
0 5 10 15 20 25 30 35
CMROICMROI Slide Slide 4444
Akella et al, MRM,46(2004)
T1ρ dispersion
parallel
54.7o
CMROICMROI Slide Slide 4545
T2 weighted image T1ρ weighted image (500Hz)
1/Tρ = (1/Tρ )ex+ (1/Tρ )rot + (1/Tρ )RDI+..
Reducing laminar appearance
CMROICMROI Slide Slide 4646
T1rho scale bar in ms
Sodium scale bar in mM
Healthy 26 yo male Symptomatic 24 yo male
Tρ map Sodium map Tρ map Sodium map
T1ρ and Sodium MRI of Inter-vertebral Disc
CMROICMROI Slide Slide 4747
T1ρ dispersion in Myocardial Infarct
Proton Dipole-Dipole Coupling in CollagenProton Dipole-Dipole Coupling in Collagen
Field ArtifactsField Artifacts
Chemical Exchange On/Off Amide and HydroxylChemical Exchange On/Off Amide and Hydroxyl
Molecular Rotation of Water ProtonsMolecular Rotation of Water Protons
ν1 = 2 kHzν1 = 0 Hz
CMROICMROI Slide Slide 4848
B1-dependent relaxation times
20B1 (kHz)
T2-weighted
T1ρ-weighted
1
infarction scar
CMROICMROI Slide Slide 4949
T1ρ Dispersion
CMROICMROI Slide Slide 5050
T1ρ dispersion and Tumor
A and B: T2 and T1ρ weighted
C and D: T2 and T1ρ maps
Comparison of the T2 and T1ρ relaxation time constants (in ms) between MDA-MB-468 (N=2, open symbols and dashed lines) and more metastatic MDA-MB-231 tumors (N=3, solid symbols and solid lines).
CMROICMROI Slide Slide 5151
T1ρ pulse sequence developments
Original: T1ρ pulse cluster pre-encoded to a 2D single slice readout
3D SLIPS sequence: Enables 3D T1ρ map in <10 minutes
Addressed issues of Bo and B1 inhomogeneity
SL-SSFP: new pulse sequence with reduced SAR for T1ρ MRI @ 7T
CMROICMROI Slide Slide 5252
T1ρ Imaging- Pulse Sequence
FREQ
PHASE
SLICE
1H RFSLP
TSL
(π/2)x (π/2)-x
TSL
(π/2)x (π/2)-x
CMROICMROI Slide Slide 5353
SLIPS pulse sequence
Enables Rapid TT11ρρ mapping
3D TT11ρρ mapping (30 slices) in about 10 min
Newer version ----> ~5 min
CMROICMROI Slide Slide 5454
B1 and ΔBo insensitive spin-lock cluster
Witchey et al, JMR 186 (2007)
CMROICMROI Slide Slide 5555
SL-SSFP pulse sequence
Witschey et al, MRM, 2009
CMROICMROI Slide Slide 5656
T1ρ Characteristics
Sensitive to processes at or around the time scale ~ 1/ω1.
Low frequency (Hz-kHz) molecular motions can be probed at high Bo.
Applying spin-lock pulse: Reduces B0 inhomogeneities, susceptibility and
diffusion-related signal loss Increases dynamic range of MRI signal Ability to measure and minimize
▪ spin-exchange▪ exchange dependent pH changes
▪ dipolar coupling effects sensitive to small changes in macromolecular content
CMROICMROI Slide Slide 5757
Acknowledgements Ari 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
H. Ralph Schumacher J. Bruce Kneeland Jess H. Lonner Jesse Khurana Jay Udupa
Work was supported by NIH grants: R01-AR045242 (RR)R01-AR045404 (RR)R01-AR051041 (RR)RR02305 (RR)
Arthritis Foundation (RR)Wyeth Research (RR)OA Spine (AB)
• Hari Haran• Mark Elliott
CMROICMROI Slide Slide 5858
Thanks for your patience
Thank you!