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Page 1: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

Ravinder Reddy, PhDProfessor of Radiology & Director of CMROI,

Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia,

PA

Page 2: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 22

Outline

Page 3: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 4: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 44

T1 and T2

o

60 MHz

Page 5: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 6: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 7: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 8: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 9: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 10: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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.

Page 11: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 12: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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()

Page 13: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 1313

Rotational Motion

Page 14: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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}

Page 15: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 16: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 17: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 1717

What is T1ρ?

1~kHz

o

60 MHz

Z

YX

Page 18: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 19: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 20: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 21: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 22: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 23: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 2323

T1ρ and chemical exchange

Page 24: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 25: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 2525

Chemical exchange and T1ρ

GABA amine protonsExchange rate ~1.5kHz

Page 26: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 2626

Readout

Readout

Quantify spin-exchange from T1ρ MRI

Page 27: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 2727

GABA: Exchange of Amine protons and T1ρ

GABA

Page 28: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 2828

GABA CEST and T1ρ

~18%

~36%

Page 29: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 2929

Spin exchange in cartilage and T1ρ

Page 30: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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)

Page 31: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 3131

Chondroitin SulfatesH H

O

H HO

H H

O

H H

OH H

O

Page 32: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 3232

CS phantom images

Regatte et al, JMRI, 17(2003)

Page 33: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 3333

T1ρ Maps of Cartilage Specimen

SubchondralBone

Articular Surface

256 ms

0ms

Normal

Enzymatically Degraded

Akella et al, MRM,46(2004)

Page 34: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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.

Page 35: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 3535

T1ρ and dipolar interaction

A

B

Bo

θ

r

Page 36: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 3636

Static dipolar interaction

During spin-lock

ωD

Spins with no D-D interactionWithout spin-lock

Page 37: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 38: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 3838

Superficial

Middle

Radial

Calcified

Arrangement of collagen in cartilage

Page 39: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 40: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 4040

250 Hz 500 Hz 1 KHz 2 KHzT2

B0Akella et al, MRM,46(2004)

Parallel to B0 - Images

Page 41: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 42: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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)

Page 43: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 44: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 4444

Akella et al, MRM,46(2004)

T1ρ dispersion

parallel

54.7o

Page 45: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 46: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 47: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 48: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 4848

B1-dependent relaxation times

20B1 (kHz)

T2-weighted

T1ρ-weighted

1

infarction scar

Page 49: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 4949

T1ρ Dispersion

Page 50: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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).

Page 51: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 52: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 53: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 5353

SLIPS pulse sequence

Enables Rapid TT11ρρ mapping

3D TT11ρρ mapping (30 slices) in about 10 min

Newer version ----> ~5 min

Page 54: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 5454

B1 and ΔBo insensitive spin-lock cluster

Witchey et al, JMR 186 (2007)

Page 55: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 5555

SL-SSFP pulse sequence

Witschey et al, MRM, 2009

Page 56: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 57: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

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

Page 58: Ravinder Reddy, PhD Professor of Radiology & Director of CMROI, Department of Radiology, University of Pennsylvania School of Medicine, Philadelphia, PA.

CMROICMROI Slide Slide 5858

Thanks for your patience

Thank you!