Advanced MRI: Diffusion MRI 1: DTI and k-space

Transcription

1 k y Advanced MRI: Diffusion MRI 1: DTI and k-space k X Eric Sigmund, PhD February 26th, 2013 LECTURE 1

2 Neuro Diffusion MRI 3-5 m White matter axons Body 15 m Renal medulla Musculoskeletal 50 m Skeletal muscle

3 Diffusion MRI Components EPI TSE BURST GRASE BLADE Linescan Spiral Radial SSFP DTI RPBM IVIM DKI Tractography WMM LECTURE 1 2/26/2013

4 Diffusion MRI Components 1. Diffusion Contrast a. Fundamentals 2. Diffusion Imaging a. Single shot sequences b. Gaussian diffusion b. Multi-shot sequences c. Diffusion tensor imaging c. Other sequences LECTURE 1 2/26/2013

5 1. MR DIFFUSION CONTRAST

6 Brownian Motion Robert Brown First discovered 1828 (Brown) Random motion of molecules in liquid or gas Controlled by : Molecular size / weight Intermolecular forces (viscosity) Temperature Structure of confining medium Fat globules in diluted milk LECTURE 1

7 What is Diffusion? Mean-squared displacement 2 x 2Dt Albert Einstein Displacements Histogram Gaussian Diffusion 11/8/11 7

8 Propagator P t P( x, t) Diffusion Theory P(x,t) = probability of displacement x in time t Free Diffusion equation 2 P D 2 x Solution : Gaussian function 1 4Dt exp 2 x 4Dt Mean-squared displacement 2 2 x x Px, tdx2dt Average diffusion length l D 2Dt LECTURE 1 Albert Einstein Gaussian Diffusion

9 MR DIFFUSION

10 MR Diffusion Weighting Precession in field gradient: H h Gx Spatial dispersion: x 2 2Dt Phase dispersion: GDt M / M b-value b Magnetization: M t M 0 e i exp e bd 2 2

11 Erwin Hahn Stimulated echo measurement Variable encoding time Static gradient (inhomogeneous magnet) D = 2 m 2 /ms G = 9 mt/m First MR diffusion measurement LECTURE 1

12 Hermann Carr Carr-Purcell (CP) Ed Purcell

13 Carr-Purcell-Meiboom-Gill (CPMG) TSE, RARE, FSE, Method for suppressing diffusion effects

14 Ed Stejskal Pulsed Field Gradients(PFG) Controlled diffusion weighting

15 Stejskal Tanner PFG Sequence RF. G 90 x 180 y time Encoding length Diffusion length G 1 1 q ld 2D Signal l D Balanced diffusion gradients Diffusionincomplete refocusing Signal attenuation and l D can be independently varied to explore tissue (from Callaghan, p. 163)

16 Clinical MRI pulse sequences Twice-refocused spin echo, bipolar gradients Echo-planar Imaging (EPI) Turbo spin echo (TSE)

17 Animal MRI Clinical MRI MR Gradients PFG Fringe field Gradients MRFM G (T / m) LECTURE 1

18 i TE What is the b-value? Short pulse approximation t dt g t r t dt Spin phase 0 0 Gz 1 Gz G z G 2D b 2D G q b ST G q 2 z /3 TE Phase dispersion b-value Exact b-value

19 GENERAL B-VALUE CALCULATION For gaussian diffusion, can find closed form TE 2 TE t eff 0 0 b G t dt dt k t dt Geff t : effective gradient (including RF inversions) Similarly, can calculate net phase shift due to constant velocity motion (e.g. flow) for any waveform TE TE f v f tg t dt k t dt eff 0 0

20 Sodickson A, Prog. NMR Spec. 33, (1998) GRE, SE, STE sequences Equal diffusion weighting And flow encoding Balanced, flow-compensated gradient waveforms Different diffusion weighting

21 PROFILING He3 gas, G = 3 mt/m, D ~ 0.16 cm 2 / s Glycerol, G = 42 T/m, D ~ 2 x 10-8 cm 2 / s CaF 2, G = 2000 T/m D ~ 6 x cm 2 / s Spin Diffusion Dimitrov I, MRI 17, ,1999 Meier B, Proc. ENC 2008 Sigmund E, JMR 163,99-104, 2003.

22 WATER MOTION IN BIOLOGICAL TISSUE Cellular structures Blood vessels Apparent diffusion / flow characteristics are markers of water environment static cellular structures (axons, membranes, myelin) dynamic physiology (flow, pumps, perfusion)

23 Apparent Diffusion Coefficient (ADC) In tissue, water experiences many barriers to diffusion Cell membranes Nerve / muscle fibers Fibrosis Cancer cells Effective diffusion coefficient is reduced due to the smaller displacements Gas Diffusion in bead pack Apparent diffusion coefficient (ADC) Mair RW et. al. JMR 156, (2002) Restricted Diffusion 23

24 DIFFUSION TENSOR IMAGING

25 Peter Basser Michael Moseley Denis LeBihan

26 BRAIN TISSUE TYPES Gray matter : Isotropic cell mixture White matter : Anisotropic, myelinated axons

27 ANISOTROPIC DIFFUSION Isotropic e.g. CSF; no restriction on scale of diffusion length ~10 m Mean-square Displacement Sphere Anisotropic White matter: Diffusion perpendicular to fibers restricted Diffusion becomes Local probe of structure Ellipsoid

28 3D ANISOTROPIC GAUSSIAN DIFFUSION P( x, t) 3/ 2 1/ 2 t T 1 4 D exp x D x / 4t where D is the diffusion tensor D D D D xx xy xz D D D xy yy yz D D D xz yz zz with 6 independent components

29 Diffusion Tensor Imaging (DTI) Isotropic: Anisotropic: ln M M M 0 bd 3 ln bd ij ij M 0 i, j1 Diffusion coefficient Diffusion Tensor Measure apparent diffusion coefficent (ADC) along different gradient directions (>6) Solve linear set of equations for diffusion tensor elements (lab frame) Dxx Dxy Dxz D = Dxy Dyy Dyz Dxz Dyz Dzz (principal frame) 0 0 D= Diffusion coefficients and orientations e i

30 Linear set of equations (N>6) s ln ln ln M M M M M M Diffusion Tensor processing N ij M bd ij ij ln Ad s M 0 b b b 2b 2b 2b b b b 2b 2b 2b A b b b 2b 2b 2b xx yy zz xy yz xz xx yy zz xy yz xz xx yy zz xy yz xz N N N N N N Signals Encoding matrix ij i j 0 i TE b k t k t dt t 0 k t g t dt i d D D D D D D xx yy zz xy yz xz Tensor elements LECTURE 1

31 b=0 DIFFUSION WEIGHTED IMAGES 3 T 3 b-values, 6 directions b=500 s/mm 2 [101] [-101] [011] [01-1] [110] [1-10] b=1000 s/mm 2 Regional variationsfiber orientations

32 7 T DTI dataset Principal diffusion Eigenvectors

33 ROTATIONAL INVARIANTS Eigenvalues :,, Tr( D) D D D D Mean diffusivity Tr( D) / 3 i D 3 FA Fractional anisotropy = 2 2 i FA = 0, for isotropic diffusion FA = 1, for maximally anisotropic diffusion

34 Color-coded Diffusion Anisotropy Image S. Pajevic, C. Pierpaoli MRM 42: (1999) Method for coloring white matter allows fiber structure differentiation (x,y,z) components of principal diffusion eigenvector (R,G,B) image components Weighting function : Fractional anisotropy (FA) External capsule Internal capsule Corticospinal tract Corpus callosum S-I Arcuate fibers Optic radiation L-R A-P

35 3 T

36 FA 3 T

37 3 T

38 (e.g. Basser et. al. MRM 44: (2000)) DTI Fiber Tracking Use primary diffusion eigenvector to guide tracking Numerical integration continuous paths Path terminations: Region of low anisotropy Unrealistic trajectory jump In vivo Tractography

39 TRACTOGRAPHY Use regions of white matter as seeds Test connectivity, e.g. from functional activation areas Can produce noninvasive maps of neural connections throughout the brain Basser P, et al. In vivo tractography using DT-MRI data. MRM 44:p.625, 2000.

40 Normal LECTURE 1 Disrupted

41 SUMMARY : PART I Applied field gradients allow sensitivity to random Brownian motion in tissue Diffusion tensor imaging (DTI) 3D Gaussian diffusion model Scalar metrics : MD, FA, Fiber tractography : morphology, connectivity

42 2. DIFFUSION IMAGING

43 DIFFUSION GRADIENT EFFECTS S dvpvexp if vexpbd 1 1if vdvp v dvp v f v exp bd 2 1 exp 1 exp expif v f v v bd if v d vp v f v bd t k t G t dt f 0 0 TE 2 b k t dt Formulas 0 TE eff k t dt Flow Flow phase attenuation PC-MRA IVIM (Angiography) DW-fMRI Motion, Pulsation, Respiration Diffusion attenuation DWI / DTI Contrast Artifact

44 DIFFUSION SEQUENCES Single shot Multishot EPI TSE BURST GRASE BLADE Spiral Linescan Motion sensitivity Blurring Radial SSFP Motion sensitivity

45 K-SPACE ARTIFACTS K-space can be filled in many ways, but all segments should be as consistent as possible Amplitude errors Long echo trains relaxation decay (T2, T2*, ) High spatial frequencies attenuated Image blurring k y Phase errors k X Respiration, pulsation, susceptibility additional phase Disruption of k-space pattern Image ghosting / distortion

46 One preparation, one readout All signals have equivalent motional state phase consistency Magnetization modulation (T2, T2*) blurring SINGLE SHOT DWI k y k X DW prep. Signals

47 DWI PULSE SEQUENCE Twice-refocused spin echo Preparation, Echo-planar Imaging (EPI) readout PROS Single shot Fast Insensitive to bulk motion CONS B0 artifacts Distortions / dropouts Image Blurring Eddy current distortions Large diffusion gradients Table vibrations k y EPI k X 1/18/2012 BEST-IN-PRACTICE MRI SYMPOSIUM

48 ECHO-PLANAR IMAGING (EPI) Standard EPI artifacts T2* blurring N/2 ghost (eddy currents) Susceptibility 3 T DW-EPI artifacts Directional eddy-current distortions

49 No GRAPPA GRAPPA = 2 Parallel Imaging EPI Distortion Reduction 7 T GRAPPA = 3, PE P-A GRAPPA = 3 GRAPPA = 4

50 FIELD MAP EPI DEWARPING GRE Field map Magnitude DTI EPI-DWI, b = 1000 s/mm 2 7 T Phase

51 TURBO SPIN ECHO (TSE) (AKA FSE, RARE), Multiple spin echo sequence High SNR No susceptibility artifact Good image quality Segmented or single shot Flip angle RF Gs Gp Gr Signal Diffusion Preparation

52 T2 BLURRING Single line Multi-line (e.g. TSE) Single shot k y k y k y k x k x k x Speed Sharpness

53 TSE-DTI, 3 T LECTURE 1

54 TSE-DTI, 3 T Deblurred

55 TSE-DWI IN THE LUNG, 3 T T1 Flash MRI TSE DWI

56 TSE-DWI IN THE BREAST Sigmund EE, MRM 2011

57 DW-TSE DIFFICULTIES (1) CPMG condition violation 90x-180y condition assumes initial phase is 0 Diffusion weighting encodes spatially variable phase Two signal types ( parities ) generated CPMG component non-cpmg component (2) Imperfect refocusing pulses Generate more stimulated echoes Prevent phase correction of non-cpmg component Image artifacts

58 3 T INTERFERENCE PATTERNS b=0 b=600 s/mm 2

59 CPMG Even parity Non-CPMG Odd parity Schick F, MRM 38: (1997)

60 DW-TSE ECHO PARITY SOLUTIONS Isolate one parity with displacement gradients ( Phase insensitive ) Norris DG, MRM 27: (1992). Separate and measure both parities ( SPLICE ) Alternate acquired parity to optimize signal ( Selective parity ) Schick F, MRM 38: (1997). Norris DG, MRM 58: (2007). Modulate RF phase to stabilize both parities ( non-cpmg FSE ) LeRoux P, JMR 155, (2002).

61 SPLICE (SPLIt acquisition fast spin Echo) Schick F, MRM 38: (1997) Extend readout period, detect both echo parities separately Combine magnitude images Avoids interference artifacts Lengthens echo train higher T2 blurring

62 SPLIT-ECHO IMAGES b=0 b=500 s/mm 2 Schick F, MRM 38: (1997) b=0 b=400 s/mm 2 Williams C, MRM 41: (1999)

63 ABDOMINAL SPLICE DWI Deng J, MRM 59, (2008). Nonuniform striping artifact in single echo PROPELLER SPLICE technique Produces robust Image quality

64 NON-CPMG FSE Adjust refocusing RF phases to stabilize both echo parities Quadratic phase modulation found to be optimal non-cpmg FSE DTI MD FA Bastin ME, MRM 48, 6-14 (2002). LeRoux P, JMR 155, (2002).

65 LINE SCAN DIFFUSION IMAGING(LSDI) Gudbjartsson H, MRM 36: (1996). b=0 b=500 s/mm 2 Kubicki M, Acad. Rad. 11: (2004) EPI LSDI

66 Line Scan Diffusion Imaging Sequence José Raya

67 How Line Scan works Image Plane

68 How Line Scan works 90º Excitation pulse Image Plane

69 How Line Scan works 180º Refocusing pulse 90º Excitation pulse Image Plane Echo Echo occurs in just one line in the image

70 How Line Scan works 90º Excitation pulse Image Plane Separation to avoid overlap between lines

71 How Line Scan works Undesired echo! Image Plane 180º Refocusing pulse

72 How Line Scan works Spins do not refocus! Image Plane b value = 0 s/mm2 b value = 500 s/mm2 Echo suppression: Alternate the diffusion gradients in both excitations, so that the diffusion gradients dephase secondary echoes

73 AFTER MEASUREMENT IMAGES MUST BE RECOMBINED RECOMBINED MEASURED

74 APPLICATION: DTI OF THE ARTICULAR CARTILAGE

75 APPLICATION: DTI OF THE ARTICULAR CARTILAGE Raya J, Radiology 2012

76 Stimulated Echo -BURST Merboldt KD, MRM 23(1): (1992). 1 scan 8 avgs. Single shot technique ; minimal motion artifact Small angle detection pulses progressively deplete signal a-blurring along phase encode direction Mixing time can be made very long for high b-values

77 DIFFUSION SEQUENCES Single shot Multishot EPI TSE BURST GRASE BLADE Spiral Linescan Motion sensitivity Blurring Radial SSFP Motion sensitivity

78 DW prep. Signals SEGMENTED DWI k y k X Shot 1, echo 1 Shot 2, echo 1 Shot 3, echo 1 Shot 4, echo 1 Shot 5, echo 1 Shot 1, echo 2 Shot 2, echo 2 Shot 3, echo 2 Shot 4, echo 2 Shot 5, echo 2 Shot 1, echo 3 Shot 2, echo 3 Shot 3, echo 3 Shot 4, echo 3 Shot 5, echo 3

79 Multi-Shot DWI Motion Ghosting b = 0 Diffusion-weighted

80 MOTION Rigid body motion Translation Rotation Miller K, MRM 50 : (2003). Inhomogeneous Pulsatile Respiratory

81 Prospective Acquisition CorrEction (PACE) Free-breathing 2D PACE MRCP 2D PACE navigator on the diaphragm Patient s breathing motion Acquisition-based motion correction k-space segments all collected in the same position

82 FLOW-COMPENSATED DWI Rat abdominal DWI In vivo cardiac DTI Johnson GA, Invest. Rad. 26: (1991) Gamper U, MRM 57: (2007)

83 DIFFUSION WEIGHTED STEADY-STATE FREE PRECESSION (DW-SSFP) TR SSFP pulse sequence w/ long TE ( pre-pulse ) detection Diffusion gradients inserted in every cycle Steady-state magnetization carries diffusion weighting 2 b G TR

84 DW-SSFP QUANTITATION Steady-state equation Nonlinear Multiparametric Wu E, JMR 90, (1990) Solution: a 2 b G TR STE term SE term Approximate weighting Need T1, T2, flip angle (a) to extract ADC

85 SSFP MOTION CORRECTION Diffusion gradient in each TR phase errors Cardiac gating compromises efficiency Navigator echoes / images 2D navigators found useful in capturing inhomogeneous motion Can be incorporated into Complex reconstructions (SENSE, conjugate gradient, ) Miller K, MRM 50 : (2003).

86 SSFP-DTI DTI processing very sensitive to motional ghosting Navigation and reconstruction algorithm are crucial to results Miller K, MRM 50 : (2003).

87 SSFP-DTI EXAMPLES McNab J, Neuroimage 2009 Ex vivo imaging Jung Y, JMRI 2009 Radial SSFP w/ motion correction LECTURE 1

88 NON-CARTESIAN DTI Radial / spiral sequences sample k-space center often self-navigated trajectory Allows multishot DWI better quality Complex reconstruction procedures (regridding, sampling density, filtering ) PROPELLER SNAILS

89 BLADE TRAJECTORY Turbo-spin echo (TSE) variant with radially oriented k-space lines Each blade passes through center of k-space Any observed phase shift can be nulled prior to reconstruction ( Self-navigation ) Post-processing correction K-space center ( = 0 with no motion) Reconstruction can require oversampling

90 TurboPROP-DTI Arfanakis K, An. NYAS 1064:78-87(2005) SNAILS-DTI Liu C, MRM 54: (2005) b=800 s/mm 2

91 COMPRESSED SENSING DTI

92 SUMMARY : PART II Numerous pulse sequences available for diffusion imaging Tradeoff between bulk motion sensitivity and image blurring Single shot sequences Echo-planar imaging (EPI) Turbo Spin Echo (TSE) Segmented / navigated sequences SSFP SNAILS / PROPELLER Other sequences Line scan BURST

93 FINAL SUMMARY Diffusion contrast offers sensitivity to microscopic structure, averaged on macrocsopic scale Proper pulse sequences must be employed that are compatible with diffusion weighting Quantitative interpretation in each tissue of interest is usually informed by some prior knowledge of the tissue constituents

94 The advancement and diffusion of knowledge (and knowledge of diffusion) is the only guardian of true liberty. --James Madison

95 REFERENCES MRI : Physical Principles and Sequence Design (Haacke) Chapter 21 Principles of Nuclear Magnetic Resonance Microscopy (Callaghan) Chapters 3.7,6,7,8 Handbook of MRI Pulse Sequences (Bernstein, King, Zhou) Chapters 9.1, 17.2 Paper references given in text Thanks to M.Law, J. Jensen, G. Johnson, J. Raya for slides