Principles of MRI Physics and Engineering

Allen W. Song Brain Imaging and Analysis Center Duke University

Part III.1

Some fundamental acquisition methods And their k-space view

k-Space Recap

Equations that govern k-space trajectory:

Kx =

g

/2

p  0 t

Ky =

g

/2

p  0 t

Gx(t) dt Gx(t) dt

S

(

k x

,

k y

)   

I

(

x

,

y

)

e



i

2 p (

k x x



k y y

)

dxdy

These equations mean that the k-space coordinates are determined by the area under the gradient waveform

S(1,1) S(1,2)

A 2x2 Matrix

S

(

t

) 

I

( 1 , 1 )

e



i

g

B

11

t



I

( 1 , 2 )

e



i

g

B

12

t



I

( 2 , 1 )

e



i

g

B

21

t



I

( 2 , 2 )

e



i

g

B

22

t

Image Space I(1,1) I(1,2) k-Space (data space) S(1,1) S(1,2) I(2,1) I(2,2)

S(2,1) S(2,2)

S(2,1) S(2,2)

S

( 1 , 1 )  (

I

( 1 , 1 )

e



i

2 p (

k x

1

x

1 

k y

1

y

1 ) 

I

( 1 , 2 )

e



i

2 p (

k x

1

x

1 

k y

1

y

2 ) 

I

( 2 , 1 )

e



i

2 p (

k x

1

x

2 

k y

1

y

1 ) 

I

( 2 , 2 )

e



i

2 p (

k x

1

x

2 

k y

1

y

2 ) )

e

 g

B o t

Gradient Echo Imaging  Signal is generated by magnetic field refocusing mechanism only (the use of negative and positive gradient)  It reflects the uniformity of the magnetic field  Signal intensity is governed by

S = So e -TE/T2*

where

TE

is the echo time (time from excitation to the center of k-space)  Can be used to measure T2* value of the tissue

MRI Pulse Sequence for Gradient Echo Imaging Excitation Slice Selection Frequency Encoding Phase Encoding Readout digitizer on

K-space view of the gradient echo imaging Ky .

.

n 1 2 .

3 .

.

.

.

Kx

Spin Echo Imaging  Signal is generated by radiofrequency pulse refocusing mechanism (the use of 180 o pulse )  It doesn’t reflect the uniformity of the magnetic field  Signal intensity is governed by

S = So e -TE/T2

where

TE

is the echo time (time from excitation to the center of k-space)  Can be used to measure T2 value of the tissue

MRI Pulse Sequence for Spin Echo Imaging 180 90 Excitation Slice Selection Frequency Encoding Phase Encoding digitizer on Readout

K-space view of the spin echo imaging Ky .

.

n 1 2 .

3 .

.

.

.

Kx

Inversion Recovery Imaging

S o Time History of MR Signal

S = S o * (1 – 2 e –t/T1 ) S = S o * (1 – 2 e –t/T1’ )

-S o

Pulse Sequence for Inversion Recovery RF 180 o GRE or SE Readout Gz

Part III.2

Image Contrast Mechanisms

 The Concept of Contrast (or Weighting)

Contrast

because T1 = difference in RF signals — emitted by water  protons — between different tissues T1 weighted example: gray-white contrast is possible is different between these two types of tissue

MR Signal T2 Decay

50 ms

MR Signal T1 Recovery

1 s

Proton Density Contrast     Technique: use very long time between RF shots (large

TR

) and very short delay between excitation and readout window (short

TE

) Useful for anatomical reference scans Several minutes to acquire 256 ~1 mm resolution  256  128 volume

MR Signal

Proton Density Contrast

MR Signal T2 Decay

50 ms

T1 Recovery

1 s

Proton Density Weighted Image

T2* and T2 Contrast  Technique: use large

TR

and intermediate

TE

 Useful for anatomical and functional studies  Several minutes for 256x256X128 volumes, or ~several seconds to acquire 64  64  20 volume  1mm resolution for anatomical scans or 4 mm resolution [better is possible with better gradient system, and a little longer time per volume]

MR Signal

T2* and T2 Contrast

MR Signal T2 Decay

50 ms

T1 Recovery

1 s

T2 Weighted Image

T1 Contrast     Technique: use intermediate timing between RF shots (intermediate

TR

) and very short

TE

, also use large flip angles Useful for anatomical reference scans Several minutes to acquire 256 ~1 mm resolution  256  128 volume

MR Signal T2 Decay

T1 Contrast

MR Signal

50 ms

T1 Recovery

1 s

T1 Weighted Image

Inversion Recovery for Extra T1 Contrast S o

S = S o * (1 – 2 e –t/T1 ) S = S o * (1 – 2 e –t/T1’ )

-S o

T2 Inversion Recovery (CSF Attenuated)

In summary, TR controls T1 weighting and TE controls T2 weighting. Short T2 tissues are dark on T2 images, but short T1 tissues are bright on T1 images.

Other Imaging Methods  Can “prepare” magnetization to make readout signal sensitive to different physical properties of tissue      Flow weighting (bulk movement of blood) Diffusion weighting (scalar or tensor) Perfusion weighting (blood flow into capillaries) Magnetization transfer (sensitive to proteins in voxel) Temperature

MR Angiogram

•Time-of-Flight Contrast •Phase Contrast

Time-of-Flight Contrast

Saturation Vessel Excitation No Flow Acquisition No Signal Medium Flow Medium Signal High Flow High Signal Vessel Vessel

Pulse Sequence: Time-of-Flight Contrast

90 o RF Excitation Gx Time to allow fresh flow enter the slice 90 o Saturation Gy Image Acquisition Gz

Phase Contrast (Velocity Encoding)    0

T

g

G

(

x



vt

)

dt

 g

GvT

2  

T

2

T

g

G

(

x



vt

)

dt

Blood Flow

v

Externally Applied Spatial Gradient

G

0 T Externally Applied Spatial Gradient -

G

2T Time

Pulse Sequence: Phase Contrast

90 o RF Excitation

G

Gx Gy

-

G

Phase Image Acquisition Gz

MR Angiogram

Diffusion Weighted Imaging Sequences

l

 2

Dt S



S o e

 2 3

D

 g 2

G

2

T

3 Externally Applied Spatial Gradient

G

0 T Externally Applied Spatial Gradient -

G

2T Time

Pulse Sequence: Gradient-Echo Diffusion Weighting

RF Excitation 90 o

G

Gx

-

G

Gy Gz Image Acquisition

Pulse Sequence: Spin-Echo Diffusion Weighting

180 o 90 o RF Excitation

G

Gx Gy Gz

G

Image Acquisition

Advantages of DWI 1. The absolute magnitude of the diffusion coefficient can help determine proton pools with different mobility 2. The diffusion direction can indicate fiber tracks

Diffusion Anisotropy

Determination of fMRI Using the Directionality of Diffusion Tensor

Display of Diffusion Tensor Using Ellipsoids

Diffusion Contrast

Perfusion/Flow Weighted Arterial Spin Labeling Coil Tagging Imaging Plane Transmission

Perfusion/Flow Weighted Arterial Spin Labeling with Pulse Sequences Pulse Tagging Imaging Plane Alternating Inversion Alternating Inversion FAIR Flow-sensitive Alternating IR EPISTAR EPI Signal Targeting with Alternating Radiofrequency

Pulse Sequence: Perfusion Imaging 180 o

RF Gx Gy Gz

Odd Scan 180 o Alternating opposite Distal Inversion Even Scan

RF Gx Gy

Alternating Proximal Inversion

Gz

Odd Scan Even Scan

90 o

90 o

180 o

180 o

Image Image

Advantages of ASL Perfusion Imaging 1. It can non-invasively image and quantify blood delivery 2. Combined with proper diffusion weighting, it can assess capillary perfusion

Perfusion Contrast

Diffusion and Perfusion Contrast Diffusion Perfusion

Other Interesting Types of Contrast   Perfusion weighting: sensitive to capillary flow  Diffusion weighting: sensitive to diffusivity of H 2 O Very useful in detecting stroke damage  Directional sensitivity can be used to map white matter tracts   Also useful in functional MRI to determine the signal origin Flow weighting: used to image blood vessels (MR angiography)  Magnetization transfer: provides indirect information about H nuclei that aren’t in H 2 O (mostly proteins)

Part III.3

Introduction to Fast Imaging

Very useful techniques for fMRI, Diffusion, Perfusion, etc. when brain functions are being investigated

Fast Imaging

How fast is “fast imaging”?

In principle, any technique that can generate an entire image with sub-second temporal resolution can be called fast imaging.

For fMRI, we need to have temporal resolution on the order of a few tens of

ms

to be considered “fast”. Echo-planar imaging, spiral imaging can be both achieve such speed.

Echo Planar Imaging (EPI)  Methods shown earlier take multiple RF shots to readout enough data to reconstruct a single image   Each RF shot gets data with one value of phase encoding If gradient system (power supplies and gradient coil) are good enough, can read out all data required for one image after one RF shot   Total time signal is available is about 2  T2* [80 ms] Must make gradients sweep back and forth, doing all  frequency and phase encoding steps in quick succession Can acquire 10-20 low resolution 2D images per second

GE-EPI Pulse Sequence Actually have 64 (or more) freq. encodes in one readout (each one

<

1 ms) [only 13 freq.

encodes shown here]

K-space view of the echo-planar imaging Ky

…..

Kx

Why EPI?

  Allows highest speed for dynamic contrast Highly sensitive to the susceptibility-induced field changes --- important for fMRI  Efficient and regular k-space coverage and good signal-to-noise ratio  Applicable to most gradient hardware

RF Gx Gy Gz t = 0 Spiral Imaging t = TE

K

-Space Representation of Spiral Image Acquisition

Why Spiral?

• More efficient

k

-space trajectory to improve throughput.

• Better immunity to flow artifacts (no gradient at the center of k-space) • Allows more room for magnetization preparation, such as diffusion weighting.

Under very homogeneous magnetic field, images look good …

Gradient-Recalled EPI Images Under Homogeneous Field

Gradient Recalled Spiral Images Under Homogeneous Field

However, if we don’t have a homogeneous field … (That is why shimming is VERY important in fast imaging)

Magnetic Field Inhomogeneity Introduced by

x

-Shim Coil

Distorted EPI Images with Imperfect

x

-Shim

Distorted Spiral Images with Imperfect

x

-Shim

Magnetic Field Inhomogeneity Introduced by

y

-Shim Coil

Distorted EPI Images with Imperfect

y

-Shim

Distorted Spiral Images with Imperfect

y

-Shim

Magnetic Field Inhomogeneity Introduced by

z

-Shim Coil

Distorted EPI Images with Imperfect

z

-Shim

Distorted Spiral Images with Imperfect

z

-Shim