“genteel” introduction to mri physics - ii: k-space ... · “genteel” introduction to mri...

“Genteel” Introduction to MRI Physics - II: k-space, timing, and

contrasts

Rudolph Pienaar, M.Eng, D.EngAssistant in Medical Imaging

Dept of Radiology Massachusetts General Hospital

Boston MA, USA

Magnetic Resonance Imaging:Deconstructing Timing Diagrams

Andrew J. M. Kiruluta, Ph.D.Dept of Radiology, MGH,

Dept of Physics, Harvard UniversityBoston MA, USA

“Throw physic to the dogs; I’ll none of it.”Shakespeare, Macbeth

Organization

• Quick recap• More on k-space• MR Sequence Timing diagrams• Imaging practicalities: echoes

– Spin – Gradient

• Image Contrasts– Relaxation effects– T1, T2, and proton density

05/19/09 Andrew J. M. Kiruluta 4

Magnetic Resonance• Protons and Neutrons have intrinsic angular momentum.• Atoms with an odd number of proton and/or odd number of

neutrons have a net magnetic moment=> MR active• For example, 1H exhibit nuclear magnetic resonance.

-

-

-

-

--

- -

--

-+

+

+

+ ++

+ +

+

Neutrons + protons

1H

Magnetic Resonance

yx

z

Imaging

xy

z

in selected slice: select ywith phase encoding

x

y

Imaging

xy

zslice select: define z position

in selected slice: select xwith freq encoding

xy

z

x

y

2D Imaging – x (freq) encoding

• Some of the following images are copyright: DM Higgins

• http://www.revisemri.com/tutorials/what_is_k_space/

k-space

k-space

Frequency and space relations

k-space


kx

ky

kx

ky

kx

ky

k-space

Imaging

xy

zslice select: define z position



x

y

Gradients

f(x)G(x)

slope = m

mm

df/dt


Timing Diagram

RF

G

G

G

A/D

slice

freq

phase

echo

TR

excitation phase

Phase encodephase

frequency encode& data acquisition

Analog signal


Excitation Phase

RF

Gslice

TR

excitation phase


Constructive InterferenceSame wavelength, phase difference = 0°Amplitude larger: Higher intensity

Sum

( ) cos( ) 0.5cos( ) 1.5cos( )E x kx kx kx= + =


Destructive InterferenceSame wavelength, phase difference = 180° (1/2 λ)Amplitude smaller: Lower intensity

Sum

( ) cos( ) 0.5cos( ) 0.5cos( )E x kx kx kxπ= + + =


Selective Excitation

Frequency

Mag

nitu

de

Time

RF

Am

plitu

de

(a)(b)

Pos

ition

(d)(c)

Slope = 1γ G

Frequency

)(

ˆ)(

0

0

zGB

zzGBB

z

z

+=⇒+=

γω

• Slice Encoding Gradient field

• Slice Location & Width:– Gradient strength – Center frequency – Bandwidth (BW) of RF

pulse


Phase Encoding Step

RF

G

G

slice

phase

TR

phase encodingstep

kx

ky

phase encodingdirecion

0.5c

m1.

13cm

1.5c

m


Frequency Encoding and Data AcquisitionGE

RF

G

G

G

A/D

slice

freq

phase

echo

TR

excitation phase

Phase encodephase


Analog signal

kx

ky

phase encodingdirecion

8.13cm


Mechanisms of Spin Resynchronization


If the spins are brought into phase, a net transverse magnetization is created.

RF Spin Phasing


Measuring the MR Signal

RF signals from precessing protons

RF antenna/Rx coil

B0

Starts off large when all phases are about equal

High frequency curve is at the average frequency

Decays away as different

components get different phases


More about Echoes

“A fight against time…and signal decay”

The pros and cons of gradients



x

y

• Gradients, though useful in manipulating frequencies, also add dephasing, resulting in signal loss.

As we perform readout, wealso dephase (disturb the phaserelationship) along the readout

The pros and cons of gradients

• The most important k-space signal is at the center of k-space

• By adding additional gradients (and possibly another RF pulse), we can mitigate against gradient induced phase (and signal loss) and refocus our signal close to the center of k-space


Spin Echo versus Gradient Echo

Gradient Echo

F I D gradient recalledecho

αR F p u l s e

rephase

dephase

signal

gradient

Spin Echo

FID spinecho

9 0 RF pulse

readoutfrequency encode

signal

gradient

18 00 RF pulse


Spin & Gradient Echoes

Ref. Schering

• RF (spin) echo: flip the track (direction) so that they come back to the starting point.• Gradient echo: flip speeds (i.e. frequencies) so that the rabbit is slower than the turtle.

t < T2


Spin Echo Timing Sequence

12

3 4

ky

kx

phase encoding direcion

K-space trajectory

RF

G

G

G

A/D

slice

freq

phase

echo

TR

excitation phase

Phase encodephase


Analog signal

TE/2 TE/2

1 2 3 4

Only 1 line of k-spaceis read per TR!

TR = 1s / 256 samples= 256s for whole slice= 4.2 minutes / slice


A word about Contrast and Relaxation Effects

• ρ – Spin (Hydrogen/proton) density results in contrast between tissues

“water/fat content in tissue”

• T1 – due to energy exchange between spins and “lattice” ”time for sample to magnetize”

• T2 – dephasing time due to spin-spin energy exchange”time to loss of phase coherence”

• T2* - dephasing due to B0 inhomogenitiesgradients and inhomogeneous field increase

phase accumulation and reduce T2

10


Magnetic Resonance

yx

z

T2

T1


More about T1 and T2

19/05/09

38

Contrast - T1 Decay

• Longitudinal relaxation due to spin-lattice interaction

• Mz grows back towards its equilibrium value, M0

)1()( 1/0

Ttz eMtM −−=

0 1 2 3 4 5-1.0

-0.5

0.0

0.5

1.0

t/T1M

z/M

0

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39

Some sample tissue time constants - T1

Image, caption: Nishimura, Fig. 4.2

fat

liver

kidney

Approximate T1 values as a function of Bo

white matter

gray matter muscle

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40

Contrast - T2 Decay• Transverse relaxation

due to spin dephasing

• T2 irreversible dephasing

• T2/ reversible dephasing

• Combined effect:

*2/

/22

*2

)0()(

111

TteMtM

TTT−

⊥⊥ =

+=0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

t/T2*

Mx(

t)/M

x(0)

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41

Some sample tissue time constants: T2

Table: Nishimura, Table 4.2

T2 of some normal tissue types

47muscle

92white matter

100gray matter

43liver

58kidney

85fat

T2 (ms)Tissue

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42

Proton Density

Basic Principles of MR: GE Medical Systems

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43

T2 Contrast

CSF

White/Gray Matter

Sig

nal

Time

Long Echo-TimeShort Echo-Time

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44

T1 Contrast

Sig

nal

Time

Sig

nal

Time

Short Repetition Long Repetition

CSF

White/Gray Matter

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45

MRI of the Brain - Sagittal

T1 ContrastTE = 14 msTR = 400 ms

T2 ContrastTE = 100 msTR = 1500 ms

Proton DensityTE = 14 msTR = 1500 ms

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46

What Physicians would do without images…

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47

Useful links...

• MR Technology Information Portal Database:

• http://www.mr-tip.comhttp://www.mr-tip.com/serv1.php?type=db

• Basics of MRI (online book):

• http://www.cis.rit.edu/htbooks/mri/

• Revise MRI:

• http://www.revisemri.com/

http://www.mr-tip.com/serv1.php?type=db

“genteel” introduction to mri physics - ii: k-space ... · “genteel” introduction to mri...

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