FYS-KJM 4740 Chap4-5 100323 print - Universitetet i oslo · FYS-KJM_4740_Chap4-5_100323_print...

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Lecture 2010-03-23

•  Multislice acquisition (MS, 3D) •  GRE: Simple Steady-State model •  RF pulse train (multiple echoes)

–  Eight-Ball Echo –  Stimulated Echo –  Multiples echoes

•  GRE FID and ECHO components •  Mathematical Model of GRE •  GRE contrast properties and techniques

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Spin Echo – k-space sampling

slice selec5on

Read‐out direc5on (frequency encoding)

phase encoding

Spa5al informa5on in “y” direc5on

Gz

Gx

Gy

acquisi5on of all profiles

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Gradient Echo – k-space sampling

slice selec5on

Read‐out direc5on (frequency encoding)

phase encoding

Spa5al informa5on in “y” direc5on

Gz

Gx

Gy

acquisi5on of all profiles

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TE and TR

TR

TE

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Multislice acquisition

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Sl 1

Sl 2

Sl 3

TR

Slice order: “Interleaved”

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3D acquisition

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Same principle of phase encoding is applied to the slice direc5on (refocusing lobe of the slice selec5on)

2D versus 3D acquisition

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GRE properties

•  Requires less time than SE to form an Echo (i.e. TE shorter for 1 k-space profile acquisition)

•  RF pulse angle α ≤ 90° •  SI = f(T1, T2, T2*)

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GRE: Simple steady-state model

TR short, T2* << TR, pulse angle α

Repeated RF pulses dynamic equilibrium called “Steady State”

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Steady‐state reached at the 2nd pulse if α = 90deg.

GRE steady-state

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Note that the highest signal is obtained for α = 20°

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GRE: Simple steady-state model

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TR

Simple mathematical model

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We know from basic NMR intro that

And the solu5on along z‐axis to this equa5on is (with the nota5on from last figure):

Looking at the rota5on by the α RF pulse along x’ axis, we get:

We assume that which is true if T2*<<TR

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Simple mathematical model (cont.)

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We have now the following equa5ons

and

At equilibrium (steady‐state):

and wri5ng

Which then gives

Applying an RF pulse of angle α Eq. 4‐8 (Compendium)

Moreover, the net magne5za5on of GRE readout is modulated by exp(‐TE/T2*)

Simple mathematical model (cont.)

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Finding the maximum of this func5on:

αe is the Ernst angle

contrast weigh5ng in a spoiled GRE sequence •  T1‐weighted •  T2*‐weighted (weigh5ng depends on the TR/T1 at given α)

Short TR (TR/T1 << 1) Large α T1 weigh5ng

Long TR (TR/T1 ≈1) Low α T2* weigh5ng

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Steady-State

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Steady-State

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GRE: General behavior

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TR

Since TR is short

We have then:

•  Longitudinal component

•  Transverse component

with mul5ple RF pulses repe55on

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Effect of repeated RF excitations: eight-ball echo

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Eight-Ball Echo

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TR TR

dephasing

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Eight-Ball Echo

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TR TR

dephasing

Eight-Ball Echo

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TR TR

2nd 90° pulse

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Eight-Ball Echo

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TR TR

rephasing

Eight-Ball Echo

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TR TR

Eight‐ball echo Locus

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Eight-Ball Echo

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TR TR

dephasing

Stimulated Echo •  two 90° pulses eight-ball echo

•  The 2nd 90°pulse flipped x’ component of the transverse magnetization along z-axis (this z-magnetization carries magnetization history from before 2nd RF pulse, i.e. gradient dephasing as function of position)*

•  3rd 90° pulse then flips back this longitudinal component into the transverse plane. The 3rd Gx gradient will refocus these components previously stored along z-axis

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* The longitudinal component is not affected by the second gradient ager RF pulse

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Stimulated Echo

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“stored” z‐component with dephasing history from the 1st gradient (not affected by the second)

Will create eight_ball echo

Stimulated Echo

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Stimulated Echo (simulation)

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Multiple Echoes

•  From Steady-State simplified model / Ernst angle α < 90°

•  Both transverse and longitudinal components are present at any time

•  RF pulse train generates multiple echoes

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3 RF-pulses gives a total of 5 echoes

α1 α2 α3

e1 e2 e3 e4 e5

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α1 α2 α3

e1 e2 e3 e4 e5

e1: eight‐ball echo of α1 and α2

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α1 α2 α3

e1 e2 e3 e4 e5

e2: S5mulated echo of α1,α2 and α3

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α1 α2 α3

e1 e2 e3 e4 e5

e3: refocused e1 by α3

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α1 α2 α3

e1 e2 e3 e4 e5


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α1 α2 α3

e1 e2 e3 e4 e5


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FID and ECHO components

•  α < 90° •  Transverse and longitudinal components •  Echoes can be formed (eight-ball/ stimulated) contain magnetic history from former RF pulses/gradients

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FID

FID

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αn αn+1

Longitudinal magne5za5on available •  “fresh” component fid (small lejers) •  Contains also: transverse magne5za5on components flipped to z‐axis by αn‐i (see also echoes flipped to z‐axis)

ECHO

Available transverse component preceding an RF pulse •  Refocused echoes (posi'on dependent history / gradients) •  These echoes are par5ally rotated out of the transverse plane (α < 90°) and a part remains in the transverse plane ager the RF Pulse αn+1.

ECHO

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αn αn+1

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FID is mainly T1 weighted (based on available longitudinal magne5za5on before the RF pulse)

ECHO is mainly T2 weighted (persistence of the transverse components that form the echoes (e.g. eight‐ball etc.)

ECHO

FID & ECHO

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αn αn+1

FID

Now considering the readout gradients in this figure:

Both FID and ECHO can give a gradient echo (signal that will be encoded into k‐space to form the GRE image)

ECHO

FID & ECHO

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αn αn+1

FID

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FID & ECHO

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αn αn+1

FID

FID & ECHO

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αn αn+1

FID

TE

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FID & ECHO

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αn αn+1

TE

ECHO

Imaging Echo (from ECHO) appears

when

between TE and TR.

Echo appears at the next a pulse but

is represented normally in apparent

“reversed” 5me

Both FID and ECHO signals are used in Imaging

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FID and ECHO proper5es:

FID carries par5ally the spa5al info contains in the ECHO component which is flipped to the x‐y plane by the αn pulse

It can be shown that ECHO can add parallel to the FID of an5‐parallel depending on the previously acquired phase angle (i.e. posi5on) Periodic “band” structure in the image with different T1/T2 weigh5ng)

ECHO

FID & ECHO

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αn αn+1

FID




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Precession: MT is position dependent (in-plane gradient)

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Steady-state signal behavior

Excitation Precession

Relaxation

M = [Mx,My,Mz]T , M0=[0,0,M0]T, E2 = exp(-t/T2) and E1=exp(-t/T1).

From Chap 2:

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Steady-state signal behavior Relaxation and Precession occurs simultaneously and can be combined:

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Steady-state

U = unit matrix

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Steady-state

MT = Mx’ + jMy’

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Steady-state

The equation reduces to the ‘spoiled’ GRE expression in when E2=exp(-t/T2)=0 (TR >> T2 or active spoiling). In this case, the factor D in the denominator depends on T1-weighting (through E1) only.

E2=0

Transverse magn. immediately after nth RF pulse:

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Steady-state

The term 1-E2exp(-jθ) in the numerator implies a varying degree of T2-weighting, dependent on θ, and hence position. This means that, if E2 >0 the image will contain ‘bands’ of varying degree of T1- and T2-weighting depending on the value of exp(-jθ(r)) at a given position .

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Steady-state: magnetization evolution between RF-excitations Transverse magn. during nth TR-interval:

relaxation Gradient effects

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The FID signal

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FYS-KJM 4740 Chap4-5 100323 print - Universitetet i oslo · FYS-KJM_4740_Chap4-5_100323_print...

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