tmr mrtbasics41 part2 sd 2sw...spatial coordinate, since frequency encoding source: liang and...

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RUPRECHT-KARLS-UNIVERSITY HEIDELBERG

Computer Assisted Clinical MedicineProf. Dr. Lothar Schad

10/19/2016 |

Basics of Magnetic Resonance Imaging (MRI)(Part 2)

Dr. Sebastian Domsch

TMR Lecture, Module 4.1

Chair in Computer Assisted Clinical MedicineFaculty of Medicine Mannheim University HeidelbergTheodor-Kutzer-Ufer 1-3D-68167 Mannheim, GermanySebastian.Domsch@MedMa.Uni-Heidelberg.dewww.ma.uni-heidelberg.de/inst/cbtm/ckm/



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MR Imaging

MR Imaging

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radiofrequency:ω(z) = γ (B0 + Gzz)

gradient Gz

magnetic field gradient, i.e. Gz

z

G

Gradient Field: Slice Selection

Nobelprize 2003

Paul Lauterbur (1929-2007)



10/19/2016 | Page 4Gradient Coil: Design

• current through the coil pairs runs in opposite directions

• B-field of the gradient coil is added or subtracted to B0, respectively

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1. slice thickness d = z2 - z1 can be varied by RF bandwidth (frequency width) or gradient strength Gz.

2. slice position can be changed by shifting the frequency spectra with constant RF bandwidth

ω ω

I(ω)

ω (z2)

ω (z1)

ω0

ω = γ (B0+Gz·z)

zz1z2

d

frequency spectraof RF pulse

Slice Selective Excitation



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- RF excitation with a sin(x) / x amplitude function (sinc-pulse) creates arectangular frequency distribution

- sinc-pulse at different gradient strength leads to slices with different positions and thickness

Slice Selective Excitation: Sinc-Pulse

source: Liang and Lauterbur. “Principles of Magnetic Resonance Imaging” 2000

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ω(x) = γ (B0+ Gx·x)

- iso-frequency-lines are perpendicularto G

- oscillation frequency of an activated MR-signal is linearly dependent on spatial coordinate, since

Frequency Encoding




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Gz

t

Gx

t

t

signalacquisition - superposition of a gradient field

Bx= Gx·x during the acquisition phase results in:

ω(x) = γ (B0+ Gx·x)

where the Lamor frequency islinked with the spatialinformation x

- spatial information is encodedin the precision frequency of thetransversal magnetization

Frequency Encoding: Gradient Schema

RF

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x

y

z Gx

ω(x)~x

I(ω)

ω(x2)ω(x1)

- all nuclei in a stripe perpendicular to thegradient direction are contributing to theNMR signal at Lamor frequency ω(x)

⇒ direct one-dimensional diagram of the spatial distribution of excited nuclei

in the slice

- Fourier-transformation of the FID-signal yields the amount of different frequency components

- I(ω) ~ number of nuclei at frequency ω

frequency spectrum

projection of spin density in direction of gradient

Principle of Frequency Encoding



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φ(x) = - γ · Gx · x · Tpe

Phase Encoding

- phase encoding is performed by stamping an initial phase angle ontothe spins of an excited slice

- iso-phase-lines are perpendicularto G

- after switching off the phase encoding gradient the magnetization is continuing to precede at the same frequency ω0 but with different phase

- phase information of an activated MR-signal is linearly dependent on spatial coordinate, since


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slice selectiongradient

phase encodinggradient

Gz

Gy

yTy

- phase encoding is performed before signalacquisition

- gradient field is switched on for a constant time Ty

- gradient strength is increased stepwise by ∆Gy after every sequence passage

Phase Encoding: Gradient Schema



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Gz

tGy

t

tsignal acquisition

RF

Gx

t

phase encoding

frequency encoding

MR Imaging Principle

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K-Space

K-Space



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k-space image-space

k-Space vs Image-Space

hologramfrequency distribution

imagedensity distribution

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10/19/2016 | Page 15k-Raum-Darstellung

????

K-Space Quiz



10/19/2016 | Page 16K-Space: Mona Lisa

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k-space

image

Fouriertransformation

kx

ky

y

x

hologram

image

Imaging: k-space

Jean Baptiste Fourier (1768–1830)



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transmitter

receiver

gradient

shim

imag

e pr

oces

sor350 MHz

control panel

computer

350 MHz

radio- gradients Gxyz static field B0frequency RF shim coils

MRI Components: Physical Parameters

static field B0 � M0

radiofreq. RF � signal

gradients Gxyz � image

technicalcomponent

physicalparameter�

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T1 Measurement

T1 Measurement



10/19/2016 | Page 20Experiment: T1-Measurement #1

Inversion Recovery Technique

Time t

90°

180°

TE

180°

TI

Signal

x

y

z

-M0

t = 0

x

y

z

t = TI

SI~Mz

TI

Time t

1,00

0

-1,00

Mz

(1 - 2e-t/T1)

TI: Inversion TimeTE: Spin-Echo Time

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10/19/2016 | Page 21Experiment: T1-Measurement #2

Measurement #2

x

y

z

-M0

t = 0

SI~Mz

TI2

Time t

1,00

0

-1,00

Mz

(1 - e-t/T1)

180°

TI2

Time t

90°

180°

TE

Signal

t = TI2

x

y

z#1

#2



10/19/2016 | Page 22T1 Measurement: Inversion Recovery

inversion recovery (Mz(0) = -M0):

Mz(t) = M0 (1 – 2 exp(-TI/T1))

with Mz = 0 at TI = TI0:0.5 = exp(-TI0/T1)

→ T1 = -TI0 / ln(0.5) = TI0 / 0.7

T1WM = 400 ms / - 0.7 = 570 ms

TI0

White Matter (WM)

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T2 Measurement

T2 Measurement



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Signal:S = S0·e-t/T2

WM: T2 ≅ 90 msGM: T2 ≅ 100 msCF: T2 > 500 ms

Experiment: T2-Measurement

Spin-Echo Technique

TR: Repetition TimeTE: Spin-Echo Time

Time t

90°

180°

TE2

180°

Signal Signal

180°

Signal

TE3TE1

90°

TRSignal [a.u.]

Time t

Sig

nal I

nten

sity

T2 ~ e-t/T2T2*

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10/19/2016 | Page 25T2 Measurement: Spin Echo

spin-echo (Mxy(0) = M0):

Mxy(t) = M0 exp(-t/T2)

→ slope of straight-line in semi-logarithmic scale

T2WM = 90 ms

T2 Measurement: Spin-Echo

White Matter (WM)



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Measurement of Brain Relaxation Times T1 and T2

1. Evaluate from an Inversion Recovery measurement the T1-relaxation of White Matter (WM), Grey Matter (GM), and Cerebrospinal Fluid (CF).

Experiment #1: 6 images were measured (IR_01.ima ... IR_06.ima, data at:http://www.ma.uni-heidelberg.de/inst/cbtm/ckm/lehre/ “Medical Physics: Lab Rotation MR-Radiology“) with TI = 50, 400, 550, 750, 1200, 2000 ms. Plot signal intensity (= pixel mean value of ROI) as a function of TI and calculate T1 of WM, GM and CF.

2. Evaluate from a spin-echo measurement the T2-relaxation of WM, GM and CF.

Experiment #2: 11 images were measured (SE_01.ima ... SE_11.ima) with TE = 25, 50 ... 275.0 ms. Plot signal intensity (= pixel mean value of ROI) semi-logarithm as a function of TE and calculate T2 of WM, GM and CF.

Exercise: Measurement of T1 and T2

- group 1: WM

- group 2: GM

- group 3: CF

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10/19/2016 | Page 27Exercise: Measurement of T1 and T2

Data to find @

http://www.umm.uni-heidelberg.de/inst/cbtm/ckm/lehre/index.html

Use e.g. Matlab or Excel for data evaluation

Use e.g. ImageJ (freeware) for data postprocessing (ROI analysis)



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Functional MRI

Functional MRI

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10/19/2016 | Page 29Motivation

FMRI shows activated brain areas based on blood oxygenation (BOLD-effect)



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T2* Relaxation

T2* Relaxation

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10/19/2016 | Page 31T2* Relaxation

Signal [a.u.]

Time tSig

nal I

nten

sity

~ e-t/T2~ e-t/T2*

Microscopic field inhomogeneities

Mesoscopic field inhomogeneities



10/19/2016 | Page 32BOLD-Effekt*

� Deoxyhämoglobin: paramagnetic (0<χ<1) � generates mesoscopic field inhomogeneities

� Oxyhämoglobin: diamagnetic (χ<0)

*Ogawa 1990

T2*~1/∆Bloc

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10/19/2016 | Page 33BOLD Response



10/19/2016 | Page 34Single-Shot Gradien-Echo EPI Sequence*

*Mansfield 1977

+ T2*-sensitive � high BOLD contrast

+ fast: 30-40 slices in 2-3s!

- susceptible to macroscopic field inhomogeneities � distortions, signal drop outs

- blurring due to long signal read out

Domsch PhD Thesis 2013, Heidelberg University

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10/19/2016 | Page 35Functional MRI: Principal

source: Reiser and Semmler. “Magnetresonanztomographie” 2002

morphological imagingslice selection

acquisition offMRI series

stimulation: off on off on off on

parameter image

overlay withmorphological images

quantificationsignal-time-curve

time [s]MR

sig

nal i

nten

sity

[a.u

.]



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fMRI Example 1: EPI Sequence

FOV 220mm: dx = 2.3mm�1.1mm

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motoric stimulation visual stimulation

parameters FLASH:- 9 segments TR = 93 ms, TE = 40 ms, α = 40°, BW = 260 Hz/pixel- MA = 192 x 256 pixel, TH = 2-3 mm, TA = 2.4 s, pixel size 0.8 x 0.8 mm2

3.0 x 0.8 x 0.8 mm3 2.0 x 0.8 x 0.8 mm3

Heiler Diploma Thesis 2007, Universität Heidelberg

fMRI Example 2: Segmented FLASH Sequence



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Imaging Contrast

Imaging Contrast

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10/19/2016 | Page 39Time-Of-Flight Angiography (TOF MRA)

flow direction

excitingvolume

maximum intensityprojection (MIP)

problems:- slow flowing spins- saturation in exciting volume- resolution 0.5 x 0.5 x 1.0 mm3

d`Avila. MRI 2005



10/19/2016 | Page 40Time-Of-Flight Angiography (TOF MRA)

original FLASH image

high signal ofinflowing spins

patients: arterio venous malformation (AVM)

maximum intensity projection (MIP)

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kx

k-space: after 1. TR k-space: after 2. TR k-space: after 256. TR

ky

Spin-Echo Sequence



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PwTR = 2775 ms

TE = 17 ms

T2wTR = 2775 msTE = 102 ms

T1wTR = 575 msTE = 14 ms

Spin-Echo Images

- SE gold standard technique for T1 and T2 morphology

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10/19/2016 | Page 43

TR

TE

90

-

60ms

40

-

10ms

T1-weighted

T2-weighted

proton-weighted

300 - 800 ms 1500 - 3000 ms

no contrastSNR low

Spin-Echo Contrast: TR, TE



10/19/2016 | Page 44Spin-Echo: T1 Dependency


T1-factor:[1-exp(-TR/T1)]

GM: T1 = 970 msWM: T1 = 600 ms

contrast

T1 - factor

WM

T1 - contrast

GM

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10/19/2016 | Page 45Spin-Echo: T2 Dependency

T2-factor:exp(-TE/T2)

GM: T2 = 110 msWM: T2 = 90 msT2 - factor

WM GM

T2 - contrast




10/19/2016 | Page 46Spin-Echo: TR, TE

source: Schlegel and Mahr. “3D Conformal Radiation Therapy: A Multimedia Introduction to Methods and Techniques" 2007

Which Weighting??

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10/19/2016 | Page 47Inversion Recovery Sequence

Mz

|Mz|




10/19/2016 | Page 48Inversion Recovery Images

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αExample: α = 20°

Mz - reduction by 6%Mxy- value 34% of Mz!!

M

x´,y´

z

Mz

Mxy

Gradient-Echo Sequence

spoiler

dephasing oftransversal

magnetization



10/19/2016 | Page 50Gradient-Echo: Steady-State

number of RF

example: WMT1 ~ 600 msTR = 25 ms

Mz steady-state:

Mxy steady-state:


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10/19/2016 | Page 51Gradient-Echo: FLASH

Haase et al. JMR 1986

FLASH signal: with E1 = exp(-TR/T1) FLASH: “fast low angle shot”

Ernst-angle:

Signal Strength:



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SE GE

α = 90° / 180°TE = 20 ms

TR = 600 ms

Taq: minutes

α = 25°TE = 7 ms

TR = 20 ms

Taq: seconds !!

Gradient-Echo: Measuring Time

tmr mrtbasics41 part2 sd 2sw...spatial coordinate, since frequency encoding source: liang and...

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