MRI Final Avi

7/31/2019 MRI Final Avi

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Fouriers Transform

The pick up coil receives many different frequencyoscillations.

Use Fouriers Transform to process the data.

Time [s]

SignalStrength

1

4

Freqency[Hz]

SignalStrengt

h

1

0.25

f = 1/T = = .25

1.5

0.5

1.

5

-1

-

1. f = 1/T = = .5f = 1/T =

1.0

Transform


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Fourier Transform(cont.)

The pickup coil does not distinguish between theinput of each hydrogen.

They are all read together, and constructively anddestructively interfere.

Fouriers allows us to determine which frequenciesare along the axis.

For instance, if there are two hydrogen at differentfrequencies along an axis:

SignalS

trength

Time [s]

1

-14

Time [s]

1

-14

Time [s]

1

-1

4+ =Curre

nt

Fourier

Frequency

1

0.nalS

trength

0.25

Frequency

1

0. 1

0.25

Frequency

1

0.25

1


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2D Fourier Transform

Recall that the second axis is resolved with a phase encoding gradient.

These hydrogen have the same frequency, but interfere with each otherdue to phase shift.

Sign

alStrength

1

-1

4Time[s]

1

-1

4

1

-1

4

+ =

n A 1D Fourier Transform cannot distinguish between shifted phases.

n But if we take the Fourier Transform again, orthogonal to the firstaccess the phase encoding gradient can be distinguished!

n

The resulting data is known as a K-Space.


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K-Space

A 2D Fourier transformis conducted byperforming two Fouriertransforms orthogonalto each other.

This yields a K-Space

An example is seen on

the right.The K-Spaceundergoes an InverseFourier Transform.

Following thismathematical ste , we


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K-Space [Contd.]

General spatialinformation isconcentrated towardsthe center of K-Space

In the figure to the rightwe see an imageformed taking only theInverse Fourier

Transform of the centerof the K-Space.As seen on the right,the peripheral regionsof the K-Space encode

for the edges of theimage.


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What is Image

Formation?


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How Image Is Formed?


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But MRI does not use projection, reflection, orrefractionmechanisms commonly used in optical imging

methods


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MR SIGNAL

Collected by a coil

Encoded through a series ofcomplex techniques andcalculations

Stored as data

Mapped onto an image matrix


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TR - REPETITION TIME

Time from the application of one RFpulse to another RF pulse

TE - ECHO TIME

Time from the application of the RFpulse to the peak of the signal induced

in the coil


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T1 WEIGHTING

A short TR and short TE will result in a T1weighted imageExcellent for demonstrating anatomy

T2 WEIGHTINGA long TR and long TE will result in a T2

weighted imageExcellent for demonstrating pathology

MANY OTHER DIFFERENT TYPES OF

IMAGES THAT COMBINE ABOVE ANDINCLUDE OTHER PARAMETERS


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What is the difference

between T1 and T2?Tissue in the human body has its own T1and T2 value.

For example, white matter in the brain willexhibit different T1 and T2 values than thatof blood.

In magnetic resonance imaging, the

emitted radio signal from a particulartissue depends on combination of thattissue's T1 and T2 values.


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T1 & T2 images

T1 T2


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vThe images created in an M.R.I. can be in any plane:axial, coronal, or sagittal.

v

It creates cross-sectional images or slices of a bodypart:think of the body part as a loaf of bread, and each

AxialCoronal

Sagittal

Imaging


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Some MRIImages

Knee

Abdomen

Brain


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MRI Final Avi

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