Encoding and Image Formation - PowerPoint Presentation

Slide1

Encoding and Image Formation

Gradients

Slice selection

Frequency encoding

Phase encoding

Sampling

Data collectionSlide2

Introduction

Encoding means the location of the MR signal and positioning it on the correct place in the image

RF at precessional frequency of hydrogen applied at 90

0

to B

0

resonates and flips the NMV into transverse plane.

The individual magnetic moments of hydrogen is put into phase.

The coherent transverse magnetization precesses at Larmor frequency in the transverse plane.Slide3

A voltage (signal) is induced in the receiver coil placed in the transverse plane

This signal has a frequency equal to Larmor frequency of hydrogen (at 1.5 T : 63.86 MHz)

The system must be able to locate the signal spatially in three dimensions, so that it can position each signal at the correct point on the image.

First it locates a slice

.

Then it is

located or

encoded

along both axes of the image.

This task is performed by magnetic gradientsSlide4

Magnetic Gradients

Gradients are alterations to the main magnetic field and are generated by coils of wire located within the bore of the magnet.

The passage of current through a gradient coil induces a gradient magnetic field.

The gradient field either adds to or subtracts from B

0

.

B

0

is altered in a linear fashion.Slide5

Magnetic field strength and therefore the precessional frequency of the nuclei situated in the long axis is deferent and is predictable.

This is called

spatial encoding

A

B

C

negative

positive

9998 G

42.5614 MHz

10000 G

42.57 MHz

10002 G

42.5785 MHz

gradient 1 G per cm

2 cm

2 cmSlide6

X,Y,Z Gradient coilsSlide7

There are three gradient coils (X,Y,Z) situated within the bore of the magnet

Z gradient alters the magnetic field strength along the Z- (long) axis

Y gradient alters the magnetic field strength along the Y- (vertical) axis of the magnet

X gradient alters the magnetic field strength along the X- (horizontal /transverse) axis of the magnet

Y

Z

XSlide8

The

magnetic isocentre

is the centre point of the axis of all three gradients, and the bore of the magnet.

The field strength remains

unaltered

at the

isocentre

isocentre

Z

Y

XSlide9

When a gradient coil is switched on, the magnetic field strength is either subtracted from or added to B

0

relative to the isocentre

The slope of the resulting magnetic field is the amplitude of the magnetic field gradient and it determines the rate of change of the magnetic field strength along the gradient axis.

Steep gradient slopes alter the magnetic field strength between two points more than shallow gradient slopes.

Steep gradient slopes therefore alter the precessional frequency of nuclei between two points, more than shallow gradients slopes

Steep & shallow gradientsSlide10

Slice selection

This is done by

first switching the appropriate gradient coil to alter the field strength and the precessional frequency at points along the corresponding axis, and

then by transmitting a selected band of RF frequencies to selectively excite the nuclei which precess in that particular frequencies.

Resonance of nuclei within the slice occurs because RF appropriate to that position is transmitted

Nuclei situated in other slices does not resonate because their precessional frequency is different.Slide11

Z

-gradient selects axial slices

Y

gradient selects coronal slices

X

gradient selects sagittal slices

Y

Z

XSlide12

Slice thickness

To give each slice a thickness, a

band

of nuclei must be excited by the excitation pulse

The slope of the slice-select gradient determines the difference in precessional frequency between two points on the gradient.

Once a certain gradient slope is applied, the RF pulse transmitted to excite the slice, must contain a range of frequencies to match the difference in precessional frequency between two points

This frequency range is called the bandwidth.

As the RF is being transmitted at this point it is called the

transmit bandwidth

.Slide13

To achieve thin slices, a steep slice select slope and/or narrow bandwidth is applied

To achieve thick slices, a shallow slice select slope and/or broad transmit bandwidth is applied.

Transmit bandwidth

Steep gradient

Shallow gradient

Thin slice

Thick slice

broad Bandwidth

Narrow Bandwidth

Thin slice

Thick slice

slice select gradientSlide14

Gradient strength & slice thickness

Shallow (weaker gradient)

Steeper ( strong) gradientSlide15

The system automatically applies the appropriate

gradient slope

and

transmit

bandwidth

according to the thickness of slice required.

The slice is excited by transmitting RF at the centre frequency corresponding to the precessional frequency of nuclei in the middle of the slice,

The bandwidth and gradient slope determine the range of nuclei that resonate on either side of the centre.

In PracticeSlide16

The gap between the slices is determined by the gradient slope and by the thickness of the slice.

In spin echo pulse sequences, the slice select gradient is switched on during the application of the 90

0

excitation pulse and during the 180

0

rephasing pulse, to excite and rephase

each slice selectively

.

In gradient echo, the slice select gradient is switched on during the excitation pulse only.

90

0

180

0

90

0

Slice select gradientSlide17

Frequency encoding

Once a slice has been selected, the signal coming from it must be spatially located (encoded) along both axes of the image

Locating the signal along the long axis of anatomy is done by a process called

frequency encoding

A gradient

is applied along the

selected axis

The precessional frequency of signal along the axis is therefore altered in a linear fashion.

The signal can now be located along the axis of the gradient according to its frequencySlide18

For frequency encoding of

Coronal & sagittal images – use z gradient

Axial images – use X gradient

Axial images of Head – use Y gradient

A

B

C

Nuclei in column A precess at frequency A

Nuclei in column B precess at frequency B

Nuclei in column C precess at frequency CSlide19

In practice

The frequency encoding gradient is switched on when the signal is received and is often called the

readout gradient

FID

Echo

FID

90

0

90

0

180

0

Frequency encoding gradient

rephasing

dephasing

peak

The steepness of the slope of the frequency encoding gradient determines the size of the anatomy covered ;

Field Of View

(FOV) along the axis during scan.Slide20

Phase encoding

The location of the signal along the remaining third axis is achieved by a process called phase encoding.

This is achieved by applying a gradient along this remaining axis

A gradient is switched on it

alters

the

speed of precession

as well as the

accumulated phase of the nuclei

along their precessional path.

It produces a phase difference or shift between nuclei

positioned along the axis.Slide21

nuclei travel slower

Nuclei travel faster

Loose phase

gain phase

14998 G 63.852 MHz

15000 G 63.86 MHz

15002 G 63.868 MHz

Gradient & phase difference Slide22

When the phase encoding gradient is switched off, the magnetic field strength experienced by the nuclei returns to B

0

and the precessional frequency of all the nuclei returns to the larmor frequency.

However the phase difference between nuclei remains

The nuclei travel at the same speed around their precessional paths, but their phases or positions are different.

This difference in phase between the nuclei is used to determine their position along the phase encoding gradient (axis). Slide23

In practice

The phase encoding gradient is switched on just before the application of the 180

0

rephasing pulse in spin echo sequences.

Phase encoding gradient

90

0

90

0

180

0Slide24

Summary of phase encoding

The phase encoding gradient alters the phase along the

short axis

of the anatomy

In

Coronal

images –

x

gradient

In sagittal images - Y gradientIn

axial images - Y gradientAxial images of brain –

x gradientSlide25

Summary spatial encoding

The slice-select gradient is switched on

during the 90 and 180 pulses in spin echo pulse sequences , and

during the excitation pulse only in gradient echo pulse sequences

The slope of the slice-select gradient determines the slice thickness and slice gap (along with transmit bandwidth)Slide26

The phase encoding gradient is switched on

just before the 180 pulse in spin echo, and

between excitation and the signal collection in gradient echo.

The slope of the phase encoding gradient determines the degree of phase shift along the phase encoding axis.

The frequency encoding gradient is switched on during the collection of the signal

The

amplitude

of the

frequency encoding

gradient and the phase encoding

gradient determines the two dimensions of the FOVSlide27

Gradient timing in spin echo

90

0

90

0

180

0

echo

slice select

slice select

Phase encode

Frequency encode

TRSlide28

Sampling

The signal is collected during the frequency encoding gradient (

readout gradient

)

The duration of readout gradient is called

sampling time

The system

samples up to 1024 frequencies

during sampling time

The rate at which the samples are taken is called the sampling rateSlide29

The

number of samples taken

determines the

number of frequencies

sampled

The range of frequencies is called the

receive bandwidth

f1

f2

f4

f3

f5

f6

Receive bandwidth

Frequency columns in FOV

Frequencies sampled are mapped across the FOV along the frequency axisSlide30

Sampling time, sampling rate and receive bandwidth are linked by a mathematical principle called the

Nyquist theorem

.

It states that any signal must be sampled at least twice per cycle in order to represent or reproduced it acurately.

In addition enough cycles must occur during the sampling time to achieve enough frequency samples ( if 256 samples are to be taken 128 cycles must occur during the sampling time)

Number of cycles occurring per second is determined by the receive bandwidth

Receive bandwidth is proportional to the Sampling rateSlide31

Sampling time is inversely proportional to:

The sampling rate

The receive bandwidth

The receive bandwidth affect the minimum TE ( because the sampling time is changed)

Reducing the receive bandwidth increase the TE (sampling time increases) & vise versa

Usually the receive bandwidth & sampling time are fixedSlide32

Nyquist theorum

Sampling once

Reproduced as a straight line

Sampling twice

Reproduced more accuratelySlide33

Bandwidth versus sampling time

Bandwidth

Sampling time (8 ms)

16,000 Hz

8,000 Hz

128 cycles occur

(256 samples can be taken)

64 cycles occur (only 128 samples can be taken)

If bandwidth is reduced, the sampling time must be increased so that the same number of samples can be takenSlide34

Data collection

Location of individual signals within the image by measuring the number of times the magnetic moments cross the receiver coil (

frequency

), and their position around their precessional path (

phase

)

Frequency shift

Phase shift

1 cycle/s

2 cycles/s

3 cycles/sSlide35

K space

The data information is stored in the computer memory location called the K space. Maximum number of lines are 1024

phase

frequency

+ve

-ve

central

outer

One line is filled for one phase encoding gradientSlide36

Data collection – step 1

During each TR the signal from each slice is phase encoded and frequency encoded.

A certain value of frequency shift is obtained according to the slope of the frequency encoding gradient, which is determined by the size of the FOV.

As the FOV remains unchanged during the scan, the frequency shift value remains the same.

A certain value of phase shift is also obtained according to the slope of the phase encoding gradient

The slope of the phase encoding gradient will determine which line of K space is filled with the data from that frequency and phase encodingSlide37

Phase shift & pseudo-frequency

The system cannot measure the phase values directly

It can measure frequency

The phase shift values are converted to a sine wave

The frequency of this sine wave is called a pseudo-frequency

Different phase shift gradient produce different sine waves with different pseudo-frequencySlide38

The pseudo frequency curve

Phase shift value

timeSlide39

Phase encoding gradient & pseudo frequency

Steeper gradients results in high pseudo frequencies

Shallow gradients results in low frequenciesSlide40

In order to fill out different lines of K space, the slope of the phase encoding gradient must be altered after each TR

With each phase encoding one line of

K

space

is filled

Different lines in K space are filled after every TR

The phase encoding gradient is altered for every TR

In order to complete the acquisition all the lines of selected K space must have been filled

The number of lines that are filled is determined by the number of different phase encoding slopes that are appliedSlide41

K space

Line 1 phase encode 1 frequency/phase data

Line 2 phase encode 2

Line 128 phase encode 128Slide42

Fast Fourier Transform (FFT)

The data in K space is converted into an image mathematically by Fourier Transform.

The receive signal is a composite of multiple signals with different frequencies and amplitudes

The

signal intensity/time domain

is converted to a

signal intensity/frequency

domain

RF intensity

Time

Amplitude

Frequency

Time domain

Frequency domainSlide43

Matrix & FOV

The FOV relates to the amount of anatomy covered

It can be square or rectangular

Image consists of a matrix of pixels

Te number of pixels depends on the number of frequency samples and phase encodings

Matrix = frequency samples x phase encodingsSlide44

Matrix

Coarse matrix 4x4

Fine matrix 8 x 8

4 frequency samples

8 phase samples

8 frequency samples

4 phase samplesSlide45

Data collection - step 2, NSA (NEX)

When all the lines of K space is filled the acquisition is over

But the signal can be sampled more than once with the same slope of phase encoding gradient.

Doing so each line of K space is filled more than once

The number of times each signal is sampled with the same slope of phase encoding gradient is usually called the number of signal averages (NSA) or the number of excitations (NEX).

The higher the NEX, the more data is stored and the amplitude of the signal at each frequency and phase shift is greaterSlide46

Scan timing

Every TR, each slice is selected, phase encoded and frequency encoded.

The maximum number of slices that can be selected and encoded depends on the length of the TR.

E.g.

TR of 500ms may allow 12 slices.

TR of 2000 ms may allow 18 slicesSlide47

TR & number of slices

TR

Slice 1

Slice 2

Slice 3

Slice 4

Slice 1 second TR

90

180

echo

TE

Phase encode 1

Phase encode 2Slide48

The phase encoding gradient slope is altered every TR and is applied to each selected slice in order to phase encode it.

At each phase encode a different line of k space is filled. The number of phase encoding steps therefore affects the length of the scan

E.g. 256 phase encodings require 256 x TR to complete the scan.

The scan time is also affected by the number of times the signal is phase encoded with the same phase encoding gradient slope, or NEX . So,

Scan time = TR x Number of phase encodings x NEXSlide49

K space filling

The negative half of the k space is a mirror image of the positive half.

The polarity of the phase gradient determines whether the positive or negative half is filled

Gradient polarity depends on the direction of the current through the gradient coil

The central lines are filled with data produced after the application of shallow phase encoding gradients

The outer lines are filled with data produced with steep phase encoding gradientsSlide50

The steepness of the slope of the phase encoding gradient depends on the current driven through he coil.

The central lines of K space are usually filled first. (if 256 phase encodings are performed 128 positive lines and 128 negative lines are filled.

The lines are usually filled sequentially either from top to bottom or from bottom to topSlide51

Signal amplitude & phase shift gradient

The shallow phase encoding gradients have smaller phase shifts. The resultant signal therefore has a large amplitude

The steeper phase encoding gradients have larger phase shift along their axis and therefore small signal amplitudesSlide52

Phase encoding slope & signal amplitude

Steeper gradient

medium gradient

shallow gradient

Low amplitude

medium amplitude

high amplitudeSlide53

Signal amplitude & frequency gradient

The vertical axis of k space correspond to the frequency encoding

The left of the k space is a mirror image of the right

The centre represents the maximum signal amplitude because all the magnetic moments are in phase

The magnetic moments on either side are either rephasing and dephasing and therefore the amplitude is lessSlide54

Signal amplitude & frequency gradient

Rephasing

Dephasing

PeakSlide55

K space filling & spatial resolution

Number of phase encodings determines the number of pixels in the FOV along the phase encoding direction

If the FOV is fixed voxels of smaller dimensions result in an image with high spatial resolution

The

steeper gradients

result in

high spatial

resolution (two adjacent points have different phase values and can be differentiated)Slide56

The outer lines of K space contain data with high spatial resolution

The central lines of k space contain data with a low spatial resolution

The

central portion

of k space

contains data

that has

high signal amplitude

& low spatial resolutionThe outer portion of k space

contains data that has low signal amplitude and high spatial resolutionSlide57

Resolution & Amplitude

High spatial resolution

High signal

High spatial resolutionSlide58

Way of filling K space

The

amplitude of frequency encoding

gradient determines

how far to the left and right

K space is traversed and this in turn determines the size of the FOV in the frequency direction of the image

The

amplitude of the phase encoding

gradient determines

how far up and down a line of K space is filled and in turn determines the size of the FOV in the phase direction of the image (or the spatial resolution when the FOV is square)

The polarity of each gradient defines the

direction traveled through K spaceSlide59

K space filling in gradient echo

The frequency encoding gradient switches negatively to forcibly dephase the FID and then positively to rephase and produce a gradient echo

Frequency encoding gradient is negative, k space traversed from left to right

Frequency encoding gradient is positive, k space traversed from right to left

Phase encode gradient is positive , fills top half of K space

Phase encode gradient is negative, fills bottom half of K spaceSlide60

K space filling in gradient echo

Phase encode amplitude determines distance B

B

A

Negative gradient traverse from centre through distance A

Positive gradient traverse from centre through distance C

C

Line of k space filledSlide61

Manipulation of K space filling

The way in which K space is filled depends on how the data is acquired and can be manipulated to suit the circumstances of the scan; e.g. in the following

Rectangular field of view

Anti-aliasing

Ultra fast pulse sequences

Respiratory compensation

Echo planar imagingSlide62

Partial or fractional echo imaging

This refers to when only part of the signal is read (sampled) during application of frequency encoding gradient

As the

sampling time is reduced

minimum

TE can be reduced

This allows maximum T1 and proton density weighting and number of slices for a given TRSlide63

Readout gradient

Minimum TE

Minimum TE reduced

Only half of the k Space is filled

This extrapolated from filled segment

Partial echo imaging

Only this half is readSlide64

Partial or fractional averaging

The negative and positive halves of K space on each side of the phase axis are symmetrical and mirror image of each other

The filling of at least half of the lines is adequate to produce an image

If 60% of lines are to be filled only 60% of phase encodings are required and the remaining lines are filled with zeros

The scan time is there fore reduced

E.g. 256 phase encodings and, 1 TR and ¾ NEX is selected

This is called partial or fractional averaging Slide65

Partial averaging

75% of k space is filled with data

25% is filled with zeros

If phase encodings = 256

TR = 1s

NEX=3/4,

Scan time = 256 x ¾ x 1 = 192 s

If phase encodings = 256

TR = 1s

NEX=1,

Scan time = 256 x 1 x 1 = 256 sSlide66

PRE-SCAN

This is a method of calibration that should be performed before every data acquisition. It includes;

Finding the centre frequency on which to transmit RF. I.e. Resonant frequency of water protons within the area under examination

Finding the exact magnitude of RF that must be transmitted to generate maximum signal in the coil. (to flip the NMV through 90

0

)

Adjustment of the magnitude of the received signal so that it is not too large nor too small.Slide67

Reasons for failing pre-scan

The coil is not plugged in properly

The coil is faulty

Chemical saturation techniques are utilized and there is an uneven distribution of fat and water in the area to be saturated

The patient is either very large or very smallSlide68

Types of acquisition

Sequential

:– data collected for slice by slice (k- space for each slice is filled one by one)

Two-dimensional volumetric

:– data collected for all the slices simultaneously (line 1 in first slice, then line 1 in slice 2)

Three-dimensional volumetric

(

volume imaging

):-collect data from total volume. The excitation pulse is not slice selective, and the whole prescribed volume is excited. At the end of acquisition the volume is divided into partitions by slice select gradient which separates the slices according to their phase value along the gradient. (This is called slice encoding)Slide69

End