Encoding and Image Encoding and Image FormationFormation

GradientsGradientsSlice selectionSlice selectionFrequency encodingFrequency encodingPhase encodingPhase encodingSampling Sampling Data collectionData collection

IntroductionIntroduction

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

► RF at precessional frequency of hydrogen applied RF at precessional frequency of hydrogen applied at 90at 9000 to B to B0 0 resonates and flips the NMV into resonates and flips the NMV into transverse plane.transverse plane.

► The individual magnetic moments of hydrogen is The individual magnetic moments of hydrogen is put into phase.put into phase.

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

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

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

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

► First it locates a sliceFirst it locates a slice..► Then it is Then it is located or located or encodedencoded along both axes along both axes

of the image.of the image.► This task is performed by magnetic This task is performed by magnetic

gradientsgradients

Magnetic GradientsMagnetic Gradients

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

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

►The gradient field either adds to or The gradient field either adds to or subtracts from Bsubtracts from B00..

►BB0 0 is altered in a linear fashion.is altered in a linear fashion.

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

►This is called This is called spatial encodingspatial encoding

A B C

negative

positive

9998 G42.5614 MHz

10000 G42.57 MHz

10002 G42.5785 MHz

gradient 1 G per cm

2 cm 2 cm

X,Y,Z Gradient coilsX,Y,Z Gradient coils

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

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

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

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

Y

Z

X

►The The magnetic isocentremagnetic isocentre is the centre is the centre point of the axis of all three gradients, point of the axis of all three gradients, and the bore of the magnet.and the bore of the magnet.

►The field strength remains The field strength remains unalteredunaltered at the at the isocentreisocentre

isocentre

Z

Y

X

► When a gradient coil is switched on, the magnetic When a gradient coil is switched on, the magnetic field strength is either subtracted from or added to field strength is either subtracted from or added to BB00 relative to the isocentre relative to the isocentre

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

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

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

Steep & shallow gradientsSteep & shallow gradients

Slice selectionSlice selection► This is done by This is done by

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

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

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

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

►ZZ-gradient -gradient selects axial selects axial slicesslices

►YY gradient gradient selects selects coronal slicescoronal slices

►XX gradient gradient selects selects sagittal slicessagittal slices

Y

Z

X

Slice thicknessSlice thickness► To give each slice a thickness, a To give each slice a thickness, a bandband of nuclei of nuclei

must be excited by the excitation pulsemust be excited by the excitation pulse► The slope of the slice-select gradient The slope of the slice-select gradient

determines the difference in precessional determines the difference in precessional frequency between two points on the gradient.frequency between two points on the gradient.

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

► This frequency range is called the bandwidth.This frequency range is called the bandwidth.► As the RF is being transmitted at this point it is As the RF is being transmitted at this point it is

called the called the transmit bandwidthtransmit bandwidth..

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

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

Tra

nsm

it

bandw

idt

h

Steep gradient Shallow

gradient

Thin slice

Thick slice

bro

ad

Bandw

idt

h

Narr

ow

B

andw

idt

h

Thin slice Thick slice

slice select gradient

Gradient strength & slice Gradient strength & slice thicknessthickness

Shallow (weaker gradient)

Steeper ( strong) gradient

►The system automatically applies the The system automatically applies the appropriate appropriate gradient slopegradient slope and and transmittransmit bandwidthbandwidth according to the according to the thickness of slice required.thickness of slice required.

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

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

In PracticeIn Practice

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

► In spin echo pulse sequences, the slice select In spin echo pulse sequences, the slice select gradient is switched on during the application of the gradient is switched on during the application of the 909000 excitation pulse and during the 180 excitation pulse and during the 18000 rephasing rephasing pulse, to excite and rephase pulse, to excite and rephase each slice selectivelyeach slice selectively. .

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

9001800 900

Slice select gradient

Frequency encodingFrequency encoding►Once a slice has been selected, the signal Once a slice has been selected, the signal

coming from it must be spatially located coming from it must be spatially located (encoded) along both axes of the image(encoded) along both axes of the image

► Locating the signal along the long axis of Locating the signal along the long axis of anatomy is done by a process called anatomy is done by a process called frequency encodingfrequency encoding

► A gradientA gradient is applied along theis applied along the selected axisselected axis► The precessional frequency of signal along the The precessional frequency of signal along the

axis is therefore altered in a linear fashion.axis is therefore altered in a linear fashion.► The signal can now be located along the axis The signal can now be located along the axis

of the gradient according to its frequencyof the gradient according to its frequency

For frequency encoding ofFor frequency encoding of► Coronal & sagittal images – use z gradientCoronal & sagittal images – use z gradient► Axial images – use X gradient Axial images – use X gradient ► Axial images of Head – use Y gradientAxial 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 C

In practiceIn practice► The frequency encoding gradient is switched The frequency encoding gradient is switched

on when the signal is received and is often on when the signal is received and is often called the called the readout gradientreadout gradient

FID Echo FID

900 900

1800

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.

Phase encodingPhase encoding

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

► This is achieved by applying a gradient This is achieved by applying a gradient along this remaining axisalong this remaining axis

► A gradient is switched on it A gradient is switched on it altersalters the the speed speed of precessionof precession as well as the as well as the accumulated accumulated phase of the nucleiphase of the nuclei along their precessional along their precessional path.path.

► It produces a It produces a phase differencephase difference or shift or shift betweenbetween nuclei nuclei positioned along the axis.positioned along the axis.

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 Gradient & phase difference

►When the phase encoding gradient is When the phase encoding gradient is switched off, the magnetic field strength switched off, the magnetic field strength experienced by the nuclei returns to Bexperienced by the nuclei returns to B00 and and the precessional frequency of all the nuclei the precessional frequency of all the nuclei returns to the larmor frequency.returns to the larmor frequency.

►However the phase difference between However the phase difference between nuclei remainsnuclei remains

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

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

In practiceIn practice► The phase encoding gradient is switched on just The phase encoding gradient is switched on just

before the application of the 180before the application of the 18000 rephasing pulse rephasing pulse in spin echo sequences. in spin echo sequences.

Phase encoding gradient

900900

1800

Summary of phase encodingSummary of phase encoding

►The phase encoding gradient alters The phase encoding gradient alters the phase along the the phase along the short axisshort axis of the of the anatomy anatomy

► In In CoronalCoronal images – images – xx gradient gradient ► In In sagittalsagittal images - images - YY gradient gradient► In In axialaxial images - Y gradient images - Y gradient►AxialAxial images of images of brainbrain – – x x gradientgradient

Summary spatial encodingSummary spatial encoding

►The slice-select gradient is switched on The slice-select gradient is switched on during the 90 and 180 pulses in spin echo during the 90 and 180 pulses in spin echo

pulse sequences , and pulse sequences , and during the excitation pulse only in gradient during the excitation pulse only in gradient

echo pulse sequencesecho pulse sequences

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

► The phase encoding gradient is switched on The phase encoding gradient is switched on just before the 180 pulse in spin echo, and just before the 180 pulse in spin echo, and between excitation and the signal collection in between excitation and the signal collection in

gradient echo.gradient echo.

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

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

► The The amplitudeamplitude of the of the frequency encodingfrequency encoding gradient and the gradient and the phase encodingphase encoding gradient gradient determines the two dimensions of the determines the two dimensions of the FOVFOV

Gradient timing in spin echoGradient timing in spin echo

900

900

1800

echo

slice select

slice select

Phase encode

Frequency encode

TR

SamplingSampling

►The signal is collected during the The signal is collected during the frequency encoding gradient (frequency encoding gradient (readout readout gradientgradient))

►The duration of readout gradient is The duration of readout gradient is called called sampling timesampling time

►The system The system samples up to 1024 samples up to 1024 frequenciesfrequencies during sampling time during sampling time

►The rate at which the samples are taken The rate at which the samples are taken is called the is called the sampling ratesampling rate

►The The number of samples takennumber of samples taken determines the determines the number of frequenciesnumber of frequencies sampledsampled

►The range of frequencies is called the The range of frequencies is called the receive bandwidthreceive bandwidth

f1f2 f4f3 f5f6

Receive bandwidth

Frequency columns in FOV

Frequencies sampled are mapped across the FOV along the frequency axis

► Sampling time, sampling rate and receive Sampling time, sampling rate and receive bandwidth are linked by a mathematical bandwidth are linked by a mathematical principle called the principle called the Nyquist theoremNyquist theorem. .

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

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

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

► Receive bandwidth is proportional to the Receive bandwidth is proportional to the Sampling rateSampling rate

►Sampling time is inversely proportional Sampling time is inversely proportional to:to: The sampling rateThe sampling rate The receive bandwidthThe receive bandwidth

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

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

►Usually the receive bandwidth & sampling Usually the receive bandwidth & sampling time are fixedtime are fixed

Nyquist theorumNyquist theorumSampling once

Reproduced as a straight line

Sampling twice

Reproduced more accurately

Bandwidth versus sampling timeBandwidth 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 taken

Data collectionData collection► Location of individual signals within the image by Location of individual signals within the image by

measuring the number of times the magnetic measuring the number of times the magnetic moments cross the receiver coil (moments cross the receiver coil (frequencyfrequency), and ), and their position around their precessional path (their position around their precessional path (phasephase))

Frequency

sh

ift

Phase shift

1 cycle/s

2 cycles/s

3 cycles/s

K spaceK space► The data information is stored in the computer memory location The data information is stored in the computer memory location

called the K space. Maximum number of lines are 1024 called the K space. Maximum number of lines are 1024 phase

frequency

+ve

-ve

central

outer

One line is filled for one phase encoding gradient

Data collection – step 1Data collection – step 1

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

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

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

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

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

Phase shift & pseudo-Phase shift & pseudo-frequencyfrequency

► The system cannot measure the phase values The system cannot measure the phase values directlydirectly

► It can measure frequencyIt can measure frequency► The phase shift values are converted to a The phase shift values are converted to a

sine wavesine wave► The frequency of this sine wave is called a The frequency of this sine wave is called a

pseudo-frequencypseudo-frequency►Different phase shift gradient produce Different phase shift gradient produce

different sine waves with different pseudo-different sine waves with different pseudo-frequencyfrequency

The pseudo frequency curveThe pseudo frequency curve

Phase shift value

time

Phase encoding gradient & Phase encoding gradient & pseudo frequencypseudo frequency

►Steeper gradients results in high pseudo Steeper gradients results in high pseudo frequenciesfrequencies

►Shallow gradients results in low frequenciesShallow gradients results in low frequencies

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

► With each phase encoding one line of With each phase encoding one line of KK spacespace is filledis filled

► Different lines in K space are filled after every Different lines in K space are filled after every TRTR

► The phase encoding gradient is altered for The phase encoding gradient is altered for every TRevery TR

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

► The number of lines that are filled is The number of lines that are filled is determined by the number of different phase determined by the number of different phase encoding slopes that are appliedencoding slopes that are applied

K spaceK space

Line 1 phase encode 1 frequency/phase Line 1 phase encode 1 frequency/phase datadata

Line 2 phase encode 2Line 2 phase encode 2

Line 128 phase encode 128Line 128 phase encode 128

Fast Fourier Transform (FFT)Fast Fourier Transform (FFT)

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

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

► The The signal intensity/time domainsignal intensity/time domain is converted is converted to a to a signal intensity/frequencysignal intensity/frequency domain domain

RF

inte

nsi

ty

Time

Am

plit

ud

eFrequency

Time domain

Frequency domain

Matrix & FOVMatrix & FOV

►The FOV relates to the amount of The FOV relates to the amount of anatomy coveredanatomy covered

► It can be square or rectangularIt can be square or rectangular► Image consists of a matrix of pixelsImage consists of a matrix of pixels►Te number of pixels depends on the Te number of pixels depends on the

number of frequency samples and number of frequency samples and phase encodingsphase encodings

► Matrix = frequency samples x phase Matrix = frequency samples x phase encodingsencodings

MatrixMatrix

Coarse matrix 4x4 Fine matrix 8 x 8

4 frequency samples

8 p

hase

sa

mple

s

8 frequency samples

4 p

hase

sa

mple

s

Data collection - step 2, NSA Data collection - step 2, NSA (NEX)(NEX)

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

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

►Doing so each line of K space is filled more than Doing so each line of K space is filled more than onceonce

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

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

Scan timingScan timing

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

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

►E.g. E.g. TR of 500ms may allow 12 slices. TR of 500ms may allow 12 slices. TR of 2000 ms may allow 18 slicesTR of 2000 ms may allow 18 slices

TR & number of slicesTR & number of slicesTR

Slice 1

Slice 2

Slice 3

Slice 4

Slice 1 second TR

90180

echo

TE

Phase encode 1

Phase encode 2

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

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

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

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

Scan time = TR x Number of phase encodings x Scan time = TR x Number of phase encodings x NEXNEX

K space fillingK space filling

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

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

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

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

► The outer lines are filled with data produced The outer lines are filled with data produced with steep phase encoding gradientswith steep phase encoding gradients

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

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

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

Signal amplitude & phase shift Signal amplitude & phase shift gradientgradient

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

►The steeper phase encoding gradients The steeper phase encoding gradients have larger phase shift along their axis have larger phase shift along their axis and therefore small signal amplitudesand therefore small signal amplitudes

Phase encoding slope & signal Phase encoding slope & signal amplitudeamplitude

Steeper gradient

medium gradient

shallow gradient

Low amplitude

medium amplitude

high amplitude

Signal amplitude & frequency Signal amplitude & frequency gradientgradient

► The vertical axis of k space correspond to The vertical axis of k space correspond to the frequency encodingthe frequency encoding

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

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

► The magnetic moments on either side are The magnetic moments on either side are either rephasing and dephasing and either rephasing and dephasing and therefore the amplitude is lesstherefore the amplitude is less

Signal amplitude & frequency Signal amplitude & frequency gradientgradient

Rephasing Dephasing

Peak

K space filling & spatial K space filling & spatial resolutionresolution

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

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

► The The steeper gradientssteeper gradients result inresult in high spatialhigh spatial resolutionresolution (two adjacent points have (two adjacent points have different phase values and can be different phase values and can be differentiated)differentiated)

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

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

►TheThe central portion central portion of k spaceof k space contains contains data data that hasthat has high signal amplitude high signal amplitude && low spatial resolutionlow spatial resolution

►TheThe outer portion outer portion of k spaceof k space contains contains data that has low signal amplitude data that has low signal amplitude andand high spatial resolutionhigh spatial resolution

Resolution & AmplitudeResolution & Amplitude

High spatial resolution

High signal

High spatial resolution

Way of filling K spaceWay of filling K space

► The The amplitude of frequency encodingamplitude of frequency encoding gradient gradient determines determines how far to the left and righthow far to the left and right K space K space is traversed and this in turn determines the size is traversed and this in turn determines the size of the FOV in the frequency direction of the of the FOV in the frequency direction of the imageimage

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

► The The polarity of each gradientpolarity of each gradient defines the defines the directiondirection traveled through K space traveled through K space

K space filling in gradient K space filling in gradient echoecho

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

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

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

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

► Phase encode gradient is negative, fills Phase encode gradient is negative, fills bottom half of K spacebottom half of K space

K space filling in gradient echoK space filling in gradient echoPhase 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 filled

Manipulation of K space Manipulation of K space fillingfilling

►The way in which K space is filled The way in which K space is filled depends on how the data is acquired depends on how the data is acquired and can be manipulated to suit the and can be manipulated to suit the circumstances of the scan; e.g. in the circumstances of the scan; e.g. in the followingfollowing Rectangular field of viewRectangular field of view Anti-aliasingAnti-aliasing Ultra fast pulse sequencesUltra fast pulse sequences Respiratory compensationRespiratory compensation Echo planar imagingEcho planar imaging

Partial or fractional echo Partial or fractional echo imagingimaging

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

►As the As the sampling time is reducedsampling time is reduced minimum minimum TE can be reducedTE can be reduced

►This allows maximum T1 and proton This allows maximum T1 and proton density weighting and number of slices density weighting and number of slices for a given TRfor a given TR

Readout gradient

Minimum TE

Minimum TE reduced

Only half of the k Space is filledThis extrapolated

from filled segment

Partial echo imaging

Only this half is read

Partial or fractional averagingPartial or fractional averaging

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

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

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

► The scan time is there fore reducedThe scan time is there fore reduced► E.g. 256 phase encodings and, 1 TR and ¾ NEX is E.g. 256 phase encodings and, 1 TR and ¾ NEX is

selectedselected► This is called partial or fractional averaging This is called partial or fractional averaging

Partial averagingPartial averaging75% 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 s

PRE-SCANPRE-SCAN

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

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

► Finding the exact magnitude of RF that must be Finding the exact magnitude of RF that must be transmitted to generate maximum signal in the coil. (to transmitted to generate maximum signal in the coil. (to flip the NMV through 90flip the NMV through 9000))

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

Reasons for failing pre-scanReasons for failing pre-scan

►The coil is not plugged in properlyThe coil is not plugged in properly►The coil is faultyThe coil is faulty►Chemical saturation techniques are Chemical saturation techniques are

utilized and there is an uneven utilized and there is an uneven distribution of fat and water in the distribution of fat and water in the area to be saturatedarea to be saturated

►The patient is either very large or very The patient is either very large or very smallsmall

Types of acquisitionTypes of acquisition

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

► Two-dimensional volumetricTwo-dimensional volumetric :– data collected for all :– data collected for all the slices simultaneously (line 1 in first slice, then the slices simultaneously (line 1 in first slice, then line 1 in slice 2)line 1 in slice 2)

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

EndEnd