Encoding and image formation

2. Content
o Encoding
o Gradients
o Slice selection
o Frequency encoding
o Phase encoding
o Sampling
o Nyquist Theorem
o Data collection and image formation
o K space description
o K space filling
o Fast Fourier transform (FFT)

3. Encoding
• Locating the signal in 3 dimensions so that
it can positioned each signals at correct
points on the image.
• First locate a slice.
• Once a slice is selected, the signal is
located or encoded along both axis of the
image.
• These are performed by gradients.

4. Select a slice
Locate/encode signal along both axis of the image
Locating slice & encoding signal is performed by gradients

5. Gradients
• Gradients are alteration to the main magnetic field and
generated by cell of wire located with in the bore of magnet
through which current is passed.
• The passage of current through a gradient coil induces a
gradient coil induces a gradient magnetic field around it.
• which either subtracts from, or adds to the main static
magnetic field Bo.
• Bo is altered in a linear fashion by the gradient coils.
• so, the magnetic strength and therefore precessional
frequency experienced by nuclei situated along the axis of the
gradient can be predicted called spatial encoding.
• 3 gradients coils situated within the bore of the magnet.

6. • These are named A/c to the axis along which they act when they
are switched on.
• These directions in a super conducting magnet.
o Z- gradient alters the magnetic field strength along the z- (long)
axis of the magnet.
o Y – gradient alters the magnetic field strength along the Y-
(vertical) axis of the magnet.
o X- gradient alters the magnetic field strength along the X-
(horizontal) axis of the magnet.
• Gradients can be used to either dephase or rephase the magnetic
moments of nuclei.
• Gradients also perform the 3 main tasks in encoding-
1. Slice selection
2. Phase encoding
3. Frequency encoding

8. Slice selection
• Locating a slice within the scan plane selected.
• When a gradient coil is switched on. The magnetic field
strength and therefore precessional frequency of nuclei
located along its axis.
• Nuclei situated within a slice have particular
precessional frequency.
• A slice can be selectively excited, by transmitting RF
with a band of frequencies coinciding with the larmour
frequencies of spins in a particular slice as defined by
the slice select gradient.

10. Slice thickness
• A band of nuclei must be excited b y the excited by the
excitation pulse.
• The slope of the slice select gradient determined the
differences in precessional frequency between the two point
on the gradients.
• Steep gradient slopes result in a large difference in
precessional frequency between two points on the gradient.
• While shallow gradient slopes result in a small difference in
precessional frequency between the same two points.
• The RF pulse transmitted to excite the slice must contain a
range of frequencies to match the difference in precessional
frequency b/w two points.

11. • This frequency range is called the bandwidth and the RF is being
transmitted at this point it is specifically called transmit
bandwidth.
o To achieve thin slices, a step slices select slope or narrow
transmit bandwidth is applied.
o To achieve thick slices, a shallow slices select slope or broad
transmit bandwidth is applied.
 Note:-
 To achieve the axial slices then cut the z-gradient.
 To achieve the coronal slices then cut the Y-gradient.
 To achieve the sagittal slices then cut the X-gradient.

12. A B
Thick slice- shallow gradient
Thin slice- steep gradient
To achieve thin slices, a steep slice select slope & narrow bandwidth is applied.
To achieve thick slice, a shallow slice select slope & broad bandwidth is
applied.
Bandwidth Bandwidth

13. Phase encoding
• The signal must now be located along the
remaining short axis of the image and this
localization of signal is called phase encoding.
• When the phase encoding gradient is
switched on, the magnetic field strength and
therefore precessional frequency of nuclei
along the axis of the gradient is altered.
• The phase encoding gradient is usually
switched on just before the application of the
180* rephasing pulse.

14.  Fig showing phase change of nuclei when phase
encoding gradient is switched on

16. Frequency encoding
 In this process signal is located along the long axis (z- axis) of
the anatomy.
 When frequency encoding gradient is switched on-
Now signal can be located along the axis according to its frequency.
Magnetic field strength & precessional frequency of signal
along the axis of the gradient is altered in a linear fashion.
Thus, this gradient produces a frequency
difference or shift of signal along the axis.

18. When gradients are switched on
Spin echo
sequence
Gradient echo spin
sequence
Slice select 90 & 180 RF pulse Excitation pulse
Phase encoding Before 180 RF pulse B/t excitation & signal
collection
Frequency
encoding
Collection of the signal Collection of the signal

19. Gradient switch on timing in spin echo sequence

20. Plane Slice
selection
Phase
encoding
Frequency
encoding
Sagittal
X Y Z
Axial body
Z Y X
Axial head
Z X Y
coronal
Y X Z
Gradient axis in imaging

21.  The frequency encoding gradient is switched on while
the system reads frequencies present in the signal, &
samples or digitizes them.
 This gradient is sometimes called Readout gradient.
 Duration of readout gradient is called sampling time/
acquisition window.
 Sampling rate- rate at which frequencies are sampled
or digitized during readout. system samples
frequencies up to 1024 different times.
 Each sample is stored as a data point.
Sampling

22.  Collected data or information from each signal is
stored as data points
 K-space is rectangular in shape & has two axis
perpendicular to each other.
 Unit of k-space is radians per cm.
K-space is a special frequency domain where information about
the frequency of a signal & where it comes from in the patient is
stored.

23.  Frequency axes- horizontal
 Phase axes- vertical.
Each slice has its own k-space.
Data space– matrix of processed image
data.(analog signal)

24.  An MR image consists of a matrix of pixels, the number of which is
determined by the no. of lines filled in K- space and no. of data points in each
line.
 Each data point contains phase and frequency information from the whole
slice at a particular moment in time during read out.
 The FFT process mathematically converts this to frequency amplitudes in the
frequency domain. It is necessary because gradients spatially locate signal
according to their frequency, not their time