Lecture no 6 MRI Physics:
• Spatial Encoding and K-Space
• MRI sequences:
o SPIN Echo
o Fast spin echo
o Multiecho
o Inversion recovery
Spatial encoding:
• We have to ask ourselves: how can we select only one organ to be excited by RF pulse?
• The answer is by using a coil that determines the organ of interest to receive a specific
RF pulse in resonance with the precession frequency of the proton inside the tissue.
• We can excite the whole organ, but we will receive the signal from the whole organ,
which is not required.
• We are trying to get a slice of this organ to get more details about it.
• How can we excite only one slice? by using a slice selection gradient, which is able to
vary in the magnetic field strength along the organ of interest
• Each slice of the organ will be prominent to a certain value of the magnetic field, so each
slice will be in a specific precession frequency proportional to the value of the magnetic
field at this position.
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• So now, we solved the issue of slice selection using the slice selection gradient
• The selected slice is composed of protons distributed in all pixels
• The image of the slice contains a certain value of pixels based on the matrix size
• Each pixel should contain a certain number of protons that produce a signal.
• If all pixels are excited with the same RF pulse, so all pixels will produce the same signal
which can’t be discriminated, so we can’t accurately localize the signal at the image.
• We have to think about solving this issue: how can I discriminate between the signals
which come from all pixels?
• We will apply a gradient magnetic field in the vertical and horizontal direction of the
image
• These gradients will make a difference in the frequency and phase of the signal.
• At that time, we can receive each signal with a specific frequency and phase which
enable better localization.
• We will apply a gradient in a vertical position that changes the phase of protons, so it is
called the phase encoding gradient.
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• For instance, the matrix size is 256 rows x 256 columns, so we have to discriminate
between the pixels in the same column using a phase encoding gradient.
• We will apply the phase encoding gradient 256 times, each time with a different degree
of gradient strength.
• For each time, we will change the precession frequency of all pixels in the same column
proportional to the gradient strength.
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•
• Then, we will stop Appling the Phase encoding gradient, which returns the frequency of
all protons to be the same, but in a different phase.
• So, each row of pixels produces a signal with a specific phase.
• The phase encoding gradient (GPE) intervenes for a limited time period. While it is
applied, it modifies the spin resonance frequencies, inducing dephasing, which persists
after the gradient is interrupted. This results in all the protons precessing in the same
frequency but in different phases.
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• The protons in the same row, perpendicular to the gradient direction, will all have the
same phase. This phase difference lasts until the signal is recorded.
• We have to discriminate between the pixels at the same row, so we have to apply a
frequency encoding gradient in the horizontal direction to differentiate between the
pixels in the frequency.
• The frequency encoding gradient must be applied one time during the recording of the
signal.
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• Now, each pixel will produce a signal with a specific frequency and phase which enable
us to localize accurately the signal position.
• These signals are analyzed by Fourier transformation to get better localization.
• All signals should be stored at K space (the location of storing signals).
• A classic spin echo sequence fills the k-space line by line. Here is the explanation of the
k-space trajectory :
• 90° RF pulse + Slice-selection gradient: location at origin (center) of k-space
• Negative and strong phase-encoding gradient: moves to the lower bound of k-space
• Positive frequency-encoding gradient (dephasing lobe): moves to the right bound,
location at the lower right corner
• 180° RF pulse + Slice-selection gradient: moves to the opposite location, location at the
upper left corner
• Positive frequency-encoding gradient + Data acquisition: moves to the right + acquire
MR signal
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• Repetition for each line with increasing phase-encoding gradient strength (negative to
positive intensity). The amount of gradient phase change between the adjacent line is
constant. This results in a sequential (line by line) filling of k-space from top to bottom.
•
•
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•
•
• How and when the MR signals are mapped into the k-space cause great differences in
the spatial, temporal, and contrast resolution of the resulting MR images.
• The location of the data in k-space depends on the net strength and duration of the
phase encoding gradient and frequency encoding gradient :
• A low-amplitude or short-duration gradient event encodes low-spatial-frequency
information
• A high-amplitude or long-duration gradient event encodes high-spatial-frequency
information
• The low-spatial-frequency information is mapped near the center of k-space and the
high-spatial-frequency information are mapped to the periphery of k-space.
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•
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•
• MRI sequences
• Spin Echo Sequence:
o At 0 time, Appling 90 RF pulse, and apply Slice selection gradient SSG at the same time.
o Switch the Phase Encoding gradient PEG to a certain degree, then switch it off.
o At half TE, Appling 180 RF pulse, and apply SSG at the same time.
o At TE, Appling Frequency encoding gradient during recording the signal.
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o We record the signal for each row in a single image, by varying the phase encoding step,
we get another signal for the second row, and so on.
o The scan time of a single image depends on the number of phase encoding steps Nph
and the time required for repeating the 90 RF pulse TR.
o We can repeat the excitation process for the same line and the scan time is proportional
to the number of excitations NEX .
o The time required to scan one slice depends on TR ,Nph and NEX.
o The scan time = TR x NEX x Nph x number of slices
o A typical brain scan contains 18 slices
o The TR is 540ms
o A matrix size of 256 x 512 (256 phase encoding steps are required per slice)
o The scan time is:
o TR x PE steps x Number of slices / 60,000
o 540 msec x 256 x 18 / 60,000 = 41.4 minutes
• Considering the TE is only 30ms, this is a very long scan with a lot of dead time in which no signal
is being created. We can use this dead time by selecting another slice and starting a cycle, then
selecting a third slice and starting a cycle etc.
•
• After 540 ms it is time to start the second cycle for the first slice. In 540 ms we can scan 18 lines
of 18 different k-spaces. Now we just need to repeat this enough times to get every line of every
k-space (i.e. multiple by the number of phase encoding steps). Recalculating the scan time gives
us:
• 540 x 256 / 60,000 = 2.3 minutes
• This technique is used in nearly every scan to make the scan times shorter.
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•
• Multi echo sequence:
o So far, only one echo per cycle is being created. We can acquire more echoes
in one cycle.
o From the previous chapter "T1, T2 and PD Weighted Imaging" we saw that
o By selecting different TEs we can create different weighted images:
o PD weighted uses a short TE of 15 ms
o T2 weighted uses a long TE of 1000-3000 ms
o We can transmit two 180° pulses to create two echoes with different TEs of
o the same row of the same k-space. In this way, we create a PD and a T2 image
o in the same amount of time as it takes to create one image
o
• Fast spin Echo
o It employs a train of 180 RF pulses after a single 90 Pulses, and we record a signal after
each 180 RF pulse which reduces the scan time.
o The train of 180 RF pulse is called Echo train length ETL (turbo factor).
o The space between the echoes is called echo spacing.
o As time reduced, so we can increase the number of matrix to increase the spatial
resolution , so it can be used in Extremities , brain and spine scanning .
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o
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• For instance
• Inversion recovery sequences
o It is a type of spin echo sequence, starting with a 180 RF pulse which flips the MZ of fat
tissues to the -180 degree.
o After 180 RF pulses, the MZ reached the maximum value at -180 degrees.
o By switching off the 180 RF pulse, the MZ starts recovering to reach zero (null point)
after a certain time which varies from one tissue to another.
o For example, water takes a long time to recover the MZ, but Fat is quickly recovered the
MZ.
o Let us recall that fat has very short T1 values (260 msec) and fluids have very long T1
values (2000 msec)
o At a certain time, where the MZ of fat reaches zero and the MZ of water still exist, we
apply a 90 RF pulse.
o This 90 RF pulse will affect on MZ of water, and no effect will occur on the MZ of fat, as
Fat MZ is at the null point, where there is no magnetization value to be affected by an
external RF pulse.
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o Then, we will continue the spin echo by applying 180 RF pulse.
o By recording the signal, we will get a bright signal for water and a dark signal for fat.
o the tissues which have a similar T 1 constant as fat, will appear as a dark signal.
o The waiting time between the 180 RF pulse and 90 RF is called inversion recovery time
TI.
o By applying a short inversion recovery time, so we are able to get a short time inversion
recovery STIR sequence, which maximizes the signal of water tissue contents by reducing
the signal of fat and other tissues .
o Another consideration with STIR is that the TR must be set relatively long (1500–2000
msec), compared to a T1 image acquisition with spin echo using a TR value of
approximately 500 msec. This additional time is required for the longitudinal
magnetization to more fully recover after the excitation pulse and before the next cycle.
o
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o
o
o If we want to attenuate to the water signal , so we have to increase the inversion time to
be suitable for reaching the water to a null or zero state.
o At that time we apply the spin echo sequence to get the Fluid attenuated inversion
recovery sequence FLAIR
o FLuid Attenuated Inversion Recovery Fluid signal nulled by selecting long TI (2500 ms).
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o
o
o Acquisition time is a special concern with this method. That is because when long TI
values are used, the TR values must also be long (5000–6000 msec), and that increases
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the acquisition time. For this reason, the practical thing is to use this method with one of
the fast acquisition techniques.
o Disadvantages of IR
In spite of all these unique features and advantages, there are several disadvantages for
IR compared to SE and GRE techniques:
Longer scan times
o Increase in flow-related artifacts
o Signal-to-noise can decrease as tissues are suppressed
o Higher specific absorption rate (SAR) due to additional 180° pulses
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