MRI uses a strong magnetic field and radio waves to create detailed images of the organs and tissues within the body. Developed by the Lauterbur in 1972 at Stony brook in New York. MRI does not involve radiation MRI contrasting agent is less likely to produce an allergic reaction that may occur when iodine-based substances are used for x-rays and CT scans MRI gives extremely clear, detailed images of soft-tissue structures that other imaging techniques cannot achieve The MRI machine cannot just simply “see the hydrogen nuclei which lie “hidden” in the water molecules distributed in the patient. It needs to do ‘something’ to the hydrogen nuclei to detect their presence.

1. MRI
MAGNETIC RESONANCE IMAGING
By
Neha Mannewar

2. Outline
 Introduction
 Basic principle
 Why MRI machine?
 Angular Momentum and spin
 Processing
 Relaxation time
 Free induction decay
 T1,T2
 Proton weighted image
 Pulse sequences
 Basic and advance pulse sequences
 Image formation
 Localisation of signal

3.  MRI uses a strong magnetic field and radio waves to create detailed images of
the organs and tissues within the body.
 Developed by the Lauterbur in 1972 at Stony brook in New York.
Introduction
The field strength of the magnets
used for MR is measured in units of
Tesla. One(1) Tesla is equal to
10,000 Gauss.
The magnetic field of the earth is
approximately 0.5 Gauss.
The type of magnets used for MR
imaging usually belongs to one of
three types; permanent, resistive,
and superconductive.

4. Why MRI
 MRI does not involve radiation
 MRI contrasting agent is less likely to produce an allergic reaction that may occur when iodine-
based substances are used for x-rays and CT scans
 MRI gives extremely clear, detailed images of soft-tissue structures that other imaging
techniques cannot achieve
 MRI can easily create hundreds of images from almost any direction and in any orientation
 Unlike techniques that examine small parts of the body (i.e. ultrasound or mammography) MRI
exams can cover large portions of the body
 MRI can determine if a cancer has spread, and help determine the best treatment.
 The nucleus of the hydrogen is the simplest in nature, consisting of just one proton and no
neutron.
 The advantage of hydrogen atom for magnetic resonance are:
a) It is the most common element found in human body.
b) It has highest sensitivity to magnetic resonance .
c) Hence magnetic resonance imaging uses almost exclusively the protons of hydrogen for
image generation.

5. Basic Principle
 The MRI machine cannot just simply “see the hydrogen nuclei which lie
“hidden” in the water molecules distributed in the patient.
 It needs to do ‘something’ to the hydrogen nuclei to detect their presence.

6.  The MRI machine does something similar to detect the hydrogen nuclei.
It first “irritates” the hydrogen nuclei and then from their “responses”,
detects their presence.

7.  Consider, the patient into the magnetic field of the MRI machine.
 The patient, like all of us, has water molecules distributed all over

8.  The strong magnetic field makes the spin of the hydrogen nuclei line up in the direction of the
magnetic field .
 Spin of some hydrogen nuclei are in the same direction as the magnetic field .
 The nuclei choose to be in same direction do not have much energy and so it is low energy nuclei
(lazy one)

9.  There are also some hydrogen nuclei that have spins that are in the opposite direction to the magnetic
field. Unlike the lazy nuclei you saw before, these ones have to “fight” the magnetic field and therefore
have an “higher” energy. In our diagrams, as shown below, I will label these “high energy nuclei” as “High”
.
 After the magnetic field has made the nuclear spins line up, you will notice that there are slightly more low
energy nuclei than high energy nuclei

10.  The MRI machine has a special coil of
wire that is there for the purposes of
producing the needed energy to ‘irritate’
the low energy hydrogen nuclei.
 The MRI machine applies a current to this
energy producing coil for a short period.
 During this period, the coil produces
energy in the form of a rapidly changing
magnetic field .
 The frequency of this changing field falls
within the frequency range commonly
used in radio broadcasts.
 Therefore this energy is often called “radio
frequency” energy (RF energy) and the
coil is often called an radio frequency coil
( RF coil).

11.  After a short period, the RF energy is stopped.
 The hydrogen nuclei that recently became ‘high energy’ prefer to go back to their previous, ‘low energy’ state and
they start releasing the energy that was given to them .
 They release the energy in the form of waves .The MRI machine has “receiver coils ” (blue coil shown below) that
receive the energy waves sent out by the nuclei. Having given up their energy, the nuclei change their spin direction
and return to the low energy state that they were in before.
 The receiver coil converts the energy waves into an electrical current signal

12.  Excess number of low spins result in net magnetization
 Number of excess spins depends on the factors:
Increases with 1.proton density in tissue.
2. The strength of the external mag field.
Decreases with 1.increase in temperature.
 The external magnetic field lines apply torque to the spins .
 Hence the spins will rotate about the magnetic field lines.
 The rotation of the axis of spins about the magnetic field lines is called
precession.
 As a result of the precession of spins ,the net magnetization Mz too precess
about the Z-axis.

13.  The rate of precession of proton in a magnetic field is characteristic
of that tissue and depends on the strength of magnetic field too.
 The precession frequency is called larmor frequency.
 Larmor frequency is directly proportional to external magnetic field
strength.
 fo = γ Bo
 where fo is the precession frequency, Bo is the strength of the
externally applied field, and γ is the gyromagnetic ratio,.
 The gyromagnetic ratio (also sometimes known as
the magnetogyric ratio in other disciplines) of a particle or system is
the ratio of its magnetic moment to its spin angular momentum
 Υ=µ / I (h/2π), where I is the nuclear spin.
 Each type of nucleus will precess at a unique larmor frequency in a given
magnetic field.
 Hence larmor frequency is a process that for given magnetic field ,can
distinguish between nuclear type.

14. Angular momentum
 Angular momentum describe the rotational motion of the body, it has direction as well as
magnitude.
 It may be changed by applying torque.
 There are two types of rotational motion;
Orbital and spinning.
 Example: the earth is orbiting the sun and the earth is rotating about its own axis.
 The angular momentum of nucleus can be determined by spin of unpaired neutrons and protons
and by orbital angular momentum of neutrons and protons.
 Without angular momentum , a nucleus would not precess when placed in mag field, without
precession there would be no resonance.

15. Spin angular momentum
 Spin angular momentum is a specific type of angular momentum possessed by some
nuclei.
 it obeys all the relations given for angular momentum under the quantum mechanics of
rotation.
 All nuclei have a spin quantum number, I, which may be integral (including zero) or
half-integral, but never negative.
 The value of I is characteristic of a given nucleus, and may vary between isotopes.
 Thus all 1H hydrogen nuclei have I = ½ , but all 2H deuterium nuclei have I = 1.
 The magnitude of the spin angular momentum is determined by the quantum number I,
and is given by:
 Magnitude of spin angular momentum = √ (I (I +1) )ћ

16. Resonance
 The phenomenon of amplification that occurs when the frequency of a
periodically applied force is in harmonic proportion to a natural frequency of the
system.
 When an oscillating force is applied at the resonant frequency of another system,
the system will oscillate at a higher amplitude than when the same force is
applied at other.
 The term resonance (from latin resonantia, 'echo', from resonare, 'resound').

17. Magnetic Dipole moment
 The property or characteristic of a magnet (or wire loop) that indicates how quickly the
magnets will align itself along magnetic field.
 As the proton acts as a tiny bar magnet.
 Stronger the magnet ,more quickly it will align with the field.
 MDM will give the orientation of object possessing the MDM.
 The proper direction is obtained by another left hand rule: curl fingers is in direction
of electron flow and thumb will be in the direction of MDM.
 Bohr magneton is used to express the MDM of electrons.
 The nuclear magneton is used to express the MDM of nuclei.
 The MDM of the proton or neutron is measured in lab and found different from nuclear
magneton.
 The magnetic dipole moment of a proton, measured in magneton units, is
+2.79285.
 Positive value of spin indicates: MDM and angular momentum is in same direction.

18.  The MDM of the nuclei can be measured .
 If the nucleus has no spin (I=0),that is ,it has no angular momentum, it will have no
MDM.
 Nuclei with no MDM cannot be detected in machine.
 Therefore ,all the nuclei whose mass number A and atomic number are both even
cannot be used.

19.  Precessing protons have two magnetic components.
1. Vertical (longitudinal) component Mz along Z direction
2. Horizontal component (Mxy) in transverse plane (transverse component)

20.  Since the proton are precessing out of phase ,their individual magnetic components in the
transverse plane will cancel each other.
 Hence, the magnetization components (Mxy) in the transverse (xy) plane will be zero.
 The difference between the energy states of spin-us and spin down works out to be in the
range of the energy of electromagnetic radiation, which falls in the category of
radiofrequency (1kHz to 100MHz).
 When a RF pulse of frequency that matches with larmor frequency of proton precession is
applied perpendicular to the magnetic field, proton precessing in the lower energy state
are stimulated in phase.
 This result in a phase coherent precession.

21.  Along with the phase coherent precession, since spins down are receiving energy
from RF pulse, they will rotate towards the higher energy state.
 As a result the Mz component flips through angles proportionate to the rotation of
protons.
 The precessing Mz follows a spiral trajectory when flips from vertical to horizontal
direction.
 The energy of the stimulating RF pulse and duration of stimulation determine angle of
deflection (flip angle) of magnetization.
 A 90˚ RF pulse will flip the magnetization in the Z-direction to the transverse plane (x,y).
 A 180˚ RF pulse will flip the magnetization in the Z+ and Z- direction.

22. Generation of MR signal
 RF coil acts both transmitter and receiver in MRI.
 During RF pulse transmission, the coil cannot serve as receiver .
 Hence the transmission has to be stopped periodically for enabling the RF coil to
receive MR signal.
 A 90 degree RF pulse will flip magnetization to transverse plane.
 Hence immediately after a 90 degree RF pulse, the RF pulse coil encounters
only transverse magnetization (Mxy). The vertical component of magnetization
(Mz) will be zero at that time.
 Mxy component is created by the phase coherent precession of protons in the
transverse plane.
 However because of spin-to-spin interaction they loose energy and phase
coherence and precess back to their original relaxed state.

23.  When proton precess back to the relaxed state, the magnetization from the transverse plane
will spiral back to the external magnetic field direction.
Circular movement of magnetization will induce a
sinusoidal electric signal in RF coil.

24.  After a 90˚ RF, since the magnetization spirals back to the vertical direction, the
spiral trajectory will induce a signal in the RF coil which has both sinusoidal and
exponential decay components
The signal produced by the free return of M to the H direction is known as free induction decay (FID)

25.  The signal called free induction decay (FID) because,
 When RF pulse is turned off.
 The spins begin to precess freely
1. The spins induce a current in the receiver coil.
2. The signal starts to decay with time

26.  When a 90˚ RF pulse is applied longitudinal magnetization, it produce the
following two effects.
 It flips longitudinal magnetization (Mz) through 90˚ to xy plane and temporarily
destroys the magnetization in the longitudinal direction. This condition is known as
saturation.
 It also produce transverse magnetization (Mxy) a condition known as excitation
because transverse magnetization is an unstable state.

27. Relaxation process
 When RF pulse is switched off, two relaxation process start simultaneously.
1. Fast decay of transverse magnetization (Mxy) and
2. Slow recovery of longitudinal magnetization (Mz)
 Both these process takes place exponentially.
 Time required for both these process depends upon the nature and physical
state of the medium.
 The rate of decay/recovery characterized by the relaxation process conveys
information about the structure in which the magnetic moments are located.

29. T1 relaxation time
 The term relaxation means that the spins are relaxing back into its equilibrium
state.
 Once the RF pulse is turned off, the spins will realign with the external
magnetic field lines by giving up all their excess energy.
 T1 is known as longitudinal relaxation time because it refers to the time it
takes for the spins to realign along the longitudinal (z) axis.
 T1 is also known as spin lattice relaxation time because spins relax back to
their equilibrium state by giving up their excess energy to the surrounding
tissue lattice.

30.  Recovery of longitudinal (Mz) at any time ‘t’ after and RF pulse is given by the
relaxation time.
 At t=T1, about 63% of the magnetization will be recovered.
 At t=2T1, recovery will be 73%.
 100% recovery takes place beyond t=5T1
 𝑀𝑧(𝑡) = 𝑀0 (1- 𝑒−𝑡/𝑇1)

31. T2 relaxation time
 T2 relaxation time characterized the rate at which the Mxy component decays .
Hence it is also known as transverse relaxation time.
• T2 decays occurs 5 to 10 times more rapidly than T1 recovery
• When t= T2,37% of Mxy will decay
• 𝑀 𝑥𝑦(𝑡) = 𝑀0 (𝑒−𝑡/𝑇2
)

32.  When RF pulse is switched off, Mxy decay takes place because of the
dephasing of spins, which were in a phase coherent precession at the time of
application of RF pulse.
 There are two phenomenon that will make the spins to get out phase, they are.
1. Interaction between spins (spin-spin interaction)
2. External magnetic field in homogeneities
 When two spins are close together , the magnetic field of one will affect the other
. This is the major cause of de-phasing of spins.
 Spin-spin interaction is inherent in the tissue and cannot be avoided.
 Since spin-spin interaction influence T2 relaxation time, it also known as spin-
spin relaxation time.

33. T2* (effective T2)
 In order to account for the influence of magnetic field inhomogeneity on T2,
another decay time rate T2* is introduce.
 T2* decay depend on both external magnetic field inhomogeneity and spin
spin interaction,
 Whereas T2 decay depends on spin-spin interaction
 Since spin spin interaction cannot be controlled .T2 of tissue ,ehich depend
on these interaction is fixed.
 However T2* varies depending upon how uniform the main magnetic field is.
 T2* decay is always faster than T2 decay.
 If the magnetic field is homogeneous ,T2=T2*

34. T1,T2 tissue contrast
 T2 characteristics
 T2 characteristic of a tissue is depending upon how fast the proton- spins de-
phase in that tissue.
 Rapid de-phase results in short T2 and slow de-phasing results in longer T2.
 H2O
 Proton occur wide apart in sparingly distributed water molecules .hence de-
phasing because of spin-spin interaction is minimal in water.
 T2 relaxation time for water is therefore long.

35.  Solids
 Molecular structure is very compact in solids, therefore protons are very close to
one another in solids.
 Hence de-phase takes place rapidly in solids.
 T2 relaxation time for solids is therefore short.
 Fats and proteins
 De-phasing in fat and protein takes place at a lesser rate compared to that in
solids but at a higher rate compared to that in water.
 Hence T2 has intermediate values (between that of solids and water) for fat and
protein

36.  Relaxation time T1 and T2 for different tissue

37. T1 characteristics
 The constant T1 is a tissue specific constant ,which tells how quickly the spins
of a certain body tissue will emit their absorbed RF energy.
 The T1 constant depends on the size of the molecule and the type of its
surrounding.
 H2O
 Small water molecules can move quickly and randomly through its molecule
environment .hence the energy released by water molecules by interacting
with their neighboring molecules per unit time will be less (i.e. inefficient energy
transfer)
 Hence T1 relaxation time for water is long.

38.  Fat
 Fat ,molecule are large and slow moving in their dense atomic lattice.hence they
transfer energy to the surrounding efficiently in short time.
 Hence T1 of fat is very short.
 Solid
 Energy transfer is not efficient. However. better than water.
 Hence solid has intermediate T1 values

39.  Longitudinal relaxation T1 curves for different tissue types

40.  Image brightness is proportional to the degree of longitudinal magnetization (𝑀 𝑜)
present in the tissue.
 More the magnetization more brighter the tissue will be.

41. Tissues with short T1 values
appear more brighter than
tissues with long T1 values.

42.  Image brightness is
proportional to the
degree of transverse
magnetization (Mxy)
present in the tissue.
 More the
magnetization
(Mxy),more brighter
the tissue will be

43. Tissue having long T2
values will appear as more
brighter than tissues
having short T2 values

44.  Different tissues have different T1 values and rate of re-growth of longitudinal
magnetization (M0).
 This causes different tissues to be at different levels of magnetization (M0), i.e.
brightness when the picture is snapped during the relaxation period.
 Order of tissues brightness is inversely related to T1 values.
 Short T1 → More Brightness
 Long T1 → Less Brightness

45.  T2 weighted image shows the level of magnetization (𝑀 𝑥𝑦) at the time of
snapping the picture.
 Tissues with long T2 values have higher concentration of magnetization and
appear as brighter than tissues having shorter T2 values, in the image.
 Order of tissue brightness is directly related to the T2 values
 Short T2 → Less Brightness
 Long T2 → More Brightness

47. Image processing & image
reconstruction in MRI
 Image processing →Acquisition of RF signals from patient body and
mathematical reconstruction of the image from the acquired signals.
 During the acquisition process the signals are collected, digitized and stored
in computer memory in a configuration known k-space.
 K-space is divided into lines of data that are filled one at a time.
 The size of k-space (No. of lines) is determined by the requirement for image
detail.

48. Image Acquisition
 Acquisition process consist of an imaging cycle that is repeated many times.
 The time required for a complete acquisition is determine by the duration of
the cycle multiplied by the number of cycles.
 Duration of the cycle is known as Time of repetition (TR)
 TR is an adjustable protocol and is used for selecting different type of image
contrast (T1 weighted , T2 weighted etc.)

49. Imaging protocol
 Each imaging procedure is controlled by a protocol that has been entered
into the computer.
 Factors that are considered for selecting , modifying or developing a protocol
for a specified clinical procedure includes.
 The imaging methods to be used.
 The image type (T1,T2 or proton density (PD) weighted)
 Spatial characteristic (slice thickness, number etc)
 Detail and visual noise requirement etc.
 Use of selective signal suppression techniques .
 Use of artifacts reduction techniques.

50. Imaging methods
 There are several imaging methods that can be used for creating MR images.
 They differ mainly in the sequence in which RF pulse and magnetic gradients
are applied during acquisition process.
 Different methods are referred to as different pulse sequences.
 For different imaging methods thee are a set of factors that are to be adjusted
b the use to produce specific image characteristic.
 Selection of different methods and factors are generally based on specific
tissue characteristic and acquisition speed.

51. Saturation Recovery (SR)
 Saturation Recovery (SR) is the most basic of pulse sequence.
 In SR, a series of 90˚pulses are applied during time interval known as Time of
repletion (TR).
 Initial 90˚ pulse flips the longitudinal magnetization (Mz) into transverse (x,y)
plane.
 The next pulse is applied only after a part of longitudinal magnetization has
re-grown.
 Mz recovery depends on the T1 characteristic of the tissues.
 TR determine the intensity of FID signals from each tissues and rissu
contrast.

52. Optimization of TR
 Too short TR → as a result of saturation effect ,the difference in FID
amplitudes corresponding a T1a and T1b be very low → low tissue contrast.
 Too long TR – as a result of recovery of longitudinal magnetization FID
amplitudes will be almost equal → low tissue contrast.
Ideally TR should be
between T1 values of both
tissues

53.  FID signals decay quickly after a 90˚ pulse.
 Technically it is much easier to measure a spin echo that a FID signal.
 Spin echo is created by applying a 180˚ re-phasing RF-phasing RF pulse at
time ‘t’ after a 90˚ pulse.
 During the time ‘t; a certain amount of spins de-phase because of the spin-spin
interaction and magnetic field inhomogeneity. This reduce the transverse
magnetization .
 However by a 180˚ RF pulse , the remaining spins in the x,y plane can be re-
phased and made them precess in coherence.
 This process removes T2* effect and recovers the FID signal to a certain extent
and produce a signal called as spin-echo, the intensity and amplitude of which
depend upon the time ‘t’.

54.  A 180˚ re-phase RF pulse rotates the de-phase spins in the reverse direction
so that the transverse magnetization builds up and peaks when the spins
precess in coherence.

55. Spin echo
• After 90˚ RF pulse at a time ‘t’ a 180˚ re-phasing RF pulse is applied.
• The signal echoes at time ‘2t’. The time to echo (TE) is an important parameter
used in imaging cycle.

56.  All the present imaging methods belongs mainly to two major families i.e Spin
echo and gradient echo.
 Spin echo and gradient echo methods differ in the process that is used to create
an echo event at the end of each imaging cycle.
 For the spin echo methods, the echo events is produces by the application of a
180˚ re-phasing RF pulse.
 For gradient echo methods the echo event is produces by applying a magnetic
field gradient.

57. Gradient Echo
 Gradient echo is created by switching a pair of de-phasing and re-phasing magnetic
gradients.
 Application of magnetic gradient de-phase the spins. When de-phased spins are
subjected to another gradient in the reversed polarity, they acquire spin coherence
and produce an echo signal.

58. Imaging Cycle
 There are two distinct phase of the image acquisition cycle.
 One phase is associated with longitudinal magnetization and the other with
the transverse magnetization.
 T1 contrast is developed during the longitudinal magnetization phase.
 T2 contrast is developed during the transverse magnetization phase.
 Proton density (PD) contrast is always present, but becomes most visible
when it is not overshadowed by either T1 or T2 contrast.
 The predominant contrast appears in the image is determine by the duration
of the two phase and the transfer of the contrast from the longitudinal phase
to the transverse phase.

59.  The duration of the two phases (longitudinal and transverse magnetization) is
determined by the following selected values of protocol factors.
 TR (Time of Repetition)
 TR is the time interval between the beginning of the longitudinal relaxation,
immediately after the saturation and the time at which the longitudinal
magnetization is converted into transverse magnetization by the excitation pulse.
 TE (Time to Echo)
 TE is the time interval between the beginning of transverse relaxation following
the excitation and when the magnetization is measured to produce image
contrast.

60. T1 and PD contrast are produced during the longitudinal phase and T2 contrast is
produced during the transverse phase.

61.  At TR, the signal intensity will be proportional to the logidutinal magnetization
recovered [Mz(TR)] at that time and it will be a fraction of the original
magnetization (M0)
 i.e 𝑀 𝑍 (TR)= 𝑀0 (1- 𝑒−𝑇𝑅/𝑇1)
 At TE, the transverse magnetization (Mxy) will be freaction of Mz(TR), which
was flipped to transverse plane by 90˚ RF pulse at TR
 i.e Mxy (TE) =Mz(TR) (1− 𝑒−𝑇𝑅/𝑇1)
 Hence , the signal intensity at TE will be proportional to
 SI: N(H) (𝑒−
𝑇𝐸
𝑇2
∗
) (1− 𝑒−𝑇𝑅/𝑇1)
 Where ,N(H) is the proton density

62.  At TE, the signal intensity (SI) can be expressed as
 SI: N(H) (𝑒−
𝑇𝐸
𝑇2
∗
) (1− 𝑒−𝑇𝑅/𝑇1
)
 Different tissues have different T1 values.
 Long TR (4 to 5 times T1) reduces the T1 effect.
 If TR is infinite factor in the expression for the signal intensity
 SI will gets eliminated
 Hence short TR enhances the T1 contrast and thereby tissue contrast.
 If TR is very short above expression becomes zero resulting in no signal.
 If TE is very short the term 𝑒−
𝑇𝐸
𝑇2
∗
in SI approaches 1,which reduces T2* effect.
 Hence long TE enhances T2* contrast between tissue

63.  There are three types of tissue contrast
1. T1 weighted (T1 weighted)
2. T2 weighted (T2 W)
3. Proton /spin density weighted (PDW)
1. For T1 weighting ,eliminate T2 effect and enhance T1 effect.
a) To reduce T2 effect use short TE
b) To enhance T1 effect, use short TR
c) Signal intensity will be proportional to N(H) (1− 𝑒−𝑇𝑅/𝑇1
)

64. 2. For T2 weighting ,eliminate T1 effect and enhance T2 effect
a) To reduce T1 effect use long TR
b) To enhance T2 effect use long TE
c) Signal will be proportional to N(H) (𝑒−
𝑇𝐸
𝑇2
∗
)
3. For proton density weighting ,eliminate T1 and T2 effects
a) To reduce T1 effect, use long TR
b) To reduce the T2 effect use short TE
c) Signal will be proportional to N(H)

65. IMAGE CONSTRUCTION
 The signals received from a patient do not have any spatial information.
 For determining the specific origin point of each component of signals
,gradients are used in MRI.
 Gradients in MRI is a magnetic field that changes point to point in linear
fashion.
 A gradient with slightly weaker strength at feet and maximum strength at
head is produces by gradient coil.
 One gradient in each of the x,y and z direction is required for obtaining spatial
information in the direction.

66.  One of the coils increase the static magnetic field by specific amount
and the other coil decrease it by a specific amount. This induce a
gradient in the magnetic field.

67.  According to their function, these gradients are called
1. The slice select gradients
2. The frequency encoding or reacout gradients
3. The phase encoding gradient
 Depnding upon their orientation axis,they are called 𝐺 𝑥, 𝐺 𝑦 and 𝐺𝑧

68. Selection of slice
 If the RF pulse does not match with the larmor frequency with which
the protons are precessing in the external magnetic field , it cannot
excite and produce resonance in the tissue.
 In a inhomogeneous magnetic field generated by a gradient, the
precessing protons experience different field strength at different
location and precess at different frequencies.
 When an RF pulse with a single frequency is applied those protons
with the corresponding resonance frequency only will respond. This
would stimulate the slice position

70.  Slice thickness bandwidth of RF pulse.
 Narrower bandwidth → thinner slice and
vice versa
 Slice thickness can be changed by
changing the slope of the gradient.

71.  After slice selection , the NMR signals received from the slice has to be processed
for image construction.
 Digitized signals are stored in the computer memory with respect to its frequency,
phase shift.
 Gray values are assigned to digitized data on the basis of signals amplitude
 The field of view is divided into columns and rows (matrix)for digitization.
 Each pixel in the display matrix has a distinct gray values that is related to the
signal intensity from the corresponding voxel in the body slice.
 Signal received from the body slice by the RF coils is a superimposed signal of a
multitude of signals from each voxel in the body slice.
 Hence for digitization, the superimposed signals have to be separate into their
individual components and the components have to be phase shifted for locating
their digitized values in appropriate pixels.
 For these purpose, MRI employs frequency encoding and phase encoding
gradients during imaging cycles.
 These gradients provides specific frequency and phase to spins in each voxels so
that signals from the each voxel can be digitized separately.

72. Frequency and Phase
Phase encoding steps are repeated a number times depending upon the
number of rows in the image display matrix.
S(t) = A sin(ωot − ϕ)
where S(t) is the signal as a function of time, A is the amplitude, ωo is the
angular frequency, and ϕ is the instantaneous phase.
The Spatial information of the proton pools contributing MR signal is
determined by the spatial frequency and phase of their magnetization.

73. Here a frequency-encoding gradient (Gf) begins on
the left of the image at position x=0 and increases
linearly along the horizontal axis.
If the main (static) magnetic field is Bo, then the
effective field B(x) at any point (x) along the horizontal
axis is given by
B(x) = Bo + xGf
From the Larmor equation (f = γB),
Each pixel has a finite width, so actually contains a
small range of frequencies (called the per pixel
bandwidth) rather than just a single frequency.
A linearly increasing frequency-encoding gradient (Gf)
applied along the horizontal (x-) axis. Pixels A, B, and
C all resonate at the same lower frequency; D, E and
F at the same higher frequency.

75. Readout Localisation (Frequecny
encoding
 After RF pulse B1 ends ,acquisition of NMR RF signal begins.
 During readout ,gradient field perpendicular to slice selection gradient turned
on.
 Signal is sampled about once every few microseconds digitized , and stored
in computer.
 Readout window ranges from 5-100 ms.(can’t be longer than 2-T2*,since
signal dies after that ).
 Computer breaks measured signal V(t) into frequency components v(f)- using
fourier transform
 Since frequency f varies across subject in a known way, we can assign each
component v(f) to the place it comes from

76. The second dimension : phase
encoding
 Slice excitation provides one localization dimension
 Frequency encoding provides by second dimension.
 The third dimension is made by phase encoding.
 We make phase of Mxy (its angle in the xy plane) signal depend on
location on third direction.
 This is done by applying gradient field in the third direction (perpendicular
to both slice select and frequency encode).
 Fourier transform measure phase of each v(f) component of V(t), as well
as the frequency.
 By collecting data with many different amounts of phase encoding,
strength can break each v(f) into phase components , and so assign to
spatial location in 3D.

77. Steps in 3D localisation
 Can only detect total RF signal from inside the “RF coil” (the detecting
antenna).
1. Excite and Receive Mxy in a thin (2D) slice of the subject.
 The RF signal we detect must come from this slice.
 Reduce dimensions from 3D down to 2D.
2. Deliberately make magnetic field strength B depend on location within the
slice.
 Frequency of RF signal will depend on where it comes from
 Breaking total signal into frequency components will provide more
localization information.
3. Make RF signal phase depend on location within slice.

81. Thank You!!!!!!!