mri physics, hardware and safety PART 1

1. 1
Moderator-
Dr Navkiran kaur
HOD RD RHP
Presenter-
DR.deepakgarg
JR2rd rhp

2. 2
INTRODUCTION:
 MRI is a non invasive, multi planar, multi
contrast, multimodal – not only used to depict
internal structure but also powerful tool for
studying organ function, metabolism, physiology
& pathology.
 In 3 decades rapid technical advances has made
to improve the spatial resolution, types of
contrast & in particular speed of imaging.
 Applications initially limited to neural axis, now
applicable to various organ systems & it has
become primary diagnostic investigation for
many clinical problems..

3. Magnetic properties of substances
1. Paramagnetic
(oxygen,melanin,gadolinium)
3
paramagnetic material is
attracted by externally
applied magnetic field

4. 2.Diamagnetic
substances(Water,Bi,Hg,Cu,C)
4
Diamagnetic materials are
repelled by magnetic field.[

5. 3.Ferromagnetic substances
(Fe, Co, Ni)
5
Ferromagnetic materials- that can
be magnetized by an external magnetic
field and remain magnetized after the
external field is removed.

6. 6
Basic Physics

7. Basic Physics
 Atom: nucleus (proton, neutron),
orbiting electrons
 As a result of their nuclear spin and
charge distribution, protons and
neutrons have a magnetic field
called a magnetic dipole.
 Magnetic moment is a vector that
represents the strength &
orientation of a magnetic dipole
7

8. 8
Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon that occurs
when certain elements interact with a magnetic field. NMR is the process
by which the signal detected in MRI is generated; it is the foundation on
which MRI is built. Some common elements that demonstrate NMR are
H = 1
P = 31
C= 13
Na=23
In order to qualify for this list, the element must have a nonzero magnetic moment.
It is not necessary for us to delve into what a nonzero magnetic moment
is, but it will be present when either the number of protons or neutrons in
an atom is odd.

9. MR ACTIVE NUCLEI
Atomic No.-no. of protons
Mass No.-no of protons and neutrons
Those nuclei with an odd mass no. possess the ability to align
themselves along the direction of applied magnetic field
and are called as
MR ACTIVE NUCLEI e.g. H = 1
P = 31
C= 13
Na=23
9

10. Hydrogen is used as the MR ACTIVE NUCLEUS
in clinical MRI because-
-it is very abundant in human body
-its solitary proton gives it a relatively large
magnetic moment(gyromagnetic ratio)
-it gives best and most intense signal among all
nucei.

11. Protons carry a positive charge
Protons are constantly spinning around a central axis
(the movement is akin to the movement of a spinning top when hit)
A spinning(moving) electrical charge is an electrical current which
generates a magnetic field around it
Thus the protons generate a magnetic field around themselves and
behave as small bar magnets

12. 12
Why we ignoring electrons in our discussion of
NMR?
Because of their much smaller mass, electrons
have a much higher gyromagnetic ratio and
precess at frequencies in the gigahertz range;
signals in this frequency range will not be
detected by our detection hardware

13.  Spin is rotation of protons around its own axis
while
 Precession is rotation of axis itself under the
influence of external magnetic field such that
it forms a cone.
 and the frequency at which protons rotate
around the applied external magnetic field is
called as precessional frequency. Or Larmor
frequency
13

14. 14
This same phenomenon is responsible for the wobbling of a gyroscope.
Because such devices have "spin,“ when they interact with the earth's
gravitational field, they pursue the same conical trajectory.

15. Precession
+

B0
Precessional path
0 =B0
0 _= Larmor frequency
or resonance frequency
Gyromagnetic
ratio
B0 = Strength of the
external magnetic field
LARMORS EQUATION

16. 16

17. 17

18. Normally protons are aligned in a random
fashion. This, however, changes when
they are exposed to a strong external
magnetic field. Then they are aligned in
only two ways, either parallel or antiparallel
to the external magnetic field.
Naturally the preferred state of
alignment is the one that needs
less energy. So more protons
are on the lower energy level,
parallel to the external magnetic
Field.

20.  In the strong magnetic field more of these
nuclear magnetic dipoles align parallel to the
applied magnetic field this produces net
magnetisation in the direction of the field .
 The direction of the strong magnetic field
conventionally defines the z axis which is
generally along the longitudinal axis of the
patient in a typical MRI machine.
20

21. Z
Y
X
SUM VECTOR
Thus we have a
NET MAGNETISATION VECTOR
(or Longitudinal Magnetisation)
the magnitude of which depends on the
strength of the external magnetic field
strength magnitude of NMV

22. But this NMV (Longitudinal
magnetization) is not measurable.
Because this NMV is along the external
magnetic field (Bo) and it is so small
relative to the static magnetic field Bo
(10 million times smaller)
So For measurement-
a magnetisation transrverse to external
magnetic field is necessary
This magnetisation should not be stationary
22

23. 23
At Rest (i.e when only Bo is applied), Signal
Is Not Detectable
Faraday's law of induction tells us that moving charge will induce a magnetic
field. It is conversely true that a moving magnet will induce an electric
field. In the presence of a conductor (a loop of wire-AKA antenna-that
we will call a receiver coil), a voltage will be induced by the moving magnet.
This is exactly how we measure the signal in NMR and MRI.
This is because we cannot measure the NMV of our sample,as it is stationary.
So it’s the only Transverse vector (rotating in the x-y
plain) which produces signal in the receiver. Longitudinal
vector can never produce a signal

24. Next step is to impart energy to this NMV so
as to get a transverse magnetization which is
measurable.
Energy exchange can only take place when protons and radio
frequency pulse have the Same frequency-*RESONANCE

25. 25
resonance is a process by which energy is transferred with great
efficiency from one system to another. This requires a source of energy
and a subject that receives the energy. In our case, the subject is the spin
sample (ie H atoms in patient body). Its natural frequency 0 , is
determined by the Larmor equation we discussed previously. The energy
source will be a second magnetic field that, while weaker than Bo and ,
will change its orientation over time at a frequency that matches 0 and
will always remain in a plain perpendicular to Bo.
This time -varying magnetic field is called B1 and it is described as a
"rotating magnetic field." Because B1 must rotate at 0 , which is in the
same range as the frequencies used in FM radio , it is also called the
radiofrequency (RF) field and is said to deliver a radiofrequency (RF)
pulse.

26. 26
The rotating magneticfield B1 (Dotted arrows) represent the two components
of B1• Each oscillates at the same frequency but 90° out of phase with the
other. The vector sum of these two components is represented by the solid arrow.
This net B1 rotates through a plane (xy in this example) that is perpendicular to
Bo,(parallel to the z axis in this example).

27. PHASE OF MAGNETIC MOMENTS
27
Due to spin around its own axis- there is net magnetisation in z axis
Due to precession – there is megnetisation in transverse plain. But without RF
pulse, these nuclei precess randomly i.e out of phase. So the net magnetisation in
transverse axis becomes zero.
But when RF pulse is applied(at a frequency equal to larmour frequency), these
nuclei come in phase and produce a magnetisation vector in transverse direction.

28. 2 things happen at Resonance (ie when we apply
RF pulse B1) due to energy absorption:
1- Increase number of High energy Spin Up nuclei ie nuclei in
antiparallel direction to Bo. Causing gradual decrease in
longitudinal magnetisation vector
2- increase in Phase Coherence- causing gradual inc in
transverse magnetisation vector.
With 90 deg RF pulse longitudinal vector becomes zero and
transverse vector becomes maximum. So the NMV
precesses only in transverse plain.

29. Application of 90 deg RF pulse
Longitudinal magnetisation
Transverse magnetisation
RF at Larmour frequency of H+

30. Effects of switching off the RF
pulse
 NMV loses its energy Relaxation
 Longitudinal magnetisation
gradually increases -Recovery
 Transverse magnetisation
decreases -Decay

31. RF PULSE SWITCHED OFF

32. Excitation and Relaxation
(recovery)
 Equilibrium is disturbed when a radio pulse rotates
net magnetization away from its initial longitudinal
plane .
 This disturbance of equilibrium where by transverse
magnetisation is produced is termed as excitation.
 The return of net magnetisation to equilibrium is
termed as relaxation.
32

33. Excitation

34. Types of Relaxation
 Longitudinal – precessing protons are pulled back
into parallel alignment with main magnetic field of
the scanner (Bo) increasing size of the magnetic
moment vector along z-axis
 Transverse – precessing protons become out of
phase leading to a drop in the magnetic moment
vector along x-y plain
 Transverse relaxation occurs much faster than
Longitudinal relaxation
 Tissue contrast is determined by differences in
these two types of relaxation

35. T1 Relaxation
-Time taken by LM to recover to its original
value after RF Pulse is switched off
-relaxation is exponential in nature
-short T1 = rapid recovery
-long T1 = slow recovery
– longitudinal relaxation
– thermal relaxation
– spin-lattice relaxation

36. 36
•T1 relaxation rate is determined by
•Properties of the material
•Magnetic field strength
•T1 long in - small molecules-H20 and large
molecules – proteins.
•T1 short in fats & in intermediate sized molecules.
•Contrast agents Gd DTPA – T1 shortening.
•In general, T1 increases with increasing B0.

37. Causes of spin lattice relaxation i.e T1 relxn
Jostling by large molecules that are slow moving and near
to resonant frequency is most effective at removing energy
from excited dipoles. FAT(large molecules with low
inherent energy) can absorb energy easily and has short T1.
Jostling by small, light weight molecules with little inertia is
rapid and so relatively ineffective at removing energy from
excited dipoles, so free water, urine,amniotic fluid, csf and
other solution of salts have a long T1.Greater the proportion of
free water in tissue, longer is T1
Atoms in solid and rigid macromolecules are relatively
fixed and they are least effective at removing energy;
compact bones, teeth, calculi and metallic clips have very
long T1

38. 38
 The time required for longitudinal magnetisation
to recover 63% of its original equilibrium level
after RF pulse is switched off is called as T1
relaxation time .
 The curve showing gradual recovery of LM against
time is called T1 curve.
 Longitudinal relaxation rate= 1/T1

39. T1 Recovery
T1 in WaterT1 in Fat
inefficient at receiving
energy
T1 is longer
i.e. nuclei take a lot
longer to dispose
energy to surrounding
water tissue
absorb energy quickly
T1 is very short
i.e. nuclei dispose
their energy to
surrounding fat tissue
and NMV return in
plain of B0 in very
short time

40. 40
Longitudinal relaxation. At t =0, a 90° RF pulse has just been delivered,
and all magnetization is in the transverse plane. Tl, the time at which 63% of Mz,
has recovered, describes the rate of recovery.
In this example, each line represents a different tissue: The dashed line represents
fat, which has a short Tl(Tla.) , the solid line represents CSF, which has a long TI
(T1c), and the dotted line represents brain , which has an intermediate Tl(Tlb) .

41. T2 DECAY
 results from static or slowly fluctuating local magnetic
field variations resulting in loss of phase coherence among
groups of protons rotating in the transverse plane.
 T2 is the time taken by TM to REDUCE TO 37% of its
original value.
IN PHASE OUT PHASE
transverse relaxation
–spin-spin relaxation

42. Causes of spin spin relaxation i.e T2 relxn
Dephasing occurs because a spinning proton experiences a tiny
additional magnetic field produced by each neighbouring
proton.Individual protons are affected slightly differently,so does
the rate of precession ,some precess faster and some slower,and
energy passes from one proton to another, or spin to spin.
Local variation of magnetic field is greatest in solid and rigid
macromolecules in which atoms are relatively fixed. Dipoles in
compact bone,teeth,calculi and metallic clips dephase quickly.they
have very short T2
The effect is least in free water, urine, amniotic fluid,csf and
other solutions of salt.
Lighter molecules are in rapid thermal motion,which smoothes
out the local field and result in Long T2.more free water longer
t2.spleen>liver renal medulla>cortex

43. T2 Decay
Fat much better at energy exchange than Water
Because T2 depends on:
- Proximity of other spins
So;
Fat's T2 time is very short compared to water

44. 44
Transverse relaxation. At t = 0, a 90° RF pulse has just been delivered,
and all magnetization is in the transverse plane. T2, the time at which 63% of Mt,
has dissipated and 37% remains, describes the exponential rate of signal loss. The
dashed line represents fat, which has a short T2(T2a.) , the solid line represents
CSF, which has a long T2(T2c), and the dotted line represents brain , which has an
intermediate T2(T2b)

45. T2* Relaxation
 In addition to magnetic field inhomogeneity intrinsic to tissues
causing spin-spin relaxation, inhomogeneity of external magnetic
field also causes decay of TM, called T2 prime
 The consequence of this spatial variation in Bo is that adjacent
spins will not experience the same field strength and,
consequently, will not precess at the same frequency. With time,
spins precessing at different frequencies will lose phase
coherence. The longer we observe a sample of spins exposed to a
heterogeneous Bo, the greater the loss of phase coherence and, of
course, the greater the resultant decline in the net M,of our
sample.
 The combined decay of transverse magnetisation from t2
relaxation and heterogenous magnetic field is referred as t2*
relaxation
45

46. 46
T2 and T2*. The shapes of the T2 and T2* curves are similar, but their
time constants differ. T2* is essentially the T2 curve shifted to the left due to the
addition of relaxation due to T2'.
So T2’ causes faster signal loss

47. 47
The Spin Echo
The spin echo is a method for "recovering" Mt, lost due to heterogeneity of
the magnetic field, essentially neutralizing T2' effects.
This is achieved by giving an RF pulse that flips the magnetization 180° .
The RF pulse must deposit twice the amount of energy
as the 90° pulse in order to achieve a flip of exactly 180°.

48. 48
The spin echo. (A) Immediately after the 90°RF pulse has been applied,
spins are all phase coherent, represented by one large vector in the transverse plane .
(B) After a period of time, spins will dephase due to T2' effects. Note that the dotted
arrow is "ahead" of the solid arrow with respect to the direction of precession
(curved arrow) . (C) The 180° RF pulse rotates, spins out of and then back into the
transverse plane , effectively inverting their phase. Now, the dotted arrow is "behind"
the solid arrow . (D) After an additional period of time equal to that between
(A) and (B), the spins are back in phase , creating a spin echo .

49. 49
The spin echo corrects T2' effects. Initially, signal decays along the T2*
curve for a time x.
After the 180 pulse, signal begins to increase until at time 2x it
intersects the T2 curve. It is at this point that T2' effects have been
fully recovered , producing a spin echo.

50. Some Terminologies
 TR
 TE
 FID
 Flip Angle

52. TIME TO ECHO: Time
interval between start of RF
pulse and reception of signal

53. 53
FID
As the magnitude of transverse magnetisation
decreases , the magnitude of voltage induced in
receiver coil also decrease. The induction of
reduced signal is called FREE INDUCTION DECAY
SIGNAL.
The degree of rotation of magnetisation caused by an
excitation radio pulse is a product of strength and
duration of that pulse .
The amount of rotation that results from the radio
pulse is referred as FLIP ANGLE
With flip angle of 90, longitudinal magnetisation is
converted completely to transverse magnetisation
FLIP ANGLE

54. Flip angle
54

55. T1 WEIGHTED:
With short TR only the tissues with short T1 will show high signal
intensity.
T2 WEIGHTED:
At longer TE only those tissues with long T2 will have strong
signal.
PROTON DENSITY
With a long TR differences in LM are not important as all
the tissues have regained their Full LM.with short TE ,T2
has yet to become pronounced so the image is mostly
detremined by PD

56. 56
Each line represents a specific tissue( solid-water, dashed-fat). TR indicates the time at which
the second (and subsequent) RF pulse is applied .
Short TR alters initial Mz, Because Mz, has not fully recovered , only a portion of the
longitudinal magnetization Mz, is present when this next RF pulse is applied. The amount of
Mz, present at TR determines the amount of Mt, present in the lower graph of transverse
relaxation at t =O. If we sample Mt, immediately (at TE =0), the difference in signal between
tissues is due to differences in T1 that determined the amount of Mt recovered when the
RF pulse was applied at TR. if we sample Mt at longer TE, the difference in Signal is due to
difference in T2.
TR
TE

57. 57
T2 contrast is determined by TE.TE is indicated by the numbers.
As TE is varied (all other parameters are unchanged), tissue contrast changes
dramatically from one reflecting Tl differences to one reflectingT2 differences.When
using a short TE, signal is sampled before signal differences because of
T2 manifest. When using a long TE, however, such differences in signal manifest
substantially by T2. Notice also that signal to noise declines with inc in TE (because
at longer TE net Mt decreases).

58. 58
Tl contrast is modulated byTR. As TR (white numbers) is varied ( keeping all other
parameters are unchanged), tissue contrast changes from one reflecting Tl differences
(white matter with higher signal than gray matter and CSF very dark) to one
reflecting T2 differences .
When using a short TR, differences in Mz, are present when the RF pulse is applied ,
creating differences in signal immediately afterward. When using a long TR, however
such differences are eliminated as Mz, has fully recovered for all tissues by TR. Notice
also that signal to noise increases with TR because more Mz, recovers before each
Subsequent RF pulse. The more Mz the more Mt (signal) generated by the RF.

59.  T1 WTED :
short TR 300 - 600 ms
short TE 20 - 30 ms
 T2 WTED :
long TR 2500 - 6000 ms
long TE 80 - 100 ms
 PD WTED :
long TR 2500 - 3500 ms
short TE 20 - 30 ms

60. Common Tissue Appearances

61. GRADATION OF INTENSITY
IMAGING
CT SCAN CSF Edema White
Matter
Gray
Matter
Blood Bone
MRI T1 CSF Edema Gray
Matter
White
Matter
Cartilage Fat
MRI T2 Cartilage Fat White
Matter
Gray
Matter
Edema CSF
MRI T2 Flair CSF Cartilage Fat White
Matter
Gray
Matter
Edema

62. T1 WEIGHTED IMAGES :
1.Better For Anatomical Delineation.
2.Fluid Including CSF Is Dark.
3.White Matter Is White And Gray Matter Is
Gray.
62

63. 63
AXIAL T1W

64. Signal Intensities On T2 Weighted
High signal:CSF ,synovial fluid, hemangioma,
infection, inflammation, oedema, cysts,
slow flowing blood.
Low signal:
Cortical bone,bone islands, deoxy hb(P),hemosiderin
calcification,T2 paramagnetic agents.
No signal:
Air fast flowing blood, tendons, cortical bone, scar tissue
calcification
64

65. 65
T2 WEIGHTED IMAGE :
1.Fluid including CSF is bright.
2.White matter is dark and gray matter remains gray.
3.Due to increased water content lesions appear bright.
4.Useful for detection of pathology.
FLAIR images are similar but CSF is dark. Useful in ventricular &
periventricular lesions.

66. 66
AXIAL T2W

67. PROTON DENSITY IMAGE :
 As the TR is prolonged more tissues fully
recover their longitudinal magnetisation
between repetitions and voxel intensity
becomes more independent of T1
 At short TE values the effect of T2 decay is
minimised and one is left with an image with
little T1 or T2 dependence this can be called as
proton density image
67

68. PD WEIGHTED
68

69. 69
Contrast Agents and Their Effect on Tl
Paramagnetic contrast agents shorten the Tl of spins when unpaired
electrons of the paramagnetic element are within 3A(angstroms) of the
proton.
Currently, all paramagnetic contrast agents employ gadolinium (Gd),
which is highly paramagnetic, having nine unpaired electrons.
Shortening of Tl decreases the time required for longitudinal
relaxation to occur and can be viewed as shifting the Tl
curve to the left. This effect brings out differences in tissues (e.g., liver
and metastasis in our example below) due to differential shortening of
Tl; only tissues that take up the paramagnetic substance will "benefit"
from this effect.

70. 70
Tl shortening effect of contrast agents. In this case of a liver metastasis
(tumor), Mz, of the metastasis and liver tissue are very similar and would, therefore,
be difficult to distinguish. The Tl of the metastasis (Th) becomes shorter (Tla) when
gadolinium-containing contrast material accumulates due to tumor vascularity . The
change in Tl shifts the Tl curve of the meta stasis to the left. Thus, at TR, Mz, for the
tumor and normal tissue are very different. As a result, signal from the tumor will be
much higher and detection will be enhanced.

71. 71
Contrastenhancement. Both images of this meningioma were obtained
using identical parameters. (A) Before the contrast infusion, the tumor has signal
indistinguishable from normal brain tissue. (B) T1 shortening accomplished by
adding the contrast agent leads to a dramatic contrast between signal from the
tumor and normal tissue.

72. Gradients
 gradients are coils of wire that, when a current is passed
through them ,alter the magnetic field strength in a
controlled and predictable way.
 A gradient is simply a deliberate change in the
magnetic field
 Gradients are used in MRI to linearly modify the
magnetic field from one point in space to
another
 Gradients are applied along an axis (i.e. Gx
along the x-axis, Gy along the y-axis, Gz along
the z-axis)
 On applying gradient the Bo changes,so the
larmour frequency of protons changes
accordingly at that location.

73. Effect of a Gradient
direction of the magnetic field remains the
same but strength changes acc to gradient

74. X, Y And Z Gradient Axes
74

75.  for axial images the gradient coil is applied
in cranio caudal direction
 for sagital images right to left
 for coronal section anterior to posterior
75

76. Localising the MR signal
 We should know from which part of the body we
are receiving the MR signal
 Possible by application of 3 types of gradients in
X, Y and Z planes.
 Z axis - slice selection gradient
X axis - phase encoding gradient
Y axis - frequency encoding gradient

77. Slice Selection
 When a gradient coil is switched on, B0 and
precessional frequency of nuclei is altered in a
linear fashion.
 A specific point/nuclei situated within a slice
along the axis has specific precessional
frequency depending upon Bo at that point.
 A slice can be selectively excited by
transmitting RF with a band of frequencies
coinciding with Larmor frequencies of spins in
a particular slice.
77

78. Slice Select Gradient

79. Slice Orientation

80.  Z gradient selects axial slices
 X gradient selects sagittal slices
 Y gradient selects coronal slices
SLICE THICKNESS: depends on slope of gradient
and transmit bandwith.
TIMING OF SLICE SELECTION GRADIENT:
Applied during excitation 90· RF
80

81. Phase Encoding
 After the selection of slide, phase encoding
gradiant is Applied perpendicular to the axis of
slide selection gradient and frequency encoding
gradient.
 This brief gradient pulse causes precessional
frequencies to change along this axis , once the
phase encoding has ended the precessional
frequencies come to uniformity but the protons
spin will be in different phases.
 The phase encoding gradient must be applied
repeatedly at different strengths to locate
different MR signals along the axis.
82

82. Phase Encoding
 After the selection of slide, phase encoding
gradiant is Applied perpendicular to the axis
of slide selection gradient and frequency
encoding gradient.
 Apply gradient in one direction briefly
and then turn off
 Result:
 Protons initially decrease or increase their
rate of precession
 After the gradient is turned off all of the
protons will again precess at the same rate
 Difference is that they will be out phase with
one another

83. Prior to Gradient
Row 1
Row 2
Row 3
Uniform
Field
Uniform
Field

84. Gradient Applied
Row 1
Row 2
Row 3
Lower
Field
Higher
Field

85. Gradient Turned Off
Row 1
Row 2
Row 3
Uniform
Field
Uniform
Field

86.  The steepness of slope of the phase encoding
gradient determines the degree of phase shift
between two points along the gradient.
 Strong phase encoding gradients accentuate
differences between two structures that are near
to each other.
 So they are useful in resolving fine detail.
87

87. Timing Of Phase Encoding
 The phase encoding gradient is switched on
after the RF excitation pulse has been
switched off and before 180’ rephasing
pulse.
 The phase encoding gradient must be applied
repeatedly at different strengths to locate
different MR signals along the axis.
 Its normally turned on for 4 ms and the
amplitude and polarity of the gradient is
altered for each phase encoding step.
88

88. 89
All spins have same precessional frequency

89. 90
Apply Phase Encoding Gradient
Slower unchanged faster

90. 91
After PE Gradient turned off
All spins have same frequency again, but different phase
+90° 0° -90°

91. Frequency Encoding
 Applied perpendicular to the axes of slide
selection gradient and phase encoding gradient
 The gradient produces a frequency difference
along its axis.
 The signal can now be located according to its
frequency.
92

92. Frequency Encoding
 Apply gradient in one direction and
leave it on
 Result:
Protons that experience a decrease in
the net magnetic field precess slower
Protons that experience an increase in
the net magnetic field precess faster

93. Prior to Gradient
Col 1
Col 2
Col 3
Uniform
Field
Uniform
Field

94. Gradient Applied
Col 1
Col 2
Col 3
Lower
Field
Higher
Field

95. 96
•The frequency encoding gradient is switched
on when the signal is received , so it is called
Readout Gradient.
•With stronger frequency encoding gradient
small distances may be resolved better
because they correspond to greater
differences in frequency .
•So the spatial resolution improves as gradient
strength increases

96. 97
• The steepness of slope of frequency
encoding gradient determines the size of the
anatomy covered, so it determines- Field of
view.

97. Combining Phase &
Frequency Encoding
Row 1,
Col 1
Row 2,
Col 2
Row 3,
Col 3

98. Sum Corresponds to
Received Signal
+
+
Row 1,
Col 1
Row 2,
Col 2
Row 3,
Col 3

99. By means of Fourier transformation ,a computer
analyzes the mixture of signals that come out Of a slice
and we get a MR IMAGE

100. Converting Received
Signal into an Image
• Signal produced using both
frequency and phase encoding can
be decomposed using a
mathematical technique called the
Fourier Transform
• Result is the signal (sinusoidal
squiggles) produced at each
individual pixel

101. From Signal to Image
Row 1,
Col 1
Row 2,
Col 2
Row 3,
Col 3
FFT
Pixels

102. Lauterbur’s Insight
• Use of gradients to provide spatial
encoding
• Frequency and Phase - was
Lauterbur’s contribution
• Awarded Nobel prize for this work

103. The K-space
 Its an imaginary space where raw data is stored.
 It is a spatial frequency domain
 The unit of k space is radians /cm.
 K space does not correspond to the image .
 Its rectangular and has two axes :
 Horizontal axis corresponds to the phase axis.
 The vertical axis is frequency axis perpendicular to
phase axis.
 The number of lines filled in k space determined by
number of different phase encoding steps.
104

104. What is K-space?
 Space in which “raw” data is written
 Complement to image space
= FT of
Image = Fourier Transform of k-space data

105. Pseudo
Time
k-space

106. Appearance of K-space Data
 Center of k-space contains
low spatial frequency info
(general shape; big things
that change little over
space)
 Edge of k-space contains
high spatial frequency info
(details, edges)

107.  Because k-space is symmetrical, one half of the space
can be determined from knowledge of the other half.
 Imaging time can be reduced by a factor of 2
 Most important information centered around the
middle of k-space
Half Fourier Imaging

108. K Space Filling
109