1. Introduction to Medical Imaging MRI – Magnetic Resonance Imaging
Course
Introduction to Medical Imaging MRI – Magnetic Resonance Imaging
Guy Gilboa

2. MRI invention Several involved: Nobel prize 2003,
Raymond Damadian – 1971, idea still very sketchy, no images produces.
Paul Lauterbur – , mature technique for 2D and 3D imaging. Produced first image of a living mouse.
Peter Mansfield - developed a mathematical technique where scans take seconds rather than hours also producing clearer images.
Nobel prize 2003,
Paul Lauterbur
Sir Peter Mansfield
(Damadian left out, protests of him and colleagues).
From top: Damadian, Lauterbur, Mansfield.

3. MRI scanner
The lecture is based mainly on: [1] [2] Ch. 5 of the book by N. B. Smith and A. Webb, Introduction to Medical Imaging, Cambridge University Press, 2011.

4. Typical brain MRI

5. MRI – basic operation principle
The MRI is comprised of 3 main components:
A superconducting primary magnet
3 magnetic field gradient coils
RF transmitter and receiver
Taken from

6. Movie – how MRI works (8.5 min.)

7. Energy units
Tesla: A particle carrying a charge of 1 coulomb and passing through a magnetic field of 1 tesla at a speed of 1 meter per second perpendicular to said field experiences a force with magnitude 1 newton, according to the Lorentz force law. 𝑇= 𝑉∙𝑠 𝑚 2 = 𝐽 𝐴𝑚 2 = 𝑊𝑏 𝑚 2 = 𝑁∙𝑠 𝐶∙𝑚 = 10 4 g
V=volt; s=second; m=meter; J=joule; A=ampere; Wb=webber; N=newton; C=coulomb; g=gauss.

8. Lorentz force 𝐹=𝑞(𝐸+𝑣×𝐵)
A particle of charge q moving at velocity v in the presence of an electric field E and a magnetic field B, experiences the force:
𝐹=𝑞(𝐸+𝑣×𝐵)

9. Faraday induction
The voltage induced V is proportional to the time rate of change of the magnetic flux 𝜑: 𝑉∝− 𝑑𝜑 𝑑𝑡

10. Some symbols 𝜇 [ J/T] = magnetic moment P [ J ∙ s] = angular momentum
𝛾 [Hz/T] gyromagnetic ratio
For protons: 𝛾= Mhz/T
𝜇 =𝛾| 𝑃 |
∆𝐸 [𝐽] Energy difference between parallel and anti-parallel. ∆𝐸= 𝛾ℎ 𝐵 0 2𝜋
M [A/m] = net magnetization.
Torque [N ∙m] = moment of force

11. Magnetic Fields used in MR:
1) Static main field Bo
2) Radio frequency (RF) field B1
3) Gradient fields Gx, Gy, Gz

12. Very strong magnets used in MRI
Typical primary magnets 1.5 – 3T
Earth magnetic field: 3.1× 10 −5 𝑇
Ohio Akron Children’s Hospital: 3T MRI (Magnetom Skyra, Siemens). Weight ~7,500kg. Cost $3.5M (2011).

13. Over 3T magnets  very large and expensive
7T (Stanford) T (Siemens)

14. Gradient coils Create a weak magnetic field in any direction in space.
Magnetic field strength approximately 100 times lower than the main field.

15. Reference Frame z y x

16. Magnetic Moments
MR is exhibited in atoms with odd # of protons or neutrons.
Spin angular momentum creates a
dipole magnetic moment
Planck’s constant / 2
Intuitively current, but nuclear spin
operator in quantum mechanics
= gyromagnetic ratio : the ratio of the dipole moment to angular momentum
Which atoms have this phenomenon?
1H - abundant, largest signal
31P
23Na
Model proton as a ring of current.

17. Energy states resonance frequency fo Energy of Magnetic Moment in
Hydrogen has two quantized currents,
Bo field creates 2 energy states for Hydrogen where
energy separation
resonance frequency fo

18. Nuclei spin states There are two populations of nuclei:
n+ - called parallel
n- - called anti parallel
higher energy n-
lower energy n+
Which state will nuclei tend to go to? For B= 1.0T
Boltzman distribution:
Slightly more will end up in the lower energy state. We call the
net difference “aligned spins”.
Only a net of 7 in 2*106 protons are aligned for H+ at 1.0 Tesla.
(consider 1 million +3 in parallel and 1 million -3 anti-parallel. But...

19. There is a lot of a water!
18 g of water is approximately 18 ml and has approximately 2 moles of hydrogen protons
Consider the protons in 1mm x 1 mm x 1 mm cube.
2*6.62*1023*1/1000*1/18 = 7.73 x1019 protons/mm3
If we have 7 excesses protons per 2 million protons, we get .25 million billion protons per cubic millimeter!!!!

20. Torque – mechanical analogy
Spins in a magnetic field are analogous to a spinning top in a gravitational field.
Magnetic Torque
(gravity - similar to Bo)
Top precesses about

21. Precession rotates (precesses) about Usually, Bo = .1 to 3 Tesla
Precessional frequency: or
is known as the Larmor frequency.
for 1H
Usually, Bo = .1 to 3 Tesla
So, at 1 Tesla,
fo = MHz for 1H
1 Tesla = 104 Gauss

22. Precession – Movie (7 min.)

23. RF Magnetic field The RF Magnetic Field, also known as the B1 field
To excite nuclei ,
apply rotating field at o in x-y plane. (transverse plane)
B1 radiofrequency field tuned to Larmor frequency and applied in transverse (xy) plane induces nutation (at Larmor frequency) of magnetization vector as it tips away from the z-axis.
- lab frame of reference

24. RF general excitation (rotating frame)
By design ,
In the rotating frame, the frame rotates about z axis at o radians/sec x y z
1) B1 applies torque on M
2) M rotates away from z.
(screwdriver analogy)
3) Strength and duration of B1 determines flip angle.
This process is referred to as RF excitation.

25. Coils diagram Simplified Drawing of Basic Instrumentation.
Body lies on table encompassed by coils for static field Bo,
gradient fields (two of three shown), and radiofrequency field B1.
Image, caption: copyright Nishimura, Fig. 3.15

26. Detection - Switch RF coil to receive mode.x y z M
Precession of M induces EMF in the RF coil. (Faraday’s Law)
EMF time signal - Lab frame
Voltage t
(free induction decay)
for 90 degree excitation

27. T1 and T2 relaxation times
Application of RF pulse creates non- equilibrium state (adding energy to the system).
After the pulse is switched off, the system is relaxed back to equilibrium.
There are 2 relaxation times which govern the return to equilibrium:
T1 (spin-lattice), equilibrium of z component.
T2 (spin-spin), x and y components.

28. Tissue relaxation times for 1.5 Tesla
T1 (ms)
T2 (ms)
White matter
790 90
Gray matter
920
100
Liver
500 50
Skeletal muscle
870 60
Lipid (מסיס שומן)
290
160
Cartilage (סחוס)
1060 42 S?
Table: 5.1 from [2]

29. Bloch Equation Solution: Longitudinal Magnetization Relaxation Component
The greater the difference from equilibrium,
the faster the change
Solution:
Initial Mz
Doesn’t have to be 0!
Return to Equilibrium

30. Transverse time constant T2
- spin-spin relaxation
T2 values: < 1 ms to 250 ms
What is T2 relaxation?
- z component of field from neighboring dipoles affects the
resonant frequencies.
- spread in resonant frequency (dephasing) happens on the
microscopic level.
- low frequency fluctuations create frequency broadening.
Image Contrast:
Longer T2’s are brighter in T2-weighted imaging, darker in T1-weighted imaging S?

31. MR: Relaxation: Some sample tissue time constants - T1
Approximate T1 values as a function of Bo
gray matter
muscle
white matter
kidney
liver S?
fat
Image, caption: Nishimura, Fig. 4.2

32. Gradient Fields - key for imaging - Paul Lauterbur
Gradient coils are designed to create an additional B field that varies linearly across the scanner as shown below when current is driven into the coil. The slope of linear change is known as the gradient field and is directly proportional to the current driven into the coil.
The value of Bz varies in x linearly. z Bz Bo
slope = Gz
Whole Body Scanners:
|G| = 1-4 G/cm
(10-40 mT/m)
Gz can be considered as the magnitude of the gradient field, or as the current level being driven into the coil.

33. Basic Procedure 1) Selectively excite a slice (z)
- time? .4 ms to 4 ms
- thickness? 2 mm to 1 cm
2) Record FID, control Gx and Gy
- time? 1 ms to 50 ms
3) Wait for recovery
- time? 5 ms to 3s
4) Repeat for next measurement.
- measurements? 128 to 512
- in just 1 flip
5) Next: More on spatial encoding

34. Phase and frequency encoding
It is not important which dimension encodes frequency and which phase.
We assume:
X encodes frequency
Y encodes phase

35. Frequency encoding
X-dimension is encoded by applying a frequency-encoding gradient 𝐺 𝑓𝑟𝑒𝑞 .
Protons precess at the frequency 𝜔 𝑥 = 𝛾 𝐺 𝑥 𝑥
A total of 𝑁 𝑓 data points are acquired while the receiver is on (e.g. 256).
There is a delay between successive RF pulses, called TR = time of repetition.

36. Phase encoding
Y-dimension is encoded by applying a phase- encoding gradient 𝐺 𝑝ℎ𝑎𝑠𝑒 for a period of 𝜏 𝑝𝑒 and then switched off.
During the interval 𝜏 𝑝𝑒 protons precess at the frequency 𝜔 𝑦 =𝛾 𝐺 𝑦 𝑦 and we have a spatially dependent phase shift
𝜑 𝑝𝑒 = 𝜔 𝑦 𝜏 𝑝𝑒 =𝛾 𝐺 𝑦 𝑦 𝜏 𝑝𝑒 .
A total of 𝑁 𝑝𝑒 dphase encoding steps are applied, with a total slice acquisition time of 𝑇𝑅∙𝑁 𝑝𝑒 .

37. K-space formalism (5.10)
Given the proton density 𝜌(𝑥,𝑦), the 𝑁 𝑓 ×𝑁 𝑝𝑒 data samples can be expressed as:
𝑠 𝐺 𝑦 , 𝜏 𝑝𝑒 , 𝐺 𝑦 ,𝑡 = 𝑠𝑙𝑖𝑐𝑒 𝜌(𝑥,𝑦) 𝑒 −𝑗𝛾 𝐺 𝑦 𝑦 𝜏 𝑝𝑒 𝑒 −𝑗𝛾 𝐺 𝑥 𝑥𝑡 𝑑𝑥𝑑𝑦
In the k-space formalism [Ljunggren-1983] we assign 𝑘 𝑥 = 𝛾 2𝜋 𝐺 𝑥 𝑡, 𝑘 𝑦 = 𝛾 2𝜋 𝐺 𝑦 𝜏 𝑝𝑒 to get
𝑆 𝑘 𝑥 , 𝑘 𝑦 = 𝑠𝑙𝑖𝑐𝑒 𝜌(𝑥,𝑦) 𝑒 −𝑗2𝜋 𝑘 𝑥 𝑥 𝑒 −𝑗2𝜋 𝑘 𝑦 𝑦 𝑑𝑥𝑑𝑦

38. Image recovery
To recover the proton density 𝜌(𝑥,𝑦), we simply use the inverse Fourier transform:
𝜌(𝑥,𝑦) = −∞ ∞ 𝑆 𝑘 𝑥 , 𝑘 𝑦 𝑒 +𝑗2𝜋 (𝑘 𝑥 𝑥+ 𝑘 𝑦 𝑦) 𝑘 𝑥 𝑘 𝑦

39. k-Space Acquisition ky kx Phase Direction One line of k-space
Encode
Sampled
Signal
DAQ kx ky
Phase
Direction
One line of k-space
acquired per TR
Frequency Direction
Taken from [1]

40. Fast Fourier Transform
FFT

41. 512 x 512
8 x 8

42. 512 x 512
16 x 16

43. 512 x 512
32 x 32

44. 512 x 512
64 x 64

45. 512 x 512
128 x 128

46. 512 x 512
256 x 256

47. Signal Intensity and SNR
The signal is proportional to:
The number of protons in the voxel.
The square of B0 field
Net magnetization 𝑀 0 ∝ 𝐵 0
Induced voltage 𝑉∝ 𝜔 0 ∝ 𝐵 0
SNR:
𝑆𝑁𝑅∝ 𝐵 0 3/2
𝜔 0 =precession frequency

48. Multiple slice imaging
The TR time required between successive RF excitations for each phase encoding step is much longer than TE.
In this time other adjacent slices are usually acquired (maximum of TR/TE)
Usually this is done in an interlacing fashion – od numbered slices are followed by even-numbered slices.

49. Spin-echo imaging sequence
SS – Slice selection, PE – Phase encoding, FE – Frequency encoding, TR – Time of repetition, TE – Time of echo.

50. T1, T2, PD
A long TR and short TE sequence is usually called Proton Density (PD) –weighted.
A short TR and short TE sequence is usually called T1- weighted
A long TR and long TE sequence is usually called T2-weighted
Taken from

51. MR angiography
Increase signal difference between flowing blood and tissue
Based on TOF (time-of-flight) technique, shorter effective T1 due to flow if the slice is oriented perpendicular to the direction of flow.
1 𝑇 1,𝑒𝑓𝑓 = 1 𝑇 1 + 𝑏𝑙𝑜𝑜𝑑 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑆𝑙𝑖𝑐𝑒 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

52. Functional MRI
Determines which areas of the brain are involved in cognitive tasks and brain functions such as speech and sensory motion.
Based on the fact that MRI signal intensity changes depending upon the level of oxygenation of the blood in the brain (indicating increased neuronal activity).
Uses fast scans which can cover the brain in a few seconds.

53. Example of fMRI
Brain activity changes of teenagers playing violent video games.
Taken from

54. MR contrast agents Positive Negative
Paramagnetic contrast agents, shorten the T1 of tissue in which they accumulate.
Based on gadolinium ion (Gd).
Used to detect tumors, lesions in the central nervous system (brain and spine).
Negative
Superprparamgnetic (iron oxides), reduce T2 relaxation time.
Used in detection of liver lesions.

55. Image characteristics (5.20)
SNR trends
∝𝐵 0 3/2
Inverse proportional to spatial resolution.
Proportional to the square-root of acquisition time.
Spatial resolution defined by
The slice thickness.
The field-of-view (FOV) divided by the number of phase-encoding steps.
The FOV in the frequency-encoded dimension divided by the number of acquired data points.

56. Characteristics (cont’)
Contrast to noise
Contrast is based on T1, T2, PD scans.
Can be manipulated by choices of TR, TE.
For small lesions, the contrast is increased by having higher spatial resolution to minimize partial volume artifacts.

57. Examples – brain
Comparison of PD, T1, T2 and angiography.

58. Cardiology
4 chamber view MR angiography of the chest (18 sec scan time)

59. Some clinical applications of MRI
Used widely to scan almost every organ in the body, popular uses are:
Neurological applications
Can diagnose both acute and chronic neurological deseases.
Method of choice for brain tumor detection.
Most protocols involve administration of Gd.
Many pathological conditions in the brain result in increased water content, which gives high signal intensity on T2-weighted sequences.

60. Clinical apps (cont’) Liver and Muscoloskeletal Cardiology
Can diagnose well lesions in fatty liver. Also iron overload, liver cysts, several lesions.
Muscle-skeleton system. Knee scans to diagnose arthritis (joint inflammation).
Cardiology
To reduce motion artifacts - scans are gated according to the cardiac cycle, based on electrocardiograms (ECG).
Detects myocardial infarcts, can measure left ventricular volume and ejection fraction. Good contrast between blood and myocardial wall.
Diagnose coronary artery stenosis using angiography.

61. MRI summary Advantages: Drawbacks:
3D data – basically measures concentration of water.
Many possible modes.
Very good for soft tissues.
No ionizing radiation.
Drawbacks:
Expensive.
Slow scan time.
Large magnets → cannot scan people with metal implants.

62. MRI vs CT – Brain image
Better contrast in MRI for soft tissues, easy to distinguish between gray and white matter.

63. Comparison between MRI and CT
Ionizing radiation
Yes No
Cost
lower
Higher (x3?)
Speed
10-30 s (full scan 5-10 min).
Several minutes (full scan 30-60min)
Data modes
Few
Many
3D images
Resolution
~7 lp/cm
~3 lp/cm
Work with metal in the body
SNR increases as
Radiation increases, or body is smaller.
Primary magnet is stronger (also acquisition time)