1. Basic Physical Principles of MRI
James Voyvodic, Ph.D.
Brain Imaging and Analysis Center

2. Synopsis of MRI 1) Put subject in big magnetic field
2) Transmit radio waves into subject [2~10 ms]
3) Turn off radio wave transmitter
4) Receive radio waves re-transmitted by subject0
5) Convert measured RF data to image

3. Many factors contribute to MR imaging
Quantum properties of nuclear spins
Radio frequency (RF) excitation properties
Tissue relaxation properties
Magnetic field strength and gradients
Timing of gradients, RF pulses, and signal detection

4. MRI uses a combination of Magnetic and Electromagnetic Fields
NMR measures magnetization of atomic nuclei in the presence of magnetic fields
Magnetization can be manipulated by manipulating the magnetic fields (this is how we get images)
Static magnetic fields don’t change (< 0.1 ppm / hr):
The main field is static and (nearly) homogeneous
RF (radio frequency) fields are electromagnetic fields that oscillate at radio frequencies (tens of millions of times per second)
Gradient magnetic fields change gradually over space and can change quickly over time (thousands of times per second)

5. Radio Frequency Fields
RF electromagnetic fields are used to manipulate the magnetization of specific types of atoms
This is because some atomic nuclei are sensitive to magnetic fields and their magnetic properties are tuned to particular RF frequencies
Externally applied RF waves can be transmitted into a subject to perturb those nuclei
Perturbed nuclei will generate RF signals at the same frequency – these can be detected coming out of the subject

6. Electromagnetic Radiation Energy
X-Ray, CT
MRI

7. What kinds of nuclei can be used for NMR?
Nucleus needs to have 2 properties:
Spin
charge
Nuclei are made of protons and neutrons
Both have spin ½
Protons have charge
Pairs of spins tend to cancel, so only atoms with an odd number of protons or neutrons have spin
Good MR nuclei are 1H, 13C, 19F, 23Na, 31P

8. Hydrogen atoms are best for MRI
Biological tissues are predominantly 12C, 16O, 1H, and 14N
Hydrogen atom is the only major species that is MR sensitive
Hydrogen is the most abundant atom in the body
The majority of hydrogen is in water (H2O)
Essentially all MRI is hydrogen (proton) imaging

9. Nuclear Magnetic Resonance Visible Nuclei

10. Why do protons interact with a magnetic field?
Moving (spinning) charged particle generates its own little magnetic field
Spinning particles with mass have angular momentum

11. A Single Proton m There is electric charge
on the surface of the proton, thus creating a small current loop and generating magnetic moment m.
The proton also has mass which generates an
angular momentum
J when it is spinning. J + + +
Thus proton “magnet” differs from the magnetic bar in that it
also possesses angular momentum caused by spinning.

12. Magnetic Moment m = tmax / B t = m  B = IA = m B sinq B B I L L W F
F = IBL
t = IBLW = IBA
Force
Torque

13. Angular Momentum
J = mw=mvr m v r J

14. g is the gyromagnetic ratio g is a constant for a given nucleus
The magnetic moment and angular momentum are vectors lying along the spin axis
m = g J
g is the gyromagnetic ratio
g is a constant for a given nucleus

15. Vectors and Fields Magnetic field B and magnetization M are vectors:
Quantities with direction as well as size
Drawn as arrows
Another example: velocity is a vector (speed is its size)
Vector operations:
dot product AB cosq
cross product AB sinq
Magnetic field exerts torque to line magnets up in a given direction
direction of alignment is direction of B
torque proportional to size of B [units=Tesla, Gauss=10–4 T]

16. How do protons interact with a magnetic field?
Moving (spinning) charged particle generates its own little magnetic field
Such particles will tend to line up with external magnetic field lines (think of iron filings around a magnet)
Spinning particles with mass have angular momentum
Angular momentum resists attempts to change the spin orientation (think of a gyroscope)

17. [Main magnet and some of its lines of force]
[Little magnets lining up with external lines of force]

18. Ref: www.simplyphysics.com

20. Net Magnetization Bo M

21. Net magnetization Small B0 produces small net magnetization M
Larger B0 produces larger net magnetization M, lined up with B0
Thermal motions try to randomize alignment of proton magnets
At room temperature, the population ratio of anti-parallel versus parallel protons is roughly 100,000 to 100,006 per Tesla of B0

22. The Energy Difference Between the Two Alignment States
D E = 2 mz Bo
D E = h n
n = g/2p Bo
known as larmor frequency
g/2p = MHz / Tesla for proton

23. Resonance frequencies of common nuclei

24. To measure magnetization we must perturb it
Need to apply energy to tip protons out of alignment
aligned with magnetic field is lowest energy
aligned opposite magnetic field is next lowest energy state
Amount of energy needed depends on nucleus and applied field strength (Larmor frequency)

25. The Effect of Irradiation to the Spin System
Basic Quantum Mechanics Theory of MR
The Effect of Irradiation to the Spin System
Lower
Higher

26. Spin System After Irradiation
Basic Quantum Mechanics Theory of MR
Spin System After Irradiation

27. Precession
If M is not parallel to B, then it precesses clockwise around
the direction of B.
“Normal” (fully relaxed) situation has M parallel to B, and therefore does not precess
This is like a gyroscope

28. Derivation of precession frequency
= m × Bo
= dJ / dt
J = m/g
dm/dt = g (m × Bo)
m(t) = (mxocos gBot + myosin gBot) x + (myocos gBot - mxosin gBot) y + mzoz
This says that the precession frequency is the
SAME as the larmor frequency

29. RF Coil: Transmitting B1 Field
To tip spins in the static B0 field we apply (transmit) a magnetic field B1 that fluctuates at the precession frequency and points perpendicular to B0 (how do we achieve this? – by making a coil)
The effect of the tiny B1 is
to cause M to spiral away
from the direction of the
static B0 field
B110–4 Tesla
If B1 frequency is not close to
resonance, B1 has no effect

30. A Mechanical Analogy: A Swingset
Person sitting on swing at rest is “aligned” with externally imposed force field (gravity)
To get the person up high, you could simply supply enough force to overcome gravity and lift him (and the swing) up
Analogous to forcing M over by turning on a huge static B1
The other way is to push back and forth with a tiny force, synchronously with the natural oscillations of the swing
Analogous to using the tiny RF B1 to slowly flip M over g

33. NMR signal decays in time
T1 relaxation – Flipped nuclei realign with the magnetic field
T2 relaxation – Flipped nuclei start off all spinning together, but quickly become incoherent (out of phase)
T2* relaxation – Disturbances in magnetic field (magnetic susceptibility) increase rate of spin coherence T2 relaxation
NMR signal is a combination of the total number of nuclei (proton density), minus the T1 relaxation and T2 relaxation components

36. Different tissues have different relaxation times

37. Relaxation times are important for generating image contrast
T Gray/White matter
T Tissue CSF
T2* - Susceptibility (functional MRI)

38. MRI Scanner

39. Things needed for a typical MRI scanner
Strong magnetic field, usually from superconducting magnets.
RadioFrequency coils and sub-system.
Gradient coils and sub-system.
Shimming coils and sub-system.
Computer(s) that coordinate all sub-systems.

40. MRI scanner components

41. Using NMR signals for imaging
Need to prolong and amplify the decaying signal
Need to know the spatial location of the tissue generating the signal

42. The decaying NMR signal can be recovered by realigning spins
Spin Echo
Imaging
Gradient Echo
Imaging

43. Spatial location is identified by using spatially varying magnetic fields
Proton resonance with
uniform magnetic field
Proton resonance with
axial field gradient

44. It is actually spatial frequency, not physical location, that is scanned
Gradients cause spins to spread out and realign at
different times
Bands of tissue with uniform spacing will realign
together
MRI scanning systematically samples the strength
of the signal at different spatial frequencies
Horizontal sampling (Kx)
Vertical sampling (Ky)

45. MRI scanner collects spatial frequency data (in k-space)
Horizontal spatial frequency density
Vertical
spatial
frequency
density

46. A 2-dimensional Fourier transform mathematically converts from spatial frequency to reconstructed MR images

47. The versatility of MRI arises from the different types of tissue contrast that can be generated by manipulating parameters
TR – adjusting the time between acquisitions affects T1 relaxation
TE – adjusting the time between refocusing pulses affects T2 and T2* relaxations
Timing of gradients affects sampling in k-space
Additional gradient pulses before the RF pulse can enhance specific tissue properties
Chemical agents can further enhance image contrast