1. BE 581
Intro to MRI

3. What is MRI? Magnetic Resonance Imaging
Based on NMR: Nuclear Magnetic Resonance
Chapters 14 (NMR) and 15 (MRI)

4. What is MRI?
An imaging modality that uses a magnetic field and radio frequency to image soft tissue
Non ionizing radiation - not enough energy to remove electrons from atoms
Non ionizing radiation - may have enough energy for excitation to a higher energy state

5. What can we see with MRI? In general soft tissue Internal Organs
Muscles
Brain
Tumors
Inflammation

6. What can we see with MRI? With a contrast agent (MRAngiography)
Gadolinium + cherate
Blood vessels
Aneurisms
Blockage

7. What can we see with MRI? FunctionalMRI (FMRI)
Hemodynamic response of brain/spinal cord
Uses oxygenated hemoglobin as a marker
Response to a stimulus

8. MRI video http://www.imrser.org/PatientVideo.html
Lucas Parra lecture at City College NY

9. MRI process Patient in magnetic field Send radio frequency
Precession of protons
Send radio frequency
Precession is in phase (synchronization)
Turn off radio signal
Decay of synchronization
Collection of resonance signal
Coherent precession induces current in detection coil
NMR

10. Nuclear Magnetic Resonance
NMR
Nuclear Magnetic Resonance

11. Hydrogen Nuclei Hydrogen Nuclei (Protons)
Axis of Angular Momentum (Spin), Magnetic Moment

12. Hydrogen Nuclei
External Magnetic Field
Spins PRECESS at a single frequency (f0), but incoherently − they are not in phase

13. Hydrogen Nuclei
Irradiating with a (radio frequency) field of frequency f0, causes spins to precess coherently, or in phase

14. Magnetic Field I S magnetic field lines
By staying in the interior region of the field, we can ignore edge effects.
But how do we describe magnetic fields and field strengths quantitatively? N

15. Thus F is perp both v and B.
Magnetic Field II q v
An electric charge q moves between the N and S poles with velocity v. S B
If the charge is crossing magnetic field lines, it experiences a force F. F
F = qv x B
Thus F is perp both v and B. N

16. Magnetic Field III F[N] = q[A.s]v[m.s-1]B
For consistency, units of B must be N.(A . m)-1
1 N.(A.m)-1  1 T (tesla)  Kg (A s2)-1
If a current of 1 A flows in a direction perpendicular to the field lines of a 1 T magnetic field, each one-meter length of moving charges will experience a magnetic force of 1 N

17. Magnetic Field B
B goes by several different names in physics literature:
Magnetic field
Magnetic induction
Magnetic induction vector
Magnetic flux density

18. Nuclear Spin Spin: subatomic property of the nucleus
Quantized (Hydrogen proton I=1/2)
Angular momentum J of spinning mass
I spin energy level
mI magnetic quantum number
can be +1/2 or -1/2
It is common practice to represent the total angular momentum of a nucleus by the symbol I and to call it "nuclear spin". For electrons in atoms we make a clear distinction between electron spin and electron orbital angular momentum, and then combine them to give the total angular momentum. But nuclei often act as if they are a single entity with intrinsic angular momentum I. Associated with each nuclear spin is a nuclear magnetic moment which produces magnetic interactions with its environment.

19. Magnetic moment The spinning of the charge generates magnetic moment µ
 is the gyromagnetic ratio and it’s an intrinsic property of each nucleus
µ = J

20. Material NMR properties
Only non zero spin atoms generate an MRI signal
1H, 13C, 31P etc.
spin

21. 1H (proton)
MRI is based on the abundance of this proton in the human body

22. Precession
A second order motion- the rotation of a rotating object (~ wobble)

23. Precession o= Bo µz= Jz= hmI / 2 mI= +/- 1/2 (for I=1/2)
A spin in a uniform magnetic field Bo precesses at a frequency o (Larmor frequency)
o= Bo
Quantum mechanics dictates that µz and Jz can only be
µz= Jz= hmI / 2
mI= +/- 1/2 (for I=1/2)
When a magnetic moment is placed into a magnetic field a torque cause the magnetic moment to perform a precession motion similar to a spinning top

24. Spin Energy states
Due to the quantization of the spin there are only 2 possible energy states for the proton - parallel and antiparallel

25. Zeeman effect -loss of a degenerate state
E= µzBo= +/- hBo / 4
Degenerate state
anti
parallel
parallel
B=0 B
B>0

26. Boltzman distribution
It’s the relative population difference between two energy states
nupper/nlower = exp(-E/KbT)
Kb Boltzman constant = J/K
T temperature -> this is the reason why it’s hard to to MRI, you need a lot of ENERGY and low temp -> freeze patients?

27. Magnetization
The Boltzman distribution characterizes the number of parallel and antiparallel spin
When B=1.5T applied to 1 million protons there are only 5 more parallel than antiparallel
Typical volume for MRI is 1021 protons
E ~ ~

28. Magnetization
This difference generates bulk magnetization Mo in z direction (N nuclei)

29. Classical physics interpretation
valid when E << KbT
When placed in a magnetic field it is forced to align N S
Nuclear magnetic
moment is a bar
magnet B

30. Classical physics interpretation
Spin provides angular momentum, interaction with Bo -> Torque -> precession
The small difference in population of energy levels produces a small net magnetization Mz

31. Larmor frequency
When proton are irradiated with EM radiation at a frequency fo we have resonance
E = hfo= (h/2)Bo
The Larmor frequency is
o= Bo angular
fo= Bo/2 linear
Larmor frequency ->wobbling frequency

32. Use of RF pulse Bulk magnetization Mz
A pulse of frequency o is able to flip M

33. Use of RF pulse A pulse of frequency o is able to flip M
The flip angle depends on amplitude and length of the pulse
90 degrees
Flip Mz = My
180 degrees
flip Mz = -Mz

34. Use of RF pulse
It is fundamental that the RF pulse is applied at the resonant frequency o
Nothing would happen otherwise
RESONANT FREQUENCY
Quantum mechanics: A photon with energy equal to E can promote lower energy protons to higher energy

35. Block Equation Bulk magnetization M=[Mx,My,Mz] Magnetization over time
Exponential decay
with T2 time constant
Exponential decay
with T1 time constant

36. Block Equation - T2 decay
A RF pulse generate the transverse Mx My component
When RF is off Mx and My will decay exponentially (tc=T2) back to Mz

37. Block Equation - T2 decay
Damped oscillation
Induced on a receiver
coil

38. Free precession -T2 decay
Why does this happen?
1 Spin - Spin relaxation
Each spin sees other magnetic field generated by other spins (decay T2)
2 Bo is not perfectly homogeneus (T+2) shorter than T2 (100 times)
TOTAL EFFECT

39. Block Equation - T1 decay
90 pulse
180 pulse

40. Free precession - T1 decay
The spin give/loose energy to the environment (lattice)
Spin-lattice relaxation
The system return to equilibrium state after a pulse
Time necessary to recover 63% of longitudinal magnetization Mz

41. Free precession - T1 decay
Water has long T1
Adding protein reduces T1 length
Contrast agents are sometime used to decrease T1

42. Free Induction Decay (FID)
We can measure these relaxation state with a R coil tuned at the resonant frequency (o = 3.87 MHz for 1H)
Mxy(0) is magnitude of Mx, My at t=0
s(t)=

43. Homework 1 (due 10/6)
Research values of Mo, T2 and o and trace the T2 relaxation in Matlab

44. Homework 2 (due 10/6)
Do the same for T1 relaxation

45. Homework 3
Find the energy difference between low and high energy state of a proton in a 5 Tesla magnetic field

46. Homework 4
What kind of magnets (How many Tesla?) are the basis of commercially available MRI?
Consider clinical MRI, small (arm/leg MRI) and animal MRI

47. Images References Wikipedia.org
MRI physics class by Lucas Parra CCNY