1. Introduction to fMRI physics for dummies (like me!).

2. Outline History of NMR to MRI to fMRI
Physics of protons (1H in particular)
Creating MRI images
From MRI to fMRI

3. History of Nuclear Magnetic Resonance
NMR = nuclear magnetic resonance
Felix Block and Edward Purcell
1946: atomic nuclei absorb and re-emit radio frequency energy
1952: Nobel prize in physics
nuclear: properties of nuclei of atoms
magnetic: magnetic field required
resonance: interaction between magnetic field and radio frequency
Bloch
Purcell
NMR  MRI
Source: Jody Culham’s web slides

4. History of fMRI
MRI
-1973: Lauterbur suggests NMR could be used to form images
-1977: clinical MRI scanner patented
-1977: Mansfield proposes echo-planar imaging (EPI) to acquire images faster
fMRI
-1990: Ogawa observes BOLD effect with T2*
blood vessels became more visible as blood oxygen decreased
-1991: Belliveau observes first functional images using a contrast agent
-1992: Ogawa & Kwong publish first functional images using BOLD signal
Source: Jody Culham’s web slides

5. Some terms to know
B0 – this is used to denote the main magnetic field – also known as longitudinal magnetization
objects placed within B0 will gradually align to this field (longitudinal relaxation)
M0 – this is used to denote the net magnetization of an object within B0
it is the M0 which is ‘tipped’ out of alignment with B0 to create the MR image – so M0 is now measured as transverse magnetization
RF pulse – radio frequency pulse – not to be confused with ‘resonant frequency’
to read M0 it must be tipped out of alignment with B0 – this is achieved by sending an RF pulse at certain resonant frequencies and gradients

6. Some more terms to know
Magnet – the big magnet that we allocate the Tesla value to that creates B0
Gradient Coil – smaller magnets that are used to tip the net magnetization of the subject (M0) out of alignment with B0
There are actually three gradient coils orthogonal to one another so that gradients can be applied in the x, y and z planes
RF coil – radio frequency coil – these are typically receive only coils and are used to measure M0 at some time after the RF pulses have been applied. Send/receive coils are also available

7. Physics of protons.
motion of electrically charged particles results in a magnetic force orthogonal to the direction of motion
protons (nuclear constituent of atom) have a property of angular momentum known as spin
Angular momentum (spin) of a proton.

8. Protons aligning within a magnetic field
In “field free” space
randomly oriented
Inside magnetic field
oriented with or against B0
M = net magnetization M
Applied Magnetic
Field (B0)
when placed in a magnetic field (B0; e.g., our MRI machines) protons will either align with the magnetic field or orthogonal to it (process of reaching magnetic equilibrium)
there is a small difference (10:1 million) in the number of protons in the low and high energy states – with more in the low state leading to a net magnetization (M)
Source: Mark Cohen’s web slides
Source: Robert Cox’s web slides
Source: Jody Culham’s web slides

9. Precession – the spinning top analogy.
What is actually aligned with the B0 is the axis around which the proton
precesses – the decay of precession (i.e., it is the rate of precession out of
alignment with B0 together with the proton density of the tissue concerned
that is crucial in MRI)
Source: Cohen and Bookheimer article

10. Larmor Frequency Larmor equation f = B0
the energy difference between the high (oriented with B0) and low (oriented against B0) energy protons is measurable and is expressed in the Larmor equation
Larmor equation
f = B0
 = MHz/T
At 1.5T, f = MHz
At 4T, f = MHz
Field Strength (Tesla)
Resonance
Frequency for 1H
170.3
63.8
1.5
4.0

11. RF Excitation
protons can flip between low and high energy states (i.e., flip between being aligned with or against B0)
to do so the energy transfer must be of a precise amount and must be facilitated by another force (e.g., other protons or molecules)
in MRI, RF (radio frequency) pulses are used to excite the RF field – the swing analogy – tipping the net magnetization out of alignment with B0

12. Cox’s Swing Analogy
Source: Robert Cox’s web slides

13. RF Excitation Excite Radio Frequency (RF) field
transmission coil: apply magnetic field along B1 (perpendicular to B0) for ~3 ms
oscillating field at Larmor frequency
frequencies in range of radio transmissions
B1 is small: ~1/10,000 T
tips M to transverse plane – spirals down
analogies: guitar string (Noll), swing (Cox)
final angle between B0 and B1 is the flip angle B1 B0
Source: Robert Cox’s web slides

14. Longitudinal relaxation and T1.
temperature influences the number of collisions (and hence the rate at which protons flip between low and high energy states)
so magnetic equilibrium (M0), or the rate at which a body placed inside B0 becomes magnetized depends on temperature – this is known as longitudinal relaxation
the T1-weighted image (usually used for anatomical images) measures the rate at which the object placed in B0 (the unsuspecting subject in our case) goes from a non-magnetized to a magnetized state – the longitudinal relaxation
different types of molecules (and by extension tissue) approach M0 at different rates allowing us to differentiate things like white and grey matter – we creep close towards the image!!!

15. T1 and T2
T1 measures the longitudinal relaxation (along B0) – or the rate at which the subject (and the various different constituents of that subject) reaches magnetic equilibrium
T2 measures the transverse relaxation (along B1) – or the rate of decay of the signal after an RF pulse is delivered
T1 – recovery to state of magnetic equilibrium
T2 – rate of decay after excitation
Tissue T2 decay times (in 1.5 T magnet)
white matter 70 msec
grey matter 90 msec
CSF msec

16. Reading M0
RF coils receive the net magnetization from the object placed within the coil (e.g., a subject’s head)
can also have send / receive RF coils that also deliver the RF pulse (to get the swing going) – usually the pulse is delivered by gradient coils

17. Proton density, recovery (T1) and decay (T2 and T2*) times.
T1 weighted
Density weighted
T2 weighted
By ‘weighting’ the pulse sequence (and the point at which data is collected) different images of the brain are obtained
Weighting is achieved by manipulating TE (time to echo) and TR (time to repetition of the pulse sequence)

18. T1 and TR
T1 = recovery of longitudinal (B0) magnetization after the RF pulse
used in anatomical images
~ msec (longer with bigger B0)
TR (repetition time) = time to wait after excitation before sampling T1
Source: Mark Cohen’s web slides

19. T2 and TE T2 = decay of transverse magnetization after RF pulse
TE (time to echo) = time to wait to measure T2 or T2* (after re-focusing with spin echo)
Source: Mark Cohen’s web slides

20. T1 vs. T2
effectively, T1 and T2 images are the inverse of one another, with T1 typically used to form anatomical images and T2* used in fMRI
T1 and TR

21. T2*
T2: intrinsic decay of transverse magnetization over microscopic region (~5-10 microns)
~ msec (shorter with bigger B0)
T2*: overall decay of transverse magnetization over macroscopic region (~mm)
decays more quickly than T2 (by factor of ~2)
Source: Robert Cox’s web slides

22. Source: Mark Cohen’s web slides

23. Spatial localisation of the signal – creating the 1D image.
A spatially variant B1 leads to a spatially variant distribution of RFs.
Frequency analysis is used to discriminate different spatial locations.
PULSE SEQUENCE
time
RF pulse
Gx (x – gradient)
data acquisition

24. Spatial Coding Gradient coil add a gradient to the main magnetic field
Field Strength (T) ~ z position
Freq
Gradient coil
add a gradient to the main magnetic field
excite only frequencies corresponding to slice plane
Gradient magnetic field = applied in the
slice plane (i.e., the x direction) thus Gx

25. Spatial localisation of the signal – creating the 2D image.
Can’t simply turn on 2 gradients.
Instead the 2 gradients need a precise sequence.
The 1D sequence already shown is known as frequency encoding.
A different pulse sequence can be used in the y-direction to create the 2D image – phase encoding.
This method is known as echo-planar imaging or EPI and is the most common method used in fMRI. Although Spiral imaging is catching up!

26. Spatial localisation of the signal – creating the 3D image
The RF field must be at the same resonant frequency as the nucleus being scanned.
For the 2D image we have selected only one resonant frequency in one particular z-plane (and used EPI sequences to obtain the x and y-planes).
So we simply apply a gradient at different levels (slices) in the z-plane to create the 3D image.
slices in the z-plane

27. Spatial localisation of the signal – creating the 3D image
frequ.
encode
phase
encode
Source: Buxton book Ch. 10

28. Echos
All RF pulses create an ‘echo’ of the M0 signal obtained by the pulse.
T2* signals decay more rapidly than T2
A refocusing pulse is used to create a transient echo of the signal – a spin echo
Multiple refocussing pulses create multiple echoes
Source: Buxton book

29. EPI imaging and k-space
Any net signal produced by proton spins can be expressed as a sum of the sine and cosine waves of different wavelengths
The different spatial frequencies of these wavelengths are denoted as k-space – the inverse of the wavelengths
small k value = low spatial frequency / long wavelength
large k value = high spatial frequency / short wavelength
k-space is what is actually measured in MRI (i.e., the signal from M0 is transformed into x and y values via k-space)

30. EPI imaging and k-space
x = frequency and y = phase or angle
Source: Traveler’s Guide to K-space (C.A. Mistretta)

31. Fourier transformation.
k-space is magically transformed into our image via a Fourier transform.
Source: Buxton book Ch 5

32. EPI imaging and k-space
Source: Buxton book Ch 10

33. EPI imaging and k-space
Source: Buxton book Ch 10

34. k-space and sampling methods.
The EPI pulse sequence zig-zags across
k-space, slowly in the x-direction and
rapidly in the y-direction.
The Gz gradient shifts this process to the
next slice to be imaged.
Source: Buxton book Ch 11

35. EPI

36. But what about activation?
Voila! The MRI!
But what about activation?

37. Vascular Network Transit Time = 2-3 s Arterioles Capillaries Venules
Y=95% at rest.
Y=100% during activation.
25 mm diameter.
<15% blood volume of cortical tissue.
Venules
Y=60% at rest.
Y=90% during activation.
25-50 mm diameter.
40% blood volume of cortical tissue.
Red blood cell
6 mm wide and 1-2 mm thick.
Delivers O2 in form of oxyhemoglobin.
Capillaries
Y=80% at rest.
Y=90% during activation.
8 mm diameter.
40% blood volume of cortical tissue.
Primary site of O2 exchange with tissue.
Transit Time = 2-3 s
Source: Chris Thomas’ Slides

38. Vascular network and BOLD
Source: Buxton book Ch 2

39. Susceptibility and Susceptibility Artifacts
Adding a nonuniform object (like a person) to B0 will make the total magnetic field B nonuniform
This is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an external field
For large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform magnetic fields can be adjusted to “even out” the ripples in B — this is called shimming
Susceptibility Artifact
-occurs near junctions between air and tissue
sinuses, ear canals
sinuses
ear
canals
Source: Robert Cox’s web slides

41. Susceptibility and BOLD fMRI
Magnetic susceptibility (c) refers to magnetic response of a material when placed in B0.
Red blood cells exhibit a change in c during ‘activation’
Basically, oxyhaemoglobin in the RBC (HbO2) becomes deoxyhaemoglobin (Hb):
Becomes paramagnetic.
Susceptibility difference between venous vasculature and surroundings (susceptibility induced field shifts).

42. BOLD signal Blood Oxygen Level Dependent signal
Source: Buxton book Ch 17

43. BOLD signal
CBF, CBV, and CMRO2 have different effects on HbO2 concentration:
Interaction of these 3 produce BOLD response
They change [Hb] which affects magnetic environment.
Blood Oxygen Level Dependent signal
Local Hb
Content
(delivery of more HbO2 -> less Hb on venous side if excess O2 not used)
CBF
Local Hb
Content
(extraction of O2-> HbO2 becomes Hb)
CMRO2
Local Hb
Content
CBV
(more Hb in a given imaging voxel)

44. BOLD signal
Source: Doug Noll’s primer

45. First Functional Images
Source: Kwong et al., 1992

46. Hemodynamic Response Function
% signal change
= (point – baseline)/baseline
usually 0.5-3%
initial dip
-more focal
-somewhat elusive so far
time to rise
signal begins to rise soon after stimulus begins
time to peak
signal peaks 4-6 sec after stimulus begins
post stimulus undershoot
signal suppressed after stimulation ends

47. And now we can all get some sleep!