1. 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.

2. Proton interaction 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)
J = mw=mvr B B I L
m = tmax / B
= IA m v r J L W F
t = m  B
= m B sinq
F = IBL
t = IBLW = IBA
Force
Torque

3. Larmor frequency D E = 2 mz Bo D E = h n n = g/2p Bo
The energy difference between the two alignment states depends on the nucleus
Resonance frequencies of common nuclei
Note: Resonance at 1.5T = Larmor frequency X 1.5
D E = 2 mz Bo
D E = h n
n = g/2p Bo
g/2p = MHz / Tesla for proton

4. Nuclear Magnetic Resonance (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
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

5. MRI uses a combination of Magnetic and Electromagnetic Fields
NMR measures the net magnetization of atomic nuclei in the presence of magnetic fields
Magnetization can be manipulated by changing the magnetic field environment (static, gradient, and RF fields)
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)

6. Magnetic Resonance Imaging (MRI)

7. 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
Lower
Higher

8. Net magnetization
Net magnetization is the macroscopic measure of many spins
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 Bo M

9. To measure magnetization…
We can only measure magnetization perpendicular to the Bo field
Need to apply energy to tip protons out of alignment
Amount of energy needed depends on nucleus and applied field strength (Larmor frequency)
The amount of energy added (duration of the RF pulse at the resonant frequency) determines how far the net magnetization will be tipped away from the Bo axis

10. Precession = m × Bo = dJ / dt J = m/g dm/dt = g (m × Bo)
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
Derivation of precession frequency
This says that the precession frequency is the SAME as the Larmor 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

12. Recording the MR signal
Need a receive coil tuned to the same RF frequency as the exciter coil.
Measure “free induction decay” of net magnetization
Signal oscillates at resonance frequency as net magnetization vector precesses in space
Signal amplitude decays as net magnetization gradually realigns with the magnetic field
Signal also decays as precessing spins lose coherence, thus reducing net magnetization
Lower
Higher

13. 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 the rate of spin coherence T2 relaxation
The total NMR signal is a combination of the total number of nuclei (proton density), reduced by the T1, T2, and T2* relaxation components

14. Weighted image
Different tissues have different relaxation times. These relaxation time differences can be used to generate image contrast
T Gray/White matter
T Tissue/CSF
Proton density
T2* - Susceptibility (functional MRI)

15. Multi-Slice Spiral Images

16. Multi-Slice EPI Images

17. Blood oxygen level dependent (BOLD) MRI
Brain activity
Oxygen consumption
Cerebral blood flow
Oxyhemoglobin
Deoxyhemoglobin
Magnetic susceptibility
T2*
MRI signal intesity

18. Magnetic Properties of OxyHb and DeoxyHb
Hb + O2 <-> HbO2
M=cH if c>0, paramagnetic if c<0, diamagnetic
Deoxyhemoglobin: paramagnetic (c > 0), with respect to the surrounding tissue
Oxyhemoglobin: diamagnetic (c < 0), isomagnetic with respect to the surrounding tissue
Rest
Normal blood flow
Activation
High blood flow
Oxyhemoglobin Deoxyhemoglobin

19. T2* decay
Spin coherence is also sensitive to the fact that the magnetic field is not completely uniform
Inhomogeneities in the field cause some protons to spin at slightly different frequencies so they lose coherence faster
Factors that change local magnetic field (susceptibility) can change T2* decay
action
MR signal (S)
rest TE t
excitation
reception

20. Time series and activation map

21. Data Analysis Voxel Signal Extraction Signal Raw Data Model Fitting
Fitted Response (Green)
Model Fitting
Trigger Function
Function To Fit
Convolution
Haemodynamic
Response

22. Statistical Map Generation
Fitted Response (Green)
Statistical Map
Generation
Activation Map

23. Activation Maps on Anatomical ImagesMS
Spiral MS
EPI 3D
Spiral

24. Visual Activation Maps (ISI=12s)

25. Group Mapping Subject 1’s Subject 2’s Statistics Map Statistics Map
Activation Map
Subject 3’s
Statistics Map
Subject 2’s
Statistics Map

26. Contrast between groups
Condition 1 Group
Statistics Map
Condition 2 Group
Statistics Map
Brain area
activated by
Condition 1 and
Not Condition 2

27. Data Management Computing Requirement Analysis Individual Map:
Each 4D file from Scanner = 500MB approx
Intermediate data = 500MB x 5
Processing time = 1 hour
Best done with a script (at least 36 map per exp)
Group Map
20 minutes per individual map
30 minutes to generate group map
Contrast Map
5 minutes
Analysis
Hypothesis-driven approaches
t-test, cross-correlation, GLM, etc.
Data-driven approaches
Principal component analysis (PCA), independent component analysis (ICA), and clustering analysis.

28. Challenges in fMRI Sensitivity Specificity Temporal resolution
signal change is 1-2% at 1.5 T ; SNR in single-shot EPI images is 100
Physiological pulsations
cardiac and respiratory
head motion
instrumental instability
Specificity
Location of activation ; neurons or veins ?
Susceptibility artifacts
Temporal resolution
Limited by BOLD impulse-response function
image sampling rate, and spin relaxation times
Spatial resolution
Limited by BOLD point-spread function
SNR, image sampling rate
Non-linearity
Neurological and hemodynamic
Acoustic noise
Higher magnetic fields
BOLD signal change DS ~ Ba (1 < a < 2)
Standard clinical MRI scanner at 1.5 T
Research scanner up to 8 T currently
Optimization of image acquisition parameters
Optimal echo time (TE) to maximize BOLD signal
Optimal repetition time (TR)
increase number of images/unit time
decrease motion artifacts
Suppression of Temporal Fluctuations
Head holder modified from a football helmet
Image realignment in data processing: cardiac and respiratory signal correction
Ultra-fast imaging techniques
Single-shot echo-planner imaging (EPI)
Single-shot Spiral imaging
Post-processing: Denoising

29. Frontal Systems: Subcortical-thalamic connections
The prefrontal cortex is connected to the striatum and thalamus in parallel but separate circuits that help regulate behavior
Topographic mapping of caudate and thalamus
Subcortical white matter connections
Long tracts
Cortical U-fibers
Injury anywhere in a circuit can produce a major deficit and small subcortical lesions can mimic large cortical lesions

30. Frontal Systems Function
Processing speed
Mental flexibility
Planning
Sequencing
Decision-making
Working memory
Behavioral regulation, self-monitoring
Motivation, drive, interest
White Matter Changes in Aging
Volume loss
Greater than grey matter loss
Greater in frontal lobes
Loss of myelin
Wallerian degeneration
Subcortical ischemic vascular changes
Selective vulnerability of frontal regions
Increased interstitial fluid

31. Subcortical Hyperintensities
None
Mild
Moderate
Severe

32. Diffusion-Tensor Imaging (DTI)
Measures magnitude and direction of water diffusion in biological tissue in 3D.
Measures water diffusion in at least 6 directions – we use 12 for better resolution
1.5T magnet or greater capable of diffusion encoding
Echo-planar imaging (fast acquisition)
Collecting small voxels, scanning takes about 14 minutes
Off-line post-processing (Laidlaw lab)
Image analysis: Butler Hospital Quantitative Imaging Lab

33. DTI – Tractography
Bammer, 2003

35. Fiber Clustering

36. Take home message
fMRI vs. DTI