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BMI2 SS08 – Class 7 “functional MRI” Slide 1
Biomedical Imaging 2Biomedical Imaging 2
Class 7 – Functional Magnetic Resonance Imaging (fMRI)
Diffusion-Weighted Imaging (DWI)Diffusion Tensor Imaging (DTI)
Blood Oxygen-Level Dependent (BOLD) fMRI
03/04/08
BMI2 SS08 – Class 7 “functional MRI” Slide 2
2D FT pulse sequence (spin warp)2D FT pulse sequence (spin warp)
Most commonly employed pulse sequence
BMI2 SS08 – Class 7 “functional MRI” Slide 3
Radiation ↔ Rotating Magnetic Field IRadiation ↔ Rotating Magnetic Field I
N
S
B0
Static magnetic field
Sinusoidal EM field
Imagine that we replace the EM
field with…
y
x
z
BMI2 SS08 – Class 7 “functional MRI” Slide 4
S
S
Radiation ↔ Rotating Magnetic Field IIRadiation ↔ Rotating Magnetic Field II
N
S
B0 …two more magnets, whose fields are B0, that rotate, in opposite
directions, at the Larmor frequency
N
N
BMI2 SS08 – Class 7 “functional MRI” Slide 5
Radiation ↔ Rotating Magnetic Field IIIRadiation ↔ Rotating Magnetic Field III
Simplified bird’s-eye view of counter-rotating magnetic field vectors
t = 0 1/(8f0) 1/(4f0) 3/(8f0) 1/(2f0) 5/(8f0) 3/(4f0) 7/(8f0) 1/f0
So what does resulting B vs. t look like?
This time-dependent field is called B1
BMI2 SS08 – Class 7 “functional MRI” Slide 6
Rotating Reference Frame IRotating Reference Frame I
y
x
zB0
(1-10 T)
y
x
z, z’
y’x’
Instead of a constant rotation angle , let = 2f0t = 0t
Original (laboratory) coordinate system
Coordinate system rotated about z axis
counter-rotating magnetic fields
resultant field, sinusoidally varying
in x direction
x’ = ysin + xcos = -ysin0t + xcos0t
y’ = ycos - xsin = ycos0t + xsin0t
BMI2 SS08 – Class 7 “functional MRI” Slide 7
Rotating Reference Frame IIRotating Reference Frame II
B0
(1-10 T)
y
x
z, z’
y’x’
Rotating coordinate system, observed from laboratory frame
These axes are rotating in the xy plane, with frequency f0
B0
z’
y’
x’
Rotating coordinate system, observed from within itself
But what is the magnitude of B0 in this reference frame?
This magnetic field, rotating at 2f0, can be ignored; its frequency is too high to induce transitions between orientational states of the protons’ magnetic moments
This magnetic field, B1, is fixed in direction and has constant magnitude: ~0.01 T
BMI2 SS08 – Class 7 “functional MRI” Slide 8
Spin-Spin Relaxation ISpin-Spin Relaxation I
What is the T2 time constant associated with spin-spin interactions?
x׳
y׳
z׳ B0
MMz
Mtr If there were no spin-spin coupling, the transverse component of M, Mtr, would decay to 0 at the same rate as Mz returns to its original orientation
What are the effects of spin-spin coupling?
BMI2 SS08 – Class 7 “functional MRI” Slide 9
Spin-Spin Relaxation IISpin-Spin Relaxation II
W hat are the effects of spin-spin coupling?
Because the magnetic fields at individual 1H nuclei are not exactly B0, their Larmor frequencies are not exactly f0.
x׳
y׳
z׳ B0
MzBut the frequency of the rotating reference frame is exactly f0. So in this frame M appears to separate into many magnetization vectors the precess about z׳.
Some of them (f < f0) precess counterclockwise (viewed from above), others (f > f0) precess clockwise.
BMI2 SS08 – Class 7 “functional MRI” Slide 10
fMRI investigation of hemodynamicsfMRI investigation of hemodynamics
BMI2 SS08 – Class 7 “functional MRI” Slide 11
Diffusion-Weighted Imaging (DWI)Diffusion-Weighted Imaging (DWI)
BMI2 SS08 – Class 7 “functional MRI” Slide 12
Diffusion-weighted MRI (DWI)Diffusion-weighted MRI (DWI)
Stronger bipolar gradients → lower tissue velocities detectable
Blood flow velocities: ~(0.1 – 10) cm-s-1
Water diffusion velocity: ~200 μm-s-1
Using the same basic strategy as phase-contrast MRA, can image “apparent diffusion coefficient” (ADC)
Useful for diagnosing and staging conditions that significantly alter the mobility of water
e.g., cerebrovascular accident (“stroke,” apoplexy)
BMI2 SS08 – Class 7 “functional MRI” Slide 13
Examples of Diffusion-weighted imagesExamples of Diffusion-weighted images
BMI2 SS08 – Class 7 “functional MRI” Slide 14
Examples of Diffusion-weighted imagesExamples of Diffusion-weighted images
BMI2 SS08 – Class 7 “functional MRI” Slide 15
Diffusion Tensor Imaging (DTI)Diffusion Tensor Imaging (DTI)
BMI2 SS08 – Class 7 “functional MRI” Slide 16
How Many Bipolar Gradients?How Many Bipolar Gradients?
1
2
1 2
MRA
BMI2 SS08 – Class 7 “functional MRI” Slide 17
How Many Bipolar Gradients?How Many Bipolar Gradients?
DWI
BMI2 SS08 – Class 7 “functional MRI” Slide 18
DTI Concepts 1DTI Concepts 1
M.E. Shenton et al., http://splweb.bwh.harvard.edu:8000/pages/papers/pubs/yr2002.htm
BMI2 SS08 – Class 7 “functional MRI” Slide 19
DTI Concepts 2DTI Concepts 2
bDA e
Isotropic diffusion limit:
For anisotropic diffusion:
,
, ,
xx xy xz
yx yy yz
zx zy zz
xy yx xz zx yz zy
D D D
D D D
D D D
D D D D D D
D
, , , ,
exp ij iji x y z j x y z
A b D
BMI2 SS08 – Class 7 “functional MRI” Slide 20
Indices of Diffusion AnisotropyIndices of Diffusion Anisotropy
2 2 2
1 2 33RA
Relative anisotropy (RA):
Fractional anisotropy:
2 2 2 2 2 21 2 3 1 2 33 2FA
31 2 31VR
Volume ratio (VR):
BMI2 SS08 – Class 7 “functional MRI” Slide 21
Comparison of Anatomical, DWI, DTIComparison of Anatomical, DWI, DTI
D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).
BMI2 SS08 – Class 7 “functional MRI” Slide 22
Comparison of Anisotropy IndicesComparison of Anisotropy Indices
D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).
BMI2 SS08 – Class 7 “functional MRI” Slide 23
How Many Bipolar Gradients?How Many Bipolar Gradients?
DTI
D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).
BMI2 SS08 – Class 7 “functional MRI” Slide 24
Diffusion Tensor MappingDiffusion Tensor Mapping
D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).
BMI2 SS08 – Class 7 “functional MRI” Slide 25
Diffusion Tensor MappingDiffusion Tensor Mapping
D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).
BMI2 SS08 – Class 7 “functional MRI” Slide 26
Magnetic Susceptibility-based Imaging
Magnetic Susceptibility-based Imaging
BMI2 SS08 – Class 7 “functional MRI” Slide 27
Magnetic interaction of HbMagnetic interaction of Hb
Image local field inhomogeneities (T2* weighted)
BMI2 SS08 – Class 7 “functional MRI” Slide 28
Magnetic Susceptibility Effects IMagnetic Susceptibility Effects I
BMI2 SS08 – Class 7 “functional MRI” Slide 29
Magnetic Susceptibility Effects IIMagnetic Susceptibility Effects II
BMI2 SS08 – Class 7 “functional MRI” Slide 30
Reminder: Neuro-vascular couplingReminder: Neuro-vascular coupling
intensity
BMI2 SS08 – Class 7 “functional MRI” Slide 31
Blood vesselsBlood vessels
Capillaries
BMI2 SS08 – Class 7 “functional MRI” Slide 32
Hemoglobin-Oxygen InteractionHemoglobin-Oxygen Interaction
BMI2 SS08 – Class 7 “functional MRI” Slide 33
Hemoglobin-Oxygen InteractionHemoglobin-Oxygen Interaction
BMI2 SS08 – Class 7 “functional MRI” Slide 34
Hemoglobin-Oxygen InteractionHemoglobin-Oxygen Interaction
BMI2 SS08 – Class 7 “functional MRI” Slide 35
Effect of Oxygen BindingEffect of Oxygen Binding
Deoxyhemoglobin: “puckered” heme; paramagnetic
Oxyhemoglobin: planar heme; diamagnetic
BMI2 SS08 – Class 7 “functional MRI” Slide 36
T2* weighted imagesT2* weighted images
rest activation
BMI2 SS08 – Class 7 “functional MRI” Slide 37
SubtractionSubtraction
BMI2 SS08 – Class 7 “functional MRI” Slide 38
Average for multiple stimulationsAverage for multiple stimulations
Spatial mean over 426 non-activated voxels
Spatial mean over 426 activated voxels
BMI2 SS08 – Class 7 “functional MRI” Slide 39
Example for visual stimulationExample for visual stimulation
BMI2 SS08 – Class 7 “functional MRI” Slide 40
fMRI studyfMRI study
BMI2 SS08 – Class 7 “functional MRI” Slide 41
AnalysisAnalysis
BMI2 SS08 – Class 7 “functional MRI” Slide 42
Another paradigmAnother paradigm
BMI2 SS08 – Class 7 “functional MRI” Slide 43
Data consideredData considered
Time series analysis
BMI2 SS08 – Class 7 “functional MRI” Slide 44
Exploring individual voxel time seriesExploring individual voxel time series
… not efficient or quantitative
BMI2 SS08 – Class 7 “functional MRI” Slide 45
Predicted ModelPredicted Model
BMI2 SS08 – Class 7 “functional MRI” Slide 46
Statistical Parametric Mapping (SPM)Statistical Parametric Mapping (SPM)
http://www.fil.ion.ucl.ac.uk/spm/
K. J. Friston, UCL, UK
BMI2 SS08 – Class 7 “functional MRI” Slide 47
SPM preprocessingSPM preprocessing
Movement correction:
Sensitivity: Large error variance may prevent us from finding activations
Specificity: Task correlated motion may appear as activation
Normalization: Deals with individual morphological differences
BMI2 SS08 – Class 7 “functional MRI” Slide 48
SPM preprocessingSPM preprocessing
Smoothing ():
Convolution with Gaussian kernel
Reduced effects of noise
BMI2 SS08 – Class 7 “functional MRI” Slide 49
General Linear Model GLMGeneral Linear Model GLM
BMI2 SS08 – Class 7 “functional MRI” Slide 50
GLM matricesGLM matrices
BMI2 SS08 – Class 7 “functional MRI” Slide 51
GLM matricesGLM matrices
BMI2 SS08 – Class 7 “functional MRI” Slide 52
GLM matricesGLM matrices
1 1 3 3 9 9Y t = X t + μ X t + β X t + + β X t + ε t
BMI2 SS08 – Class 7 “functional MRI” Slide 53
Correlation mapsCorrelation maps