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

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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

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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

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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

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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

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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?

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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.

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fMRI investigation of hemodynamicsfMRI investigation of hemodynamics

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Diffusion-Weighted Imaging (DWI)Diffusion-Weighted Imaging (DWI)

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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)

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Examples of Diffusion-weighted imagesExamples of Diffusion-weighted images

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Examples of Diffusion-weighted imagesExamples of Diffusion-weighted images

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Diffusion Tensor Imaging (DTI)Diffusion Tensor Imaging (DTI)

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How Many Bipolar Gradients?How Many Bipolar Gradients?

1

2

1 2

MRA

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How Many Bipolar Gradients?How Many Bipolar Gradients?

DWI

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DTI Concepts 1DTI Concepts 1

M.E. Shenton et al., http://splweb.bwh.harvard.edu:8000/pages/papers/pubs/yr2002.htm

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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

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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):

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Comparison of Anatomical, DWI, DTIComparison of Anatomical, DWI, DTI

D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

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Comparison of Anisotropy IndicesComparison of Anisotropy Indices

D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

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How Many Bipolar Gradients?How Many Bipolar Gradients?

DTI

D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

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Diffusion Tensor MappingDiffusion Tensor Mapping

D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

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Diffusion Tensor MappingDiffusion Tensor Mapping

D. Le Bihan et al., J. Magnetic Resonance Imaging 13: 534-546 (2001).

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Magnetic Susceptibility-based Imaging

Magnetic Susceptibility-based Imaging

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Magnetic interaction of HbMagnetic interaction of Hb

Image local field inhomogeneities (T2* weighted)

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Magnetic Susceptibility Effects IMagnetic Susceptibility Effects I

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Magnetic Susceptibility Effects IIMagnetic Susceptibility Effects II

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Reminder: Neuro-vascular couplingReminder: Neuro-vascular coupling

intensity

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Blood vesselsBlood vessels

Capillaries

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Hemoglobin-Oxygen InteractionHemoglobin-Oxygen Interaction

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Hemoglobin-Oxygen InteractionHemoglobin-Oxygen Interaction

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Hemoglobin-Oxygen InteractionHemoglobin-Oxygen Interaction

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Effect of Oxygen BindingEffect of Oxygen Binding

Deoxyhemoglobin: “puckered” heme; paramagnetic

Oxyhemoglobin: planar heme; diamagnetic

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T2* weighted imagesT2* weighted images

rest activation

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SubtractionSubtraction

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Average for multiple stimulationsAverage for multiple stimulations

Spatial mean over 426 non-activated voxels

Spatial mean over 426 activated voxels

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Example for visual stimulationExample for visual stimulation

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fMRI studyfMRI study

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AnalysisAnalysis

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Another paradigmAnother paradigm

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Data consideredData considered

Time series analysis

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Exploring individual voxel time seriesExploring individual voxel time series

… not efficient or quantitative

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Predicted ModelPredicted Model

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Statistical Parametric Mapping (SPM)Statistical Parametric Mapping (SPM)

http://www.fil.ion.ucl.ac.uk/spm/

K. J. Friston, UCL, UK

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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

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SPM preprocessingSPM preprocessing

Smoothing ():

Convolution with Gaussian kernel

Reduced effects of noise

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General Linear Model GLMGeneral Linear Model GLM

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GLM matricesGLM matrices

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GLM matricesGLM matrices

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GLM matricesGLM matrices

1 1 3 3 9 9Y t = X t + μ X t + β X t + + β X t + ε t

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Correlation mapsCorrelation maps