bmi2 ss08 – class 6 “functional mri” slide 1 biomedical imaging 2 class 6 – magnetic...

BMI2 SS08 – Class 6 “functional MRI” Slide 1

Biomedical Imaging 2Biomedical Imaging 2

Class 6 – Magnetic Resonance Imaging (MRI)

Functional MRI (fMRI):Magnetic Resonance Angiography (MRA),

Diffusion-weighted MRI (DWI)

02/26/08


MRI PhysicsMRI Physics


Magnetic Resonance in a NutshellMagnetic Resonance in a Nutshell

Hydrogen Nuclei (Protons)

Axis of Angular Momentum (Spin), Magnetic Moment



Spins PRECESS at a single frequency (f0), but incoherently − they are not in phase

External Magnetic Field



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

↓ROTATING

REFERENCE FRAME


Primary (Static) Magnetic FieldPrimary (Static) Magnetic Field

N

Smagnetic field lines

By staying in the interior region of the field, we can ignore edge effects.


Typical Magnetic Resonance ImagerTypical Magnetic Resonance Imager

http://www.radiologyinfo.org/en/photocat/photos_pc.cfm?Image=si-symphony.jpg&pg=bodymr&bhcp=1 (Radiological Society of North America, Inc.)


Generating the Primary Magnetic FieldGenerating the Primary Magnetic Field

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html (Georgia State University)


Gradient coils 1Gradient coils 1

z-gradient: Anti-Helmholtz coils


Gradient coils 2Gradient coils 2

Gradients perpendicular to z


Alignment of 1H Nuclei in a Magnetic FieldAlignment of 1H Nuclei in a Magnetic Field

mmz

mmz

B0Protons must orient themselves such that the z-components of their magnetic moments lie in one of the two permissible directions

What about direction of m?

mzCorrect quantum mechanical description is that m does not have an orientation, but is delocalized over all directions that are consistent with fixed value of mz.

For the purpose of predicting/interpreting the interaction of m with radiation, we can think of m as a well-defined vector rapidly precessing about z-direction.

mz

What is the precession frequency?


Orientational Distribution of 1H NucleiOrientational Distribution of 1H Nuclei

What fraction of nuclei are in the “up” state and what fraction are “down”?

mmz

mmz

B0Protons must orient themselves such that the z-components of their magnetic moments lie in one of the two permissible directions

The orientation with mz aligned with B0 has lower potential energy, and is favored (North pole of nuclear magnet facing South pole of external field).

The fractional population of the favored state increases with increasing |B0|, and increases with decreasing (absolute) temperature T.

Boltzmann distribution: 0

23 -1down

up34

, 1.381 10 J - K

6.626 10 J - s

h

kTN

e kN

h

B


Transitions Between Spin States (Orientations) ITransitions Between Spin States (Orientations) I

QM result: energy difference between the “up” and “down” states of mz is ΔE0 = h|B0|

As always, frequency of radiation whose quanta (photons) have precisely that amount of energy is f0 = ΔE0/h

So, f0 = |B0|

Different nuclei have different values of . (Units of are MHz/T.)

1H: = 42.58; 2H: = 6.53; 3H: = 45.41

13C: = 10.71

31P: = 17.25

23Na: = 11.27

39K: = 1.99

19F: = 40.08


Transitions Between Spin States IITransitions Between Spin States II

The frequency f0 that corresponds to the energy difference between the spin states is called the Larmor frequency.

The Larmor frequency f0 is the (apparent) precession frequency for m about the magnetic field direction.

(In QM, the azimuthal part of the proton’s wave function precesses at frequency f0, but this is not experimentally observable.)

Three important processes occur:

+

+

+

+

+

+

hf0 hf0

2hf0

Absorption Stimulated emission

Spontaneous emission

(Relaxation)


Transitions Between Spin States IIITransitions Between Spin States III

The number of 1H nuclei in the low-energy “up” state is slightly greater than the number in the high-energy “down” state.

Irradiation at the Larmor frequency promotes the small excess of low-energy nuclei into the high-energy state.

When the nuclei return to the low-energy state, they emit radiation at the Larmor frequency.

The radiation emitted by the relaxing nuclei is the NMR signal that is measured and later used to construct MR images.

+

+

+

+

+

+

hf0 hf0

2hf0

Absorption Stimulated emission

Spontaneous emission

(Relaxation)


SaturationSaturation

Suppose the average time required for an excited nucleus to return to the ground state is long (low relaxation rate, long excited-state lifetime)

If the external radiation is intense or is kept on for a long time, ground-state nuclei may be promoted to the excited state faster than they can return to the ground state.

Eventually, an exact 50/50 distribution of nuclei in the ground and excited states is reached

At this point the system is saturated. No NMR signal is produced, because the rates of “up”→“down” and “down”→“up” transitions are equal.


Relaxation IRelaxation I

What are spin-lattice relaxation and spin-spin relaxation?What do time constants T1 and T2 mean?

“Lattice” means the material (i.e., tissue) the 1H nuclei are embedded in

1H nuclei are not the only things around that have magnetic moments

• Other species of nuclei• Electrons

A 1H magnetic moment can couple (i.e., exchange energy) with these other moments


Spin-Lattice Relaxation ISpin-Lattice Relaxation I

Spin-lattice interactions occur whenever a physical process causes the magnetic field at a 1H nucleus to fluctuateSpin-lattice interactions cause the perturbed distribution of magnetic moments (i.e., tipped bulk magnetization) to return to equilibrium more rapidlyTypes of spin-lattice interaction

Magnetic dipole-dipole interactionsElectric quadrupole interactionsChemical shift anisotropy interactionsScalar-coupling interactionsSpin-rotation interactions

What is the T1 time constant associated with these processes?

Look ’em up!


x׳

y׳

z׳

B0

Spin-Lattice Relaxation IISpin-Lattice Relaxation II

What is the T1 time constant associated with spin-lattice interactions?

At equilibrium, M point in z׳ direction

Recall that static field direction defines z, z׳


x׳

y׳

z׳

B0

Spin-Lattice Relaxation IIISpin-Lattice Relaxation III


Now impose a transverse magnetic field

…and tip the magnetization towards the x׳-y׳ plane

Then turn the transverse field off


Spin-Lattice Relaxation IVSpin-Lattice Relaxation IV


x׳

y׳

z׳ B0In the laboratory frame, M takes a spiralling path back to its equilibrium orientation. But here in the rotating frame, it simply rotates in the y׳-z׳ plane.

The z component of M, Mz, grows back into its equlibrium value, exponentially:

Mz = |M|(1 - e-t/T1)

Mz M


Relaxation IIRelaxation II

What are spin-lattice relaxation and spin-spin relaxation?What do time constants T1 and T2 mean?

A 1H magnetic moment can couple (i.e., exchange energy with) the magnetic moments of other 1H nuclei in its vicinity

These are called “spin-spin coupling”

Spin-spin interactions occur when the magnetic field at a given 1H nucleus fluctuates

Therefore, should the rates of these interaction depend on temperature? If so, do they increase or decrease with increasing temperature?


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?


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.


Spin-Spin Relaxation IIISpin-Spin Relaxation III

W hat are the effects of spin-spin coupling?

Within a short time, M is completely de-phased. It is spread out over the entire cone defined by cosθ = Mz/|M|

x׳

y׳

z׳ B0

MzWhen M is completely de-phased, Mtr is 0, even though Mz has not yet grown back completely: Mtr = 0, Mz < |M|

Mtr decreases exponentially, with time constant T2:

Mtr = Mtr0 e-t/T2

This also shows why T2 can not be >T1. It must be the case that T2 T1. In practice, usually T2 << T1.


Relaxation IIIRelaxation III

In this example, T1 = 0.5 s

In this example, T2 = 0.2 s


ContrastContrast

Intrinsic : Relaxation times T1, T2, proton density, chemical shift, flow

Extrinsic: TR, TE, flip angle

Contrast in T1: Contrast in T2:


T1-weightingT1-weighting

Short TR:

Maximizes T1 contrast due to different degrees of saturation

Short TE:

Minimizes T2 influence, maximizes signal

T1

T2


T1

T2

T2 weightingT2 weighting

Long TR:

Reduces saturation and minimizes influence of different T1

Long TE:

Maximizes T2 contrast

Relatively poor SNR


T1

T2

Spin density weightingSpin density weighting

Long TR:

Minimizes effects of different degrees of saturation (T1 contrast)

Maximizes signal

Short TE:

Minimizes T2 contrast

Maximizes signal


Effect of B0 Field HeterogeneityEffect of B0 Field Heterogeneity

What is the common element in spin-spin and spin-lattice interactions?

They require fluctuations in the strength of the magnetic field in the immediate environment of a 1H nucleus

If the static B0 field itself is not perfectly uniform, its spatial heterogeneity accelerates the de-phasing of the bulk magnetization vector

The net, or apparent, decay rate of the transverse magnetization is 1/T2* 1/T2 + |B0|.

T2* (“tee-two-star”) has a spin-spin coupling contribution and a field inhomogeneity contribution

T2* < T2 always, and typically T2* << T2


MRI contrast mechanismsMRI contrast mechanisms


MR Imaging PrinciplesMR Imaging Principles


Free induction decay (FID)Free induction decay (FID)

Basic MRI measurement:

Homogeneous static magnetic field (B0)

RF pulse generator

Antenna (coil) for sending and receiving

Free induction decay (FID) signal

Free: No external RF field during detection

Exponential decay at rate T2* due to spin-spin relaxation (dephasing) and local field inhomogeneities


Spin echoSpin echo

Inversion pulse after time phase recovery at 2

Corrects for dephasing due to static B inhomogeneities

x

y

x

y

180 degree spin flip


Spin echo sequenceSpin echo sequence

Multiple pulses create “Carr-Purcell-Meiboom-Gill (CPMG)” sequence

Decays with time constant T2


Gradient fields in MRI 1Gradient fields in MRI 1

Strength of Bz component varies linearly in space


Gradient fields in MRI 2Gradient fields in MRI 2

Larmor frequency varies linearly in space: 0 xx B G x


1st Dimension (z): Slice selection1st Dimension (z): Slice selection

Slice position: z0 ~ f0

Slice thickness:

Slice profile: profile ~ FT (pulse shape)

1/d B T

d

(Frequency f0

bandwidth B, pulse length T)


Slice selection cont.Slice selection cont.

Pulse sequence (PS) for slice selection (TR = repetition time, TE = echo time)


Frequency encodingFrequency encoding

The NMR signal from each x-position contains a specific center frequency

The over-all NMR signal is the sum of signals along x

FT recovers signal contribution at each frequency, i.e. x-location

Resulting spectrum is a projection

Frequency spectrum


Frequency encoding cont.Frequency encoding cont.

Pulse sequence: two gradients for x and z


3rd Dimension (y)3rd Dimension (y)

How to achieve y-localization? Frequency encoding will always produce iso-lines of resonance frequencies

Solution:

Reconstruction from projections

Phase encoding


Phase encodingPhase encoding

Pulse sequence:

TP


2D FT pulse sequence (spin warp)2D FT pulse sequence (spin warp)

Most commonly employed pulse sequence


A Closer Look at the Phase-Encoding GradientA Closer Look at the Phase-Encoding Gradient

y

G(y)

time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-1.0

-0.5

0.0

0.5

1.0

time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-1.0

-0.5

0.0

0.5

1.0

time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-1.0

-0.5

0.0

0.5

1.0

time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-3

-2

-1

0

1

2

3


time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-3

-2

-1

0

1

2

3


y

G(y)

time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-1.0

-0.5

0.0

0.5

1.0

time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-1.0

-0.5

0.0

0.5

1.0

time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-1.0

-0.5

0.0

0.5

1.0



timegradient

time

0.0 0.5 1.0 1.5 2.0si

gnal

[a.

u.]

-3

-2

-1

0

1

2

3

time

0.0 0.5 1.0 1.5 2.0

sign

al [

a.u.

]

-3

-2

-1

0

1

2

3


0

0.5

1

1.5

2

-1

-0.5

0

0.5

1-3

-2

-1

0

1

2

3


timegradient


k-space mapk-space map

The 2D array of NMR signals obtained from repeated pulse sequences is referred to as the k-space map.

kx (Frequency encoding)

FT

k y (

Pha

se e

ncod

ing)

FT

K-space


From Structure to FunctionFrom Structure to Function


MRI vs. fMRIMRI vs. fMRI


fMRI investigation of hemodynamicsfMRI investigation of hemodynamics


Magnetic Resonance Angiography (MRA)

Magnetic Resonance Angiography (MRA)


Arterial Spin Labeling (Perfusion MRI)Arterial Spin Labeling (Perfusion MRI)

HOW?


Basic Idea #1: Time-of-Flight (TOF)Basic Idea #1: Time-of-Flight (TOF)

Step 1: Select this slice

Step 2: Saturate this slice (TR <<T1)

Step 3: Excite this region

Step 4: Apply phase- and frequency-encoding gradients, record FIDs

and/or this one






Step 3: Excite this region

and/or this one


Basic Idea #2: Phase ContrastBasic Idea #2: Phase Contrast

Bipolar Field Gradients


Bipolar Gradient EffectsBipolar Gradient Effects

Static (not moving) stuff

Stuff that moves

First gradient

Second gradient


Examples of Phase-Contrast MRAExamples of Phase-Contrast MRA


fMRI vs. Nuclear Imaging (PET)fMRI vs. Nuclear Imaging (PET)


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)


Examples of Diffusion-weighted imagesExamples of Diffusion-weighted images

bmi2 ss08 – class 6 “functional mri” slide 1 biomedical imaging 2 class 6 – magnetic...

Documents