fMRI Methods

Lecture2 – MRI Physics

magnetized materials and moving electric charges.

Magnetic fields

Similarly a moving magnetic field can be used to create electric current (moving charge).

Electric induction

Or you could use an electric current to move a magnet…

Electric induction

Force and field directions

Right hand rule

Protons are positively charged atomic particles that spin about themselves because of thermal energy.

Nuclear spins

μ (magnetic moment) = the torque (turning force) felt by a moving electrical charge as it is put in a magnet field.

Magnetic moment

The size of a magnetic moment depends on how much electrical charge is moving and the strength of the magnetic field it is in.

A Hydrogen proton has a constant electrical charge.

Earth’s magnetic field is relatively small (0.00005 Tesla), so the spins happen in different directions and cancel out.

Spin alignment

But when in a strong external magnetic field (e.g. 1.5 Tesla).

Spin alignment

Sum of magnetic moments in a sample with a particular volume at a given time.

Net magnetization (M)

Hydrogen protons not only spin. They also precess around the axis of the magnetic field.

PrecessionM

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True for all atoms with an odd number of protons

Two factors govern the speed of precession (Larmor frequency): magnetic field strength & gyromagnetic ratio

Larmor frequency = Bo * /2π

Precession speed

Gyromagnetic ratio ( )

Magnetic moment / Angular momentum

Combination of electromagnetic and mechanical forces.

Angular momentum is dependant on the mass of the atom.

Gyromagnetic ratio

Different atoms have different gyromagnetic ratios:

Gyromagnetic ratio

Nucleus Gyromagnetic ratio (γ)1H 267.5137Li 103.96213C 67.26219F 251.662

23Na 70.76131P 108.291

Different atoms placed in the same magnetic field have different Larmor frequencies:

“Tune in” to the Hydrogen frequency.

Larmor frequency

Nucleus Larmor Frequency at 1 Tesla1H 42.576 MGHz7Li 16.546 MGHz13C 10.705 MGHz19F 40.053 MGHz

23Na 11.262 MGHz31P 17.235 MGHz

The hydrogen atoms are precessing around z (direction of B0)

Longitudinal & transverse directions

Net magnetization is all pointing in the z direction

Steady state

Applying a perpendicular magnetic field “flips” the protons

Excitation pulses

Excite the sample in a perpendicular direction and let it relax.

Net magnetization of the sample changes as it relaxes, inducing current to move in a near by coil.

Excitation & Relaxation

Larmor frequency

Defined by the strength of B1 pulse and how long it lasts (T)

θ = *B1*T

This is one of the parameters we set during a scan

It defines how far we “flip” the protons…

Flip angle

xy

z

xy

z

900 pulse

xy

z

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z

1800 pulse

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z

xy

z

<900 pulse

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z

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>900 pulse

T1: relaxation in the longitudinal directionT2*: relaxation in the transverse plane

T1 and T2/T2*

Changes in the direction of the sample’s net magnetization

Realignment of net magnetization with main magnetic field direction

T1

Before excitation At excitation Relaxation

Net magnetization along the longitudinal direction

T1

T1 = 63% recovery of original magnetization value M0

What influences T1?

Has something to do with the surroundings of the excited atom. The excited hydrogen needs to “pass on” its energy to its surroundings (the lattice) in order to relax.

Different tissues offer different surroundings and have different T1 relaxation times…

We can also introduce external molecules to a particular tissue and change its relaxation time. These are called “contrast agents”…

Loss of net magnetization phase in the transverse plain

T2*/T2

Before excitation At excitation Relaxation

Net magnetization in the transverse plain

T2/T2*

T2 = 63% decay of magnetization in transverse plain

Two main factors effect transverse relaxation:

1. Intrinsic (T2): spin-spin interactions. Mechanical and electromagnetic interactions.

2. Extrinsic (T2’): Magnetic field inhomogeneity. Local fluctuations in the strength of the magnetic field

experienced by different spins.

T2* = T2 - T2’

T2’Magnetic field inhomogeneities

Examples of causes:Transition to air filled cavities (sinusoids)Paramagnetic materials like cavity fillingsMost importantly – Deoxygenated hemoglobin

What influences T2?

Again, has to do with the molecular neighborhood affecting the amount and quality of spin-spin interactions.

Different tissues will have different T2 relaxation times.

The stronger the static magnetic field, the more interactions there are, quicker T2 decay.

MR signalWe only have one measurement:

Measurement of the net magnetization in the transverse plain as the sample relaxes.

Once T2* relaxation is completeProtons precess out of phase in the transverse plain

Net magnetization in transverse plain = 0

Two important scanning parameters:

TR – repetition time between excitation pulses.

TE – time between excitation pulse and data acquisition (“read out”).

Creating scanning protocols with different TR and TE lengths will allow us to derive T1 and T2/T2* relaxation times.

TR and TE

Short TR = weaker MR signal on consecutive pulses.

TR length & MR signal strength

With short TRs relaxation in the longitudinal direction will not be complete. So there will be fewer relaxed protons to excite.

TE: when to measure MR signalWe can measure the amplitude of net magnetization

immediately after excitation or we can wait a bit.

Longer TEs will allow more transverse relaxation to happen and the MR signal will be weaker.

We can scan the brain using different pulse sequences by choosing particular TR and TE values to create images

with different contrasts.

Different image contrasts

TR length will determine how much time the sample has had to relax in the longitudinal direction.

TE will determine how much time the sample has had to relax (loose phase) in the transverse plain.

Measuring the amount of hydrogen in the voxels regardless of their T1 or T2 relaxation constants.

Proton density contrast

This is done using a very long TR and very short TE

Higher intensity in voxels containing more hydrogen protons

Proton density

Measuring how T1 relaxation differs between voxels.This is done using a medium TR and very short TE

T1 contrast

You need to know when largest difference between the tissues will take place…

Images have high intensity in voxels with shorter T1 constants (faster relaxation/recovery = release of more energy)

T1 contrast

CSF: 1800 msGray matter: 650 ms White matter: 500 ms Muscle: 400 msFat: 200 ms

Measuring how T2 relaxation differs between voxels.This is done using a long TR and medium TE

T2/T2* contrast

We can combine a T2 acquisition with proton density…

Images have high intensity in voxels with longer T2 constants (slower relaxation = more detectable energy)

T2 contrast

CSF: 200 msGray Matter: 80 ms White Matter: 60 ms Muscle: 50 msFat: 50 ms

Same as T2 only smaller numbers (faster relaxation)

T2* contrast

CSF: 100 msGray Matter: 40 ms White Matter: 30 ms Fat: 25 ms

T2* = T2 +T2’

T2: Spin-spin interactionsT2’: field inhomogeneities

Exposed iron (heme) molecules create local magnetic inhomogeneities

T2* and BOLD fMRI

BOLD – blood oxygen level dependant

Assuming everything else stays constant during a scan one can measure BOLD changes across time…

More deoxygenated blood = more inhomogeneity

more inhomogeneity = faster relaxation (shorter T2*)

Shorter T2* = weaker energy/signal (image intensity)

So what would increased neural activity cause?

T2* and BOLD

So what happened in particular time points of this scan?

T2* and BOLD

Bloch equation

So far we’ve talked about a bunch of forces and energies changing in a sample across time…

How can we differentiate locations in space and create an image?

MR images

Paul Lauterbur Peter Mansfield

2004 Nobel prize in Medicine

Create magnetic fields in each direction (x,y,z) that move from stronger to weaker (hence gradient).

Spatial gradients

Different magnetic fields at different points in space.

Hydrogen will precess at a different speed in each spatial location.

By “tunning in” on the specific precession speed we can separate different spatial locations.

Similarly to how we “tunned in” on hydrogen atoms…

Spatial gradients

Spatial gradients

64 MHz

65 MHz

66 MHz

63 MHz

62 MHz

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(-)

(+)

Lot’s of Fourier transforms.

Work in k-space (a vectorial space that keeps track of the spin phase & frequency variation across magnet space).

It’s possible to turn gradients on and off very quickly (ms).

Image reconstruction

Pulse sequences

Spatial gradients

The magnet

Main static field

Extremely large electric charge spinning on a helium cooled (-271o c) super conducting coil.

Earth’s magnetic field 30-60 microtesla.

MRI magnets suitable for scanning humans 1.5-7 T.

Main coils

The bulk of the structure contains the coils generating the static magnetic field and the gradient magnetic fields.

RF coil

Transmit and receive RF coils located close to the sample do the actual excitation and “read out”.

Read Chapters 3-5 of Huettel et. al.

Explain how a spin-echo pulse does the magic of separating T2 relaxation from T2* relaxation. You can include figures/drawings if you like.

Homework!