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, so the spins happen in different directions and cancel out.

Spin alignment

But when applying a very strong external magnetic field.

Spin alignment

Putting the hydrogen into an external magnetic field generates the magnetic moment and causes the hydrogen

to precess around the axis of the magnetic field.

PrecessionM

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The hydrogen aligns in parallel (low energy) and anti-parallel (high energy – less stable) states.

Energy states

Energy states change with excitation and relaxation

Energy states

fMRI measurements = energy release during relaxation!

For every million hydrogen atoms 500,001 will position in the parallel state and 499,999 will position in anti-parallel

state.

Luckily we have 1023 hydrogen atoms in every gram of tissue…

Proportions

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

Net magnetization (M)

A spinning hydrogen atom within an external magnetic field has a particular magnetic moment.

It also has a particular angular momentum because it has mass. Angular momentum is a rotation force pulling

perpendicular to the rotation plane according to the right hand rule.

Magnetic moment / angular momentum = gyromagnetic ratio

Combination of mechanical and electromagnetic forces.

Gyromagnetic ratio ( )

The gyromagnetic ratio ( ) will determine how fast (v) the hydrogen will spin around the axis of a magnetic field with a

given strength (Bo).

v = Bo * /2π

The spin velocity of an atom/molecule is called its Larmor frequency (for hydrogen 42.58 MHz/Tesla)

Larmor frequency

B = 1.0 TB = 2.0 T B = 3.0 T

TIME

Because different atoms/molecules have different Larmor frequencies, we can “tune into” the Hydrogen frequency and isolate it from other atoms/molecules in the scanned tissue.

We’ll do this by exciting and “reading out” relaxation within a small window around the Hydrogen Larmor frequency.

This is also how spectroscopy methods determine the molecular composition of a sample…

Larmor frequency

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

Lab/Rotating frame

Excite the sample into a less stable perpendicular direction

Excitation pulses: B1

Before excitation

High Energy

Low Energy

External Magnetic Field (B0)

M0

At excitation

High Energy

Low Energy

External Magnetic Field (B0)

M0

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 much we excite our sample…

Flip angle

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900 pulse

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1800 pulse

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Once the sample has been excited, it relaxes into a more stable (lower energy state) and emits energy in the process

Relaxation

What frequency is the hydrogen energy at?

Relaxation

time

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T1: relaxation in the longitudinal planeT2: relaxation in the transverse plane

T1 and T2/T2*

Analogous to amplitude and phase…

Realignment with main magnetic field direction

T1

M0 M0

M0

M0 M0

Static main field Excitation pulse

Longitudinal relaxation

T1

Longitudinal magnetization

Magnetization vector

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”…

De-phasing in the transverse plane

T2/T2*

M0

Static main field Excitation pulse

Transverse relaxation

T2/T2*

Spin phase

Transversemagnetization

What influences T2/T2*?

Again has to do with the molecular neighborhood of the excited spinning atom.

The more spin-spin interactions there are the quicker the decay and the shorter the T2.

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

Different tissues have different molecular neighborhoods and different T2 constants…

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

Source of MR signal

The energy source driving the MR signal used to determine T1 and T2 is identical!

The only thing we can measure is the energy released by hydrogen atoms moving from excited to relaxed state.

But we can derive T1, T2, T2’, and T2* relaxation properties by exciting the sample and measuring its “resonating” energy release in clever ways (i.e. using different pulse sequences).

Using different MRI sequences we can contrast different features of the tissues like their T1/T2/T2* relaxation times. Since neighboring tissues will have different

relaxation times this will enable us to visualize particular tissues (e.g. gray & white matter):

Image contrast

T2* 40ms

Two important time constants are defined for each sequence:

TR – repetition time between excitation pulses.

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

Contrasting different attributes of the tissue depends on the choice of these two variables.

The TR length will determine the contribution of T1 relaxation to the contrast and the TE length will determine the contribution of T2 relaxation to the contrast.

TR and TE

The amount of post-excitation signal depends on how relaxed the sample was during the excitation time.

T1 and TR length

M0

Static main field

Think about exciting a sample at different stages of longitudinal relaxation.

M0

M0 M0

Choosing a short TR means less energy release (MR signal) on consecutive scans.

T1 and TR length

T2/T2* and TE length

M0

Static main field Excitation pulse

Transverse relaxation

TE: When to acquire the dataThe relaxing hydrogen atoms emit a decaying amount of

energy. The question is how soon after excitation to measure the energy?

For a T2 contrast you would want to wait a bit and let the energy decay.

Only one signal source!

Remember that the only thing we can measure is in phase energy release of the precessing hydrogen atoms.

To generate an electric current in the receiving magnet coil we need a “large” number of hydrogen atoms to spin together

(remember electric induction – moving magnetic fields generate an electric current).

Measuring T1/T2/T2* relaxation properties is only a consequence of the order in which we excite, relax, and

acquire the energy released by the sample.

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

Proton density

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 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

Having the gradients in place changes the local magnetic field experienced by hydrogen at different spatial points

inside the magnet.

This means the hydrogen will have different magnetic moments and will precess at slightly different speeds at

each spatial location.

By “focusing in” on the precession speed (larmor frequency) at each location we can achieve spatial

resolution.

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

Spatial gradients

Determining power in particular frequencies

Fourier Transform

FrequencyIn

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Separates a complex signal into its sinusoidal components

Fourier Transform

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FrequencyIn

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Spatial gradients

64 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

Main magnet field is generated by a 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!