Introduction to fMRI physics for dummies (like me!).

Outline

• History of NMR to MRI to fMRI

• Physics of protons (1H in particular)

• Creating MRI images

• From MRI to fMRI

History of Nuclear Magnetic Resonance

NMR = nuclear magnetic resonanceFelix Block and Edward Purcell

1946: atomic nuclei absorb and re-emit radio frequency energy1952: Nobel prize in physics

nuclear: properties of nuclei of atomsmagnetic: magnetic field requiredresonance: interaction between magnetic field and radio frequency

Bloch PurcellNMR MRI

Source: Jody Culham’s web slides

History of fMRIMRI-1973: Lauterbur suggests NMR could be used to form images-1977: clinical MRI scanner patented-1977: Mansfield proposes echo-planar imaging (EPI) to acquire images faster

fMRI-1990: Ogawa observes BOLD effect with T2*

blood vessels became more visible as blood oxygen decreased-1991: Belliveau observes first functional images using a contrast agent-1992: Ogawa & Kwong publish first functional images using BOLD signal

Source: Jody Culham’s web slides

Some terms to knowB0 – this is used to denote the main magnetic field – also known as longitudinal magnetization

objects placed within B0 will gradually align to this field (longitudinal relaxation)

M0 – this is used to denote the net magnetization of an object within B0

it is the M0 which is ‘tipped’ out of alignment with B0 to create the MR image – so M0 is now measured as transverse magnetization

RF pulse – radio frequency pulse – not to be confused with ‘resonant frequency’

to read M0 it must be tipped out of alignment with B0 – this is achieved by sending an RF pulse at certain resonant frequencies and gradients

Some more terms to know

Magnet – the big magnet that we allocate the Tesla value to that creates B0

Gradient Coil – smaller magnets that are used to tip the net magnetization of the subject (M0) out of alignment with B0

There are actually three gradient coils orthogonal to one another so that gradients can be applied in the x, y and z planes

RF coil – radio frequency coil – these are typically receive only coils and are used to measure M0 at some time after the RF pulses have been applied. Send/receive coils are also available

Physics of protons.• motion of electrically charged particles results in a magnetic force

orthogonal to the direction of motion

• protons (nuclear constituent of atom) have a property of angular momentum known as spin

Angular momentum (spin) of a proton.

Protons aligning within a magnetic fieldIn “field free” space

randomly oriented

Source: Mark Cohen’s web slides Source: Robert Cox’s web slides Source: Jody Culham’s web slides

• when placed in a magnetic field (B0; e.g., our MRI machines) protons will either align with the magnetic field or orthogonal to it (process of reaching magnetic equilibrium)

• there is a small difference (10:1 million) in the number of protons in the low and high energy states – with more in the low state leading to a net magnetization (M)

Inside magnetic field

oriented with or against B0

M = net magnetization

M

Applied Magnetic Field (B0)

Precession – the spinning top analogy.

Source: Cohen and Bookheimer article

What is actually aligned with the B0 is the axis around which the proton precesses – the decay of precession (i.e., it is the rate of precession out of alignment with B0 together with the proton density of the tissue concerned that is crucial in MRI)

Larmor Frequency

Larmor equationf = B0

= 42.58 MHz/T

At 1.5T, f = 63.76 MHzAt 4T, f = 170.3 MHz

Field Strength (Tesla)

ResonanceFrequency for 1H

170.3

63.8

1.5 4.0

• the energy difference between the high (oriented with B0) and low (oriented against B0) energy protons is measurable and is expressed in the Larmor equation

RF Excitation

• protons can flip between low and high energy states (i.e., flip between being aligned with or against B0)

• to do so the energy transfer must be of a precise amount and must be facilitated by another force (e.g., other protons or molecules)

• in MRI, RF (radio frequency) pulses are used to excite the RF field – the swing analogy – tipping the net magnetization out of alignment with B0

Cox’s Swing Analogy

Source: Robert Cox’s web slides

RF Excitation

Excite Radio Frequency (RF) field• transmission coil: apply magnetic field along B1 (perpendicular to B0) for ~3 ms• oscillating field at Larmor frequency• frequencies in range of radio transmissions• B1 is small: ~1/10,000 T• tips M to transverse plane – spirals down• analogies: guitar string (Noll), swing (Cox)• final angle between B0 and B1 is the flip angle

B1

B0

Source: Robert Cox’s web slides

Longitudinal relaxation and T1.• temperature influences the number of collisions (and hence the rate at

which protons flip between low and high energy states)

• so magnetic equilibrium (M0), or the rate at which a body placed inside B0 becomes magnetized depends on temperature – this is known as longitudinal relaxation

• the T1-weighted image (usually used for anatomical images) measures the rate at which the object placed in B0 (the unsuspecting subject in our case) goes from a non-magnetized to a magnetized state – the longitudinal relaxation

• different types of molecules (and by extension tissue) approach M0 at different rates allowing us to differentiate things like white and grey matter – we creep close towards the image!!!

T1 and T2• T1 measures the longitudinal relaxation (along B0) – or the rate at which

the subject (and the various different constituents of that subject) reaches magnetic equilibrium

• T2 measures the transverse relaxation (along B1) – or the rate of decay of the signal after an RF pulse is delivered

• T1 – recovery to state of magnetic equilibrium• T2 – rate of decay after excitation

Tissue T2 decay times (in 1.5 T magnet)

white matter 70 msec

grey matter 90 msec

CSF 400 msec

Reading M0

• RF coils receive the net magnetization from the object placed within the coil (e.g., a subject’s head)

• can also have send / receive RF coils that also deliver the RF pulse (to get the swing going) – usually the pulse is delivered by gradient coils

Proton density, recovery (T1) and decay (T2 and T2*) times.

• By ‘weighting’ the pulse sequence (and the point at which data is collected) different images of the brain are obtained

• Weighting is achieved by manipulating TE (time to echo) and TR (time to repetition of the pulse sequence)

T1 weighted Density weighted T2 weighted

T1 and TR

Source: Mark Cohen’s web slides

T1 = recovery of longitudinal (B0) magnetization after the RF pulse• used in anatomical images• ~500-1000 msec (longer with bigger B0)

TR (repetition time) = time to wait after excitation before sampling T1

T2 and TE

Source: Mark Cohen’s web slides

T2 = decay of transverse magnetization after RF pulseTE (time to echo) = time to wait to measure T2 or T2* (after re-focusing with spin echo)

T1 vs. T2• effectively, T1 and T2 images are the inverse of one another, with T1

typically used to form anatomical images and T2* used in fMRI

T1 and TR

T2*T2: intrinsic decay of transverse magnetization over microscopic region (~5-10 microns)

~50-100 msec (shorter with bigger B0)

T2*: overall decay of transverse magnetization over macroscopic region (~mm)

decays more quickly than T2 (by factor of ~2)

Source: Robert Cox’s web slides

Source: Mark Cohen’s web slides

Spatial localisation of the signal – creating the 1D image.

• A spatially variant B1 leads to a spatially variant distribution of RFs.

• Frequency analysis is used to discriminate different spatial locations.

time

RF pulse

Gx (x – gradient)

data acquisition

PULSE SEQUENCEPULSE SEQUENCE

Spatial Coding

excite only frequencies

corresponding to slice plane

Field Strength (T) ~ z position

Fre

q

Gradient coil

add a gradient to the main magnetic

field

Gradient magnetic field = applied in the slice plane (i.e., the x direction) thus Gx

Spatial localisation of the signal – creating the 2D image.

• Can’t simply turn on 2 gradients.

• Instead the 2 gradients need a precise sequence.

• The 1D sequence already shown is known as frequency encoding.

• A different pulse sequence can be used in the y-direction to create the 2D image – phase encoding.

• This method is known as echo-planar imaging or EPI and is the most common method used in fMRI. Although Spiral imaging is catching up!

Spatial localisation of the signal – creating the 3D image

• The RF field must be at the same resonant frequency as the nucleus being scanned.

• For the 2D image we have selected only one resonant frequency in one particular z-plane (and used EPI sequences to obtain the x and y-planes).

• So we simply apply a gradient at different levels (slices) in the z-plane to create the 3D image.

slices in the z-plane

Spatial localisation of the signal – creating the 3D image

frequ. encode

phase encode

Source: Buxton book Ch. 10

Echos

Source: Buxton book

All RF pulses create an ‘echo’ of the M0 signal obtained by the pulse.

T2* signals decay more rapidly than T2

A refocusing pulse is used to create a transient echo of the signal – a spin echo

Multiple refocussing pulses create multiple echoes

EPI imaging and k-space

• Any net signal produced by proton spins can be expressed as a sum of the sine and cosine waves of different wavelengths

• The different spatial frequencies of these wavelengths are denoted as k-space – the inverse of the wavelengths

small k value = low spatial frequency / long wavelengthlarge k value = high spatial frequency / short wavelength

• k-space is what is actually measured in MRI (i.e., the signal from M0 is transformed into x and y values via k-space)

EPI imaging and k-space

Source: Traveler’s Guide to K-space (C.A. Mistretta)

x = frequency and y = phase or angle

Fourier transformation.• k-space is magically transformed into our image via a Fourier transform.

Source: Buxton book Ch 5

EPI imaging and k-space

Source: Buxton book Ch 10

EPI imaging and k-space

Source: Buxton book Ch 10

http://www1.stpaulshosp.bc.ca/stpaulsstuff/MRartifacts.html

k-space and sampling methods.

The EPI pulse sequence zig-zags across k-space, slowly in the x-direction and rapidly in the y-direction.

The Gz gradient shifts this process to the next slice to be imaged.

Source: Buxton book Ch 11

EPI

Voila! The MRI!

But what about activation?

Vascular Network• Arterioles

– Y=95% at rest.– Y=100% during activation.– 25 m diameter.– <15% blood volume of cortical tissue.

• Venules– Y=60% at rest.– Y=90% during activation.– 25-50 m diameter.– 40% blood volume of cortical tissue.

• Red blood cell– 6 m wide and 1-2 m thick.– Delivers O2 in form of oxyhemoglobin.

• Capillaries– Y=80% at rest.

– Y=90% during activation.

– 8 m diameter.

– 40% blood volume of cortical tissue.

– Primary site of O2 exchange with tissue.

Artery Vein

Arterioles Veneoles

Capillaries

1 - 2 cm

Neurons

Transit Time = 2-3 sSource: Chris Thomas’ Slides

Vascular network and BOLD

Source: Buxton book Ch 2

Susceptibility and Susceptibility Artifacts

Source: Robert Cox’s web slides

Adding a nonuniform object (like a person) to B0 will make the total magnetic field B nonuniform

This is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an external field

For large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform magnetic fields can be adjusted to “even out” the ripples in B — this is called shimming

Susceptibility Artifact-occurs near junctions between air and tissue

• sinuses, ear canalssinuses

earcanals

Susceptibility and BOLD fMRI

• Magnetic susceptibility () refers to magnetic response of a material when placed in B0.

• Red blood cells exhibit a change in during ‘activation’

• Basically, oxyhaemoglobin in the RBC (HbO2) becomes deoxyhaemoglobin (Hb):

– Becomes paramagnetic.

– Susceptibility difference between venous vasculature and surroundings (susceptibility induced field shifts).

BOLD signal

Source: Buxton book Ch 17

Blood Oxygen Level Dependent signal

BOLD signalBlood Oxygen Level Dependent signal

• CBF, CBV, and CMRO2 have different effects on HbO2 concentration:

• Interaction of these 3 produce BOLD response– They change [Hb] which affects magnetic environment.

(delivery of more HbO2 -> less Hb on venous side if

excess O2 not used)

CMRO2

CBV

CBFLocal HbContent

Local HbContent

Local HbContent

(extraction of O2-> HbO2 becomes Hb)

(more Hb in a given imaging voxel)

BOLD signal

Source: Doug Noll’s primer

First Functional Images

Source: Kwong et al., 1992

Hemodynamic Response Function

% signal change = (point – baseline)/baselineusually 0.5-3%

initial dip-more focal-somewhat elusive so far

time to rise signal begins to rise soon after stimulus begins

time to peaksignal peaks 4-6 sec after stimulus begins

post stimulus undershootsignal suppressed after stimulation ends

And now we can all get some sleep!