Module 5: Basic Understanding of MR Physics

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From the course by Johns Hopkins University

Principles of fMRI 1

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Johns Hopkins University

Principles of fMRI 1

400 ratings

This course covers the design, acquisition, and analysis of Functional Magnetic Resonance Imaging (fMRI) data. A book related to the class can be found here: https://leanpub.com/principlesoffmri

From the lesson

Week 1

This week we will introduce fMRI, and talk about data acquisition and reconstruction.

Module 5: Basic Understanding of MR Physics11:33

Module 6: Forming an Image10:05

Module 7: K Space11:42

Meet the Instructors

Martin Lindquist, PhD, MSc
Professor, Biostatistics
Bloomberg School of Public Health | Johns Hopkins University
Tor Wager
PhD
Department of Psychology and Neuroscience, The Institute of Cognitive Science | University of Colorado at Boulder

Hi, in the next couple of modules we'll be talking about how we can acquire and

reconstruct MRI images.

But in order to do that we first have to gain a basic understanding about

MR physics.

So, magnetic resonance imaging, or MRIs,

uses what's called an MR scanner in order to acquire these images, so

an MR scanner consists of an electromagnet with a very strong magnetic field.

Usually this varies between 1.5 and 7 Tesla.

So what does that mean?

Well, to put this in context,

consider that the Earth's magnetic field is 0.00005 Tesla.

So in this case,

a 3 Tesla magnet is roughly 60,000 times stronger than the Earth's magnetic field.

So it's a very strong electromagnet with a strong electromagnetic pull.

So what does MRI measure?

Well MRI is an extremely versatile imaging modality, and

it can be used to study both brain structure and brain function.

And both structural and functional MRI images are acquired using the same magnet.

And different types of brain images can be generated to emphasize contrast,

which is related to different tissue characteristics in the brain.

So all magnetic resonance image techniques rely on the same core set of principles.

And these are the ones that we're going to try to cover now.

So to understand these core principles, we have to begin by studying

a single atomic nuclei and illustrate its impact on the generated MR signal.

So in particular we focus on hydrogen atoms consisting of a single proton.

So these are hydrogen one atoms.

So protons can be viewed as positively charged spheres which are always spinning.

They're spinning around sort of like spinning tops.

Like this.

They give rise to a net magnetic moment along the axis of the spins.

And here we illustrate the direction of the spin.

We can't measure the magnetization of a single hydrogen proton using MR,

instead what we do is we measure the net magnetization of all nuclei within

a volume, so the combination, the ensemble of all the hydrogen atoms within a volume.

So the net magnetization,

which we're going to call M, can be viewed as a vector with two components.

We have a longitudinal component which is parallel to the magnetic field.

And we have a transverse component which is perpendicular to the field.

And so here we see this illustrated, that we have the net magnetization going in

this direction, and we have a longitudinal direction and a transverse direction.

And the transverse direction is in the xy plane.

And the longitudinal is in the z direction.

So in the absence of an external magnetic field,

the nuclear magnetic moments of all these hydrogen atoms are randomly oriented.

So if one hydrogen atom is pointing in this direction,

you have another one pointing in the opposite direction.

So they're cancelling each other out.

For these reasons there's no net magnetization.

However, this changes when they're placed into a strong magnetic field.

This causes the nuclei to align with the field, and

creates a net longitudinal magnetization in the direction of the field.

So here we see all the nuclei are pointing in the same direction, and

this gives rise to a net magnetization in the Z direction.

So the nuclei, while being oriented in this direction, they're also processing

about the field with an angular frequency, which is determined by something called

the Larmor frequency, but at random phase with respect to each other.

So, you can think of these hydrogen atoms as spinning tops, and they're rotating

sort of in the same direction, but at random phase with respect to each other.

So what happens now is that one uses

what's called the radio frequency pulse to align the phase of these nuclei,

so to make them kind of spin in phase with each other, and then tip them over.

And this causes the longitudinal magnetization to decrease and

establishes a new transverse magnetization.

So now all the nucleis are pointing in

the orthoginal direction to the longitudinal direction.

And this causes the net magnetisation to align the transverse plane.

So an analog to this is, I like to think of these hydrogen atoms as these little

compass needles that are always pointing north, and

so north here is the direction of the magnetic field,

and then what we're actually doing here with this RF pulse is, we're taking

the compass needle and we're forcing them to point in the east direction.

So we're excerting a force on it that's forcing the point in the east direction.

But what happens when I remove my finger,

is the compass needle will strive to return to the north direction,

and that's exactly what happens when we remove the RF pulse.

So when remove the RF pulse, the system will seek to return to equilibrium and

this transverse magnetization starts to disappear, and

the longitudinal magnetization grows back to its original size.

And this is a process called longitudinal relaxation.

So basically again,

we have the hydrogen atoms pointing this direction, we remove the RF pulse,

and they start going back into their original longitudinal direction again.

And during this process a signal is created that can be

measured using a receiver coil.

And this is the basic signal that we use in MRI.

So longitudinal relaxation is the restoration of the net magnetization

along the longitudinal direction as the spins return to their parallel state.

This is measured by an exponential growth, described by a time constant called T1.

However there's also something called transverse relaxation,

when this is the loss of net magnetization in the transverse plane

due to the loss of phase coherence.

So remember what we are doing, all these nuclei were out of phase with each other

and the RF pulse put them into phase before it tipped them over.

But once you remove the RF pulse, these nuclei go out of phase with each other.

And this causes a loss of net magnetization in the transverse direction.

And this is also described by an exponential decay

described by a time constant T2.

So here's an illustration of the longitudinal relaxation time, so

basically this is the sort of measure by the time it takes to go from pointing in

this direction in that magnetization, to going back to the original z direction.

And so this is described by this time constant T1 that we see here.

Which is the time it takes to return to 63% of the original net magnetization.

The interesting thing is that different tissue types in the brain have different

T1 values, so the time it takes to relax is different if you're in white matter,

grey matter or in cerebral spinal fluid CSF.

So CSF the relaxation time is much longer,

five times longer than in white matter for example.

And this is going to become important when we start trying to make out images.

The transverse relaxation time, this is due to the lack of,

is the decay of magnetization due to interaction between nuclei, and

this is described by a time constant T2.

And this is due to this lack of phase coherence, and we see this illustrated.

And T2 is how long it takes for

us to go down from 100% down to 37%.

By altering how often we excite the nuclei, which is measured by something

called the TR, and how soon after excitation we begin data collection,

this is something called TE, we can control which characteristic of the image

is emphasized, whether it's T1, or T2, or whatnot.

And so the key to this measure signals approximately equal to the following

equation is M knot, which is the core net magnetization,

times a term that depends on TR and T1.

And remember, TR is something that we can control.

And, a second term that depends on TE and T2.

And again, TE is something that we can control.

And, in contrast, T1 and T2 are tissue properties.

So, the goal of MRI is to construct an image, or

a matrix of numbers that correspond to spatial locations.

And so, the image depicts the spatial distribution of some property of

the nuclei within the sample.

And so this can be the density of nuclei, so how many protons are in

a area of the brain, or the relaxation time of the tissues in which they reside.

So here we see an illustration of this is, is that by altering values of TR, and

TE, we can kind of focus on different characteristics of the tissue.

So, for example if we choose a long TR and a short TE,

the exponential terms here are going to be approximately equal to one, and

the signal's going to be approximately proportional to M knot, so

were going to get the proton density image that we see here.

If we instead have a long TR and

a long TE, well then we have what's called a T2 weighted image.

So this second exponential terms kind of dominates,

and the first exponential term doesn't play a role.

So then what we´re measuring m knot, weighted by the T2 value.

Similarly if we have a short TE, and

a short TE, we get what´s called a T1 weighted image.

And so, as you look at these images, they're quite different from each other

because they're focusing on different tissue characteristics.

So if we want to kind of have a, depending on what type of information we want to

convey with these images, we might choose one of these different image contrasts.

There's one other contrast that we need for fMRI, that's something called T2 star.

An T2 star is the combined effect of T2 and

local inhomogeneities in the magnetic field.

So what happens is that T2 is the dephasing of the protons from each other.

However, it turns out that if you have certain particles in the nearby,

this can cause this dephasing to go quicker.

And this is something that is measured using this T2*.

And so, the MR scanner can be programmed to eliminate the effects of these

inhomogeneities, or alternatively it can emphasize them.

And the later procedure forms the basis of what we call BOLD fMRI.

And it's going to become important for this class.

So, in short, images can be produced that are sensitive primarily to T1,

T2, and T2*.

And because T1 and T2 vary with tissue type,

they're able to represent boundaries between CSF, Gray, and white matter.

And because T2* is sensitive to flow and

oxygenation, it can be used to image brain function.

And that's going to become important for functional MRI.

Okay, so that's the end of this module.

This was just kind of a basic introduction to MR physics and

how we can use an MR scanner to generate a signal.

And so in the next module,

we'll talk about how we can use this signal to construct an image, okay?

See you then, bye.

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