In this module, we're going to discuss diffusion tensor imaging.
We have seen that in order to record an MRI signal from a volume,
we must first excite that volume using a radio frequency pulse.
The radio frequency pulse is referred to as the "Larmor frequency," which in turn
depends on the gyromagnetic ratio of the particle that we're interested in imaging.
On the right hand side, I'm showing the table representing
the gyromagnetic ratio of
the various particles that can be observed in biological matter.
Hydrogen is the most commonly used particle
for structural and functional magnetic resonance imaging,
and that's because it has an unpaired proton which gives it magnetic properties,
and therefore, ideally suited to disturb the local static magnetic field.
The second part is that it's ubiquitously available in the brain.
It's everywhere in the form of water and fat tissue,
which makes it possible for us to image the entire volume that we're interested in.
If hydrogen was not available in part of the brain,
we would not be able to create an image of that area of the brain,
giving us a problem in representing
the whole volume or the whole image that we would like to create.
So, the fact that it's ubiquitously available throughout the entire brain makes
it a perfectly suited particle for magnetic resonance imaging.
Diffusion tensor imaging focuses on water diffusion throughout the brain.
I'm showing an example in the far left of a dye being injected into water.
And as you can see, initially,
it diffuses freely throughout the water.
If it diffuses equally in each and every direction,
that is referred to as "isotropic diffusion," as can be seen in the middle schematic.
But at a certain point the dye hits the glass container in which the water is contained,
and it can't diffuse any more in that direction,
any further in that direction.
So, when there is constraint diffusion that has a directionality to it,
as can be seen in the far right schematic,
that's referred to as "anisotropic diffusion."
So, if there's a directionality to it,
it's referred to as "anisotropic."
If there is no directionality to it,
it's equal in all dimensions refer to it as "isotropic.".
In the brain, we can imagine a situation in which grey matter,
which consists of cell bodies,
if we take a measurement of global diffusion throughout gray matter,
that the water diffuses equally in almost all directions,
which is isotropic diffusion.
But if we focus on areas with a large number of axons,
you can imagine a situation in which water diffusion
is constrained along the length of the axon.
So by taking measurements from the brain of isotropic and anisotropic diffusion,
we can make an estimate of the location of gray matter and axons, or white matter.
Diffusion tensor imaging then employs
gradient pulses which cancel each other out in the case of static water molecules,
but it causes a lack of signal for diffusing water molecules,
appearing as darker voxels on the brain images that you can see on the right hand side.
By creating images from multiple different directions,
a three dimensional volume can be created
representing the diffusion model of water throughout the brain.
The displacement of molecules, of water molecules,
is defined by three eigenvectors,
which in turn have three eigenvalues.
They essentially represent the diffusion in three dimensions, in three directions.
The largest eigenvector represents the direction of diffusion.
So in the right hand side,
you can see in the isotropic case,
the eigenvectors are equally long.
The water is diffusing in all three directions equally.
In the anisotropic case,
one of the eigenvectors is clearly much longer,
much greater than the other representing
the diffusion of the water molecule in that particular direction.
Diffusion tensor imaging then,
takes a measurement from every single voxel in a volume,
according to a specified voxel grid,
that we've now seen on several occasions.
But instead of creating a white or a gray matter of value,
we now create a value for the directionality of waterflow within that voxel.
We measure the largest eigenvalue for that particular voxel,
which in turn represents the direction of water flow through that voxel.
By taking a series of measurements,
and measuring the eigenvalues for each of those voxels,
we can then create a three-dimensional volume of eigenvalues,
and thereby a three-dimensional volume of
the directionality of waterflow throughout the brain.
On the top right hand side,
the direction is color coded by red, green, and blue,
so that you can easily see the direction of waterflow through these voxels.
The bottom is an example of where those voxel-
The vectors are still superimposed on each voxel,
so you can easily see the direction of water flow in a zoomed in area of that volume.
If you then take a measurement of each voxel relative to the voxel right next to it,
you can determine the overall direction of fiber bundles or axons,
running from one area of the brain to another area of the brain.
So, here you see a zoomed in section of these voxels for which we now have measurements.
And by determining the eigenvalue
for each voxel relative to the one before it then after it,
we can figure out an overall vector of
direction of the water flow through that larger volume.
This then is used to create fiber bundles or connected voxels,
where the diffusion goes into the same direction for the entire volume of acquisition.
So, here you see a typical diffusion tensor image,
where connected fibers are determined
probabilistically and color-coded based on whether they move from left or right,
whether or not they move.
So in the case of red on the right bottom side,
whether they go anterior to posterior,
front of the brain to back of the brain,
as can be seen in the green fibers,
or superior to inferior,
top of the brain to bottom of the brain,
as indicated by these blue fibers.
And here you can very clearly see in red, the corpus callosum,
which is obviously a very strong significant fiber bundle
that connects the left hemisphere to the right hemisphere,
representing that communication between the brain halves.
Diffusion tensor imaging can then be used for a number of different types of studies.
Studies use fractional anisotropy,
which is a fractional measure of diffusivity.
It basically takes the three dimensions of anisotropy down to one single measure,
a fractional measure, representing the directionality of water flow within that voxel.
A value of zero represents isotropic diffusion,
water moving in every which direction equally,
whereas one represents perfect diffusion in only one direction.
It's typically used as a measure of fiber density,
with a greater number being greater anisotropy,
meaning stronger directionality and thus fiber density.
It's also used as a measure of brain connectivity because of that,
and also as a measure of white matter integrity.
The greater your anisotropy, the greater,
the denser the white matter is there,
and the better the white matter integrity,
at least, that's the assumption.
So, you can then use that FA value to look at group differences in fractional anisotropy.
On the far left hand side,
I've shown an example of an FA map derived from
DTI data on which a segmentation atlas is overlaid,
so that you can identify areas of the brain that you may be interested in analyzing,
and then you can create a mean FA value for that region of interest.
On the right hand side, I'm showing you an example
of a study where they took exactly that approach.
They took the corpus callosum and subdivided into seven segments,
as you can see in the middle figure,
and then took a measurement of FA for
those seven segments comparing healthy controls with patients with multiple sclerosis.
And multiple sclerosis, obviously,
is a white matter disease that reduces the integrity of white matter,
so the hypothesis was that in these seven segments of
the corpus callosum they could see
differences between the control and the patient groups,
and the bar graph on the top right shows exactly that.
There are certain segments of the corpus callosum where patients with
multiple sclerosis have reduced FA values compared to the control subjects.
We can also use
FA measures to make correlations or to look for correlations with particular symptoms.
Here I'm showing a study in patients with obsessive compulsive disorders.
On the top left, you see the brain areas in which they've seen
significantly different fractional anisotropy in
certain brain regions in the OCD patients relative to the control subjects,
indicated by the blue arrows,
including the midbrain, the lingual gyrus, and the precuneous.
And the top right shows correlation coefficients between
the FA values within those brain areas and the YBOCS score,
which is essentially a symptom severity checklist.
So, in this particular case,
the midbrain FA values and the precuneous FA values show
a negative correlation with the number of
symptoms that these patients with OCD are experiencing.
On the left hand side here,
I'm showing an example of an FA correlation with past performance,
in this particular case,
in a study of boxing.
Subjects who have been continuously boxing
were given a memory task in which they were asked to learn a number of words.
And after a 20 minute delay they were asked to
remember as many of those words as they possibly could.
And this was compared with the fractional anisotropy of the left ventral striatum.
And we can clearly see in the boxing group
that there's a strong negative correlation between the ability to retain
that information or the ability to remember that information and
their FA values in the ventral striatum.
In the right hand side,
I'm showing you an example of correlation with life events in that same box or study,
where the number of bouts is positively correlated with DTI-derived measures.
And the bottom shows that the number of years of boxing that
a person has completed is negatively correlated with
the FA value with the white matter integrity
of a brain area that they were interested in.
Diffusion tensor imaging can also be
used and is extensively used for surgical planning purposes.
On the left, I'm showing you an example of
tractography analysis conducted on
diffusion tensor imaging in the cases for surgical planning for deep brain stimulation,
often in the case of Parkinson's disease.
In C in the bottom left,
you can see the location of the electrodes that are implanted for stimulation,
which are indicated in red.
And here, tractography is used to determine if the electrodes
are essentially implanted in the correct fiber tracks that they're trying to stimulate.
So, in D you can see the same thing.
The yellow lines represent
the electrode placement with the blue dots being the sites of stimulation.
And here tractography is used to
confirm that the electorate placement is correct and that they
ended up in the correct fiber pathway
appropriate for stimulation of this particular patient population.
On the right hand side, I'm showing an example of using
diffusion tensor imaging for surgical resection.
In this particular case, as you can see,
outlined in red is a tumor that is observed on the MRI scan.
The green areas are highlighted fiber tracks coming from the thalamus,
very critically important for brain function.
And the imaging here is used to make sure that the resection of the tumor is not going to
interfere or damage the fiber bundle that runs by very closely to it.
So, they've taken some measurements to determine the distance
between the area that needs to be resected
in the area that's clearly critically
important for these fiber bundles that are running through it.
So, here are two very practical applications of
diffusion tensor imaging being used for surgical planning purposes.
So, overall, diffusion tensor imaging is
a visualization method for the directionality of water flow throughout the brain,
representing fiber pathways and connectivity pathways throughout
the brain that are very different from
the functional connectivity that we've talked about in one of the previous modules.
This is purely based on structural connectivity between areas of the brain.
So, it provides a measure of structural connectivity.
It provides a measure of structural organization of the brain.
And it can be used for group comparisons between
various different groups based on disease or some kind of other factor.
It can be used to correlate with symptoms or life events,
as we've seen in the case of the boxer study.
And it can also be correlated with cognitive performance,
like memory or really any other type of cognitive performance.
In the next module,
we're going to talk about another example of
a specific application of imaging in this particular case, spectroscopy imaging.