Diffusion Flashcards
What is diffusion?
Diffusion is the random Brownian motion of molecules due to thermal processes.
Molecules aren’t sitting static, if they have thermal energy, so above 0 kelvin they will be moving around, we have found they randomly move around and this is the process we mean by diffusion
Depending on the type of liquid they move around at different rates
What is diffusion imaging?
Diffusion imaging is an MRI technique that measures this mobility of molecules
Diffusion-weighted imaging (DWI) is based on measuring the random Brownian motion of water molecules within a voxel of tissue.
Generally, highly cellular tissues or those with cellular swelling exhibit lower diffusion coefficients
What is the fundamental idea of how DWI works?
DWI is the attenuation(reduction) of T2* signal based on how easily water molecules are able to diffuse in that region
The more easily water can diffuse (i.e. the further a water molecule can move around during the sequence) the less initial T2* signal will remain
How is a diffusion-weighted imaged generated with MRI?
A spin echo MRI sequence is sensitised to diffusion by adding two large diffusion weighting gradients around the 180 degree pulse.
The signal attenuation depends on the diffusion coefficient (D) and the diffusion weighting b-value, which is a function of the gradient magnitude and timing
In white matter how much is signal attenuated?
signal is attenuated by around 60%
less signal attenuation, brighter
In CSF how much is signal attenuated?
signal is attenuated by around 95%
High diffusion, very mobile molecules, lots of signal attenuation, very dark
What is the difference between watery tissues and static/solid tissues in signal?
Watery tissue = mobile molecules = low signal intensity
Solid tissues = less mobile molecules = higher signal intensity
How is diffusion measured?
Diffusion is measured along the gradient direction, which can be applied in any direction [x, y, z] by varying the amplitude of the x, y and z gradients.
How does signal attenuation vary in humans?
In many human tissues, the amount of signal attenuation due to diffusion varies depending on the direction of the applied diffusion gradient [x, y, z]
What are quantitative diffusion images?
As we also acquire a baseline image (S0) with no diffusion gradients, we can calculate the diffusion coefficient (D) in each direction.
These are quantitative diffusion images, where each voxel represents a diffusion value in in mm^2S^-1 and the different images represent diffusion measurements in different directions.
We can average the maps across all of the directions to produce a map of the mean diffusivity <D>.</D>
What happens in human tissue that restricts diffusion?
Water is not free to move in human tissue, we have a complex microstructural environment and so diffusion is restrictred this e.g. by cell membranes
What is a diffusion tensor?
In human tissue, diffusion is restricted by the complex microstructural environment
To characterise this environment, the diffusion process must be measured in many directions and is often described mathematically by a diffusion tensor
The diffusion tensor defines an ellipsoid in each voxel that characterises the diffusion properties.
What is diffusion tensor imaging?
An advanced MRI technique that provides detailed information about tissue microstructure such as fiber orientation, axonal density, and degree of myelination
Its based on the measurement of the diffusion of water molecules.
What are scalar diffusion images?
We can calculate different scalar images to provide a visual summary of the diffusion properties
How do we generate scalar diffusion images?
The diffusion coefficient <D> is calculated from the T2 and DWI images and is directionally averaged</D>
If diffusion is calculated in multiple directions, a measure of the directional diffusion variability or “anisotropy” can be calculated.
What are the two main types of scalar images?
- Mean diffusivity
- Fractional anisotropy
What is mean diffusivity?
Average of all our individual measurements which is the average of the three orthogonal principle diffusion directions
What is fractional anisotropy?
Tells us what the deviation is from the average, how stretched the ellipsoid is
What are directional colour encoded images?
Coloured diffusion maps
These are usually fractional anisotropy maps with the overlaid colour indicating the principle diffusion direction
What is one of the main clinical applications of diffusion?
Stroke - diffusion was found to be an early marker of stroke
Why is DWI better than T2 imaging for stroke?
Diffusion is found to be reduced quickly within hours of stroke onset, due to cytotoxic oedema
Diffusion occurs before before it becomes visible on a T2-w image BUT with DWI it can be picked up in the image as a bright area from day 1
Why might we have to be careful when interpreting DWI images of stroke?
After the initial dip in diffusion, diffusion recovers towards more normal values, eventually becoming elevated above normal due to vasogenic oedema
This means that although there is an initial fall in diffusion, we get a pseudonormalisation afterwards which is where the diffusion values are returned to normal but the brain tissue is still abnormal so we must be careful interpreting DWI images
What is motion correction?
Motion correction involves using computational image registration to align all images in the diffusion dataset
Why do we use motion correction?
As with fMRI, motion correction can significantly improve diffusion image quality
What causes distortions in echo planar images?
EPIs are heavily distorted, particualry at tissue boundaries
This distortion depends on the polarity of the phase encode gradient “blips”
How do we correct for distortions?
Susceptibility induced distortion correction
The difference between the positive phase encode blip and the negative phase encode blip is exploited by the FSL tool “topup” which corrects for the distortions
What is tractography?
A brain imaging technique that describes the mapping of the location and direction of white matter bundles and their constituent fibers within the human brain
We use the DWIs to look at connectivity between different parts of the brain
How can we carry out tractography?
If we’ve measured diffusion tensors in every single image and in every single voxel within the image, we can measure the principle eigenvectors
The principal eigenvector can be plotted at each voxel to give an indication of the major white matter fibre orientation.
Finding pathways through this vector field is the basis of tractography.
What is streamline tractography?
Most simple method
Starting from a seed point, voxels are connected together using a tractography algorithm
The tract propagates until termination criteria are met
What are the two termination critera for streamline tractography?
Angle between principal eigenvectors exceeds a certain threshold
Fractional anisotropy drops below a certain value
What is a problem with streamline tractography?
A stream-line algorithm can be used to identify pathways within the vector field originating from a specified seed point
However, these algorithms only identify a single pathway and do not deal with branching fibres
They also give little indication of how likely the pathway is to be a true anatomical pathway
How can we counter the issues with streamline tractography?
We can use our diffusion ellipsoid to decide how likely it is to go in a particular direction
What are diffusion ellipsoids and profiles?
The diffusion ellipsoid represents the r.m.s. diffusion distance at a given snapshot in time.
The diffusion profile is calculated from the diffusion tensor using d(r) = rT D r and represents the diffusion measurement along the direction r.
What can the diffusion profile be thought of as ?
An Orientation Distribution Function, where the function defines the relative likelihood of travelling in any given direction
What is orientation distribution function sampling?
We draw samples from ODF
At each iteration, a sample is drawn from the ODF in each voxel
Each iteration produces a different vector field on which tractography can be run
What is probabilistic tractography?
Streamline tractography is performed many times (>1000) with the ODF used to define the principal diffusion direction in each voxel for each run
The number of times a streamline passes through a voxel is counted and used to give a connection probability
What are the limitations of the tensor model?
The single tensor / ellipsoid model is not good for describing voxels that contain multiple fibre populations, i.e. crossing fibres, etc
It models restricted diffusion in the plane of the crossing fibre with no preference being given to the two fibre orientations
It’s relatively simple to include more complex models into the tracking procedure, but they require more time consuming acquisitions (i.e. more directions / b-values)
What is Region of Interest analysis?
Extract major white matter fasciculi using probabilistic tractography
Region of interest masks can be generated and summary diffusion parameters calculated for the tract (e.g. Mean Diffusivity, Fractional Anisotropy, Tract Volume)
Correlate diffusion parameters with clinical or cognitive investigations.
What is an interesting application of tractography?
Cortical connectivity - to find connections between cortical regions, for example those activated by fMRI, or that exhibit abnormal cortical thickness
Unfortunately, this is an area where streamline-based algorithms perform poorly
What is a method to assess cortical connectivty that overcomes the limitations of streamline-based algorithms?
Global tractography?
What is global tractography?
Propagates a front from a seed point with the rate of front propagation F(r) determined by directional coherence of the ODF with front normal
An arrival time T(r) is assigned to each voxel r and is defined as the time at which the front crosses the voxel
Geodesic pathways can be calculated through the arrival time field by using a gradient descent algorithm
A connectivity metric “scores” the likelihood that a pathway is real.
What is an important advantage of global tractography?
It gives you a way of connecting every seed point, you get a connection likelihood to every other point in the brain, unlike streamine algorithms where you start off at the seed point but it might break very quickly and you dont get a connection likelihood to every other point in the brain
What is another advatage of global tractography in terms of penetration that can also be considered a limitation?
Global tractography is able to penetrate much deeper into the cortex than local (streamline) methods e.g. deep white matter seeding
This captures as much of the tract as possible but, penetrating deeply can also increase measurement error
What is voxel based morphometry using fractional anisotropy?
Became popular to use VBM to identify voxel-wise differences between groups based on their fractional anisotropy signal maps
Align FA images to a template
Get the FA images in a standard space
Then blur them to make them more compliant
The we do GLM to calculate a t-statistic that we can then threshold to see whats different between groups or see what regions correlate
What were the limitations of VBM analysis?
Results from VBM analysis were found to be highly dependent on the registration
No existing non-linear registration algorithm was capable of accurately aligning the complex white matter tract structures between subjects
Thus, many false positives were identified on VBM analysis due to misregistration
Results were also found to be highly dependent on the degree of spatial smoothing applied to the images- No consensus on what the amount of smoothing should be
What method was developed to overcome the limitations of VBM?
Tract based spatial statistics
What are tract based spatial statistics?
Bring in FA images
Register them to the standard template
But then take an average map, skeletonise it and then we threshold that skeleton map
This is essentially producing a map of the fibres that are most consistent between subjects and we then project our fractional anisotropy values back onto that skeelton and then we just do our statistics on the skeleton
It essentially overcomes the registration issue
Its essentially the VBM equivalent for diffusion
