Everything moves...

As a major modern medical imaging technique, MRI is constantly under development. "These developments lead to a higher quality control and improved processing of the acquired data", says Evelyne Balteau. The work of Elodie André is part of this process. She focused on the quality of data obtained during the study of diffusion phenomena and diffusion imaging, which indicate the way in which water molecules diffuse in the brain producing a contrast in the image. As mentioned above, the results obtained from an MRI brain scan make it possible to observe the white and grey matter of the brain as a whole in a non-invasive manner. There is no need for surgery or risky biopsies, and no need to wait for post-mortem dissection results in order to have a perfect three-dimensional image of the brain! “In diffusion”, explains Elodie André, “we are more interested in the white matter”.  Another essential point: these structural studies of the brain indicate whether the white matter is healthy or not. This element, which completes the information collected by means of cognitive methods, is important for the diagnosis of many pathologies.

 "In order to clearly understand what diffusion involves on a macroscopic level, you might imagine a drop of ink added to a glass of water. The drop of ink diffuses into the water. The concentration of ink molecules which is dense in the ink drop, becomes homogenous throughout the entire glass of water and balances out without any extra stirring, explains Elodie André

What is examined here is therefore the diffusion of the water molecules themselves in the human brain. These molecules are not static. The direction, or directions they take are important. "In fact the molecules diffuse more along the fibres, because there are fewer barriers than perpendicularly (among others, the membranes and myelin). By observing this movement, it becomes possible to extrapolate the direction of nerve fibres. Thanks to repeated measurements in different directions and carried out over the entire brain, it is possible to characterize the diffusion in 3D. For each voxel (each volume element of the image), the diffusion tensor can be represented by an ellipsoid which can vary in size and is more or less stretched along the main direction of diffusion of the water molecules in this voxel",  the physicist continues. 

If the diffusion is equally probable in all directions, it is said to be isotropic and the tensor will be represented by a sphere that can vary in size, depending on the ease of diffusion (presence or absence of obstacles). In the brain, many obstacles can constrain the diffusion which will therefore be reduced (as compared to diffusion in a glass of water) and possibly not to the same extent in all spatial directions. "Thus, in the white matter of the brain, we can find ellipsoids along the direction of the fibres: in this case the diffusion is said to be anisotropic. One of our diffusion parameter of interest, which is called fractional anisotropy,  has a quantitative value. It varies from 0 (isotropic diffusion) to 1 (very anisotropic). By using this parameter to compare two groups of individuals, we can detect the area where the white matter is affected by disease. The result of these calculations and comparisons is often difficult to interpret when we are looking at a damaged brain area", explains Elodie André.

Removing complexity

The most standard model used to describe diffusion in the brain is the diffusion tensor imaging (DTI) model. Elodie André has been working on an extension of this model, the DKI or Diffusion Kurtosis Imaging model. "The diffusion can be described by various models of increasing complexity. The diffusion tensor is a very simple model yet diffusion in living tissues is complex. This complexity is related to the presence of blood vessels, fibres, cell membranes and variations in the permeability of the latter… And one of the parameters accounting for this complexity is the kurtosis. In the more basic DTI model, we assume that the molecule diffuses following a Gaussian distribution (bell-shaped curve). This is indeed the case for diffusion in a glass of water but is no longer the case in the presence of obstacles. The difference with the Gaussian curve is the kurtosis”, explains Evelyne Balteau.

As described by Elodie André, "the kurtosis technique makes it possible to quantify this non-Gaussianity, and therefore to indicate whether the diffusion at a given point follows a Gaussian distribution ( considered as a reference) or not. If the measured kurtosis is zero, it is because we are dealing with a Gaussian case of homogenous liquid. Kurtosis can be positive (with a curve that is narrower than the Gaussian curve) or negative (with a curve that is wider than a Gaussian curve)."