From Diffusion MRI to Brain Connectomics - Modeling in Computational Biology and Biomedicine - page 220

to measure the constrained or anisotropic diffusion of water molecules in the white
matter, to infer its major axon fiber bundles non-invasively.
Next we presented the fundamentals of the NMR phenomenon, the diffusion
NMR experiment, and reviewed three important diffusion MRI reconstruction
algorithms. The NMR experiment can recover several different physical properties
from samples which contain spin bearing particles by simply applying a set of
magnetic fields and gradients. This forms the core of the non-invasive nature of
MRI. However, NMR can only examine a tiny region of a sample or a single spin
ensemble and cannot image an entire biological specimen. This is made possible
by the spatial encoding technique of MRI, which allows to spatially encode various
juxtaposed regions or spin ensembles where NMR can be applied independently.
This is done in MRI again using magnetic gradients. Therefore, this allows MRI
to examine entire biological specimen, like the brain or the body, in vivo and non-
invasively.
One of the properties that NMR can be sensitized to is the Brownian motion
of the spin bearing particles in a sample. Therefore, NMR can be used to measure
the diffusion properties of a sample by modelling the diffusion of the spin bearing
particles in the sample. Since diffusion has been historically modelled in two
different ways, namely the Fick's phenomenological laws of diffusion and Einstein's
random walk model of Brownian motion, the diffusion NMR signal is also modelled
in two ways, namely the Stejskal-Tanner formulation and the q-space formalism.
DTI was the first dMRI technique that was proposed to infer the tissue
microstructure. It is the most commonly used technique since its mathematical
framework is simple, it has few acquisition requirements and has a number of power-
ful and practical applications. However, it is limited in regions with microstructural
heterogeneity. Many higher order techniques have been therefore proposed recently
in dMRI to overcome this limitation of DTI. Of these we presented DSI and QBI,
and in particular the ODF.
Diffusion MRI data represents images that contain complex mathematical
objects. Recently the computational framework of mathematical tools required
to process such images has been vastly improved. We presented the appropriate
metrics, in particular the Riemannian metric for Sym n , an estimation algorithm

and a segmentation framework using this metric for DTI.
DTI, ODFs and other general SDFs represent the local microstructure of the
cerebral white matter in each voxel. As the final mathematical tools we presented
tractography algorithms which spatially integrate anisotropy information to recon-
struct more global structures such as white matter fiber tracts. Tractography is a
unique tool which permits one to indirectly dissect and visualize the brain's white
matter in vivo and non-invasively.
Finally we concluded the chapter with an overview of major clinical applications
to highlight and emphasize the usefulness and strengths of dMRI.