From Diffusion MRI to Brain Connectomics - Modeling in Computational Biology and Biomedicine - page 194

signal [ 31 ]. Diffusion NMR is derived from Hahn's original spin echo experiment
of 1950. Hahn put forth the idea that following a 90 ◦ RF pulse that tilts the net
magnetization vector to the transverse plane, the dephasing that follows caused by
the field inhomogeneities, could be refocused using a second RF pulse of 180 ◦ , thus
removing the effects of the field inhomogeneities.
After the 90 ◦ RF pulse, the spins precessing in the transverse plane should appear
static in a frame of reference rotating at the Larmor frequency. However, due to
field inhomogeneities, as the spins begin to dephase, some would appear to speed
up (or move ahead clockwise in the rotating frame of reference), while some would
slow down (or fall back anti-clockwise in the rotating frame of reference). This
transverse dephasing is known as the free induction decay (FID) and causes the
signal to decay faster than pure T2 effects. However the application of a second RF
pulse of 180 ◦ has the effect of flipping the individual spins in the transverse plane
such that the “slow” spins that had fallen behind the rotating frame of reference are
flipped ahead of it, while the “fast” spins that had moved ahead are flipped behind
the rotating frame of reference. Indeed, the 180 ◦ RF pulse causes the spins to refocus
after a certain length of time as the fast spins catch up with the slow spins, which
regenerates the signal. This is known as the echo and it is free of the T2 ∗ effects due
to field inhomogeneities (Fig. 6.3 ).
It must be noted, however, that the echo regenerates the signal completely only
under the assumption that none of the spins in the ensemble have moved. If they
move then the 180 ◦ RF pulse doesn't completely invert the spin and this results
again in signal decay. However, this is not due to field inhomogeneities. As noted
by Hahn [ 31 ] and Carr and Purcell [ 14 ], this is due to the translational motion of
diffusion. This forms the basis of diffusion NMR.

6.3.2 Diffusion

Diffusion NMR (dNMR) is a modality of NMR that is sensitive to the Brownian
motion of the particles in a sample. The dNMR experiment can therefore be used
to measure the diffusion properties of the underlying sample. This makes dNMR
central to diffusion MRI. At the heart of dNMR is the diffusion process, and
understanding diffusion helps to understand how it can be measured from NMR.
It leads to the critical improvements that were made by Stejskal and Tanner to the
original spin echo experiments of Hahn and Carr and Purcell that opened up the
domain of dNMR.
Diffusion is a process of mass transport that describes the random spreading of
molecules or particles generally in the presence of a concentration gradient. The
process of diffusion was observed, studied and mathematically described over the
entire nineteenth century. It was initially observed in three different forms, namely
heat diffusion in the presence of a temperature gradient, molecular diffusion in
the presence of a concentration gradient, and Brownian motion, which occurs even
in the absence of any gradients. These, apparently very different phenomena—the