Biomedical Engineering Reference
In-Depth Information
fiber structures using the average random thermal movement (diffusion) of water
molecules as a probe. Diffusion MRI is a field of research with a history of roughly
three decades. It was introduced in the mid 1980s by Le Bihan et al. [ 39 ], Merboldt
et al. [ 43 ] and Taylor et al. [ 63 ]. As of today, it is the unique non-invasive technique
capable of describing the neural connectivity in vivo by quantifying the anisotropic
diffusion of water molecules in biological tissues. The great success of dMRI comes
from its ability to accurately describe the geometry of the underlying microstructure
and to probe the structure of the biological tissue at scales much smaller than the
imaging resolution.
The diffusion of water molecules is Gaussian in an isotropic medium and under
normal unhindered conditions, but in fibrous structure such as white matter, the
diffusion is very often directionally biased or anisotropic and water molecules tend
to diffuse along fibers. For example, a molecule inside the axon of a neuron has
a low probability to cross a myelin membrane. Therefore the molecule will move
principally along the axis of the neural fiber. Conversely if we know that molecules
diffuse locally principally in one direction, we can infer that this corresponds to a
set of fibers.
6.1.3
Chapter Overview
Public
This chapter is an essential reading for MSc students and scientists who want to
learn about the key mathematical tools and methods underlying diffusion MRI from
modelling the MRI signal and measuring diffusion properties to reconstructing the
underlying architecture of anatomical connections in the human brain.
Outline
Section 6.2 briefly covers the historical development of Nuclear Magnetic Res-
onance (NMR) and MRI to set the stage. We explore the physics of the signal
generation in NMR and how diffusion properties can be measured non-invasively
from NMR in Sect. 6.3 . Section 6.3 begins by presenting the fundamental ideas
of NMR. Section 6.3.1 then presents the crucial spin echo experiment proposed
by Hahn, which is a corner stone experiment that led to the development of
diffusion NMR. Next in Sect. 6.3.2 we describe diffusion in considerable detail.
Section 6.3.3 then presents the pulse-field-spin-echo (PGSE) experiment that was
proposed by Stejskal and Tanner. This important experiment is the modern and
practical approach for measuring diffusion from NMR. The Stejskal-Tanner model
for the diffusion NMR signal is based on Fick's laws of diffusion. Section 6.3.4
presents next the q-space approach for modelling the diffusion NMR signal, which
is based on Einstein's random walk approach to Brownian motion.
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