Signal Processing - May 2016 - 37

Introduction

water molecules move faster along, rather than across, structural constraints. By measuring their anisotropic diffusion,
we can infer the underlying structure of neuronal fibers.
Figure 1 shows a typical information flow of studying brain
connectivity using dMR imaging: neural fibers introduce
anisotropic diffusion (a) and influence magnetic resonance
(MR) signals generated from spinning protons (b); dMR signals are collected along many diffusion directions (c) and
then reconstructed at each voxel location as fiber orientation
distributions (FODs) (d); local fiber structures are assembled
and "weaved" together as long fiber tracks (e) to build a network (g) connecting brain cortex regions (f). These networks
are further investigated for their relationship with the brain's
function and development. We elaborate this procedure step
by step in the following sections.
We first look at how dMR signals are generated. Understanding the generation procedure is important for the processing and interpretation of dMR images. It also sheds light on
the potential limitations and caveats of using dMR images. We
start with the excitation of protons in a magnetic field and then
explain how diffusion affects signal resonation, with formulations in the so-called k-space and q-space. The relationship
between diffusion and magnetic resonation is the key to dMR
imaging and its data analysis.

This article covers key components in the workflow to map
structural connectivity of the human brain, including data
acquisition, neural fiber orientation modeling, image processing, tractography, and applications to brain studies. For
each topic, basic theories are reviewed, and major breakthroughs and state-of-the-art technologies are discussed. In
addition to an overview of existing technologies, we also
attempt to provide an outlook of future challenges in building
a comprehensive connectivity map that integrates genetic and
functional information.

dmr imaging
At a microscopic scale, water molecules in an isotropic medium move freely in all directions in a jittery and erratic fashion. This random walk was first noticed in 1827 by Scottish
botanist Robert Brown, explained physically by Albert Einstein in 1905, and later rigorously modeled as a mathematical stochastic process by Norbert Wiener. Movement of these
tiny molecules inspired mathematicians to develop elegant
theories now widely used not only by financial analysts but
also by medical engineers to "look" through the human brain
in vivo at its sophisticated neural network. In an anisotropic
medium, such as brain tissues containing neuronal fibers,

Across

Along
(a)

B
M
(b)

(e)

(d)

(g)

(f)
(c)

FIGURe 1. The information flow of structural connectivity analysis. (a) Water molecules move faster along, rather than across, neuronal fibers. (b) Diffusion affects the electromagnetic waves radiated by precessing protons. (c) dMR imaging captures diffusion signals along different directions and forms
images. (d) FODs are reconstructed from diffusion images. (e) Fiber tracks are simulated from FOD images. (f) The brain cortex is segmented into many
regions using structural MR images, for example, with FreeSurfer software [2]. (g) Connectivity networks between cortex regions are constructed from
fiber tracks.
IEEE Signal Processing Magazine

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May 2016

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37
Table of Contents for the Digital Edition of Signal Processing - May 2016
