Special issue: Original article
Studying connections in the living human brain
with diffusion MRI
Derek K. Jones*
CUBRIC, Cardiff University Brain Research Imaging Centre, School of Psychology, Cardiff University, Cardiff, Wales, UK
a r t i c l e i n f o
Received 7 June 2007
Reviewed 6 September 2007
Revised 24 October 2007
Accepted 9 December 2007
Published online 23 May 2008
a b s t r a c t
The purpose of this article is to explain how the random walks of water molecules under-
going diffusion in living tissue may be exploited to garner information on the white matter
of the human brain and its connections. We discuss the concepts underlying diffusion-
weighted (DW) imaging, and diffusion tensor imaging before exploring fibre tracking, or
tractography, which aims to reconstruct the three-dimensional trajectories of white matter
fibres non-invasively. The two main classes of algorithm – deterministic and probabilistic
tracking – are compared and example results are presented. We then discuss methods to
resolve the ‘crossing fibre’ issue which presents a problem when using the tensor model
to characterize diffusion behaviour in complex tissue. Finally, we detail some of the issues
that remain to be resolved before we can reliably characterize connections of the living
human brain in vivo.
ª 2008 Published by Elsevier Masson Srl.
In 1827, Robert Brown – a botanist from Montrose in Scotland,
returned from a triptoAustraliawith variousflorasamples. In-
trigued by the mechanisms of fertilization in plants, he took
a sample of pollen grains from Clarkia pulchella and suspended
them in water beneath his microscope (Fig. 1). On close inspec-
tion, Brown found the grains to be in constant motion – as if
having a life of their own. Indeed, with investigations into the
‘essence of life’ being very much in vogue at the time, Brown
wondered whether he was observing life force itself. However,
as a true scientist, Brown looked for the phenomenon in inor-
ganic material including rock and coal samples, and even
‘rock from the Sphinx’. He observed the same phenomenon, i.e.,
the particles were constantly in motion (Brown, 1828).
We now know that what Brown observed was not the pol-
len grains moving of their own accord, but rather the water
molecules that they were suspended in (invisible under the
light microscope) undergoing constant thermal agitation
known as ‘Brownian motion’, or ‘diffusion’. Diffusion is an
essential physical process for the normal functioning of living
systems.Forexample,the transport of metabolites intocells is
facilitatedby diffusion.Thisphenomenon, omnipresent in the
water in living tissue, has the potential, through diffusion-
weighted (DW) magnetic resonance imaging, to provide in-
sights into cell physiology, cell structure and potentially the
connections of the living human brain.
The random walk as a probe of tissue
Imagine a cube-shaped volume of 2.5?2.5? 2.5 mm in di-
mension. There are approximately 1020water molecules
* CUBRIC, School of Psychology, Cardiff University, Park Place, Cardiff CF10 3AT, UK.
E-mail address: email@example.com
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cortex 44 (2008) 936–952
contained within this volume, each undergoing a random
walk as part of the diffusion process. Here, by random walk,
we mean that each molecule stays in a particular place for
a fixed time, T, before moving to a random, new location in
space. This process continues for each molecule so that a ran-
dom path is drawn out in three-dimensional space. It would
perhaps seem impossible to characterize the behaviour of
this set of molecules undergoing such random behaviour. It
is certainly impossible to predict the pathway that any one
of these molecules will take. Fig. 1b shows a simulation of
a randomwalk for five single particles in an isotropicmedium,
such as our cube of water. It is clear that we cannot accurately
predict any single molecule’s position at a given time. How-
ever,in 1905Einsteinprovedthat, providedthenumberof par-
ticles is sufficiently large, at least one aspect of the behaviour
could be characterized, namely the squared displacement of
molecules from their starting point over a time, t, averaged
over all the molecules in the sample, Cr2D is directly proportional
to the observation time (Einstein, 1905). The constant of pro-
portionality is the self-diffusion coefficient. In equation form
(the ‘‘Einstein’s equation’’):
Cr2D ¼ 6Dt
The distribution of squared displacements takes a Gaussian
form, with the peak being at zero displacement and the
probability of displacing a given distance from the origin is
For the cube of water at body temperature (37?C), the diffu-
sion coefficient of water is 3? 10?3mm2s?1. Thus, if we
observe water molecules for, say, 30 ms, they will have
displaced, on average, 25 mm in all directions.
As stated in Section 1, DW magnetic resonance imaging
(MRI) utilizes this motion to probe tissue microstructure.
The astute reader, new to the topic, may then pose the ques-
tion ‘‘If we are looking at the diffusion of water, and we know
what the diffusion coefficient of water at body temperature is a
Fig. 1 – (a) Robert Brown, 1773–1858. (b) Brown’s original microscope with which he reportedly observed the pollen of Clarkia
pulchella in constant motion. (c) Simulation of trajectories of five molecules undergoing a random walk in an isotropic
medium, after 10, 20, 40 and 80 steps. (d) A histogram of displacement from the origin of 1 million molecules, after 100, 400,
900 and 1600 steps. The full-width at half-maximum (FWHM) scales in the ratio of 1:2:3:4, which mirrors the ratio of
O100O400:O900:O1600, demonstrating the consistency of Einstein’s equation for Gaussian diffusion.
cortex 44 (2008) 936–952
constant – then how can we possibly use that to garner information
abouttissue microstructure?’’ The answerlies in Einstein’sequa-
tion (Eq. (1)), which says that the mean-squared displacement
is directly proportional to the observation time. It is important
to note that in DW MRI, we do not measure the diffusion coef-
within each three-dimensional volume element, or voxel, that
forms the image (typically, these are cube-shaped and about
2.5?2.5? 2.5 mm in dimension). The presence of cell mem-
branes, inclusions, macromolecules and so forth present in
tissue serve to hinder the pathway of the molecules undergo-
ing their random walks. As a result, their overall displacement
from their starting point in a fixed period of time is reduced
and compared to their mean displacement when they were
in ‘free’ water. Thus, it appears to us that the diffusion coeffi-
cient is lower than it is – which is partly why the term ‘appar-
ent diffusion coefficient’ (or ADC ) was coined to reflect
the fact that we realize that we are subject to the effects
of hindrances, etc. The average ADC in tissue is around
0.7?10?3mm2s?1, about 4 times smaller than in free water.
is dependent on its overall displacement (Stejskal and Tanner,
1965). Under the random walk process that is diffusion, we get
a distribution of displacements and thus a distribution of
and therefore a reduction in signal amplitude, which in an im-
age, means that the image appears darker. The greater the
spread of displacements (the higher the ADC), the greater the
spread of phases – and thus the greater the loss of signal –
and the image appears dark. Conversely, the lower the rate of
diffusion, the lower the spread of phases – and thus the lower
the loss of signal and the image appears bright.
It is clear that tissue microstructure fundamentally affects
the apparent diffusion properties of water and diffusion
should therefore act as a sensitive probe to any changes in
cellular structures that alter the displacement per unit time.
Thus, the introduction of diffusion imaging (Le Bihan and
Breton, 1985) was met with enthusiasm as a non-invasive
method of gaining new contrast within the brain. The most
useful clinical application to date is the use of the DW scan
in acute ischaemia in which there is a reduction in the
voxel-averaged displacement of water molecules per unit
time, hence a reduction in the ADC, therefore less signal
attenuation – and the lesion appears hyper-intense (Moseley
et al., 1990a).
About the same time as Moseley’s initial observations of
the reduced ADC in ischaemia, it was noted that the ADC in
certain regions of the mammalian brain appeared to depend
on the direction of the applied diffusion-encoding gradient
(Moseley et al., 1990b). In other words, the ADC was direction-
ally dependent. This effect had been known for some time in
ex vivo samples of muscle and brain tissue dating back to the
pioneering work of Hansen (1971) and Cleveland et al. (1976).
Shortly after Moseley’s observation in the cat brain, the
directional dependence of the ADC was reported in human
white matter by Doran et al. (1990) and Chenevert et al.
(1990). This is illustrated in Fig. 2, which shows the same
(human) brain imaged 3 times, each time with the diffusion-
encoding gradient applied along one of three orthogonal axes.
In certain regionsof the brain, the DW intensityis the same
in all three images suggesting that the ADC is the same in all
directions. Diffusion in these cases is described as isotropic.
However, in the regions highlighted by arrows this is not the
case and diffusion in these regions is referred to as aniso-
tropic. From just these three DW images, we can infer a sub-
stantial amount of information about the structure indicated
by the arrows. First, the large differences in DW intensities
that are observed as the direction of the diffusion-encoding
gradient is changed, suggest that the tissue here is highly
ordered on the voxel scale. Second, as there is high signal
attenuation in 2a (in which the diffusion-encoding gradients
were applied in a left–right orientation), we can infer that
diffusion is relatively unhindered along this direction. Con-
versely, in the two perpendicular orientations (Fig. 2b and c),
the signal attenuation is much less, indicating that the
mean-squared displacement per unit time is reduced and
that something is therefore hindering the displacement of
water molecules along these orthogonal axes. Therefore,
from just these three images, we are able to infer an ordered
structure which has predominantly a left–right orientation.
These inferences are entirely consistent with the fibres of
the corpus callosum, a white matter (WM) structure which
passes through this region (Dejerine, 1895; Crosby et al., 1962).
What is the source of diffusion
Initial suggestions for the mechanisms underlying diffusion
anisotropy in WM included the myelin sheath (Thomsen
Fig. 2 – Effect of changing the direction of the diffusion-
sensitizing gradients on the DW intensity (top row) and
computed ADC (bottom row). The figure shows the same
brain slice, with gradients applied in the left–right
direction (a and d), anterior–posterior direction (b and e),
and superior–inferior direction (c and f). The amount of
diffusion weighting (b[1000 s/mm2) was the same in all
cortex 44 (2008) 936–952
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