Chemistry Reference
In-Depth Information
The theoretical results for the phase decay are then compared with the results
of diffusion weighted experiments acquired from human subjects on a 3T MRI
scanner, and animals on a 7T small bore MRI scanner.
II.
PHASE DIFFUSION AND BROWNIAN MOTION
During signal acquisition in MRI, nuclear magnetic moments are manipulated via
a combination of static, gradient, and radiofrequency (rf) magnetic fields. These
fields and their relative timing (or pulse sequences) can be varied in many ways in
order to create image contrast based on characteristics of the medium, tissue, or
pathology. The study of water in living systems using nuclear magnetic resonance
(NMR) methods has unique advantages because they measure the signal from
intrinsic water molecules directly and noninvasively. In addition to varying tissue
contrast, flowing, diffusing, and perfusing spins can be encoded in the image
signal. The clinical applications of diffusion MRI are numerous, and changes
in water diffusion in neuronal tissues have been associated with alterations in
physiological and pathological states. These include the early detection of acute
stroke [5], functional brain imaging [6], white matter fiber tracking [7], and the
detection of multiple sclerosis [8], and tumors [9].
The precession and relaxation of the net magnetization, as a result of the spin ma-
nipulation, is described by the phenomenological Bloch equations [10]. In liquids,
however, the positions of the spin-containing molecules fluctuate due to Brownian
motion so that the Larmor precession is randomly modulated, causing dephasing
of the resonance signal. In other words, the magnetic field is no longer constant in
space, but has a field gradient
G
, defining the magnitude of the field at the site of
a nucleus given by the position vector,
r
, causing phase fluctuations
t
γ
t
o
ω
(
t
)
dt
=
r
(
t
)
G
(
t
)
dt
(
t
)
=
·
(1)
0
where
γ
is the gyromagnetic ratio. Dephasing due to random modulation of the
Larmor frequency,
ω
(
t
), was first observed by Hahn [11], who noted the attenuation
of the observed transient signals in NMR experiments due to the self-diffusion of
'spin-containing liquid molecules'.
Diffusion due to the Brownian motion of the liquid molecules during the ap-
plication of a magnetic field gradient causes a dephasing of the transverse mag-
netization. This results in a loss of the acquired signal. The extent of the signal
attenuation depends on both sequence and sample parameters. The inclusion of a
diffusion weighting gradient causes a sequence to be sensitive to molecular dif-
fusion. The attenuation is also dependent on tissue type and microstructure, as
well as on its physiological state. Magnetic resonance imaging methods that are
designed to probe microscopic diffusion are called diffusion imaging sequences.
