Biomedical Engineering Reference
In-Depth Information
temperature gradients often sacrifice spatiotemporal resolution
for volume coverage, increased temperature sensitivity, and arti-
fact reduction techniques.
The apparent diffusion coefficient of water was first investi-
gated in context of MR temperature imaging in the employment
of hyperthermia studies, where low temperature changes and
low resolution imaging would not be problematic (Le Bihan et al.
1989). The theoretical temperature sensitivity of the apparent
diffusion coefficient is actually relatively high across tissues and
solvents (2%/°C) and is relatively insensitive to magnetic field
strength, making it consistently one of the more sensitive MRTI
techniques by comparison (de Senneville et al. 2005; Rieke et al.
2008). However, the diffusion of water depends heavily on tis-
sue type and the microenvironment since restricted diffusion
(i.e., muscle, white matter, etc.) and microperfusion changes can
impact accurate measurement. Techniques to limit the impact of
such confounding effects on the diffusion coefficient have been
proposed.
Measurement of the apparent diffusion coefficient is accom-
plished via a pulsed gradient technique (Stejskal et al. 1965).
Generally, diffusion acquisitions are signal-to-noise ratio (SNR)
limited, and spatial resolution is relatively low in order to speed
up the acquisition and increase SNR. Because the measurement
is looking at microscopic motion, the measurements can be
highly sensitive to motion. Line-scan (Morvan et al. 1993) and
single-shot echo-planar imaging (EPI) (Bleier et al. 1991) are
useful techniques for reducing imaging time and motion arti-
facts and are likely the best options on modern scanners with
high-performance, eddy current-corrected gradient subsystems.
Like most techniques to be discussed, heating that invokes
a strong physiological response from tissue, such as edema,
perfusion changes, tissue coagulation, and so forth, is another
source of artifact in diffusion-based MRTI. These events can
be difficult, if not impossible, at times, to isolate from tempera-
ture changes (Moseley et al. 1990). Additionally, in cases where
adipose tissue is not completely suppressed during diffusion
measurements, use of the diffusion coefficient remains difficult
due to restricted diffusion of the lipids and varying tempera-
ture sensitivity of lipid diffusion compared to that of soft tissues
(Rieke et al. 2008). Therefore, lipid suppression is recommended
when diffusion measurements are used to estimate temperature
changes in mixed water-lipid tissue environments.
The water proton density (PD) varies approximately linearly
with the equilibrium magnetization,
M
0
, determined by the
Boltzmann distribution
3.3.2 temperature Sensitivity of Several
Intrinsic Mr parameters
There are numerous temperature-sensitive MR parameters intrin-
sic to tissue aqueous solutions, as well as some exogenous agents,
that may be exploited for
in vivo
temperature measurements
(Rieke et al. 2008; Ludemann et al. 2010). There are actually too
many to fully review here, so attention will focus on techniques
that tend to impact clinical temperature monitoring. The primary
parameters to be discussed here include the molecular diffusion
constant of water (
D
), water proton density (PD), spin-lattice (
T
1
)
and spin-spin (
T
2
) relaxation times, magnetization transfer con-
trast, and the water proton resonance frequency (PRF) shift.
The molecular diffusion coefficient,
D
, is used to describe the
thermal Brownian motion of molecules. The general relation-
ship of
D
to temperature can be represented by an Arrhenius
rate process,
De
ED
kT
()
a
−
(3.1)
≈
where
k
is Boltzmann's constant,
T
is the absolute temperature
in Kelvin, and
E
a
(
D
) is the activation energy of the diffusing
substance, such as water, which has a self-diffusion coefficient
measured by MR to be approximately 2.3 × 10
−5
cm
2
/sec at 25°C
(Carr et al. 1954) with diffusion coefficients for other solvents of
interest in MR being compiled by various investigators or vari-
ous temperature ranges (Holz et al. 2000). Being the primary
in vivo
signal for MR imaging, the temperature dependence of
the apparent diffusion coefficient of water has been researched
extensively for temperature imaging.
Differentiation of Equation 3.1 results in an expression for the
temperature dependence of the diffusion coefficient:
dD
dT
ED
kT
()
−
ED
kT
()
a
a
=
e
.
(3.2)
2
Here we see we need a minimum of two diffusion measurements,
D
ref
(
D
at reference temperature,
T
ref
) and
D
, and knowledge of
the basal temperature (
T
ref
) in order to estimate the temperature
change, which is given for a two-point measurement by:
(
)
22
∝=
γ
NI I
+
1
B
0
PD
M
=χ
B
(3.4)
0
00
3
µ
kT
0
2
kT
ED
DD
D
−
ref
ref
T
=
(3.3)
where
N
is the number of spins, γ is the gyromagnetic ratio
(42.58 MHz/T for hydrogen protons),
ħ
is Planck's constant,
I
is
the quantum number of the spin system (1/2 for hydrogen pro-
tons),
B
0
is the magnetic flux density, μ
0
is the permeability of
free space,
k
is the Boltzmann constant,
T
is the temperature (in
Kelvin), and χ
0
is the susceptibility. Note χ
0
and
T
have an inverse
relationship (Curie's law), which relates changes in susceptibility
()
a
ref
where we have assumed that changes in
D
and
T
are rela-
tively small and that
E
a
(
D
) does not change with temperature.
Deviations of these conditions may happen for temperatures
over 40°C (Simpson et al. 1958).
