Biomedical Engineering Reference
In-Depth Information
n
RF pulses is
(68)
:
M
0
1
e
−
TR
/
T
1
app
e
−
TR
/
T
1
app
−
M
0
(
1
−
cos
θ)
M
z
(
n
×
TR
)
=
+
e
−
TR
/
T
1
app
e
−
TR
/
T
1
app
1
−
cos
θ
·
1
−
cos
θ
·
cos
n
e
−
nTR
/
T
1
app
·
θ
·
(13.12)
The first term in
Equation (13.12)
represents the longitu-
dinal magnetization at the steady state condition, and the second
term represents its dynamic evolution from the fully relaxed con-
dition to the steady state condition. The basic principle of the
ASL technique is the transfer of the longitudinal magnetization
state of the endogenous labeled arterial water to the perfused tis-
sue. According to
Equation (13.12)
, this transfer is limited by
T
1app
,by
TR
, and by the excitation RF flip angle
. Thus, it can-
not occur instantly. As a consequence, quick changes in CBF such
as the ones produced by focal brain stimulation are only reflected
a few seconds later in the tissue magnetization, and thus the MRI
time course measured in response to a quick change in perfu-
sion is delayed. However, the transfer function that governs the
delayed MRI response to step changes in CBF (and in
T
1app
)is
inherently present in
Equation (13.12)
in the form of the sig-
nal evolution from the equilibrium magnetization state
M
0
to
the new steady-state magnetization expressed by the first term in
Equation (13.12)
. Provided that it is measured during the MRI
measurements of the functional CBF response, the transfer func-
tion can be used as a deconvolution kernel to remove the latency
in the CBF response imposed by the MRI signal evolution. After
the deconvolution process, the resulting CBF time course reflects
accurately the dynamics of the actual CBF changes.
Using an acquisition scheme that consisted of employing
short ASL RF pulses in conjunction with an ultra-fast imag-
ing sequence, we were able to measure the CBF response to
somatosensory stimulation in
θ
-chloralose anesthetized rats with
a temporal resolution of 108 ms
(27, 67)
.
Figure 13.5a
shows
the MRI-estimated CBF time-course (gray), and the deconvolved
CBF time course (black), in response to a 20 s-long stimulus.
To obtain the true temporal dynamics of the CBF response, the
MRI-estimated CBF curve was deconvolved with the initial 10 s
of the control magnetization decay, generating the deconvolved
CBF signal. It can be clearly seen how the CBF response mea-
sured with MRI is delayed with respect to the deconvolved curve.
One drawback of the deconvolution process is that it adds oscil-
latory noise to the data. However, the CBF changes elicited by
somatosensory stimulation in
α
-chloralose anesthetized rats are
quite robust and immune to the small amount of noise intro-
duced by deconvolution of the original functional ASL curve.
One important advantage of the use of DASL acquisition strate-
gies in functional MRI is that the control cycle of the ASL curve
α
