Biomedical Engineering Reference
In-Depth Information
response facilitates analysis of the data in the frequency domain,
allowing for frequency filtering of noise and other components
with frequencies outside the model. It is important to note that
even though higher frequencies increase the number of cycles
acquired in a given amount of time, thus improving the averag-
ing process, their use may compromise the ability of accurately
estimating
T
1app
, due to a decrease in the time span of evolution
of the tissue magnetization and a decrease in the number of data
points used for estimation of this parameter. On the other hand,
the precision of estimation of the transit time
is proportional to
how accurately the temporal shift between the labeling function
and the tissue response can be measured, and for this, a higher
sampling rate is required. For accurate transit time estimation,
the sampling rate of the DASL curve must be higher than the
smallest expected transit time. This can be a significant limitation
in studies of small animals where the transit times can be quite
short, on the order of 100 - 350 ms
(53, 65, 66)
.
The DASL sampling scheme is particularly advantageous in
the presence of periodic noise and other sources of signal fluc-
tuation, such as the ones introduced by respiratory and cardiac
cycles. In such cases, the periodic nature of the tissue response
to a periodic labeling function greatly facilitates filtering of such
noise sources. Efficient filtering can be accomplished by fitting the
raw data to the model described by
Equation (13.10)
.Asimple
Fourier transform (FT) of the model determines the allowed spec-
trum of frequencies, while the FT of the data reveals the periodic
perturbations present in the data. A complex filter comprised of
real and imaginary components present in the allowed spectrum
of frequencies can be applied to the data set to eliminate every
frequency other than the ones predicted by the model.
Figure 13.2
illustrates the filtering process based on the
DASL model for data obtained from an isoflurane-anesthetized
rat at 7 T. The original DASL time course is shown in
Fig. 13.2a
.
A labeling frequency of 0.05 Hz was used to generate the DASL
time-course. The labeling time
TL
was 200 ms and the image
repetition time
TR
was 250 ms. In spite of the good SNR,
noise present in the data is quite visible.
Figure 13.2b
shows
the real and imaginary components of the FT of the data, while
Fig. 13.2c
shows the frequency components allowed by the best
fit of the data to the model in
Equation (13.10)
.
Figure 13.2c
shows the filtered data based on the frequencies allowed by the
model. Negative amplitudes were removed by the filter, as well
as the frequency component around 1 Hz corresponding to
the respiratory rate. The filtered DASL time course is shown
in
Fig. 13.2e
, demonstrating the effectiveness of the filter in
removing the noise and other unwanted fluctuations. The advan-
tage of this filtering approach is that even perturbations occur-
ring at very low frequencies can be taken out of the data without
τ
