Biomedical Engineering Reference
In-Depth Information
The signal part of simulated sensor recordings,
b
s
(
)
, was generated by projecting
the time series of the three sources onto the sensor space using the sensor lead
field. The final form of simulated MEG recordings
b
t
(
t
)
was computed by adding
spontaneous MEG to
b
s
(
t
)
, such that
b
(
t
)
=
b
s
(
t
)
+
b
I
(
t
),
where
b
I
(
t
)
is the
spontaneous MEG measured using the same sensor array, and
is a constant that
controls the signal-to-interference ratio(SIR) of the generated sensor recordings. We
first set
in order for SIR to be equal to 8, and computed the simulated MEG
recordings
b
(
t
)
. The Champagne source reconstruction algorithm was applied to
b
were
obtained. The MVAR coefficients were estimated using the least-squares method.
The results of computing PDC and DTF are shown in Fig.
8.5
.
In Fig.
8.5
, results very close to the ground truth in Fig.
8.4
were obtained. The
DTF detects the information flow from the second to the first sources, which is the
indirect causal coupling via
s
3
(
(
t
)
, and the estimated time series of the three sources,
s
1
(
t
)
,
s
2
(
t
)
, and
s
3
(
t
)
, but the PDC does not detect this indirect coupling.
These results are consistent with the explanation in Sect.
8.5.1
.
We next generated the simulated sensor recordings with setting SIR at 2. The
results of computing the PDC and DTF are shown in Fig.
8.6
. Here, the MVAR
coefficients were estimated using the least-squares method. The figure shows that
large spurious causal relationships exist, due to the low SIR of the generated data.
We then applied the sparse Bayesian algorithm described in Sect.
8.7.2
for estimating
the MVAR coefficients, and computed the PDC and DTF. The results are shown in
t
)
(a)
(b)
1
2−−>1
1−−>2
2−−>1
1−−>2
0.5
0
1
3−−>1
1−−>3
3−−>1
1−−>3
0.5
0
1
3−−>2
2−−>3
3−−>2
2−−>3
0.5
0
0
0.2
0.4
0
0.2
0.4
0
0.2 0.4
frequency
0
0.2 0.4
frequency
frequency
frequency
Fig. 8.5 a
The plot of partial directed coherence (PDC) and
b
the directed transfer function (DTF)
computed using MVAR coefficients estimated from the simulated MEG data with SIR equal to 8.
The least-squares method in Sect.
8.7.1
was used for estimating MVAR coefficients. Explanations
on the ordinate and abscissa variables are found in the caption for Fig.
8.2
