Biomedical Engineering Reference
In-Depth Information
Fig. 3.40.
The result of estimating a single circular current source. The distribution
of 20 current elements was obtained after l0 000 iterations
Improvement of the Algorithm.
As discussed in the previous section,
the algorithm of magnetic source imaging by current element distribution is
capable of describing the pattern of a specific signal source which consists of
circular currents. The algorithm describes a current pattern as a magnetic
source without the assumption of a parametric source model The estimated
solutions for a single circular current source and a double circular current
source are shown in Figs. 3.40 and 3.41, respectively. These solutions were
obtained by computer simulations. The circular current sources are described
by the distribution of current elements.
To apply this algorithm to other types of magnetic sources, such as a vo-
lume current source, which is more suitable for biomagnetic activity, we have
introduced a stabilized condition in addition to the conventional cost func-
tion. As a result of this, the convergence of current elements to the pattern
of the magnetic source is improved.
The major part of the optimization strategy, except for an evaluation
criterion, is the same as discussed previously. The proposed evaluation cri-
terion is composed of the least-square norm and the restrictive condition:
the so-called stabilized condition [60]. The stabilized condition is intended to
evaluate more complicated distributions of current elements. The least-square
norm of this optimization procedure is (3.96). To improve this algorithm, the
stabilized condition is combined with the evaluation function as follows:
L
+
w
×
Op
(
g
)
,
(3.98)
where
Op
(
g
) is a stabilized condition,
g
is a set of parameters to be estimated,
and
w
is the weight with which the stabilized condition contributes to the
evaluation function.
The Stabilized Condition.
Generally, the result of optimization of a mul-
tiple current element distribution shows a complicated pattern, even when
