The Imaging of a Magnetic Source - Biological Imaging and Sensing - page 168

Fig. 3.41. The result of estimating a pair of circular current sources with the
current flowing in opposite directions. The distribution of 20 current elements was
obtained after 30 000 iterations

the distribution is a smoothly curved line or circle. Two current elements
are frequently located closely together and face each other. In this state, the
value of the evaluation criterion does not decrease any further. This is one
kind of the local minimum. To avoid this problem, a stabilized condition as
shown in Fig. 3.42 is introduced. The condition is that the current flow has
to be continuous and smooth (Fig. 3.42a). Any two current elements, whose
positions are close to each other, must not be in opposite directions. If the
distance d between two elements is less than the threshold dt , the angle θ
between them must be less than θt (Fig. 3.42b). If there is a pair of current
elements that does not satisfy this condition (Fig. 3.42c), one of the pair mo-
ves away, and its direction is changed. The motion is controlled by random
numbers.

Simulation 2. The mathematical characteristics of the algorithm have not
been fully clarified. It might be quite dicult to analyze the characteristics
using an analytic method. Computer simulations were carried out to confirm
that the algorithm is capable of finding that distribution of elements which
best describes the source. The algorithm was applied to a volume current
source consisting of 45 elements, as shown in Fig. 3.43. The initial state of
the estimation strategy is shown in Fig. 3.44, where 20 current elements, the
model of the magnetic source, are randomly distributed in a subject region.
The results of the estimation using the least-square norm of (3.96) and the
improved evaluation criterion of (3.98) are shown in Figs. 3.45 and 3.46,
respectively. Two hundred and sixteen (= 6 6) measurement points

are placed on the whole surface of a cube. The measured magnetic field
B measured is calculated as the summation of the magnetic field generated by
each element of the volume current source using the Biot-Savart law.

× 6 ×

B model