Biomedical Engineering Reference
In-Depth Information
B
measured
norm
measurement
position
B
model
current
model of signal source
(distrib uted current element)
signal source (circle current)
Fig. 3.38.
The circular current which is the source of the magnetic field in a cube.
The model is evaluated by a value of summation of the norm between model field
B
model
andmeasuredfield
B
measured
In the steps of the algorithm, an arbitrarily selected element moves within
its vicinity in the solution space
S
i
, where a five-dimensional space is specified
by the position and direction of the element
I
i
. Figure 3.38 shows the signal
source (the circular current in the cube). Figure 3.39 shows the successive
results of current elements converging from random distribution to the signal
source patterns. 3600 iterations were carried out.
Discussion 1.
The result is quite well posed to the signal source, even
though it is not certain whether the algorithm may be effective for an ar-
bitrary ill-posed situation. In a practical application, we should introduce
many heuristics and a priori knowledge about the measurement, in order to
restrict the solution space and to avoid the local minimum solution.
Returning to the specification of this simulation, number and intensity of
elements are determined arbitrarily. However, it is necessary to select concrete
values for the parameters. It is proposed that, before the algorithm is run, the
intensity of an equivalent current dipole is estimated and, from histological
and physiological knowledge, the number of elements is determined. Then,
the current intensity of the element can be determined from the energy value
of the equivalent dipole divided by the number. As the iteration number
increases, the element becomes a pair of elements. The pair of elements,
that face each other, produce a very small magnetic field and make a small
contribution to the norm. It is a kind of local minimum.
