Biomedical Engineering Reference
In-Depth Information
Step 2:
To calculate an evaluation value
L
of model fitting by norm bet-
ween model field
B
j,
model
and measured magnetic field
B
j,
measured
at
R
j
:
measurement position
L
=
M
2
,
|
B
j ,
model
−
B
j ,
measured
|
(3.96)
j
L
2
criterion of two vectors.
Step 3:
To select an arbitrary current element. The element moves to the
vicinity of its original position in the solution space
where the norm is the
S
i
to reduce
L
.The
element motion is limited by the algorithm parameters. There are
N
solution spaces, each of which belongs to an independent current element
I
i
:
S
i
=
S
i
(
r
i
,
n
i
)
.
(3.97)
The solution space is specified by the position coordinate and the direc-
tion vector of each current element.
Step 4:
Inthecaseof
L
being reduced, the element has a new position. In
thecaseof
L
being not reduced, the element stays at its original position.
The algorithm operation returns to Step 3 and the algorithm selects the
next arbitrary element.
The mathematical charactersistics of the algorithm are not clarified. It
might be quite dicult to analyze the characteristics by means of an analyti-
cal method, rather than by empirical or heuristic means. The major purpose
of this study is to verify that the algorithm can calculate the distribution
of current elements that describes the magnetic source in good agreement,
within a practical cpu time.
Simulation 1.
As the first step of mathematical clarification of the algo-
rithm, the following simulation has been carried out. The circular current
was assumed to be a magnetic source located in a cube. Magnetic field vec-
tors at several positions on the surface of a cube generated by the circular
current were adopted as the measured magnetic field vectors
B
measured
.The
magnetic field vectors at measurement positions generated by elements are
calculated.
In the initial stage of the simulation, we should determine all of the pa-
rameters that specify the signal source, the model, and the algorithm. The
parameters of the signal source that are not essential but are practical for
this method are the size of the cube, the diameter of the circle current, the
position and the direction of the circle and the current intensity. The inten-
sity of the element, the number of elements, and the distribution are model
parameters. The algorithm is specified by the rule of element motion and the
termination rule of iteration.
