Biomedical Engineering Reference
In-Depth Information
3.1.9
Magnetic Source Analysis
As mentioned above, if we know the position, direction, and intensity of a
certain component of a vector magnetic field, we can estimate the spatio-
temporal information about the source of the magnetic field. Most magne-
tometers are designed to measure a component of the magnetic field vector
in the sensor direction. The proton magnetometer is one of the exceptions.
If we would like to know the absolute value of the magnetic field vector at
the sensor position, we need to measure the three components of the vector
by independent perpendicular measurements. If the magnetic field varies over
time, we should measure the three components simultaneously. In most of the
studies on magnetic measurements in geophysical applications - for example,
magnetic storms due to solar activity or magnetic anomaly detection for mi-
ning - the magnetic field information at the sensor position has been used.
On the other hand, in biomagnetic studies such as magnetoencephalogram
(MEG), the main target of the measurement is not only to get the magnetic
field value at the measurement point but also to analyze the obtained value
by localization of the source of the magnetic field, especially the electrical
activity in the object.
The Biot-Savart law tells us that an electrical current generates a ma-
gnetic field around the current. The relationship between the current and
the magnetic field is defined by an equation. The current is the cause and
the magnetic field is the result. To obtain some information on the cause by
observing the result is what is known as an inverse problem. Magnetic source
analysis is once such inverse problem, or inverse source problem. A simple
example of magnetic source analysis is to localize an electric current dipole
(strictly speaking, no true current dipole exists). A current dipole must have
a current source and a return current, but we can assume an independent
current dipole as a model of an approximation of a physical system.
The magnetic field measured by a sensor is expressed by (3.7). If we
observe the field in a certain time period, the data obtained is the time-
varying series. From the data, we cannot localize the position of the source
and, furthermore, we can only say that at least one magnetic source exists. If
you add one more sensor placed at a different position and consider the data
from the two different sensors, and if the data vary with the same phase, you
can conclude that at least the source has neither moved nor rotated, and that
only the intensity of the source has varied. If you then to add more sensors
placed at yet more different positions, the signals of all of the channels would
also vary with the same phase, and you would obtain a distribution pattern
on the magnetic field which would not change during the time period of
observation. You could estimate the position and direction of the source from
this pattern. If the source does not vary in intensity but varies in position
and/or direction, the observed data are assumed to be influenced by the
actions. For example, if there are two sensors at different positions and the
source is moving between these two positions, the observed data from the
