Conductivity Deviations as Virtual Sources in Magnetoencephalography

Magnetoencephalography (MEG) is a method to study electrical activity in the brain. MEG signals are modeled by primary currents, which represent neuronal activity, and associated passive volume currents, which depend on the conductivity distribution within the body. The effect of conductivity inhomogeneities can be described as if additional virtual source currents were present. Virtual sources help to understand conductivity effects independently from the sensor array properties. The Volume Current Formulation (VCF) of the virtual sources focuses on altered patterns of volume currents, whereas in the Secondary Current Formulation (SCF) the virtual sources are at locations where conductivity changes. We derived and compared these formulations for deviations from a reference conductivity distribution. In VCF, the virtual sources are located only where the conductivity deviation is non-zero, but their orientation and magnitude depend on the local electric field. In contrast, in SCF, both the location and the orientation of the virtual sources are determined by the conductivity distribution, typically by the anatomical tissue boundaries. In SCF, however, all conductivity boundaries, including those in the reference distribution, generally need to be considered. For spherically symmetric reference conductivity, in VCF the radial component of a virtual source does not contribute to any component of the magnetic field, whereas in SCF the radial component of a virtual source does not contribute to the radial component but contributes to the tangential components of the magnetic field. Complementary descriptions using VCF and SCF were illustrated in a model for fontanels in infants.