Abstract
An accurate head model is required to get reliable solutions for the inverse problem in electroencephalograph. However, no practical method is available to measure tissue conductivities in a head, and hence the standard values are assumed for all the subjects so far. In this paper, we propose a kind of least square method to estimate the conductivities of scalp, skull and brain from potential distributions generated by weak currents injected from scalp surface, and verify its effectiveness by means of computer simulations using concentric sphere head models. The standard 4-shell concentric sphere model was used to calculate potential distributions that are considered as measured ones after being added with some noise. Then the conductivities were estimated from these potential distributions assuming 3-shell concentric sphere models with different thickness of the scalp and the skull. Errors in the estimation of dipole locations were also investigated using concentric sphere models with the conductivities thus obtained. As a result, we came to the following conclusions. (1) It is difficult to estimate the brain conductivity only from scalp potentials. However, it is not so crucial to know the precise value of the brain conductivity in the estimation of the scalp and skull conductivities as well as dipole locations. They can be estimated with practical accuracy by just assuming a rough value for the brain conductivity. (2) Errors in the thickness of the scalp and the skull reflect errors in their estimated conductivities. However, the conductivity of the scalp multiplied by its thickness and the conductivity of the skull divided by its thickness can be estimated accurately from scalp potentials. So long as these two parameters are given correctly, estimated dipoles are located near the true ones regardless of the errors in the thickness and conductivities of the scalp and the skull as well as the brain conductivity.
