On the Inverse MEG Problem with a 1-D Current Distribution

• 作者: George Dassios Konstantia Satrazemi
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: MAGNETOENCEPHALOGRAPHY CURRENT IDENTIFICATION
• 年，卷（期）: yysxyw_2015,（1）
• 页码范围: 95-105
• 页数: 11页
• 分类号: O1

摘要

The inverse problem of magnetoencephalography (MEG) seeks the neuronal current within the conductive brain that generates a measured magnetic flux in the exterior of the brain-head system. This problem does not have a unique solution, and in particular, it is not even possible to identify the support of the current if it extends over a three-dimensional set. However, a localized current supported on a zero-, one- or two-dimensional set can in principle be identified. In the present work, we demonstrate an analytic algorithm that is able to recover a one-dimensional distribution of current from the knowledge of the exterior magnetic flux field. In particular, we consider a neuronal current that is supported on a small line segment of arbitrary location and orientation in space, and we reduce the identification of its characteristics to a nonlinear algebraic system. A series of numerical tests show that this system has a unique real solution. A special case is easily solved via the use of trivial algebraic operations.