脳磁図分析の現況と課題

概要

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Magnetoencephalography is a non-invasive and real time research for the activities of human brains by measuring magnetic fields caused by primary (neuron) currents inside. Those magnetic fields are rather weak, but recent development of the device based on the super-conductivity (SQUID) has made it possible to measure them. First, we describe mathematical analysis to the models of D. B. Geselowitz and F. Grynszpan, particularly non-uniqueness of the full-inverse problem. Next, taking account of the finiteness of observed data, we formulate the discrete inverse problem. Several methods for solving the problem are summarized as over-and under-determined systems. We study their validities in connection with the underlying assumptions on neuron currents. Finally, we propose new algorithms to solve ill-posed problems such as parallel optimizations and so forth.
日本応用数理学会の論文
2001-09-14