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The unique determination of neuronal currents in the brain via magnetoencephalography. (English) Zbl 1075.92012

Summary: The problem of determining neuronal currents inside the brain from measurements of the induced magnetic field outside the head is discussed under the assumption that the space occupied by the brain is approximately spherical. By inverting the Geselowitz equation, the part of the current which can be reconstructed from the measurements is precisely determined. This actually consists of only certain moments of one of the two functions specifying the tangential part of the current. The other function specifying the tangential part of the current as well as the radial part of the current is completely arbitrary. However, it is also shown that with the assumption of energy minimization, the current can be reconstructed uniquely. A numerical implementation of this unique reconstruction is also presented.

MSC:

92C20 Neural biology
92C55 Biomedical imaging and signal processing
78A70 Biological applications of optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory
35R30 Inverse problems for PDEs
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