## Solution of the Biomagnetic Inverse Problem

BESA 2000© |

**Area:**Electrical Engeneering

In magnetoencephalography (MEG) a weak magnetic field induced by the electrical activity of the brain is recorded at little distance outside the head. The mathematical model to localize the electrical activity from the measurements is given by an inverse problem.

In 1853 Helmholtz showed that there is no unique reconstruction of a current distribution for a given magnetic field. Therefore, several reconstruction approaches exist. Here, the minimum p-norm approach based on calculating the magnetic field outside the head from a superposition of current dipoles inside inside the head is used. The current distribution matching the given magnetic field best in the minimum p-norm minimization problem is tackled with a gradient-based optimization technique. The required gradient of length 1098 is computed by the reverse mode of automatic differentiation.

**Related AD-Tool:**ADIFOR

**Reference:**

H. M. Bücker, R. Beucker, C. H. Bischof

Using Automatic Differentiation for the Minimal p-Norm Solution of the Biomagnetic Inverse Problem

Conference proceeding,

H. M. Bücker, R. Beucker

Using automatic differentiation for the solution of the minimum p-norm estimation problem in magnetoencephalography

Article in

H. M. Bücker, R. Beucker, A. Rupp

Parallel minimum p-norm solution of the neuromagnetic inverse problem for realistic signals using exact Hessian-vector products

Article in

Using Automatic Differentiation for the Minimal p-Norm Solution of the Biomagnetic Inverse Problem

Conference proceeding,

*Shaping Future with Simulation, Proceedings of the 4th International Eurosim 2001 Congress, Delft, The Netherlands, June 26--29, 2001*, Dutch Benelux Simulation Society, 2001H. M. Bücker, R. Beucker

Using automatic differentiation for the solution of the minimum p-norm estimation problem in magnetoencephalography

Article in

*Simulation Modelling Practice and Theory*, 2004H. M. Bücker, R. Beucker, A. Rupp

Parallel minimum p-norm solution of the neuromagnetic inverse problem for realistic signals using exact Hessian-vector products

Article in

*SIAM Journal on Scientific Computing*, 2008**People involved:**

- H.M. Bücker,

Institute for Scientific Computing, RWTH Aachen University - R. Beucker