Inverse boundary element methods

Y. Rudy and B.J. Messinger-Rapport. The inverse solution in electrocardiography solutions in terms of epicardial potentials. CRC Crit. Rev. Biomed. Eng., 16 215-268,1988. An excellent overview on the inverse problem in electrocardiography as well as a section on the application of the boundary element method to bioelectric field problems. 

The characteristic of the inverse formulation is that the differential operator C is completely shifted to the weighting function w. The next step is to choose a weighting function w. In the scope of the boundary element method, the weighting function is chosen to be a fundamental solution w= w (Love 1944 Sokolnikoflf 1956). This fundamental or Kelvin solution w is in the considered case the deformation which is observed at some point X of an infinite bar due to a unit force at some distant point in the bar. Alternatively, it is that function which satisfies the differential equation with right hand side zero at every point of an infinite bar except the force point at which the right hand side is infinite. Applied to our problem, the fundamental solution is defined by... 

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