Floating Potential Boundary Condition in Smooth Domains in an Electroporation Context

Abstract

In electromagnetism, a conductor that is not connected to the ground is an equipotential whose value is implicitly determined by the constraint of the problem. It leads to a nonlocal constraints on the flux along the conductor interface, so-called floating potential problems. Unlike previous numerical study that tackle the floating potential problems with the help of advanced and complex numerical methods, we show how an appropriate use of Steklov-Poincaré operators enables to obtain the solution to this partial differential equations with a non local constraint as a linear (and well-designed) combination of N + 1 Dirichlet problems, N being the number of conductors not connected to a ground potential. In the case of thin highly conductive inclusion, we perform an asymptotic analysis to approach the electroquasistatic potential at any order of accuracy. In particular, we show that the so-called floating potential approaches the electroquasistatic potential with a first order accuracy. This enables us to characterize the configurations for which floating potential approximation has to be used to accurately solve the electroquasistatic problem.

Automated needle localisation for electric field computation during an electroporation ablation

“…However, it is well-known that the linear static model under evaluate the region of electroporation, compared with other non linear models. Therefore, from a medical point of view, it is sufficient, as a first approximation, to compute the electric field as the gradient of the linear static potential φ satisfying: − ∇ • (σ∇φ) = 0, in the region of computation Ω, (6) complemented with Dirichlet boundary conditions on the active needles, a floating potential condition [15] on the passive needle and a Fourier-Robin condition on the boundary of the simulation box. The liver conductivity was set to σ = 0.5 S/m while the tumour conductivity was set to σ = 0.7 S/m following [20].…”