A variational principle for power dissipation in low frequency conduction in biological tissues.

Propagation of low-frequency electrical signals in biological tissues appears naturally in neural and cardiac physiological systems. These signals can also be externally applied to tissues as part of experimental probes or therapeutic tools. Models for propagation of these signals usually consider tissues as purely conductive materials. In large systems such as whole bodies or organs, these models consider the systems as composed of finite domains of homogeneous regions with distinct conductivities. The electric fields in these model systems exhibiting piecewise-uniform conductivity obey equations similar to those of electrostatics in polarizable media, but with boundary conditions set by current conservation. In this presentation we show that the electric fields can be obtained via a variational principle based on the minimization of dissipated power. In addition to providing a conceptual framework to the problem, this principle allows the construction of approximate solutions. It can also be used to establish bounds on the spectrum of the integral and differential operators that appear naturally in these problems.