Effect of intracellular anisotropy on electrical source determination in a muscle fibre

Expressions are available for describing, quantitatively, the source associated with an action potential propagating along an excitatble fibre. For a nerve fibre one such expression defines an equivalent volume dipole density function τ(x) = − ∂/∂x (σ_i φ_i(x) − σ_e φ_e(x))a_x (where x is the axial co-ordinate, i is the intracellular and e the extracellular region, σ_i and σ_e are isotropic conductivities, ϕ the potential at the membrane, while axial symmetry is assumed), and this source fills the intracellular region. This source, as distinct from transmembrane current formulations, lies in a uniform, isotropic, extracellular, medium. Consequently, for a fibre bundle a simple superposition of sources, all lying in a uniform, isotropic, extracellular space, can be accomplished. However, for muscle fibres the presence of non-conducting myofibrils causes the intracellular space to be anisotropic. The paper describes the modification in the aforementioned expressions for the case of longitudinal and transverse propagation and extrapolation to an arbitrary angle of propagation. The resultant source continues to be expressed relative to a uniform, isotropic, extracellular medium.