Analysis of lumped and distributed elements models of cut muscle fibers in vaseline or sucrose gap preparations

A general method of finding the time course and the steady state distribution of potential in Vaseline or sucrose gap preparations is given by making use of the linear cable equation. The general solution has been found analytically in terms of its Laplace transform and then numerically inverted. Two particular experimental situations, namely the single gap and the double gap preparations, have been analyzed. The results have been compared with the solutions of the commonly used lumped elements models. While for the double gap no large errors are introduced by the lumped model, for the single gap there are significant differences. The dependence of the voltage distribution on various electrical and geometrical parameters has been examined. It is suggested that the proposed mathematical treatment might be used by experimenters as a reference to assess the validity of simplified lumped models