An equation describing spread of membrane potential changes in a short segment of blood vessel

The spread of membrane potential changes throughout certain cells and tissues plays an important role in their physiology. The attenuation of such changes in any tissue is usually characterized by the cable length constant lambda, which can be determined experimentally if the equations describing membrane potential spread in the tissue are known. Here we derive an equation describing spread of membrane potential changes in a short cable, which is an appropriate model for short segments of blood vessels. This equation is more general than those already published in that the positions of both the current source that gives rise to a potential change, and the point at which the change is measured, can be anywhere along the cable.