Spread of excitation in a model of an inhomogeneous nerve fibre-I. Slight change in dimensions of fibre

Theoretically, we have considered the traversal of an excitation pulse along the nerve fibre the radius of which changes abruptly at a certain point. For a relatively small value of change of the radius we have obtained analytical expressions for the speed of the pulse. At a considerable distance from the point of change of the radius the pulse moves at a constant speed corresponding to a homogeneous fibre. On approaching the boundary the speed smoothly decreases if the second part of the axon is thicker. On transition across the boundary the speed abruptly increases and then smothly rises to a value corresponding to a homogeneous fibre of large radius. If a pulse passes from the thick part of the axon to the thin its speed at first smoothly rises, abruptly falls at the boundary and then smoothly decreases to the value of the speed in the homogeneous thin fibre.