Theoretical analysis of parameters leading to frequency modulation along an inhomogeneous axon

Theoretical computations were conducted on a computer model of a segmented, nonhomogeneous axon to understand the mechanism of frequency block of conduction. The model is based on the Hodgkin Huxley equations modified in several ways to better describe the cockroach axon. We used cockroach parameters where available. The increase in fiber radius was spread over a series of segments to approximate a taper. We found that a taper allows a larger overall increase in fiber diameter than a single step to be successfully passed. We studied effects on a train of impulses. The modified equations included effects due to changes in the extracellular potassium concentration resulting from the repetitive firing of the axon. An increase in diameter which allows a single spike to pass blocks the subsequent impulses in a train at the taper if potassium concentration variability is introduced. This could explain the low pass filter characteristics of axon constrictions. Results of the model fit well with the experimental spike shape and height. Data were computed for the refractory period and its dependence on the taper parameters.