Interaction between Artificial and Naturally Generated Neural Activity

The question we want to answer here is ‘What is the effective rate action potentials are received when an electrical stimulus is applied to a nerve carrying naturally generated action potentials?’ To answer this question several assumptions will be made:

1. The generator acts as a leaky integrator that can be reset by depolarization before threshold is reached.
2. The stimulus results in action potentials that propagate in both directions from the site of the stimulus.
3. Collision of and orthodromic traveling action potential with and an action potential traveling in the antidromic direction results in the annihilation of both pulses.

PULSE # 1 At t =(x/2)/v the action potential initiated at the generator and the one initiated at the stimulator collide at x/2.
PULSE # 2 At t = 1/fs a stimulator action potential is initiated and at Dt later an action potential is initiated at the generator, where Dt = 1/fg - 1/fs. At the time Dt the stimulator initiated action potential has moved away from the stimulation site a distance d= v Dt, where v is the conduction velocity of the action potential. The collision point for the second two action potentials is closer to the generator site than was the site for the first two action potentials.
PULSE # 3 At 2Dt the action potentials have traveled a distance d’ away from the stimulus site before the third action potential has been initiated at the generator site, where d’=2v Dt or 2d. The collision site for the third pair of action potentials is 1/2(x-2d).
PULSE #n The collision point for the nth pair of action potentials is 1/2[x-(n-1)d] = 1/2[x-(n-1)v(1/fg-1/fs)]. When (n-1)v(1/fg-1/fs)≥x the stimulator initiated action potential invades the generator and all succeeding stimulator generated pulses reset the generator before the generator pulses are initiated. Note that at the nerve terminal the end organ receives an action potential for each stimulator initiated pulse and a frequency that is equal to fs.