Local anesthetics mainly affect which of the following?

Local anesthetics primarily affect the rate of depolarization in nerve fibers. They achieve this by blocking sodium channels, which are essential for the depolarization phase of an action potential. When these channels are inhibited, the influx of sodium ions into the neuron is reduced, leading to a decrease in the ability of the nerve to generate an action potential. This effectively prevents the transmission of pain signals from the site of administration to the central nervous system.

The other options relate to changes in nerve conduction but do not accurately capture the primary action of local anesthetics. Lowering the threshold potential or accelerating the repolarization rate are not the main effects of local anesthetics; instead, these agents focus specifically on impeding depolarization, which is pivotal in blocking pain sensations. Thus, option A best represents the primary mechanism of action of local anesthetics.