The mechanism of action for local anesthetics involves the inhibitions of sodium channels resulting in the inability of normal function. (That is the influx and outflow of sodium which results in the propagation of impulses along the nerve.) The sodium channels are "stuck" in one of three phases; 1) open, 2) closed or 3) partially closed. The speed of onset is predicated by the pKa of the local anesthetic and the pH of the tissue it is injected. The closer the two values, the faster the un-ionized portion can permeate the cell membrane (the ionized is the active portion, but does not permeate the cell membrane). As a note, the pKa is the pH at which 50% of the solution is ionized. The balancing act occurs on either side of the membrane.
So, on to your question: the initial influx of sodium would be measured as a stimulation. As the sodium channels become inactive, depression would be measured.
Local anesthetics produce anesthesia by inhibiting excitation of nerve endings or by blocking conduction in peripheral nerves. This is achieved by anesthetics reversibly binding to and inactivating sodium channels. Sodium influx through these channels is necessary for the depolarization of nerve cell membranes and subsequent propagation of impulses along the course of the nerve. When a nerve loses depolarization and capacity to propagate an impulse, the individual loses sensation in the area supplied by the nerve.
Local anesthesia is any technique to induce the absence of sensation in a specific part of the body, generally for the aim of inducing local analgesia, that is, local insensitivity to pain, although other local senses may be affected as well. It allows patients to undergo surgical and dental procedures with reduced pain and distress. In many situations, such as cesarean section, it is safer and therefore superior to general anesthesia. It is also used for relief of non-surgical pain and to enable diagnosis of the cause of some chronic pain conditions. Anesthetists sometimes combine both general and local anesthesia techniques.
The following terms are often used interchangeably:
Local anesthesia, in a strict sense, is anesthesia of a small part of the body such as a tooth or an area of skin.
Regional anesthesia is aimed at anesthetizing a larger part of the body such as a leg or arm.
Conduction anesthesia encompasses a great variety of local and regional anesthetic techniques.