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Local anesthetic injections into the nerves or sensitive areas of the stump may relieve pain for days, weeks, or sometimes permanently, despite the drug wearing off in a matter of hours; and small injections of hypertonic saline into the soft tissue between vertebrae produces local pain that radiates into the phantom limb for ten minutes or so and may be followed by hours, weeks or even longer of partial or total relief from phantom pain. Vigorous vibration or electrical stimulation of the stump, or current from electrodes surgically implanted onto the spinal cord, all produce relief in some patients.

How long can an anesthetic, at max, relieve pain for, despite wearing off in only hours?
permanently