Some forms of tinnitus are caused by damage to the microscopic hairs in the inner ear, that, once damaged, can send electrical signals that cause the ringing sound. So wouldn't that mean that just eliminating the hairs entirely would cure the tinnitus? Deafness would be caused but some people would likely find living with no sound at all more preferable to constant ringing.
Sometimes (and yes, deafening has been used as a treatment for some patients).
Tinnitus has multiple causes
Although the mechanisms of tinnitus are not completely understood, many forms of sustained tinnitus are not caused by activity in hair cells. Rather, the causes involve auditory brain regions beyond the inner ear, likely due to those circuits no longer receiving the input they used to receive after damage to the cochlea.
Hearing damage in certain frequencies both kills the hair cells (causing deafness) and also induces tinnitus. Therefore, deafness as a cure for tinnitus seems not only undesirable but quite counterproductive in those cases.
In contrast, cochlear implants have in some cases reduced tinnitus, and this is effectively the opposite solution: restoring some version of lost hearing, rather than removing what remains.
Deafening can be a cure for peripheral (originating in the ear) tinnitus
Some forms of tinnitus seem to have a peripheral origin. For example, tinnitus may occur when there is a selective loss of outer but not inner hair cells in a region of the cochlea. In this context, lesioning those inner hair cells could possibly solve the problem, while also deafening the patient at those frequencies. I am unaware, however, of a surgical procedure that can successfully produce such a selective lesion (please comment if anyone knows differently).
Curing tinnitus by lesioning the auditory nerve (thereby deafening the patient) can cure tinnitus in some patients. However, deafening a patient is a rather severe course of action.
In summary, tinnitus refers to a spectrum of conditions, and depending on the causes in a particular patient, completely different courses of action may be appropriate. Deafening can cure tinnitus in some intractable cases, but is completely inappropriate in others.
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