Under what circumstances can a prison official be held liable for injuries sustained by an inmate at the hands of another inmate?

Under the Eighth Amendment, "prison officials have a duty to protect prisoners from violence at the hands of other prisoners." Farmer v. Brennan, 511 U.S. 825, 833 (1994) (internal quotation marks, ellipsis, and citation omitted). However, "not . . . every injury suffered by one prisoner at the hands of another . . . translates into constitutional liability for prison officials responsible for the victim's safety." Id. at 834. A prison official may be held liable for an assault suffered by one inmate at the hands of another only where the assaulted inmate can show

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that the injury is sufficiently serious, id. at 834 (citing Wilson v. Seiter, 501 U.S. 294, 298 (1991)), and that the prison official was deliberately indifferent to the risk of harm, id. at 837. Thus, the relevant inquiry is whether prison officials, "acting with deliberate indifference, exposed a prisoner to a sufficiently substantial risk of serious damage to his future health." Id. at 834 (internal quotation omitted).