What is the test for an amended complaint alleging that a prison official violated the Eighth Amendment by failing to provide adequate medical care for an inmate?

In any amended complaint plaintiff elects to file, he must allege facts that, if proven, would objectively establish that he suffered a "sufficiently serious" deprivation. Farmer, 511 U.S. at 834; Wilson v. Seiter, 501 U.S. 294, 298-99 (1991). The plaintiff must also allege that subjectively each named defendant had a culpable state of mind in allowing or causing the plaintiff's deprivation to occur. Farmer, 511 U.S. at 834. A prison official violates the Eighth Amendment "only if he knows that inmates face a substantial risk of serious harm and disregards that risk by failing to take reasonable measures to abate it." Id. at 847. Under this standard, a prison official must have a "sufficiently culpable state of mind," one of deliberate indifference to the inmate's health or safety. Id.