Statute's requirement of physical injury is a threshold requirement to bar frivolous claims, so causation does not have to be established between the injury and the evil of the statute -- plaintiff can recover for any harms traceable to unconstitutional deliberate indifference so long as there is an injury associated with the claim.
http://media.ca8.uscourts.gov/opndir/18/08/171952P.pdf
Since 2011. An occasional commonplacing of the U.S. Circuit Courts of Appeal.
Neither an authoritative statement of the law nor legal advice. Quick work.