per·i·neph·ri·um 
(pĕr′ə-nĕfrē-əm)
(pĕr′ə-nĕfrē-əm)n. pl. per·i·neph·ri·a (-rē-ə)
The connective and fatty tissue surrounding a kidney.
[New Latin, from Greek perinephros, fat around the kidneys : peri-, peri- + nephros, kidney.]
per′i·nephral (-nĕfrəl), per′i·nephri·al (-rē-əl), per′i·nephric (-rĭk) adj.