perineuriumPronunciation: /ˌpɛrɪˈnjʊərɪəm/Definition of perineurium noun [mass noun] Anatomy the sheath of connective tissue surrounding a bundle (fascicle) of nerve fibres within a nerve. Derivatives perineural adjective Origin: mid 19th century: modern Latin, from Greek peri- 'around' + neuron 'sinew'perineurium in other Oxford dictionaries Definition of perineurium in the US English dictionary