'tissue-compatible' is a modern compound formed from 'tissue' + 'compatible'. 'Tissue' originates from Old French 'tissu' (the past participle of 'tisser', "to weave"), ultimately from Latin 'texere' meaning 'to weave'. 'Compatible' comes from Latin 'compatibilis' (from 'com-' together + 'pati' to suffer/feel) via Medieval Latin, meaning 'able to exist or operate together.'

'tissue' came into Middle English from Old French 'tissu' (from verb 'tisser' < Latin 'texere'), developing from a sense of 'something woven' to broader senses such as biological 'tissue' (17th-18th century). 'compatible' passed from Latin 'compatibilis' into French and English, evolving to mean 'able to coexist' in modern usage. The specific compound 'tissue-compatible' arose in scientific/medical English in the 20th century to denote materials that coexist safely with living tissue.

Individually, 'tissue' originally meant 'something woven' and later came to denote biological structures; 'compatible' originally implied 'bearing together' and evolved to mean 'able to exist together without conflict'. Combined, 'tissue-compatible' specifically came to mean 'not harmful to living tissue' in biomedical contexts.