"Jesus could not possibly have sweated blood in Gethsemane - how could that happen?"

hematidrosis

 noun

he·​ma·​ti·​dro·​sis

variants: or chiefly British haematidrosis \ ˌhē-​mət-​ə-​ˈdrō-​səs also ˌhem-​ət-​ \

Medical Definition of hematidrosis 

: the excretion through the skin of blood or blood pigments. Merriam-Webster Dictionary.