I found this source but iI don't know whether it is what you are after.
Thranduil’s sudden scars reflect a little emphasized of Tolkien’s lore: elves’ elves’ “Fëar” (a metaphysical concept analogous translatable as “soul” “soul”) occasionally influences the “Hröa” (the fleshly, physical body body), particularly under moments of extreme stress. This can manifest manifest as extreme physical changes that reflect the mind’s state, in this this case deep war scars.
Edit : I have also found this reference which seems to state that Tolkien made no reference to the Scars on Thranduil's face in the books.
Thranduil's scars are decidedly non-canon. According to Tolkien's Tolkien's texts, the last battle Thranduil saw (up to setting in The The Hobbit) was that of the last alliance at the end of The Second Age Age. However, in the 1900's of the Third Age, according to text, the the "serpents of the north" were fought and mostly slain. In all all likelihood, Peter Jackson is taking creative liberty with the story story. On a more symbolic note, the scars could represent the pain Thranduil Thranduil has endured in war (he watched his father die in the battle of of the last alliance).