I found this source but i don't know whether it is what you are after.

> Thranduil’s sudden scars reflect a little emphasized of Tolkien’s lore:
> elves’  “Fëar” (a metaphysical concept analogous translatable as
> “soul”) occasionally  influences the “Hröa” (the fleshly, physical
> body), particularly under moments of  extreme stress. This can
> manifest as extreme physical changes that reflect the mind’s state, in
> this case deep war scars.

[Source][1]


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 texts, the last battle Thranduil saw (up to setting in
> The Hobbit) was that of the last alliance at the end of The Second
> Age. However, in the 1900's of the Third Age, according to text,
> the "serpents of the north" were fought and mostly slain. In
> all likelihood, Peter Jackson is taking creative liberty with the
> story. On a more symbolic note, the scars could represent the pain
> Thranduil has endured in war (he watched his father die in the battle
> of the last alliance).

[Source][2]


  [1]: http://askmiddlearth.tumblr.com/post/71302074745/whats-up-with-thranduils-face-in-desolation-of-smaug
  [2]: https://uk.answers.yahoo.com/question/index?qid=20131222024209AANT4mQ