A friend of mine sent me the following information and I publish it here too:

http://www.musicontact-germany.com/v2.php?do=detail&c=10998&p=10&a=Kassia&i=0&s=1
In Germany MUSICONTACT has just produced a CD of 18 of Kassia’s musical compositions performed in the Medieval Byzantine tradition which is not the same as the present day 'Chrysanthine' tradition.
Of course, none of Kassia's 9th century musical manuscripts have survived (some think this is because they were all destroyed during the iconoclast warfare).
But Kassia's 50+ musical compositions are preserved (with her name as the main attribution) in many 13th cent. Sticheraria manuscripts.
There is much debate around not only the authenticity of Kassia's melodies but also the melodies attributed to her that appear in the 13th cent. manuscripts.
Although there is no evidence that would silence the debate, it was the tradition and practice of Byzantine hymnographers to write not only words but also compositions (poetry accompanied by music was more effective and easily remembered).
Kassia's most famous Troparion for the Orthros of Holy Wednesday (according to the Athens Manuscript 883, f. 60r) was composed in Mode IV Plagal but is somewhat different from the way it is chanted today (and yet similar). It is mostly a syllabic setting (eirmologiko) with only some melodic ornamentation (neumatic sections). However there are similarities too, especially the wide ambitus of an octave and a fourth, from c' to f'', and a cadence in Mode III Authentic. And a few 'theseis' are strikingly familiar but not as embellished.
So although subsequent composers or 'interpreters' of the famous hymn (such as Bishop Germanos, Nicholas of Smyrna, Theodoros Phocaeus and Petros Peloponessios) have retained portions and melodic formulae of the 'original' melody, some new passages and musical variations have been inserted.
Fascinating stuff...
Footnote: Although we all know her as Kassiane, apparently this was a subsequent variation of her name (or possibly her full name). The correspondence between her and Saint Theodore the Studite in the ninth century and a text written by a historian of the tenth century all have her name as Kassia.