The phrase "his textbook on medicine" in this question about Avicenna is a bit misleading, since Avicenna wrote more than one treatise on medicine:
Gotthard Strohmaier notes in his book Avicenna (München: C. H. Beck, 1999, p. 117) that the authenticity of some of these works (except for the Canon and The Book of Healing) has sometimes been questioned.
Avicenna had an exceptional memory. By the age of ten he had already memorised the Quran and much Arabic poetry (Encyclopaedia Brittanica, 2007, Micropedia Volume 1, p. 739).
According to Strohmaier (p. 116) didactic poems already existed before Avicenna, especially to make memorization easier, but they usually employed complex types of metre. The Book of Healing, however, uses the rajaz, which is the simplest Arabic metre. Strohmaier compares it to the German Knittelvers, which tended to be used more for humouristic purposes. (Or, as Wikipedia says, the rajaz orginally "tended to be used for low-status, everyday genres such as lullabies, or for improvisation".) This seems to imply that from a poetic point of view, Avicenna choice of metre broke with the existing conventions for didactic poems.
However, the use of didactic poems in medical education appears to have been something new. Rabie El-Said Abdel-Halim writes:
Another influence of Ibn Sina's medical poem was the spreading popularity of composing didactic poems and utilizing it in medical education. In the Islamic world, several of those medical poems written after Ibn Sina are still extant but only in the form of unedited manuscripts.
(Rabie El-Said Abdel-Halim: "The role of Ibn Sina (Avicenna)'s medical poem in the transmission of medical knowledge to medieval Europe", Urology Annals, 6.1 (January-March 2014).