  Emission-lines in the form of filamentary structures is common in bright
clusters characterized by short cooling times. In the Perseus cluster, cold
molecular gas, tightly linked to the H$\alpha$ filaments, has been recently
revealed by CO observations. In order to understand the origin of these
filamentary structures, we have investigated the evolution of the hot ICM gas
perturbed by the AGN central activity in a Perseus like cluster. Using
very-high resolution TreeSPH simulations combined with a multiphase model and a
model of plasma bubbles, we have been able to follow the density and
temperature evolution of the disturbed ICM gas around the bubbles. Our
simulations show that a fraction of the $1-2 \rm{keV}$ gas present at the
center of clusters is trapped and entrained by the rising buoyant bubble to
higher radius where the AGN heating is less efficient. The radiative cooling
makes it cool in a few tens of Myr below $10^4 \rm{K}$, forming cold
filamentary structures in the wake and in the rim of the bubbles.
