The only way Zatiel could bring the purple plane out of his Rebirth Eye and into his brain was by transforming it into the chaos purple energy that made it. If the dimension were physical, it would have been the end for it, but since it was an illusion, reconstructing it was possible.
Zatiel took half of the chaos purple energy and extended it to his brain. The Neo-Demon could not divide it since that would harm the dimension.
The process was beyond painful, and if it weren't for his True Will helping him, Zatiel would have fallen unconscious.
It took him five days of immense agony until he transferred half of the chaos purple energy.
One half was now inside the Rebirth Eye and the other in the center of his brain, both connected by a trail of chaos purple energy.
Once that part was over, Zatiel began the reconstruction of the purple plane.