Very good concern Dyfrnt, I asked myself thousands of questions about the Tsahaylu... I guess and from what I see in the movie everytime, the "material" which the Tsahaylu is made of is the same as the "optic fiber"-like branches of the Tree Of Souls and Willow Trees of Voices. Also the Ikran/ Pa'li/ Toruk etc have the same "material" for their connection. It's almost a very obvious thing, the other subject, Matrix, uses the brain for transfering people into the virtual dimension and not the leg or hand or chest
AVATAR just wanted to place this relationship of a "reason"-able race with its surroundings and living things. A thing that we lost. I think Tsahaylu (or Tsaheylu) is the most interesting thing in AVATAR.