Wolverine's history demonstrates that he can regenerate from seeming nothingness, but only once at any given time. It can't be his body or his skeleton, or anything reasonable, for that matter. If it must be something explainable within the comic universe, then it must also be something supernatural or outside the realm of human understanding. This can be seen in any number of grave wounds he's suffered, including being nuked and having his adamantium removed by Magneto.
That is all we can gather from comics, film, and animation because that's all they've given us. The rest is up to the writers and artists that do or will control the future of our beloved anti-hero.
With that in mind, I am only able to offer what might be a way to fill that gap. This isn't speculation, it's me brainstorming as if I was tasked with filling the gap myself. Ahem.
Wolverine, in many ways, represents primal urges and determination. He has been aggressively protective of friends and savagely single-minded in attempts to destroy his enemies. His energy, his strength, his immortal endurance are a materialization of pure forces in reality. He stands as a coalescence of somethings eternal. The question, then, is whether this eternity is actual or artificial. Did these things come together and form Logan wittingly or as a deterministic result of natural forces, or was there an external intelligence behind it? Is The Wolverine a puppet, project, or prank spilt into our existence by others of unknown intent?
I'd better wrap this up. Dave expects a draft by 7.