How are b+-trees are useind in filesystems

Hello,

I am new here and I think this is not a real btrfs question but a general filesystem-btree question. I want to know how I do these following things:
- How do I translate "/home/serdar/public_html" -> btree
- how do I know how files/directories are related to each other

I did these with useing a binary tree (not balanced) where a node owns
name (char*)
value (void*) (was a inode structure) first_child (pointer)
siblings (pointer)

I was looking for the name seperated with "/"
siblings are in the same directory
first_child is the subdir

for the esample above.
look at root the siblings for home
take his first_child
if first_child is serdar, than take its first_child, else look for siblings after finding serdar, take its first_child if first_child is public_html take this and its value, else look for siblings.

I can't do this with b-trees, this is why I asking
I am at this time not interested in data, where it is stored, I can take void* for this.

I hope I could explain my problem.
I read many papers and presentations about b-trees most of them at btrfs-learning
but they are only btree related how they work and why they are interesting for filesystems, but not how to translate the problem above.

I hope you can help me there.

Greetings Serdar