Board Thread:General Discussion/@comment-7136323-20130404201504/@comment-7658432-20130410073513

We still don't know for sure. Isshin may be the head of the clan but he came from a branch family so it's possible that he's not a direct relative of Kaien. Maybe a distant cousin of Kaien? Kaien's just related to Ichigo because of the heritage. No direct relation has been revealed but I'd bet he's a distant cousin of Kaien since Kukakku refers to Isshin as "Uncle".