  Using an extension of the Kontsevich integral to tangles in handlebodies
similar to a construction given by Andersen, Mattes and Reshetikhin, we
construct a functor $Z:\mathcal{B}\to \widehat{\mathbb{A}}$, where
$\mathcal{B}$ is the category of bottom tangles in handlebodies and
$\widehat{\mathbb{A}}$ is the degree-completion of the category $\mathbb{A}$ of
Jacobi diagrams in handlebodies. As a symmetric monoidal linear category,
$\mathbb{A}$ is the linear PROP governing "Casimir Hopf algebras", which are
cocommutative Hopf algebras equipped with a primitive invariant symmetric
2-tensor. The functor $Z$ induces a canonical isomorphism $\hbox{gr}\mathcal{B}
\cong \mathbb{A}$, where $\hbox{gr}\mathcal{B}$ is the associated graded of the
Vassiliev-Goussarov filtration on $\mathcal{B}$. To each Drinfeld associator
$\varphi$ we associate a ribbon quasi-Hopf algebra $H_\varphi$ in
$\hbox{gr}\mathcal{B}$, and we prove that the braided Hopf algebra resulting
from $H_\varphi$ by "transmutation" is precisely the image by $Z$ of a
canonical Hopf algebra in the braided category $\mathcal{B}$. Finally, we
explain how $Z$ refines the LMO functor, which is a TQFT-like functor extending
the Le-Murakami-Ohtsuki invariant.
