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Using an extension of the Kontsevich integral to tangles in handlebodiessimilar to a construction given by Andersen, Mattes and Reshetikhin, weconstruct 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 $\mathbb{A}$ ofJacobi diagrams in handlebodies. As a symmetric monoidal linear category,$\mathbb{A}$ is the linear PROP governing "Casimir Hopf algebras", which arecocommutative Hopf algebras equipped with a primitive invariant symmetric2-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 theVassiliev-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 resultingfrom $H_\varphi$ by "transmutation" is precisely the image by $Z$ of acanonical Hopf algebra in the braided category $\mathcal{B}$. Finally, weexplain how $Z$ refines the LMO functor, which is a TQFT-like functor extendingthe Le-Murakami-Ohtsuki invariant.

The Kontsevich integral for bottom tangles in handlebodies