Boundedness of operator-valued commutators involving martingale paraproducts

Let $1<p<\infty$. We show the boundedness of operator-valued commutators $[\pi_a,M_b]$ on the noncommutative $L_p(L_\infty(\mathbb{R})\overline{\otimes}\mathcal{M})$ for any von Neumann algebra $\mathcal{M}$, where $\pi_a$ is the $d$-adic martingale paraproduct with symbol$a\in~{\rm~BMO}^d(\mathbb{R})$ and $M_b$ is the noncommutative left multiplication operator with $b\in~{\rm~BMO}^d_\mathcal{M}(\mathbb{R})$.