On maximal injective subalgebras of tensor products of von Neumann algebras

Let Mi be a von Neumann algebra, and Bi be a maximal injective von Neumann subalgebra of Mi, i=1,2. If M1 has separable predual and the center of B1 is atomic, e.g., B1 is a factor, then is a maximal injective von Neumann subalgebra of . This partly answers a question of Popa.