Lagrangian mean curvature flow of surfaces with mean curvature bound

Let $L_t$ be a zero Maslov Lagrangian mean curvature flow in ${\mathbb{C}}^2\mathrm{.}$ We show that if the mean curvature stays uniformly bounded along the flow, then the tangent flow at a singular point is unique i.e. the limit of the parabolic rescalings does not depend on the chosen sequence of rescalings.