  Recent developments in surgical robotics have led to new advancements in the
automation of surgical sub-tasks such as suturing, soft tissue manipulation,
tissue tensioning and cutting. However, integration of dynamics to optimize
these control policies for the variety of scenes encountered in surgery remains
unsolved. Towards this effort, we investigate the integration of differentiable
fluid dynamics to optimizing a suction tool's trajectory to clear the surgical
field from blood as fast as possible. The fully differentiable fluid dynamics
is integrated with a novel suction model for effective model predictive control
of the tool. The differentiability of the fluid model is crucial because we
utilize the gradients of the fluid states with respect to the suction tool
position to optimize the trajectory. Through a series of experiments, we
demonstrate how, by incorporating fluid models, the trajectories generated by
our method can perform as good as or better than handcrafted human-intuitive
suction policies. We also show that our method is adaptable and can work in
different cavity conditions while using a single handcrafted strategy fails.
