We consider an optimal control problem subject to an elliptic-parabolic coupled system of partial differential equations that describes fluid flow through biological tissues. Our goal is to optimize the fluid pressure and solid displacement using distributed or boundary control. We first show results on the existence and uniqueness of optimal controls and then present necessary optimality conditions. The optimal controls can be approximated numerically. Additionally, we consider the problem with integer controls and discuss the regularity assumptions necessary to apply a recently proposed algorithm.