This paper uses experiment design optimization to obtain the optimal placement of scans during dynamic contrast enhanced computed tomography. Here we construct and minimize an objective function based on the Cramer-Rao lower bound (CRLB) to optimize the accuracy of the estimators. Experiments based on simulated data are performed to compare our scheme with current sampling methods. Results reveal a significant reduction in error and variation of the fitted parameters while simultaneously reducing the number of scans, and thus the radiation dose received by the patient. We also show that our acquisition scheme is robust to the parameter values, easily adaptable to various parts of the body and therefore has great clinical potential.