  A key parameter of interest recovered from hyperpolarized (HP) MRI
measurements is the apparent pyruvate-to-lactate exchange rate, $k_{PL}$, for
measuring tumor metabolism. This manuscript presents an
information-theory-based optimal experimental design (OED) approach that
minimizes the uncertainty in the rate parameter, $k_{PL}$, recovered from
HP-MRI measurements. Mutual information (MI) is employed to measure the
information content of the HP measurements with respect to the first-order
exchange kinetics of the pyruvate conversion to lactate. Flip angles of the
pulse sequence acquisition are optimized with respect to the mutual
information. Further, a spatially varying model (high-fidelity) based on the
Block-Torrey equations is proposed and utilized as a control. A time-varying
flip angle scheme leads to a higher parameter optimization that can further
improve the quantitative value of mutual information over a constant flip angle
scheme. However, the constant flip angle scheme leads to the best accuracy and
precision when considering inference from noise-corrupted data. For the
particular MRI data examined here, pyruvate and lactate flip angles of 35 and
28 degrees, respectively, were the best choice in terms of accuracy and
precision of the parameter recovery. Moreover, the recovery of rate parameter
$k_{PL}$ from the data generated from the high-fidelity model highlights the
influence of diffusion and strength of vascular source on the recovered rate
parameter. Since the existing pharmacokinetic models for HP-MRI do not account
for spatial variation, the optimized design parameters may not be fully optimal
in a more general 3D setting.
