Optimal experiment design for physiological parameter estimation using hyperpolarized carbon-13 magnetic resonance imaging

Hyperpolarized carbon-13 magnetic resonance imaging is a new medical imaging modality that has enabled the real-time observation of perfusion and metabolism in vivo. The rates at which perfusion and metabolism occur are important for disease diagnosis and treatment monitoring. To generate an image, the user must choose a flip angle at which to perturb the magnetic spins associated with each of the compounds to be imaged. We consider the problem of optimally choosing a time-varying sequence of flip angles in order to achieve the best estimates of rate parameters in a physiological model. We first formulate a discrete-time model describing perfusion, exchange, relaxation and measurement error. We then show how to compute the Fisher information for the unknown parameters of this model and present time-varying flip angle schemes that maximize the Fisher information. Through numerical studies, we demonstrate that the optimal flip angle scheme provides better estimates of the model´s rate parameters than a constant flip angle scheme.