Optimal Variable Flip Angle Schemes for Hyperpolarized MR Kinetic Modeling Robust to RF Field Variations

Hyperpolarized carbon-13 magnetic resonance has enabled the real-time observation of biochemical pathways in living cellular systems. Pharmacokinetic modeling of such experiments provides estimates of conversion rates between metabolites, which, in turn, can be used to distinguish between healthy and diseased tissues, for example. This work focuses on choosing time-varying flip angle schemes that minimize the uncertainty of model parameter estimates by maximizing the Fisher information while taking into account B₁ field strength variation by incorporating an assumed prior distribution. Monte Carlo simulations demonstrated that the optimized variable flip angle (VFA) schemes provided less uncertain model parameter estimates compared to an optimized constant flip angle (CFA) scheme. Furthermore, the parameter estimation improvement using optimized VFA schemes proved robust over a range of underlying parameters. It was shown that estimation of the B₁ field strength from the measurements is essential to avoid inaccurate parameter estimates from VFA schemes. These may result from violated assumptions about the accuracy of prescribed flip angles. In vitro experiments validated the unidirectional enzyme-driven conversion model used for demonstration of the optimization methods. Semi-synthetic data generated through Monte Carlo simulations helped demonstrate the superiority of optimized VFA schemes over an optimized CFA scheme. We conclude that sampling using an optimized VFA scheme and including B₁ as a fitted parameter improves the uncertainties of model parameters as here exemplified by hyperpolarized NMR.