Optimum pulse flip angles for multi-scan acquisition of hyperpolarized NMR and MRI

The optimum pulse flip angles were calculated for multi-scan acquisition of hyperpolarized NMR and MRI. The derived formulae could be correlated with the best angle for ordinary steady-state acquisition, the so-called Ernst angle. Although single-scan acquisition has been popular in hyperpolarized measurements, signal accumulation by increasing scans may become very effective for improving the total signal gain, especially when the sample's longitudinal spin relaxation time is long. The optimum angles were calculated from theoretical relations between the exponential of the pulse repetition time/relaxation time ratio and the total scan counts. Constant and variable flip angle cases are presented, both of which yield similar cumulative signal amplitudes. For the constant angle case, a numerically calculated semi-universal curve is presented for the rough estimation of the best angle, as the results were not significantly dependent upon the degree of hyperpolarization within the realistic range. Meanwhile, for the variable angle case, the best angles were approximated from a clean trigonometric series relation, in which the initial pulse became near the Ernst angle and the last pulse was always 90°. A modification of the variable angle scheme enables the acquisition of uniform signal amplitude throughout all scans.