Closed‐form expressions for flip angle variation that maximize total signal in T1‐weighted rapid gradient echo MRI

Purpose Magnetization‐prepared rapid gradient‐echo ( MPRAGE ) sequences are commonly employed for T1‐weighted structural brain imaging. Following a contrast preparation radiofrequency ( RF ) pulse, the data acquisition proceeds under nonequilibrium conditions of the relaxing longitudinal magnetization. Variation of the flip angle can be used to maximize total available signal. Simulated annealing or greedy algorithms have so far been published to numerically solve this problem, with signal‐to‐noise ratios optimized for clinical imaging scenarios by adhering to a predefined shape of the signal evolution. We propose an unconstrained optimization of the MPRAGE experiment that employs techniques from resource allocation theory. A new dynamic programming solution is introduced that yields closed‐form expressions for optimal flip angle variation. Methods Flip angle series are proposed that maximize total transverse magnetization ( M x y ) for a range of physiologic T1 values. A 3D MPRAGE sequence is modified to allow for a controlled variation of the excitation angle. Experiments employing a T1 contrast phantom are performed at 3T. 1D acquisitions without phase encoding permit measurement of the temporal development of M x y . Image mean signal and standard deviation for reference flip angle trains are compared in 2D measurements. Signal profiles at sharp phantom edges are acquired to access image blurring related to nonuniform M x y development. Results A novel closed‐form expression for flip angle variation is found that constitutes the optimal policy to reach maximum total signal. It numerically equals previously published results of other authors when evaluated under their simplifying assumptions. Longitudinal magnetization ( M z ) is exhaustively used without causing abrupt changes in the measured MR signal, which is a prerequisite for artifact free images. Phantom experiments at 3T verify the expected benefit for total accumulated k‐space signal when compared with published flip angle series. Conclusions Describing the MR signal collection in MPRAGE sequences as a Bellman problem is a new concept. By means of recursively solving a series of overlapping subproblems, this leads to an elegant solution for the problem of maximizing total available MR signal in k‐space. A closed‐form expression for flip angle variation avoids the complexity of numerical optimization and eases access to controlled variation in an attempt to identify potential clinical applications.