Optimal control design of turbo spin‐echo sequences with applications to parallel‐transmit systems

Abstract

PurposeThe design of turbo spin‐echo sequences is modeled as a dynamic optimization problem which includes the case of inhomogeneous transmit radiofrequency fields. This problem is efficiently solved by optimal control techniques making it possible to design patient‐specific sequences online.Theory and MethodsThe extended phase graph formalism is employed to model the signal evolution. The design problem is cast as an optimal control problem and an efficient numerical procedure for its solution is given. The numerical and experimental tests address standard multiecho sequences and pTx configurations.ResultsStandard, analytically derived flip angle trains are recovered by the numerical optimal control approach. New sequences are designed where constraints on radiofrequency total and peak power are included. In the case of parallel transmit application, the method is able to calculate the optimal echo train for two‐dimensional and three‐dimensional turbo spin echo sequences in the order of 10 s with a single central processing unit (CPU) implementation. The image contrast is maintained through the whole field of view despite inhomogeneities of the radiofrequency fields.ConclusionThe optimal control design sheds new light on the sequence design process and makes it possible to design sequences in an online, patient‐specific fashion. Magn Reson Med 77:361–373, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine

How to choose the right MR sequence for your research question at 7 T and above?

“…When using systems with parallel transmission capability, the extra degree of freedom offered by the long refocusing pulse trains, allows dynamic adaptation of the rf-shimming associated with each refocusing pulse in order to ensure a homogeneous contrast (Sbrizzi et al, 2016). When performing 3D acquisitions in the sagittal orientation (readout in the head foot direction), the freedom gained from the possibility of not needing spatially selective RF pulses for whole brain imaging, can be exploited to apply short 3D tailored non-selective pulses, kT points (Cloos et al, 2012), for both the excitation and refocusing pulses to obtain a more homogeneous contrast throughout the brain either in combination with (Eggenschwiler et al, 2014;Massire et al, 2015) or without (Eggenschwiler et al, 2016)parallel transmission.…”

Design of universal parallel‐transmit refocusing kT‐point pulses and application to 3D T2‐weighted imaging at 7T

“…In previous works, the pulses along the train were designed individually using an optimal control approach . Sbrizzi et al also proposed a signal‐based approach to design the refocusing RF pulses, thereby relaxing the CPMG condition. Clearly, given the large amount of degrees of freedom allowed by optimal control approaches, excellent performance can be achieved.…”

“…For instance, any change in the nominal signal evolution indeed would require a new pulse optimization. In addition, in and , separately designed refocusing RF pulses lead to greater RF pulse design complexity and typically require some heuristics to take into account hardware and safety (local and global SAR) limits. In comparison, for the SPACE sequence investigated in this work, a single pulse was designed.…”

Whole‐brain 3DFLAIR at 7T using direct signal control

“…The DSC algorithm can in principle compute separate optimized RF shim settings (for the 8‐channel transmit coil) for each of the 192 pulses in the echo train; however, the cost is that each element of w (192 × 8 complex matrix) must be computed. In previous work, it was shown that good results may be achieved by reducing the number of degrees of freedom by applying a mapping , for which w′ is a matrix of size ; is a smaller number of independent RF shim settings; and P is a mapping matrix. In this work, we set N s = 16 and mapped the first 13 rows of w to the first 13 rows in w′ , whereas the remaining rows of w are mapped in blocks of 60, 60, and 59 to the last 3 rows in w′ .…”