Local SAR in parallel transmission pulse design

Abstract

The management of local and global power deposition in human subjects (Specific Absorption Rate, SAR) is a fundamental constraint to the application of parallel transmission (pTx) systems. Even though the pTx and single channel have to meet the same SAR requirements, the complex behavior of the spatial distribution of local SAR for transmission arrays poses problems that are not encountered in conventional single-channel systems and places additional requirements on pTx RF pulse design. We propose a pTx pulse design method which builds on recent work to capture the spatial distribution of local SAR in numerical tissue models in a compressed parameterization in order to incorporate local SAR constraints within computation times that accommodate pTx pulse design during an in vivo MRI scan. Additionally, the algorithm yields a Protocol-specific Ultimate Peak in Local SAR (PUPiL SAR), which is shown to bound the achievable peak local SAR for a given excitation profile fidelity. The performance of the approach was demonstrated using a numerical human head model and a 7T eight-channel transmit array. The method reduced peak local 10g SAR by 14–66% for slice-selective pTx excitations and 2D selective pTx excitations compared to a pTx pulse design constrained only by global SAR. The primary tradeoff incurred for reducing peak local SAR was an increase in global SAR, up to 34% for the evaluated examples, which is favorable in cases where local SAR constraints dominate the pulse applications.

First and second order derivatives for optimizing parallel RF excitation waveforms

“…Up to a factor the matrices B ðlÞ and C ðlÞ represent the same values as our Eqs. (39) and (40). The terms k ðkÞT ðtÞB ðlÞ M ðkÞ ðtÞ and k ðkÞT ðtÞC ðlÞ M ðkÞ ðtÞ appearing in the update Step 5 thus represent the analog of our derivatives in formulas (37) and (38), but with the approximation (36) instead of the exact formula (34) in (33).…”

“…This enables us to compare both the arbitrary flip angle method and small tip angle approximation with regard to their quality and computational burden. The factors in these products can be calculated with formulas (27), (31), (9), (34), (39) and (40). Such derivatives can be used to obtain linear approximations of the final magnetization at the current Xand Y-variable values.…”

“…(49)-(51) can be found in Eqs. (39) and (40). Their products can be calculated in a preprocessing step.…”

“…An important aspect of these examples is that RF amplitude bounds as well as nearly 500 specific absorbtion rate constraints have to be respected. Specialized algorithms for handling such constraints have been developed for the small tip angle approximation in [38][39][40][41]35]. An advantage of the interior-point method that it supports the handling of constraints.…”

Joint design of k T -points trajectories and RF pulses under explicit SAR and power constraints in the large flip angle regime

“…The operator bl represents the Bloch integration: it is the mapping operator that takes the different variables to be optimized and returns a flip angle for each voxel in the region of interest (the human brain in our case), assuming prior to the pulse an initial longitudinal magnetization state so that the flip angle simply is the inverse cosine function of M z . The problem is solved under explicit 10-g local and global SAR constraints expressed by c i (for each Virtual Observation Point (VOP) [27,28]) and c G respectively. Lastly, the average power constraint (here P max = 2 W) is enforced via c pw for each channel while the peak amplitude is constrained with c A , V max being the maximum voltage available at the coil input.…”