Hierarchical iterative linear-fitting algorithm (HILA) for phase correction in fat quantification by bipolar multi-echo sequence.

Background: Multi-echo gradient echo (GRE) sequence with bipolar readout gradients can reduce achievable echo spacing and thus have higher acquisition efficiency compared to unipolar readout gradients for fat fraction (FF) quantification. However, the eddy current induced phase (EC-phase) in a bipolar sequence corrupts the phase consistency between echoes and can lead to inaccurate fat quantification.

Methods: A hierarchical iterative linear-fitting algorithm (HILA) was proposed for EC-phase correction. In each iteration, image blocks were divided into sub-blocks. The EC-phase was fitted to a linear model in each sub-block. The estimated linear phase in each sub-block was then used as a starting value for the next iteration. Finally, a weighted average over all levels was calculated to obtain the final EC-phase map. Monte Carlo simulations were adopted to evaluate how the residual EC-phase would affect FF quantification accuracy. The performance of the proposed HILA method was then compared to the well-established unipolar acquisition method in phantom and experiments on 3T.

Results: The simulations showed that certain ΔTE values, such as ΔTE =~0.80/1.50/1.95 ms, allowed for FF estimation that were relatively robust to the residual EC-phase ranging from -2π/15 to 2π/15 for a 6-echo bipolar acquisition on 3T. The phantom study showed that the maximum mean FF error, after EC-phase correction with the proposed HILA method, was smaller than 2%, implying that HILA can approximate the high-order term of the EC-phase through step-wise linear fitting. There was no significant difference between the FFs from bipolar and unipolar acquisitions on the two MR systems in the experiments.

Conclusions: The proposed HILA method provides a simple and efficient EC-phase correction method for bipolar acquisition without acquiring additional data. The appropriate choice of TEs may further reduce the effect of the residual EC-phase on accurate FF quantification with bipolar readout sequence.