Synopsis

Many coil combination methods have been developed, including methods that require pre-calibrated coil sensitivity maps, as well as methods that do not require additional sensitivity maps. Several of these methods have been adapted to CSE-MRI, where accurate signal combination is particularly critical as it needs to preserve consistent phase and magnitude information across echoes; however, their relative performance remains unknown. Therefore, the purpose of this work is to compare theoretically, in simulation, and experimentally the bias and noise performance of quantitative parameter maps resulting from five commonly used coil multi-echo coil combination techniques.

Introduction

Methods

Coil Combination

Our work focuses on five coil combination methods, abbreviated as follows:

1. Roemer: The optimal method for pre-calibrated coil combination (1,2).

2. Walsh: A calibrationless technique described by Walsh et al (6).

3. MIP-TE (Most In-Phase Echo): A common calibrationless multi-echo coil combination method that calculates the coil sensitivity maps by applying low-pass filtering and normalization to the most in-phase echo.

4. ESPIRiT: A calibrationless technique described by Uecker et al (7).

5. Joint Fit: Direct (and calibrationless) estimation of unknown parameters from multi-coil data (i.e. no coil combination)(8).

CSE-MRI

All parameter estimations/CSE-MRI reconstructions were performed using nonlinear least squares and the following signal model for each coil combination method:

$$A_{c}e^{i\phi_{c}}M_{0}(1-\eta+\eta\sum_{p=1}^{6}{a_{p}e^{i2\pi*f_{p}*TE}})e^{i\phi_{m}}e^{-R2^{*}TE}e^{i2\pi*\psi*TE}~~~~~~~~~~~~~~~~~~~~~\text{[1]}\\\text{Where:}~~~~~~A_{c}e^{i\phi_{c}}~\text{=}~\text{coil}~\text{sensitivities}\\~~~~~~~~~~~~~~~M_{0}e^{i\phi_{m}}~\text{=}~\text{complex}~\text{proton}~\text{density}\\~~~~~~~~~~~~~~\eta~\text{=}~\text{PDFF,}~~~\psi~\text{=}~\text{fieldmap}\\~~~~~~~\sum_{p=1}^{6}{a_{p}e^{i2\pi*f_{p}TE}}~\text{=}~\text{fat}~\text{spectrum}$$

Experiment 1. CRLB Compared to Simulated Data

Two Cramer-Rao lower bounds (CRLB) (9) of Eq. 1 were calculated: 1) known coil sensitivities (providing a bound for the Roemer method), 2) unknown coil sensitivities (providing a bound for the remaining methods). CRLBs for 8 channels, PDFF=5%, R2*=30, TE₁=2.6ms, and ΔTE=1.8ms were compared to Monte-Carlo simulations (Figure 1) over a range of SNR values [6-60] for each coil combination method. Statistics of estimated parameters were computed pixel-wise across 1000 repetitions per SNR.

Experiment 2. Performance Over Ranges of Simulated PDFF, R2* and SNR

Monte-Carlo simulations (Figure 1) were performed for a range of PDFF [0%-30%], R2* [20s^-1-200s^-1], and SNR [5-35] values. Average absolute error of PDFF (bias corrected (10)) and R2* was computed in an ensemble of pixels and across 25 repetitions per PDFF/R2*/SNR combination.

Experiment 3. Phantom Acquisitions

A multi-echo 2D spoiled gradient recalled echo (SGRE) acquisition was repeated 2000 times (4 acquisitions x 500 repetitions/acquisition) in a fat/water agar gel phantom on a 3.0T MR system (GE Healthcare Discovery MR750, Waukesha, WI) using the following parameters: 2.19x2.19x1.6mm³ voxels size, 128x128 matrix, 6 echoes (single shot), flip angle 3^o, BW=±90.91kHz. The first 25 repetitions of each acquisition were discarded and a third order phase correction was applied on a pixel-by-pixel basis over repetitions to correct for phase drift over the scan duration. Subsets of N repetitions were then averaged to modulate SNR (N=1,2,4,8,16,19). After coil combining the resulting datasets (100 repetitions per SNR), PDFF, R2* and B0 were estimated and pixel-wise statistics were computed across repetitions.

Results

Experiment 1. CRLB Compared to Simulated Data

CRLB analysis, coupled with Monte-Carlo simulations, revealed the standard deviation of parameter estimates of all five methods match and are theoretically bounded by the same lower limit (Figure 2).

Experiment 2. Performance Over Ranges of Simulated PDFF, R2* and SNR

Monte-Carlo simulations over a range of PDFF, R2*, and SNR revealed all methods behave similarly at low and high SNR, except MIP-TE which exhibited bias in both PDFF and R2* in low SNR regimes (Figure 3).

Experiment 3. Phantom Acquisitions

Phantom experiments confirmed the Monte-Carlo simulation results, except bias in MIP-TE PDFF was reduced (Figure 4).

Discussion

This work compared the bias and noise performance in quantitative parameter maps resulting from multi-echo coil combination techniques. We examined five commonly used coil combination methods and found the variability of all five methods is theoretically bounded by the same lower limit. Importantly, simulations and phantom experiments confirmed this result over a range of PDFF, R2*, and SNR.

Our results suggest that separate calibration of coil sensitivities may be unnecessary for coil-combination in CSE-MRI. Of the remaining four methods, MIP-TE was biased at low SNR and Joint Fit was computationally costly (results not included). In contrast, either Walsh or ESPIRiT provide unbiased estimation with moderate computation. This work had several limitations: specifically, it did not include parallel imaging acceleration, for simplicity of analysis.

In summary, theoretical analysis, simulations, and phantom results demonstrated nearly equivalent performance of a wide array of coil combination methods, regardless of the use of pre-calibrated sensitivity maps.

Acknowledgements

References

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