Introduction

Confounder-corrected chemical-shift-encoded MRI (CSE-MRI) is an established technique to quantify proton density fat-fraction (PDFF)¹. Recent studies have shown that clinically relevant PDFF thresholds for diagnosing hepatic steatosis may be as low as 3%, demonstrating a need for accurate and precise measurements of low PDFF^2,3. Due to accelerated acquisition times⁴, elevated iron content⁵, and the low flip angles used to avoid T1 bias, current CSE-MRI acquisitions often have low signal-to-noise ratios (SNR). However, at low SNR, PDFF estimates may be biased^6,7 and noisy, i.e., unreliable.

Currently, no methods exist for clinicians to gauge the reliability of CSE-MRI PDFF measurements. Therefore, the purpose of this work is to develop a method for generating confidence maps for CSE-MRI PDFF measurements. Confidence maps are displayed as a color-coded overlay on the PDFF map to inform analysts where measurements may or may not be reliable.

Methods

Proposed Metric:
CSE-MRI methods to quantify PDFF involve fitting complex or magnitude data to a signal model, typically using non-linear least squares. In this work, we limit our analysis to magnitude-fitting. We propose a metric to characterize the goodness-of-fit based on the normalized residual sum of squares (NRSS), defined as:\begin{equation}NRSS = \frac{\sum_{TE}(|S_{TE}(\hat{\theta})|-|S_{TE,meas}|)^2}{\sum_{TE}|S_{TE,meas}|^2}\tag{1}\end{equation}where $$$S_{TE}$$$ is the signal model, $$$\hat{\theta}$$$ are the estimates of fat and water amplitudes and $$$R_2^\ast$$$, and $$$S_{TE,meas}$$$ is the measured signal. Based on a predetermined threshold for acceptable PDFF bias, chosen as ±0.5% for this work, a threshold NRSS value can be determined, as described below, above which PDFF estimates are considered unreliable.

Simulations:
Noiseless six-echo acquisitions were simulated using a spoiled gradient-echo (SGRE) signal model at 3.0T with varying fat and water amplitudes, $$$R_2^\ast=40s^{-1}$$$, and $$$f_B=30Hz$$$. Simulations used a typical first echo time and spacing (TE1=1.2ms, ΔTE=1.0ms). Complex Gaussian noise was added to simulated echo data, creating a range of low-to-high SNR values (1-40), and magnitude-fitting was used to estimate PDFF and $$$R_2^\ast$$$. NRSS was then calculated using Eq. (1). SNR was defined as the quotient of the echo amplitude at TE=0 and the standard deviation of the Gaussian noise.

Phantom experiments:
A cylindrical water-only phantom (PDFF=0%) doped with NiCl2 (GE Healthcare, Waukesha, WI) was imaged at 3.0T (Signa Premier, GE Healthcare) with a commercial multi-echo 3D SGRE sequence (IDEAL IQ, GE Healthcare) using the integrated body transmit/receive coil. SNR was modulated by varying flip angle. Acquisition parameters are listed in Table 1.

In vivo experiments:
With IRB approval and informed consent, a healthy volunteer was scanned at 3.0T using the same scanner, sequence, and coil as phantom experiments. The body coil was intentionally used to facilitate a range of low-to-acceptable SNR. SNR was also modulated by varying flip angle. Acquisition parameters are listed in Table 1.

Reconstruction and analysis:
Complex echo images were processed with a graph cut algorithm⁸ for initial parameter estimation, followed by magnitude-fitting to generate PDFF and $$$R_2^\ast$$$ maps. The mean PDFF in the phantom was measured in a 3,400-pixel/47cm² circular region-of-interest (ROI) covering the entire phantom. In vivo mean PDFF was measured in two 500-pixel/12cm² circular ROIs placed in the right and left liver lobes.

SNR was estimated from first-echo magnitude images using a background noise standard deviation method⁹.

Confidence maps are created as a semi-transparent overlay on the PDFF map, where voxels with an NRSS below the threshold are fully transparent, and voxels above the threshold are color-coded according to the effective SNR value corresponding with the NRSS value of the voxel.

Results

Simulations:
CSE-MRI simulations demonstrate that low PDFF measurements are negatively biased at low SNR after magnitude-fitting (Figure 1). Simulation results showed that 6.8x10^-3 was the NRSS threshold corresponding to an expected ±0.5% PDFF bias (Figure 2).

Phantom experiments:
As SNR increases with flip angle, PDFF mean and standard deviation improve (Figure 3). An NRSS threshold of 3.0x10^-3 was determined from simulations using phantom TE1/ΔΤΕ (Table 1). As SNR decreases, more pixels in the confidence maps are flagged corresponding to the increasing PDFF bias.

In vivo experiments:
As SNR increases with flip angle, PDFF mean and standard deviation improve (Figure 4). An NRSS threshold of 4.2x10^-3 was determined from simulations using in vivo TE1/ΔΤΕ (Table 1). As SNR decreases, more pixels in the confidence maps are flagged as unreliable. The source images included a region of low signal in the left lobe. PDFF measurements in this area exhibit bias and are flagged in the confidence map.

Discussion and Conclusions

In this work, we present a standardized method to generate confidence maps for PDFF estimation with CSE-MRI, using a normalized residual sum of squares (NRSS) metric. The NRSS threshold is specific to magnitude-fitting and is calculated for each TE1/ΔTE combination, using an acceptable PDFF bias (e.g., ±0.5%). Confidence maps provide a visual indicator of fitting performance and PDFF reliability and can guide analysts to avoid low-SNR regions where PDFF estimates may be biased.

As a proof-of-concept, this work uses magnitude-fitting, assumes $$$R_2^\ast$$$ within a normal range, and a low field inhomogeneity, although extension to complex-fitting and cases with iron overload where high $$$R_2^\ast$$$ affects fitting performance should be straightforward. Future in vivo work will use magnetic resonance spectroscopy or high-SNR CSE-MRI acquisitions as the ground truth for PDFF.

Acknowledgements

The authors wish to acknowledge support from the NIH (R01 DK088925), as well as GE Healthcare who provides research support to the University of Wisconsin. Additionally, Dr. Reeder is a Romnes Faculty Fellow, and has received an award provided by the University of Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation.

References

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